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1. Spectrum sequence of colors Circle reading Minimum deviation red Line of sight Yellow Red end Blue end Calculations stow work Index of Refraction for Yellow Light Don t forget units continued 445 www ATIBOOK ir EXPERIMENT 30 The Prism Spectrometer Laboratory Report RV QUESTIONS 1 Show that the angle between the two telescope settings of the reflected slit images is equal to 2A Procedure 4 2 Judging on the basis of your experimental results what is the speed of yellow light in the prism 3 What is the range of indices of refraction of the prism for the wavelengths of visible light 446 www ATIBOOK ir Section Date Name Lab Partner s EX PERIMENT 3 1 Line Spectra and the Rydberg Constant RV Advance Study Assignment Read the experiment and answer the following questions 1 Distinguish between continuous spectra and line spectra and describe their causes 2 Why does a gas discharge tube for example a neon light have a certain color 3 What are a the Balmer series and b the Rydberg constant 447 continued www ATIBOOK ir EXPERI MIEN TF 8 1 Advance Study Assignment 4 Explain briefly how the prism spectrometer is calibrated 5 Explain briefly how the Rydberg constant is determined experimentally 448 www A TIBOOK ir EX PE RI Line Spectra and the Rydberg Constant MENT 3 1 INTRODUCTION AND OBJECTIVES I
2. Lab Partner s EX PERIMENT 2 7 Reflection and Refraction RV Advance Study Assignment Read the experiment and answer the following questions 1 What is the law of reflection and does it apply to all reflecting surfaces 2 Distinguish between regular and irregular reflection Give an example of each 3 Why is light refracted when it passes from one medium into an optically different medium 393 continued www A TIBOOK ir EXPERIMENT 27 Advance Study Assignment 4 Show by Snell s law that if the speed of light is less in a particular medium then a light ray is bent toward the normal when entering that medium What happens if the speed of light is greater in the medium 5 What is the difference between the relative index of refraction and the absolute index of refraction Explain why the absolute index of refraction can be determined experimentally fairly accurately using air as a medium 394 www A TIBOOK ir EX PE RI ENT 2 7 Reflection and Refraction INTRODUCTION AND OBJECTIVES Reflection and refraction are two commonly observed properties of light The reflection of light from smooth and polished surfaces such as ponds of water and mir rors enables us to view the images of objects including ourselves When light passes from one medium into another it is bent or refracted As a result a stick in a pond or a pencil in a glass of water appears to be bent Fig 27 1 As part of geo
3. n sin 05 where n is the index of refraction of the glass and sin 0 sin 90 04 cos 0 Thus sin 0 sin 0 tan n sin 4 cos0 or tand n TI 29 2 This expression is sometimes called Brewster s law and 6 is called Brewster s angle TI Example 29 1 A glass plate has an index of refraction of 1 48 What is the angle of polarization for the plate Solution With n 1 48 0 tan 1 48 56 Notice from TI Fig 29 4 that the reflected beam is hor izontally polarized Sunlight reflected from water metallic surfaces for example from a car and the like is partially polarized If the surface is horizontal the reflected light has a strong horizontal component This fact is used in polarizing sunglasses The transmission axis of the lenses is oriented vertically so as to absorb the reflected horizon tal component and reduce the glare or intensity Unpolarized beam Linearly polarized beam electric vectors normal to page Almost linearly polarized in plane of page TI Figure 29 4 Polarization by reflection Maximum polar ization occurs for a particular polarization angle 0 which depends on the index of refraction of the material Note that the transmitted beam is partially polarized After its discoverer David Brewster 1781 1868 a Scottish physicist EXPERIMENT 29 Polarized Light 425 Also notice that the refracted beam is partially polar ized
4. EXPERIMENT 27 Reflection and Refraction Laboratory Report b Explain why reflection images are easily seen at night in a window pane from inside the house whereas during the day they are not Judging on the basis of your experimental data draw conclusions about a the relationship of the distance of the object in front of a plane mirror and the distance of its image behind the mirror and b the image magnification that is how much bigger the image is than the object 3 Explain the situation shown in Fig 27 8 How can this be done without hurting one s hand Hint The fearless author s hand extends inside the sliding glass windowed door of a laboratory cabinet Figure 27 8 See Question 3 Cengage Learning continued 401 www ATIBOOK ir EXPERIMENT 27 Reflection and Refraction Laboratory Report 4 Prove mathematically that when a plane mirror is rotated an angle 0 about an axis through its center Part A of the experiment the angle of deflection of a light ray is equal to 20 Draw a diagram and show the work involved in your proof Attach an additional sheet if necessary 5 Referring to the situation in Fig 27 7 show theoretically that ray C C is parallel to ray CR Compute the displacement d of the ray passing through the glass plate Compare this with the measured experimental displacement 6 Using the experimentally determined n for the glass plate compute the speed of light in the gl
5. EH THEORY See TI CI General Theory at the beginning of the experiment SETTING UP DATA STUDIO T Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There EQUIPMENT SETUP are seven channels to choose from Digital channels 1 2 3 and 4 are the small buttons on the left ana 1 The cart string bracket and the fan accessory are log channels A B and C are the larger buttons on the mounted on top of the cart right as shown in CI Figure 4 2 2 The rotary motion sensor RMS is mounted to one 3 Click on the Channel 1 button in the picture A win side of the track with the small pulley of the RMS IDS dow with a list of sensors will open adapter mounted on the opposite end of the same side of 4 Choose the Rotary Motion Sensor from the list and the track CI Fig 4 1 is a diagram of the setup press OK 3 The string makes a full loop connecting the cart string 5 The diagram now shows you the properties of the bracket with the large pulley of the RMS sensor and RMS sensor directly under the picture of the interface the small pulley on the opposite bracket That string See CI Fig 4 2 should be tense but not tight 6 Connect the sensor to the interface as shown on the 4 Adjust the height of the string so that the fan blade computer screen to channels 1 and 2 clears the string as it spins The RMS and the small 7 Adjust
6. Slope discharging Average slope R C from slope R C from given values Percent error www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 25 TheRC Time Constant Manual Timing Laboratory Report RV QUESTIONS 1 Show that the magnitude of the charge on a capacitor is given by Q Q 1 e and Q Q e for charging and discharging respectively 2 What is the voltage across a capacitor after a time of two constants when a charging from zero voltage and b discharging from a fully charged condition 3 With V Vie 6 it mathematically takes an infinite time for a capacitor in an RC circuit to discharge Practically how many time constants does it take for a capacitor to discharge to less than 1 of its initial voltage continued 373 www ATIBOOK ir EXPERIMENT 25 TheRC Time Constant Manual Timing Laboratory Report 4 Show that the time for the voltage in the RC circuit to rise to V 2 half max is tin 71n2 5 A 2 0 uF capacitor in a circuit in series with a resistance of 1 0 MQ is charged with a 6 0 V battery How long would it take to charge the capacitor to three fourths of its maximum voltage 374 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 26 The RC Time Constant Electronic Timing RV Advance Study Assignment Read the experiment and answer the following questions 1 Compare the voltage
7. constant m1 New Remove Accept symb l Value 0 55 Units kg 4 Accept 3 Enter the value of this constant and the units b CI Figure 7 4 The expanded calculator window a After the Experiment Constants button is pressed the calculator window expands to full size b The Experiment Constants section is the lower part of the expanded calculator This section is used to define parameters that are to remain constant during the experiment The diagram shows the steps needed to enter experi mental constants into the calculator Reprinted courtesy of PASCO Scientific www ATIBOOK ir 118 12 13 14 15 16 EXPERIMENT 7 Conservation of Linear Momentum b Click the lower Accept button c Click on the New button again and enter the name of the constant as m2 the value as the mass of Car 2 measured before and the units as kg d Click the lower Accept button e Close the experiment constants portion of the calculator window by pressing the button marked Experiment Constants again Calculation of the total momentum of the system a In the same calculator window clear the definition box and enter the following equation TotalP ml smooth 10 v1 m2 smooth 10 v2 This is the calculation of the total momentum Proa mv M a that we will call TotalP The smooth function will help produce a cleaner graph b Press the top Accep
8. or mv MV MV mv In one dimension the directions of the velocity and momentum vectors are commonly indicated by plus and minus signs that is v and y The internal forces of a system do not change the total momentum because according to Newton s third law F F the force on object 1 due to object 2 is equal to and opposite in direction minus to the force on object 2 due to object 1 Thus the change in momentum for one object will be equal in magnitude and opposite in direction to the change in momentum for the other object and the total mo mentum will be unchanged TIn two or three dimensions the momentum is conserved in both or all directions That is p p p 0 and p 0 and p 0 Why Note p Xp and p Xp www ATIBOOK ir 108 EXPERIMENT 7 Conservation of Linear Momentum AY EXPERIMENTAL PROCEDURES procedure twice for each of the three cars and record U the data in the TI Trial Data Table Review the operation of the air track in Experiment 4 Method B Two Timers Set the car in motion if necessary The two observers should start and stop their indi LD aeth nn d diei vidual timers as the leading edge of the car passes So GLE RHE PIG mass OF Cac hear ant TGBOTCE t m tie their respective reference mark set Carry out this TI Trial Data Table Let the masses of the two cars procedure twice for each of the three cars and re of nearly equal mass be m and m and the
9. 5 Using the values of the average thickness per page determined in Procedures 2 and 3 and the overall average thickness of the manual from Procedure 4 compute the number of pages sheets of paper in Be sure the pages are compacted as much as possible before you take the measurements your manual For example if the average thickness per page is 0 150 mm and the average overall thick ness is 35 5 mm 3 55 cm the calculated number of papers is 35 5 mm 0 150 mm page 236 6666 237 pages Determine the actual number of pages sheets of paper in the manual Remember to subtract any pages handed in from Experiment 1 the Advance Study Assignment for this experiment and any others that might be missing Compute the percent error for each of the two experimentally determined values C Density Determinations Js 10 11 12 The densities of the materials of the various objects are to be determined from mass and volume length measurements Taking the mass and length measure ments will give you experience in using the laboratory balance and the vernier and micrometer calipers Using the appropriate measuring instrument s take several measurements to determine the average dimensions of the regularly shaped objects so that their volumes can be calculated Record the data in Data Table 3 Remember to make a zero correction for each reading if necessary Calculate the volume of each of the o
10. Decade box Temperature resistance L L Thermistor resistance TC RC fC 0 C R2UJLORC T Ra Temperature C 3 Ty Te 273 1 T 1 T VT RIR In R R Slope 8 Accepted B Percent error continued 331 www ATIBOOK ir EXPERIMENT 22 The Temperature Dependence of Resistance Laboratory Report fr questions A Metal Conductor 1 What is the value of a for copper in terms of Fahrenheit degrees If the resistance is a linear function on the Celsius scale will it be a linear function on the Fahrenheit scale Explain 2 Replot the copper data for R versus T with a smaller temperature scale extending to 300 C and extrapolate the line to the temperature axis At what temperature would the resistance go to zero What are the practical electrical implications for a conductor with zero resistance It is interesting to note that the value of a is roughly the same for many pure metals approximately 543 or 0 004 C This is the same as the value of the coefficient of expan sion of an ideal gas Also some metals and alloys do become superconductors or have zero resistance at low temperatures Some high temperature ceramic materials show superconductivity at liquid nitrogen temperatures 77 K or 196 C or 321 F 3 A coil of copper wire has a resistance of 10 0 Q and a coil of silver wire has a resistance of 10 1 Q both at 0 C A
11. or TI 26 2 V 0 63 V o That is the voltage across the capacitor is 0 63 or 6396 of its maximum value TI Fig 26 1 For a dc voltage source the capacitor voltage further increases to V and maintains this voltage unless discharged However for an ac voltage source the capacitor voltage increases and decreases as the voltage of the applied signal alternately increases and decreases For example suppose that a square wave ac signal as illustrated in TI Fig 26 2 is applied to the circuit This has the effect of continuously 379 charging and discharging the capacitor The voltage across the capacitor increases according to TI Eq 26 1 and then decreases according to the relationship ye ye RC TI 26 3 On an oscilloscope the time base or the magnitude of the horizontal time axis is determined by the SWEEP TIME DIV From this control setting you can determine time functions for traces on the screen For example suppose two complete wave cycles of a stationary sinusoidal pattern cover 6 66 horizontal divisions with a SWEEP TIME DIV Voltage V Vo V V 1 e7 0 63V t RC Time t TI Figure 26 1 Voltage rise A typical graph of voltage ver sus time for a capacitor charging in an RC circuit In a time t RC the capacitor charges to 63 of its maximum value The square wave generator actually is constantly reversing the charge on the capacitor but the tra
12. 2 Show that the magnification factor for a mirror or lens M d d sign convention omitted is the lateral magnification or the ratio of the height lateral size of the image to that of the object Hint Draw a ray diagram 3 Explain what characteristics make convex spherical mirrors applicable for store monitoring and concave spherical mirrors applicable as flashlight reflectors 4 Prove that for a converging lens for the case d d that d d 2f Laboratory Report continued 417 www ATIBOOK ir EXPERIMENT 28 Spherical Mirrors and Lenses Laboratory Report 5 Using the thin lens equation and the magnification factor show that for a spherical diverging lens the image of a real object is always virtual upright and reduced Does the same apply for a spherical diverging mirror 6 Optional a Using the experimental value of f for the biconvex converging lens and n 1 5 compute the radius of curvature of the lens s surfaces using the lensmaker s equation The radius of curvature for each surface is the same b A student incorrectly assumes that f R 2 for the lens and computes f using the value of R found in part a Compare this computed value of f with the experimental value c The index of refraction of the lens could have a different value n of glass varies generally from 1 5 to 1 7 Would this make a difference Explain 418 www A TIBOOK ir Name Section Date Lab Part
13. E 9 and the logs of the endpoints of the slope interval or their ratio must be found explicitly The ordinate and abscissa values on the log log plot are y and x not log y and log x As in the case of the semi log plot the value of a in y ax can be read directly from the y intercept of the graph However in this case the intercept is not at x 0 but at x 1 since the intercept log y log a requires that log x Oand log 1 0 www A TIBOOK ir Conversion Factors Mass Length Area Volume Time Angle Speed Force Pressure Energy Power Rest mass energy equivalents 1 g 10 kg 1 kg 10 g metric ton 1000 kg lu 1 66 X 10 g 1 66 X 10 kg 1 cm 10 m 0 394 in m 10 km 328 ft 39 4 in 1 km 10 m 0 621 mi 1 in 2 54 cm 2 54 X 10 m 1 ft 12 in 30 5 cm 0 305 m 1 mi 5280 ft 1 609 m 1 609 km 1 cm 107 m 0 1550 in 1 08 X 102 ft 1 m 10 cm 10 76 ft 1550 in 1 in 6 94 X102 f 6 45 cm 645 X10 m 1 ft 144 in 9 29 x 10 n 929 cm 1 cm 10 n 3 53 X 10 gt ft 6 10 X 102 i 1 m 10 cn 10 L 35 3 f 6 10 X10 in 264 gal 1 liter 10 cm 10 n 1 056 qt 0 264 gal 1 in 5 79 X 10 ft 16 4 cm 1 64 X10 n 1 f 1728 in 7 48 gal 0 0283 n 28 3 liters 1 qt 2 pt 946 5 cm 0 946 liter 1 gal 4 qt 231 in 3 785 liters 1 h 60 min 3600s 1 day
14. Photo Courtesy of Sargent Welch TI Example 32 1 In an experiment using a diffrac Then for first order n 1 interference by TI Eq 32 3 tion grating with 600 lines mm the angle between the corresponding lines of a particular component of dsin6 A the first order spectrum on either side of the incident beam is 41 30 What is the wavelength of the spec tral line A dsin6 1 67 X 107 nm sin 20 65 589 nm Solution Given 20 41 30 or 0 20 65 and with a grating ruling of N 600 lines mm the grating constant d or is TI Eq 32 2 TV EXPERIMENTAL PROCEDURE 1 1 67 X 10 mm 1 Review the general operation of a spectrometer if N 600 mm necessary Experiment 30 Record the number of lines per mm of your diffraction grating in the labo ratory report Mount the grating on the spectrometer table with the grating ruling parallel to the collimator slit and the plane of the grating perpendicular to the d 1 67 X 10 mm 10 nm mm 1 67 X 10 nm collimator axis When doing several calculations it is convenient to express the grating constant in nanometers nm Convert ing to nanometers 1 mm 106 nm yields www ATIBOOK ir EXPERIMENT 32 The Transmission Diffraction Grating Measuring the Wavelengths of Light 465 DETERMINATION OF THE WAVELENGTH RANGE OF THE VISIBLE SPECTRUM 2 Mount an incandescent light source in front of the Caution Work very carefully as the discharge 4 tube o
15. xy to choose a data point that is close to the beginning of the motion but for which the position is not zero Record the position and the time of this point in CI Data Table 1 as the first data points x and t Find the position at a time f 2f That is where was the car when the previous time doubled Record x Repeat for times ft 3t t4 4t as many mul tiples of t as you can get from the graph The longer the track you use the more you can get UDIN se BET Fh Ed Exeimec Widow Owpuy Hep Summary wm Setup gt Stor 0000 0 E Cocone Cure Fe FTO j IT LITE Data icons gt Peera o S S 8l ja 2 7 Are wl Al Bho ovs x i Pow h 1 amp 2 No Dat Graph display f option aR F all x lt Position graph lt Velocity graph CI Figure 4 3 Graph displays The graph display in this picture has been maximized to occupy most of the screen Reprinted courtesy of PASCO Scientific www ATIBOOK ir 8 Determine by what factor the distance traveled at time t is greater than the distance at time f Then deter mine by what factor the distance traveled at time f is greater than the distance at time Continue until CI Data Table 1 is complete Now click anywhere on the velocity versus time graph to activate it Use the Smart Tool to find the velocity of the cart at each of the times f t t Record the E
16. z Reading line Ratchet o s ao Sleeve Thimble 25 bi Reading of 5 785 mm Figure 2 5 A micrometer caliper and an example of a micrometer reading a This particular mike has the 1 0 mm and 0 5 mm scale divisions below the reading line b In this diagram as on some mikes the 1 0 mm divisions are above the reading line and the 0 5 mm divisions are below it The thimble in the diagram is in the second rotation of millimeter movement as indicated by its being past the 0 5 mm mark The reading is 5 500 0 285 mm or 5 785 mm where the last 5 is the estimated figure Photo courtesy of Sargent Welch going from 0 50 to 1 00 so that two complete rotations go through 100 cents or 1 00 of the main scale Some micrometers have a scale that indicates the 0 5 mm marks of the main scale divisions and hence tells which rotation the thimble is in see Fig 2 5 Cheaper mikes do not have this extra graduation and the main scale must be closely examined to determine which rotation the thimble is in If a mike does not have the 0 5 mm scale you must de termine whether the thimble is in its first rotation in which case the thimble reading is between 0 00 and 0 50 mm cor responding to the actual engraved numbers on the thimble or in the second rotation in which case the reading is be tween 0 50 and 1 00 mm the actual thimble scale read ing plus 0 50 This can be done by judging whether the edge of the th
17. 200 g is at the 60 cm position Remember to add the masses of the hanger clamps if used Record this value in the data table ii Check your results experimentally and compute the percent error of the experimental value of r4 taking the previously calculated value as the accepted value Case 3 Unknown mass The balance principle A balance scale essentially uses the method of moments to compare an unknown mass with a known mass Some balances have constant and equal lever arms and others do not see Experiment 2 Fig 2 1 This procedure will illustrate the balance principle Figure 12 4 Torque apparatus Example of experimental setup and equili brium conditions Photo Courtesy of Sargent Welch www ATIBOOK ir EXPERIMENT 12 Torques Equilibrium and Center of Gravity 197 a With the meter stick on the support stand at x suspend the unknown mass m near one end of the meter stick for example at the 10 cm posi tion Suspend from the other side of the meter stick an appropriate known countermass m for example 200 g and adjust its position until the meter stick is in balance or equilibrium Record the value of the known mass and the moment arms in Data Table 1 b Remove the unknown mass and determine its mass on a laboratory balance c Compute the value of the unknown mass by the method of moments and compare it with the mea sured value by calculating the percent error 6 Case 4 Instr
18. 3 cm Notice from the relationship that y mx b so that when x 0 then y b If the intercept is at the origin 0 0 then b 0 The equation of the line in the graph in Fig 1 8 is d 7 5t 3 The general equation for uniform motion has the form d vt d Hence the initial displacement d 3 cm and the speed v 7 5 cm s Some forms of nonlinear functions that are common in physics can be represented as straight lines on a Cartesian graph This is done by plotting nonlinear values For example if y ar b is plotted on a regular y versus x graph a parabola would be obtained But if x7 x were used the equation becomes y ax b which has the form of a straight line This means plotting y versus x would give a straight line Since x x the squared values of x must be plotted That is square all the values of x in the data table and plot these numbers with the corresponding y values Other functions can be straightened out by this pro cedure including an exponential function y Ae In this case taking the natural logarithm of both sides In y InA Ine or Iny ax InA where In e x Plotting the values of the natural base e logarithm versus x gives a straight line with slope a and an intercept In A Similarly for y ax using the common base 10 logarithm log y log a log x and log y nlogx loga where log x n log x www ATIBOOK ir 12 EXPERIMENT 1
19. 377 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir T J EXPER MENT 2 6 The RC Time Constant Electronic Timing RV EQUIPMENT NEEDED Function generator square wave Oscilloscope Three capacitors 0 05 uF 0 1 uF and 0 2 uF or capacitor substitution box Three resistors 5 KQ 10 kQ and 20 kQ or resistance box Connecting wires 2 sheets of Cartesian graph paper Optional Unknown resistor wrapped in masking tape to conceal value AY THEORY When an RC circuit is connected to a de voltage source charge must flow into the capacitor before the voltage across the capacitor can change This takes time As the voltage across the capacitor becomes closer to that of the source the flow of charge becomes slower and slower The capacitor voltage approaches the supply voltage as an asymptote coming ever closer but never getting there When the capacitor starts with no voltage across it V Oat t 0 the subsequent changing voltage is given by the equation V Wy eS TI 26 1 WW e where eis the base of the natural logarithms e 2 718 V is the voltage of the dc source R the resistance in the circuit and C the capacitance The quantity 7 RC is the time constant of the circuit See the Theory section in Experiment 25 After a time of one time constant t 7 RC the voltage is V V1 amp ROR y 1 e V 0 63
20. Equivalent resistance R Current J Voltage drops Vi Experimental measurements Currents h I I Vi h I fr questions 1 Discuss the sources of error in the experiment 346 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 23 Resistances in Series and Parallel Laboratory Report 2 Suppose that the resistors in the various circuit diagrams represented the resistances of lightbulbs When a lightbulb burns out the circuit is open through that particular component that is R is infinite Would the remaining bulbs continue to burn for the following conditions If so would the bulbs burn more brightly draw more current or burn more dimly draw less current if a R burned out in the circuit in Part A b R burned out in the circuit in Part B c Then R also burned out in the circuit in Part B d R burned out in the circuit in Part C continued 347 www ATIBOOK ir EXPERIMENT 28 Resistances in Series and Parallel Laboratory Report e Then R also burned out in the circuit in Part C 3 Explain the effect of replacing R with R in Procedure 12 Explain theoretically even if Procedure 12 of the experiment was not done 4 For the circuit in Fig 23 3 V 12 V f 4 Q R 6 Q and R 3 Q Show that the power supplied by the battery P IV is equal to that dissipated in the resistors R What principle
21. Laboratory balance These procedures will greatly assist in understanding some of the most basic physical principles After perform ing the experiment and analyzing the data you should be able to do the following 1 Explain the use of conservation laws linear momen tum and mechanical energy in determining the initial velocity of a projectile using the ballistic pendulum 2 Describe the components of motion and how they are used in determining the velocity of a projectile with range fall measurements 3 Tell how the range of a projectile varies with the angle of projection Masking tape Wooden blocks e 1 sheet of Cartesian graph paper Safety glasses Carbon paper may or may not be needed THEORY A The Ballistic Pendulum Types of ballistic pendula apparatus are shown in Fig 8 1 The ballistic pendulum is used to experimentally deter mine the initial velocity of a horizontally projected object a metal ball fired from a spring gun The projectile is fired into a stationary pendulum bob suspended by a rod and on collision the pendulum and the embedded projec tile swing upward A catch mechanism stops the pendulum at its highest position of swing By measuring the vertical distance that the center of mass of the pendulum ball system rises the initial velocity of the projectile can be computed through the use of the conservation of linear momentum and the conservation of mechanical energy neglecting rota
22. Name Section Date Lab Partner s BAe EX PERIMENT 8 Projectile Motion The Ballistic Pendulum fy Experimental Planning Vy j ew v l h h Before l After GL Figure 8 1 Ballistic pendulum parameters See Experimental Planning text for description A The Ballistic Pendulum The ballistic pendulum allows the experimental determination of the speed of a projectile that is launched horizontally This is done using two conservation principles and a few simple measurements The parameters of a ballistic pendulum system are shown in GL Fig 8 1 A projectile of mass m is fired with velocity v into a stationary pendulum bob of mass M and becomes embedded The horizontal momentum of the system can be expressed in terms of the variables given in GL Fig 8 1 What is the momentum of the system immediately after the projectile is fired that is just before it hits the pendulum bob 1 In terms of the variables given in GL Fig 8 1 what is the momentum of the system immediately after the mass m becomes embedded in the pendulum bob 2 If the horizontal momentum is considered to be conserved in the collision what can you say about the two expressions for momentum that you determined above 3 Write an equation for the conservation of momentum for this collision Designate it Eq 1 continued 127 www A TIBOOK ir EXPERIMENT Experimental Planning 4 Verify that your equati
23. R 5 7 N x 0 tan relative to the x axis or 180 42 138 relative to the x axis It is convenient to measure all component angles as acute angles from the x axis The minus R and positive R indicate that the resultant is in the second quadrant l Figure 5 4 Component method Rather than using the head to tail method of vector addition it is generally more convenient to use the component method in which all vec tors are drawn originating from the origin and resolved into components Although it is customary to measure angles counterclockwise from the positive x axis this procedure of measuring angles from the nearest x axis is convenient in eliminating the need for double angle equations www ATIBOOK ir 78 EXPERIMENT 5 The Addition and Resolution of Vectors The Force Table C Methods of Vector Addition Experimental THE FORCE TABLE The force table is an apparatus that makes possible the experimental determination of the resultant of force vec tors Fig 5 5 The rim of the circular table is calibrated in degrees Forces are applied to a central ring by means of strings running over pulleys and attached to weight hang ers The magnitude mg of a force vector is varied by adding or removing slotted weights and the direction is varied by moving the pulley The resultant of two or more forces vectors is found by balancing the forces with another force weights on a hanger so
24. Signal generator output voltage of the 750 interface CI Figure 26 2 The experimental setup The signal gener ator of the 750 Interface will be the voltage source for this experiment A positive square wave voltage function will be used to periodically charge and discharge the capacitor A voltage sensor will keep track of the voltage across the capacitor Period CI Figure 26 3 A positive square wave The voltage period ically turns ON and OFF To make sure the time it remains ON is enough to charge the capacitor fully the time needed will be approximated to seven time constants 77 and the frequency of the signal will be adjusted accordingly The circuit is shown in CI Fig 26 2 The voltage source is the signal generator of the PASCO Science Workshop 750 Interface A voltage sensor will keep track of the volt age across the capacitor A positive square wave is shown in CI Fig 26 3 The voltage source will periodically turn on and off charging and discharging the capacitor To make sure that the capacitor gets fully charged before the source turns off it will be necessary to set up the square wave so that the time it remains ON is at least seven time constants as explained by CI Eq 26 4 The experimental procedure contains detailed instructions on how to do this B Discharging a Capacitor When the voltage source is turned off the charge in the capacitor flows back through the res
25. and so on for more added weights The linear relation ship of Hooke s law holds provided that the deformation or elongation is not too great Beyond the elastic limit a spring is permanently deformed and eventually breaks with increasing force Notice that Hooke s law has the form of an equation for a straight line F kO yo or F ky ky which is of the general form y x b www A TIBOOK ir 224 EXPERIMENT 14 Simple Harmonic Motion B Simple Harmonic Motion When the motion of an object is repeated in regular time intervals or periods it is called periodic motion Examples include the oscillations of a pendulum with a path back and forth along a circular arc and a mass oscillating lin early up and down on a spring The latter is under the influ ence of the type of force described by Hooke s law and its motion is called simple harmonic motion SHM simple because the restoring force has the simplest form and harmonic because the motion can be described by harmonic functions sines and cosines As illustrated in TI Fig 14 2 a mass oscillating on a spring would trace out a wavy time varying curve on a mov ing roll of paper The equation for this curve which describes the oscillatory motion of the mass can be written as 4 2t COS Y T where T is the period of oscillation and A is the amplitude or maximum displacement of the mass The amplitude A depends on the initial conditions of
26. solution www ATIBOOK ir Name Section Date Lab Partner s x EX PERIMENT 3 The Scientific Method The Simple Pendulum aj Experimental Planning The Simple Pendulum 1 Scientists use models and theories to describe physical phenomena When a new model is developed it must be tested to find out if it is an accurate representation No theory or model of nature is valid unless its predictions are in agreement with experimental results The laboratory provides an environment where extraneous factors can be minimized and specific predictions can be tested The process of making testing and refining models is usually called the scientific method An example of this method will be demonstrated in this experiment for a simple pendulum A simple pendulum is one in which a small but substantial mass is suspended on a relatively light string like the one pictured in Fig 3 1 If one were to observe the motion of the mass swinging back and forth which of the following statements do you think would be the most accurate It is understood that the motion takes place in a single plane The time for the mass to swing back and forth from point A to B and back to A in Fig 3 1 a changes randomly from one swing to the next b gets consistently bigger from one swing to the next c gets consistently smaller from one swing to the next d stays about the same from one swing to the next 2 The time for the mass to sw
27. ticles cannot be detected directly by our senses Hence some observable detection method employing the interac tion of nuclear decay particles with matter must be used There are several methods but the most common is the Geiger tube In a Geiger tube the particles from radioac tive decay ionize gas molecules giving rise to electrical pulses that can be amplified and counted The total instru ment is referred to as a Geiger counter In this experiment the characteristics of a Geiger tube and the inverse square relationship for nuclear radiation will be investigated After performing this experiment and analyzing the data you should be able to 1 Explain the principle of operation of the Geiger coun ter and its major disadvantage 2 Describe how the count rate of a Geiger counter varies with its distance from a radioactive source Sometimes referred to as a Geiger Miiller tube or G M tube A proto type was developed in 1913 by the German physicist Hans Geiger 1882 1945 who worked in England on experiments that led to our present nuclear model of the atom The tube was improved in 1928 in collabora tion with the German physicist S Miiller EQUIPMENT NEEDED Geiger counter rate meter or scaler type Radioactive source for example Cs 137 beta gamma Laboratory timer or stopwatch Calibrated mounting board or meterstick 2 sheets of Cartesian graph paper or 1 sheet of Cartesian and optiona
28. where m and b are constants When the values of such quantities are plotted the graph is a straight line as shown in e Fig 1 8 The m in the algebraic relationship is called the slope of the line and is equal to the ratio of the intervals Ay Ax Any set of intervals may be used to determine the slope of a straight line graph for example in Fig 1 8 Ay 15cm 7 5 cm Aw 2 08 eee Ay 45cm 7 The straight line of best fit for a set of data points on a graph can be determined by a statistical procedure called linear regression using what is known as the method of least squares This method determines the best fitting straight line by means of differential calculus which is beyond the scope of this manual The resulting equations are given in Appendix D along with the procedure for determining the slope and intercept of a best fitting straight line The mean deviation and standard deviation are discussed in Appendix C and D respectively They give an indication of the dispersion of a set of measured values These methods are optional at your instructor s discretion Points should be chosen relatively far apart on the line For best results points corresponding to data points should not be chosen even if they appear to lie on the line The bin the algebraic relationship is called the y intercept and is equal to the value of the y coordinate where the graph line intercepts the Y axis In Fig 1 8 b
29. 15 3 The vibrator and pulley should be clamped to support posts at the opposite ends of the laboratory table to give an active string length of about 150 cm This length may vary for a given setup Measure the total length of the string and determine its mass on a laboratory balance Record these values in the data table and compute the linear mass density u m L Note L is the total length of the string Attach the string to the vibrator and suspend a weight hanger from the other end as shown in Fig 15 3 Make certain that the string is aligned properly and that it is parallel to the table surface Measure the distance be tween the vibrator arm and the point of contact of the string on the pulley Record this length L in the data table Turn on the vibrator Try to produce different standing wave patterns in the string by alternately lifting and carefully pulling down on the weight hanger It is helpful to fold a thin strip of paper in half and hang it on the string to observe vibrating action The number of loops should increase with less tension Why Also try grasping the string at a node and antinode of a given pattern to see what happens When you are familiar with the operation of the appa ratus add enough weights to the weight hanger so that a standing wave pattern of two loops is formed in the string nodal point at the center Adjust the tension by adding or removing some small weights until the loops are
30. 2 3 and 4 are the small buttons on the left analog channels A B and C are the larger buttons on the right 3 Click on the channel A button in the picture A win dow with a list of sensors will open 4 Choose the Light Sensor from the list and press OK 5 Connect the sensor to channel A of the interface as shown on the computer screen 6 In the same window under Measurement select Light Intensity and deselect all others Set the Sample Rate to 20 Hz 7 Now click on the Channel 1 button in the picture to access the list of sensors again 8 Choose the Rotary Motion Sensor RMS from the list and press OK 9 Connect the RMS to channels 1 and 2 of the interface as shown on the computer screen 10 On the same window adjust the properties of the RMS as follows First Measurements tab select Position Ch 1 amp 2 and deselect all others Rotary Motion Sensor tab set the Resolution to high 1440 divisions rotations and set the Linear Scale to Rack amp Pinion Set the Sample Rate to 20 Hz The Data list on the left of the screen should now have three icons one for voltage one for light inten sity and one for the position data www A TIBOOK ir Ele Edt Experiment Window Display Heb Rg betel Y Voltage ChA V T Light Intensity Ch A rr a Position Ch 122 mj 42 Light Intensity Ch A vs Pc 1 Digits kh FFT p Graph ic Graph 1 WA Histogram 7 Meter E Workbeok Double click a display
31. 24h 1440 min 8 64 X 10 s 1 year 365 days 8 76 X 10 h 5 26 X 10 min 3 16 X 107 s 360 27 rad 180 v rad 1 rad 57 3 90 7 2 rad 60 7 3 rad 1 0 0175 rad 45 7 4 rad 30 7 6 rad 1 rev min 77 30 rad s 0 1047 rad s 1 m s 3 6 km h 3 28 ft s 2 24 mi h 1 km h 0 278 m s 0 621 mi h 0 911 ft s 1 ft s 0 682 mi h 0 305 m s 1 10 km h 1 mi h 1 467 ft s 1 609 km h 0 447 m s 60 mi h 88 ft s 1 N 0 225 Ib 1 lb 4 45 N Equivalent weight of 1 kg mass on the Earth s surface 2 2 lb 9 8 N 1 Pa N m 1 45 X10 Ib in 7 4 X 10 torr mm Hg 1 torr mm Hg 133 Pa N m 0 02 Ib in 1 atm 14 7 lb in 1 013 X10 N m Pa 1 Ib in 6 90 x 10 Pa N m 1 bar 10 N m Pa 1 millibar 10 N m Pa 1 J 107 ergs 0 738 ft lb 0 239 cal 9 48 x 10 Btu 6 24 X 10 8eV 1 kcal 4186 J 3 968 Btu 1 Btu 1055 J 778 ft lb 0 252 kcal 1 cal 4 186 J 3 97 x 103 Btu 3 09 ft lb 1 ft lb 1 356 J 1 29 x 10 Btu 1 eV 1 60 x 107 J 1 kWh 3 6 x 106 1 W 0 738 ft Ib s 1 34 X 10 hp 3 41 Btu h 1 ft Ib s 1 36 W 1 82 X 10 hp 1 hp 550 ft Ib s 745 7 W 2545 Btu h 1 u 1 66 X 1077 kg lt gt 931 MeV 1 electron mass 9 11 X 10 kg 5 49 X 10 u 0 511 MeV 1 proton mass 1 673 X 107 kg 1 00728 u lt gt 938 3 MeV 1 neutron mass 1 675 X 1077 kg 1 00867 u lt gt 939 6 MeV www ATIBOOK ir
32. 4 5A v 2yj t are not the actual instantaneous velocities of the falling ob ject since it had a nonzero initial velocity or was in motion at the first spot line y TI Eq 4 4A really applies to the situation and 2y t v v Note that the instantaneous velocities you computed 2y t included v Even so plot the computed v s on a v versus t graph and determine the slope This will still be an experimental value of g Compute the percent error of your experimental result Accepted value g 9 80 m s 980 cm s You will notice on your graph that the line does not intercept the y axis at the origin t 0 This is because t 0 usually was measured not at the actual time of release but at some time later From TI Eqs 4 4A and 4 1A we see that at t 0 in the measurement time frame 2y 29 Ving ty where y and f are respectively the distance and time measured by the zero values from the point of release www ATIBOOK ir The initial velocity at the first line spot is then Vo Yoto This gives you the extra bonus of being able to determine v from your graph since Visa w i 2 EXPERIMENT 4A Uniformly Accelerated Motion 69 where v is the intercept value Compute the initial la 0 velocity that the falling object had at your first line spot and record in TI Data Table 1 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Sectio
33. 7 in the material is found to be proportional to the voltage Z V The resistance R of the material is defined as the ratio of the applied voltage and the resulting current that is TI 20 1 definition of electrical resistance For many materials the resistance is constant or at least approximately so over a range of voltages A resistor that has constant resistance is said to obey Ohm s law or to be ohmic From TI Eq 20 1 it can be seen that the unit of resistance is the volt ampere V A However the combined unit is called the ohm Q in honor of Georg Ohm 1787 1854 a German physicist who developed this relationship known as Ohm s law Note that to avoid confusion with a zero the ohm is abbreviated with a capi tal omega Q instead of a capital O A plot of V versus J for an ohmic resistance is a straight line TI Fig 20 1 Materials that do not obey e Voltage a e I Current TI Figure 20 1 Ohmic resistance A voltage versus current graph for an ohmic resistance is a straight line the slope of which is equal to the value of the resistance R V I 295 Ohm s law are said to be nonohmic and have a nonlinear voltage current relationship Semiconductors and transis tors are nonohmic In common practice Ohm s law is written IR TI 20 2 where it is understood that R is independent of V Keep in mind that Ohm s law is not a fundamental law such as Newton
34. AQ oup and stirrer and Hes Tm T My Cy Ts Ta MesCes Te Ty my Cw MesCos Ts a T Solving for Cm u MyCy F macs X Tr Ty 7 My Tm Ti 17 4 C where 7 is the final intermediate equilibrium temperature of the system The other subscripts indicate the masses specific heats and initial temperatures of the respective components Hence Eq 17 4 may be used to determine the specific heat c of the metal if all the other quantities are known EXPERIMENTAL PROCEDURE 1 Weigh out 400 g to 500 g 0 4 kg to 0 5 kg of one kind of dry metal shot Do this by first determining the mass of the empty boiler cup in which the metal shot is heated and then adding an appropriate amount of metal shot to the cup and reweighing Record the mass of the metal m and the room temperature 7 in the data table Your instructor may prefer to use a solid piece of metal with a string at tached instead of metal shot In this case it is neces sary to weigh only the piece of metal 2 Insert a thermometer well into the metal shot or into the cup with a piece of metal if used place the cup and shot in the boiler and start heating the boiler water Caution If a mercury thermometer is used special care must be taken If the thermometer should break and mercury spill into the hot metal immediately www ATIBOOK ir 4 notify your instructor The cup should be removed from the room
35. Define the term linear mass density Also what is implied if it is assumed that the linear mass density of an object is uniform 192 www A TIBOOK ir EXPERI ENT 1 2 Torques Equilibrium and Center of Gravity INTRODUCTION AND OBJECTIVES In introductory physics forces act on particle objects That is we consider an object to be a particle which gen erally responds linearly to a force In reality an object is an extended collection of particles and where a force is applied makes a difference Rotational motion becomes relevant when the motion of a solid extended object or a rigid body is considered A rigid body is an object or sys tem of particles in which the distances between particles are fixed and remain constant A quantity of liquid water is not a rigid body but the ice that would form if the water were frozen is Actually the concept of a rigid body is an idealiza tion In reality the particles atoms and molecules of a solid vibrate constantly Also solids can undergo defor mations Even so most solids can be considered to be rigid bodies for the purposes of analyzing rotational motion An important condition of rigid bodies in many prac tical applications is static equilibrium Examples include girders in bridges and the beam of a laboratory beam balance when taking a reading They are at rest or in static equilibrium In particular the balance beam is in rotational static equilibrium when ba
36. Examples of the ray dia gram method for determining the image characteristics for a a biconvex or converging lens and b a biconcave or diverging lens The bi indicates two surfaces for example biconvex two convex surfaces www ATIBOOK ir 408 EXPERIMENT 28 Spherical Mirrors and Lenses If the image is formed on the side of the lens opposite to the object it is real and can be observed on a screen However if the image is on the same side of the lens as the object it is virtual and cannot be seen on a screen The spherical thin lens equation and magnification factor for analytically determining the image character istics are identical to the equations for spherical mirrors Eqs 28 2 and 28 3 The sign convention is also similar see Table 28 1 It should be noted that this lens equation applies only to thin lenses Example 28 2 An object is placed 30 cm from a biconcave lens with a focal length of 10 cm corre sponding to the case in Fig 28 4b Determine the image characteristics analytically Solution With d 30 cm and f 10 cm negative by convention for a concave lens using Eq 28 2b yields d f 30 cm 10 cm d d f 30cm 10cm 300 _ cm 30cm _ 75cm 40 cm 4 Then d 30 4 y 76 904 1 d 30 4 Thus the image is virtual negative d upright posi tive M and reduced by a factor of However the relationship between the focal l
37. Experimental Uncertainty Error and Data Analysis H EN Period T of spring oscillation E BE Vs mass m suspended on a spring LL 6 0 5 0 E 4 0 4 MNNEEN Seen E oa m EENE NEN o 2 1 Eje ai 5 n 3 0 cI Co ERETTE Coo Coo 2 0 1 0 H tt 1 LE Name 4e4e3ee 0 0 1 Date October 15 2009 0 0 025 0 10 0 15 0 20 0 25 3 0 Mass kg Figure 1 7 Error bars An example of graphically presented data with error bars An error bar indicates the precision of a measurement In this case the error bars represent mean deviations Plotting the values of log y versus log x gives a straight line with slope n and intercept log a See Appendix E EXPERIMENTAL PROCEDURE Complete the exercises in the Laboratory Report showing calculations and attaching grap
38. Ez Graph 1 fi Histogrsm 7 Meter L H So Scope x 5 fi a LE Table Time s C93 Wurkhiu ik otalKE No Data 7 a T7 TT fi Time s CI Figure 7 5 Data Studio setup Data for velocity of each car total momentum and total kinetic energy will appear simulta neously on four plots with matching time axes The graph window may be maximized to occupy the whole screen in order to display the experimental results better Reprinted courtesy of PASCO Scientific Velcro tabs a to E ports 3 4 Magnetic ends N T IDS track collision cars e RMS Been Car 1 Thread Car 2 E e T Car 1 F Sunneciste Car string brackets ports 1 2 IDS track pulley brackets CI Figure 7 6 Experimental setup Two collision carts are installed on the same track Each cart is connected to its own rotary motion sensor on one side and to its own IDS RMS adapter track pulley bracket on the other side An elastic collision can be performed by having the magnetic ends of the cars face each other An inelastic collision can be performed by having the nonmagnetic sides face each other and putting clay or Velcro on the ends of the cars www A TIBOOK ir 120 EXPERIMENT 7 Conservation of Linear Momentum IDS track pulley IDS track bracket IDS mount accessory To computer interface CI Figure 7 7 Mounting the RMS and
39. If a stack of glass plates is used the transmitted beam becomes more linearly polarized C Polarization by Refraction In a sense the preceding case of a polarized transmitted beam from a stack of glass plates might be thought of as polarization by refraction since the refracted beam is polar ized However polarization by refraction generally refers to the double refraction exhibited by some crystals In an optically isotropic medium such as glass light travels with the same speed in all directions As a result the material is characterized by a single index of refrac tion In certain anisotropic crystals however the speed of light is not the same in all directions The crystal cal cite CaCO Iceland spar for example exhibits double refraction or birefringence and is characterized by two indices of refraction When an unpolarized beam of light enters a calcite crystal it splits into two polarized rays with polarizations in mutually perpendicular directions TI Fig 29 5 One beam is called the ordinary 0 ray and the other the extraordinary e ray Because of this property when something that is a printed line is viewed through a cal cite crystal a double image is seen corresponding to the two emergent rays D Polarization by Scattering Scattering is the process of a medium absorbing light then reradiating it For example if light is incident on a gas the electrons in the gas atoms or molecules can abs
40. In this experiment it is convenient to think of fas being in revolutions per second EXPERIMENTAL PROCEDURE A Manual Centripetal Force Apparatus 1 A type of hand operated centripetal force apparatus is shown in Fig 9 2 By rolling the rotor between the thumb and fingers the operator sets a suspended mass bob into circular motion with the centripetal force be ing supplied by a spring The horizontal support arm b Figure 9 2 Hand operated centripetal force apparatus a The suspended weights used to determine the centripe tal force supplied by the spring are not attached to the bob when the apparatus is operationally rotating b Appara tus in action See text for description Photos Courtesy of Sargent Welch www ATIBOOK ir is counterbalanced for ease of operation the position of the counterbalance is not critical A pulley mounted to the base of the apparatus is used to make direct measurement of the spring tension supplying the centripetal force for uniform circular motion of a particular radius indicated by the distance between the vertical pointer rod P and the axis of rotation Remove the bob and determine its mass on a labo ratory balance Record the mass value in Data Table 1 Adjust the position of the vertical pointer rod if possible to the smallest possible radius distance between the pointer tip and the center of the vertical rotor shaft Measure this distance and record Attach the bob
41. Inclined Plane The AMA of an inclined plane is somewhat difficult to determine experimentally That is manually determine F by pulling a load up the incline at a constant speed with a spring scale So for this simple machine the focus will be on the TMA This is given by TMA 1 sin0 where is the angle of incline 1 Several angles are listed in Data Table 1 Compute the TMA for each angle 2 Plot a graph of TMA versus 0 and comment on the result Compute the TMA for 0 90 What does this tell you B Lever 3 Use a load of 0 40 kg to 0 50 kg or what is provided and record the mass in Data Table 2 and compute its weight in newtons N Assemble the lever as shown in Fig 13 2b using the pivot block meter stick and load The load should be on the table It may be nec essary to tape the load to the stick Begin with the fulcrum at the 50 cm mark L L 50 cm 4 Attach the spring scale to the stick at the end opposite the load Tape or some other means may be used here Then pull vertically downward on the scale with enough force so that the load moves upward with approximately a constant speed Try several pulls to get familiar with the equipment Also it may be necessary to put the fulcrum block near the edge of the table so as to have room to pull the scale Then during a pull take a scale reading Your lab partner should take the reading Why Record in Data Table 2 Repeat the procedure for a t
42. Read the experiment and answer the following questions 1 What is the significance of the half life of a radioactive isotope in terms of a the amount of sample or number of nuclei and b the activity of the sample 2 What is the decay constant Is it the same for each decay process What are the units of the decay constant 3 How is the half life related to the decay constant of a radioactive process 4 What is meant by milking a cow Give the technical terms for milking and cow 491 continued www A TIBOOK ir EXPERIMENT EA Advance Study Assignment 5 Ba 137m is a nuclear isomer of Ba 137 Explain what this means 6 Ifa particular radioactive sample undergoes four half lives what fraction of the original material remains 492 www A TIBOOK ir EXPER MENT 3 4 Radioactive Half Life INTRODUCTION AND OBJECTIVES The decrease in the activity of a radioactive isotope is characterized by its half life This is the time required for one half of the nuclei of a sample to decay Of course the nuclei of a sample cannot be counted directly but when one half of the sample has decayed the activity or the rate of emission of nuclear radiation has also decreased by one half Thus as we monitor the sample with a Geiger counter when the count rate counts per minute cpm has decreased by one half one half life has elapsed In this experiment the half life of a radioactive isotope will be determined After
43. Tighten the clamp screw and record in Data Table 1 the meter stick read ing or the distance of the balancing point x from the zero end of the meter stick 3 Case 1 Two known masses a With the meter stick on the support stand at x suspend a mass m 100 g at the 15 cm position on the meter stick that is 15 cm from the zero end of the meter stick b Set up the conditions for static equilibrium by adjusting the moment arm of a mass m 200 g suspended on the side of the meter stick opposite m Record the masses and moment arms in Data Table 1 If clamps are used instead of string do not forget to add the masses of the clamps Remem ber the moment arms are the distances from the pivot point to the masses that is r x xol c Compute the torques and find the percent differ ence in the computed values that is compare the clockwise torque with the counterclockwise torque Case 2 Three known masses Case a i With the meter stick on the support stand at xo suspend m 100 g at the 30 cm position and m 200 g at the 70 cm position Suspend m 50 g and adjust the moment arm of this mass so that the meter stick is in static equilib rium Record the data in Data Table 1 ii Compute the torques and compare as in Proce dure 3 Case b i Calculate theoretically the lever arm r3 for the mass m3 50 g for the system to be in equilib rium if m 100 g is at the 20 cm position and m
44. a Plot the weight force or the force of kinetic friction F fi versus the normal force N for these data on the same graph as for Part A Draw a straight line that best fits the data Since fk WN the slope of the straight line is uy Determine the slope and record it in TI Data Table 2 Calculate the percent decrease of uy from the u value ELEVATED BOARD INCLINED PLANE 9 10 Elevate the pulley end of the board on a support to form an inclined plane TI Fig 10 3 see Fig 11 3 for a similar setup Note in Fig 10 3 the magnitude of the normal force perpendicular to the plane is equal to a component of the weight force With the block laying on a side of its larger sur face area determine the angle 0 of incline that will al low the block to slide down the plane with a constant speed after being given a slight tap No suspended weight is used in this case Note The maximum an gle before slipping without tapping gives u whereas the angle of constant velocity with tapping gives py Using a protractor measure the angle 0 and record in TI Data Table 3 Also with a meter stick measure the length L of the base along the table and the height h of the inclined plane Record the ratio h L in TI Data Table 3 TI Figure 10 3 Coefficient of kinetic friction Experimental setup to determine ux See text for description www ATIBOOK ir 162 EXPERIMENT 10 Friction 11 Repeat this procedure for the blo
45. and acceleration Use y for length and g for acceleration Hence we have a simple equation that involves only length time and acceleration along with the equipment to measure length and time for a falling object to find g Solve the equation for t which is the time of fall that will be measured Answer the following questions 1 What effect might the distance of fall have on your experimental measurements and results Hint Consider the following extreme cases a How long would it take the object to reach the floor if you dropped it from a height of 0 50 m Could you measure this accurately with a stopwatch b What if an object were dropped from a height of 10 m Could you measure this distance accurately with a meter stick Would the acceleration remain constant 48 www ATIBOOK ir Name Section LL Date Lab Partner s EXPERIMEN 7 4 Advance Study Assignment 2 From the preceding calculation it should be obvious that to experimentally time the distance of fall for a dropped object is critical To gain an appreciation of how the distance of fall varies with time consider the daring experimenter shown in GL Fig 4 1 Jo Jo will illustrate the time distance relationship of free fall by stepping off a high vertical cliff with a timer in one hand and a marker in the other For each second of fall he makes a mark on the cliff face But wait Jo Jo wants you to determine how far he would fall during each second
46. as in this picture or independently if resized to fit the full screen Reprinted courtesy of PASCO Scientific www A TIBOOK ir 236 EXPERIMENT 14 Simple Harmonic Motion Support rod Rotary motion i sensor Light rod Pendulum bob CI Figure 14 7 The experimental setup The light rod with the bob at the end is attached to the front screw of the rotary motion sensor 2 The rotary motion sensor will set its zero at the location of the pendulum when the START button is pressed If we want the position 0 0 to correspond with the equilibrium position of the pendulum it is very important that the START button be pressed while the pendulum is at rest in the equilibrium position 10 11 After pressing the start button displace the pendulum a small angle x 10 to the side and let it go Collect data for about 5 or 6 seconds and then press the STOP button Print the graphs and paste them to the laboratory report Read from any of the position graphs what was the maximum amplitude of the pendulum and record it in CI Data Table 1 Determine from the graph the period of oscillation of the pendulum and record it in the table From the kinetic energy graph look at the first clear complete cycle of the motion and find the maximum kinetic energy during that cycle Record it in the table Record also the position of the pend
47. available from PASCO Scientific THEORY A Types of Experimental Uncertainty Experimental uncertainty error generally can be classified as being of two types 1 random or statistical error and 2 systematic error These are also referred to as 1 indeterminate error and 2 determinate error respec tively Let s take a closer look at each type of experimental uncertainty RANDOM INDETERMINATE OR STATISTICAL ERROR Random errors result from unknown and unpredictable variations that arise in all experimental measurement situa tions The term indeterminate refers to the fact that there is no way to determine the magnitude or sign too large too small of the error in any individual measurement Conditions in which random errors can result include 1 Unpredictable fluctuations in temperature or line voltage Mechanical vibrations of an experimental setup 3 Unbiased estimates of measurement readings by the Observer P Repeated measurements with random errors give slightly different values each time The effect of random errors may be reduced and minimized by improving and refining experimental techniques SYSTEMATIC DETERMINATE ERRORS Systematic errors are associated with particular measure ment instruments or techniques such as an improperly calibrated instrument or bias on the part of the observer The term systematic implies that the same magnitude and sign of experimental uncertainty are obtained w
48. f Conclusions continued 413 www ATIBOOK ir EXPERIMENT 28 Spherical Mirrors and Lenses Laboratory Report B Spherical Lenses Convex lens Ray diagrams f d lt 2f d 2f Calculation of d for object at o Experimental focal length f Average 414 www ATIBOOK ir Name Section Lab Partner s EXPERIMEN T 26 DATA TABLE 2 Spherical Mirrors and Lenses Purpose To determine the image distance and magnification Laboratory Report Experimental Computed di 6 M factor estimated d percent difference d gt 2f fed of do lt f Calculations show work continued 415 www ATIBOOK ir EXPERIMENT 28 Spherical Mirrors and Lenses Laboratory Report Concave lens Ray diagrams dy gt BF Conclusions F F Fe dy Bf F F if Focal length determination F F fa focal length of the combination f focal length of convex lens f focal length of concave lens RV QUESTIONS 1 A plane mirror essentially has a radius of curvature of infinity Using the mirror equation show that a the image of a plane mirror is always virtual b the image is behind the mirror the same distance as the object is in front of the mirror and c the image is always upright 416 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 28 Spherical Mirrors and Lenses
49. of the pendulum at any moment during its motion can eas ily be determined The kinetic energy of a pendulum of mass m moving with a linear speed v is given by CI 14 3 The potential energy measured with respect to the equilib rium position depends on the height above the equilibrium at a particular time That is U mgh mg L L cos0 CI 14 4 See CI Fig 14 2 A A 0 L cos 0 L Y AE L Lcos0 Es CI Figure 14 2 The elevation of a pendulum with respect to the equilibrium position The elevation of a pendu lum with respect to the equilibrium lowest position can be expressed in terms of L the length of the pendulum and of 0 as L L cos0 The angular displacement has been exaggerated in the illustration For simple harmonic motion 0 must be small www ATIBOOK ir 232 EXPERIMENT 14 Simple Harmonic Motion In this experiment a sensor will keep track of the angular position 0 of the pendulum as it swings The sen sor will also keep track of the angular speed w A0 At of the pendulum The linear speed v can then be deter mined as v wL where L is the length of the pendulum and also the radius of the circular arc described by its motion The kinetic and potential energies of the pendu lum at any time can then be calculated BEFORE YOU BEGIN 1 Measure the mass of the pendulum bob M and record it in the laboratory report in kilograms 2
50. www A TIBOOK ir 26 EXPERIMENT 2 Measurement Instruments Mass Volume and Density Similarly if the error is negative or the vernier zero lies to the left of the main scale zero measurements will be too small and the zero correction must be added to the measurement readings Summarizing these corrections in equation form Corrected reading actual reading zero reading For example for a positive error of 0 05 cm as in Fig 2 4 Corrected reading actual reading 0 05 cm If there is a negative correction of 0 05 cm then Corrected reading actual reading 0 05 cm actual reading 0 05 cm C The Micrometer Caliper The micrometer caliper 6 Fig 2 5a commonly called a mike provides for accurate measurements of small lengths A mike is particularly convenient in measuring the diameters of thin wires and the thicknesses of thin sheets It consists of a movable spindle jaw that is advanced toward another parallel faced jaw called an anvil by rotating the thimble The thimble rotates over an engraved sleeve or barrel mounted on a solid frame Most micrometers are equipped with a ratchet ratchet handle is to the far right in the figure that allows slippage of the screw mechanism when a small and constant force is exerted on the jaw This permits the jaw to be tightened on an object with the same amount of force each time Care should be taken not to force the screw particularly if the micro
51. www A TIBOOK ir TI Figure 29 7 Optical stress analysis with polarized light A transparent bar reveals stress concentrations near the support and loading point because of optical activity Cengage Learning Incident light Reflected light Mirror Polarizer Liquid Polarizer crystal a Incident light No reflected light TI Figure 29 8 LCD liquid crystal display a A liquid crystal has the property of being able to twist or rotate the plane of linearly polarized light by 90 b When a voltage is applied to the crystal this property is lost With no light reemerging the crystal appears dark Voltage b have the ability to rotate or twist the plane of polarization of polarized light In a so called twisted nematic display a liquid crystal is sandwiched between crossed polarizing sheets and backed by a mirror e TI Fig 29 8 Light falling on the surface of an LCD is polarized twisted reflected and twisted again and then leaves the display Hence the display normally appears light because the doubly twisted polarized light coming back from the surface is seen However when a voltage is applied to the crystal the polarized light is not twisted the last time EXPERIMENT 29 Polarized Light 427 and hence is absorbed by the final polarizing sheet Such dark regions of the crystal are used to form numbers and letters in the display RV EXPERIMENTAL PROCEDURE A Plane of Polariza
52. 18 Archimedes Principle Buoyancy and Density 273 SO Sp gr p 18 4 That is the specific gravity is equal to the numerical value of the density of a substance when expressed in g cm For example the density of mercury is 13 6 g cm and mercury has a specific gravity of 13 6 A specific gravity of 13 6 indicates that mercury is 13 6 times more dense than water p sp gr p or that a sample of mercury will weigh 13 6 times as much as an equal volume of water Archimedes principle can be used to determine the specific gravity and density of a submerged object By Eq 18 2 sp gf 07 18 5 where w is the weight of the object w is the weight of the water it displaces and by Archimedes principle ww Fy For a heavy object that sinks the net force as it does so is equal to w Fy Why If attached to a scale while submerged it would have a measured apparent weight and w w F Thus F w c and Eq 18 5 may be written Wo sp gr f Ow Wo T Wo or in terms of mass measured on a balance m w g sp gr p 18 6 of a heavy object that sinks where p is the magnitude of the density of the object in g cm This provides us with an experimental method to determine the specific gravity and density of an object that sinks To measure the specific gravity and density of an object that floats or is less dense than water usin
53. 2 Resistance measurement Another basic ar rangement for measuring resistance with an ammeter and a voltmeter The ammeter measures the current through R but the voltmeter is across R and the ammeter Therefore the true value of R is less than the measured value if the measured value is taken to be V I where R is the resistance of the ammeter When R lt lt R the voltage drop across R that is V IR is small compared to that across R which is Vg JR Taking the voltage drop or the resistance of the ammeter into account V Vg V IR IR K R R IR and R R R 21 5 Solving for R and substituting for R from the first equation R R 21 6 B Wheatstone Bridge Method The basic diagram of a Wheatstone bridge circuit is shown in Fig 21 3 In its simplest form the bridge circuit con sists of four resistors a battery or voltage source and a sensitive galvanometer The values of R R and R are all known and R is the unknown resistance Switch S is closed and the bridge is balanced by ad justing the standard resistance R until the galvanometer shows no deflection indicating no current flow through the galvanometer branch As a result the Wheatstone bridge is called a null instrument This is analogous to an ordinary double pan beam balance which shows a null or Zero reading when there are equal masses on its pans Assume that the Wheatstone bridge is balanced
54. 200 5 2 2 1 g masses and a similar de scending mass m 260 g 50 g hanger 200 10 g masses Mass increments larger than 1 and 2 g may have to be used depending on the pulley friction Friction may not be uniform so a greater mass difference may be needed to initiate motion 2b 3b 4b Measure the frictional mass as done previously in Procedure A4a Record the data in the asterisked column in TI Data Table 2 The value of m from these data may be used in the calculations for all trials in TI Data Table 2 since the total mass and presumably the friction will now be constant Leaving mj in place transfer 1 g from m to m in order to create a net unbalanced force without affecting the total mass Make three measurements of the travel time as in Procedure 5a Record all pertinent data in the Trial 5 column Leaving rn and the previously transferred 1 g mass in place a transfer an additional 2 g for Trial 6 b transfer an additional 2 g for Trial 7 c transfer an additional 5 g for Trial 8 C Comments on Experimental Technique 1 The masses must start from rest during the accelera tion trials A good technique is as follows a Hold m down against the floor b Simultaneously release m and start the timer c Stop the timer at the instant m strikes the floor The best results are obtained when the same per son releases m and operates the timer Why Some of the masses
55. 23 2 8 The default form of the signal generator function is a sine wave Change it to a Positive Up Ramp Wave by selecting from the drop menu 349 9 Setthe amplitude to 2 0 V and the frequency to 0 20 Hz 10 Click on the Measurements and Sample Rate button on the Signal Generator window A list of measurements will open Choose to measure the output current Deselect the measurement of the output voltage 11 Press the Sampling Options button on the top tool bar of the Experiment Setup window The Sampling Options window will open Under Automatic Stop set the time to 4 5 seconds Click OK 12 Click on the Calculate button on the main toolbar The calculator will open Follow the next steps a Clear the definition box at the top and enter the following formula in it Voltage smooth 20 x b Press the top Accept button after entering the formula Notice that the variable x will appear waiting to be defined c To define the variable click on the drop menu button on the side of the variable Define x as a Data Measurement and when prompted choose Voltage ChA www A TIBOOK ir 350 EXPERIMENT 23 Resistances in Series and Parallel r Sample Rate r Sensor Samping Options Setup Timers Calbeate Sensors Samping Options Choose Intedace A B C Sga Generator CI NE RES CI Figure 23 1 The Experiment Setup window The voltage sensor is connected to Channel A and wor
56. 3 taking a series of measurements at approximately 10 C temperature intervals until a final temperature of about 90 C is reached 5 Optional Repeat the foregoing procedures using the constantan wire coil starting near room temperature Use Data Table 1A 6 Compute R of the coil s at the various temperatures and plot a graph of R versus T with a temperature range of 0 C to 100 C Draw the straight line s that best fit s the data and extrapolate the line s to the y axis Determine the slope and y intercept of the line s www ATIBOOK ir EXPERIMENT 22 The Temperature Dependence of Resistance 327 From the slope find the temperature coefficient resistance measurements since a thermistor shows of resistance for the specimen s and compare with considerable variation in resistance with temperature the accepted value found in Appendix A Table A6 by computing the percent error 8 a Find the quantities listed in the second part of Data Table 2 B Thermistor b Plot a graph of y In R R versus x 1 T 4 7 Replace the coil with the thermistor in the bridge circuit de rapit draw DI State dC Mae that bestiis and repeat the previous measurement Procedures 1 4 starting at a temperature near room temperature In this portion of the experiment exercise great care in order to have temperatures as constant as possible when making c Determine the slope of the line which is the value of B Compare thi
57. 519 second quadrant y first quadrant X third quadrant fourth quadrant TT IER x Ssin y sin d A cos 8 F tan 8 cma x 0 rad sin 0 cos 0 tan 0 0 0 0 1 0 30 77 6 0 500 0 866 0 577 45 77 4 0 707 0 707 1 00 60 7 3 0 866 0 500 1 73 90 7 2 1 0 oo The sign of trigonometric functions depends on the quadrant or sign of x and y for example in the second quadrant x y x r cos 0 and x r sin 6 or by Reduction Formulas 0 in second quadrant 0 in third quadrant sin cos0 0 90 sin 0 180 cos sin 0 90 cos 0 180 Fundamental Identities sin cos 1 sin 20 2 sin 0 cos 6 cos 0 cos 0 sin 2cos 8 1 1 2 sin 8 sin 4 1 cos 20 cos id cos 20 For half angle 0 2 identities replace 0 2 for example sin 9 2 X 1 cos 0 cos 0 2 5 1 cos 0 sin a B sina cos B cos a sin B cos a B cosa cos B sina sin B Law of sines a b c sina sing siny Law of cosines a c 2bc cos a bD a e 2ac cos B C a b 2ab cos y 0 in fourth quadrant cos 0 270 sin 0 270 For very small angles cosQ 1 sin 0 0 radians tan 0 0 www ATIBOOK ir APPENDIX C Absolute Deviation and Mean Absolute Deviation ABSOLUTE DEVIATION Having obtained a set of measurements and determined the mean valu
58. 8 a Sketch a ray diagram for a convex lens with the object at its focal point As with the concave mirror Procedure 1 the image is formed at infinity b Using the lens equation determine the image characteristics for an object at infinity c Experimentally determine the focal length of the lens by a procedure similar to that used for the concave mirror The lens may be placed in a lens holder and mounted on a meter stick In general for a lens f 4 However it can be shown for the case of d d that d 2f See Question 4 at the end of the experiment Arrangements for experimental procedures for a spherical mirrors and 9 Repeat the four cases for the lens as was done for the concave mirror in Procedures 3 to 6 with R replaced by 2f see Fig 28 5 It is initially instructive to move the lens continuously toward the object light source de creasing d from a d gt 2f and to observe the image on the screen which also must be moved continuously to obtain a sharp image In particular notice the change in the size of the image as d approaches f CONCAVE LENS 10 Repeat the procedures carried out for the convex 11 mirror in Procedure 7 for the concave lens with R replaced by 2f It is possible to determine the focal length of a con cave lens experimentally by placing it in contact with a convex lens so as to form a lens combination The combination forms a real image If two lenses of focal length
59. APPENDIX A Material Properties 513 TABLE A7 Wire Sizes American Wire Gauge AWG Temperature Resistivity p coefficient Substance Q cm C Aluminum 2 8 X 10 0 0039 Brass 7 X 10 0 002 Constantan 49 x 10 6 0 00001 Copper 1 72 x 1075 0 00393 German silver 1896 Ni 33 x 1075 0 0004 Iron 10 x 1075 0 005 Manganin 44 X 107 0 00001 Mercury 95 8 X 107 0 00089 Nichrome 100 x 1075 0 0004 Nickel 7 8 x 1075 0 006 Silver 1 6 X 1075 0 0038 Tin 11 5 x 1075 0 0042 Gauge Diameter No in cm 0000 0 4600 1 168 000 0 4096 1 040 00 0 3648 0 9266 0 0 3249 0 8252 1 0 2893 0 7348 2 0 2576 0 6543 3 0 2294 0 5827 4 0 2043 0 5189 5 0 1819 0 4620 6 0 1620 0 4115 7 0 1443 0 3665 8 0 1285 0 3264 9 0 1144 0 2906 10 0 1019 0 2588 11 0 09074 0 2305 12 0 08081 0 2053 13 0 07196 0 1828 14 0 06408 0 1628 15 0 05707 0 1450 16 0 05082 0 1291 17 0 04526 0 1150 18 0 04030 0 1024 19 0 03589 0 09116 20 0 03196 0 08118 21 0 02846 0 07229 22 0 02535 0 06439 23 0 02257 0 05733 24 0 02010 0 05105 25 0 01790 0 04547 26 0 01594 0 04049 27 0 01419 0 03604 28 0 01264 0 03211 29 0 01126 0 02860 30 0 01003 0 02548 31 0 008928 0 02268 32 0 007950 0 02019 33 0 007080 0 01798 34 0 006304 0 01601 35 0 005614 0 01426 36 0 005000 0 01270 37 0 004453 0 01131 38 0 003965 0 01007 39 0 003531 0 008969 40 0 003145 0 007988 www A TIBOOK ir 514 APPENDIX A Material Properties TABLE A8 Major Visi
60. ATIBOOK ir EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis Laboratory Report RV QUESTIONS 1 Read the measurements on the rulers in Fig 1 9 and comment on the results BI Ruler 1 cm 0 1 2 3 4 5 6 DE XE ix 1 r Ruler 2 cm 0 i 2 3 4 5 6 prs xx Ruler 3 TTTTTTTTTTTTTT TTTTTTTTT TTTTTTTTT TTTTTTTTTTTTTT TTTTTTTTT cm 0 1 2 3 4 5 6 Figure 1 9 2 Were the measurements of the block in part b of Procedure 2 all done with the same instrument Explain 3 Referring to the dart analogy in Fig 1 3 draw a dart grouping that would represent poor precision but good accuracy with an average value 4 Do percent error and percent difference give indications of accuracy or precision Discuss each 5 Suppose you were the first to measure the value of some physical constant experimentally How would you provide an estimate of the experimental uncertainty 20 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 Measurement Instruments Mass Volume and Density RV Advance Study Assignment Read the experiment and answer the following questions 1 What is the least count of a measurement instrument and how is it related to the number of significant figures of a measurement reading 2 Does a laboratory balance measure weight or mass Explain 3 What is the function of the vernier scale on the vernier caliper Does it extend a
61. ATIBOOK ir IE OS PE TR Ul IM IE IN 1 Experimental Uncertainty Error and Data Analysis Laboratory Report c Data Table 4 shows data taken in a free fall experiment Measurements were made of the distance of fall y at each of four precisely measured times Complete the table Use only the proper number of significant figures in your table entries even if you carry extra digits during your intermediate calculations DATA TABLE 4 Purpose To practice analyzing data Time f Distance m Optional g s y M Js Y4 Y5 d 0 0 0 0 0 0 0 50 1 0 1 4 1 1 1 4 1 5 0 75 2 6 9 2 2 8 2 5 3 1 1 00 4 8 4 4 5 1 4 7 4 8 1 25 8 2 7 9 T3 8 1 7 4 Calculations show work 18 d Plot a graph of y versus t optional with 2d error bars for the free fall data in part c Remember that t 0 is a known point e The equation of motion for an object in free fall starting from rest is y 5 gf where g is the acceleration due to gravity This is the equation of a parabola which has the general form y ax Convert the curve into a straight line by plotting y versus That is plot the square of the time on the abscissa Determine the slope of the line and compute the experimen tal value of g from the slope value Experimental value of g from graph units www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis
62. Apparatus for measurement of specific heats Metal shot or a piece of metal right is heated with boiling water in the container on the hot plate The metal is then placed in a known amount of water in the calorimeter which insulates the system from losing heat The inner calorimeter cup is shown with its dark insulating ring lying in front of the outer cup A thermometer and stirrer extend through the calorimeter cover Cengage Learning The specific heat of a material can be determined experimentally by measuring the temperature change of a given mass of material produced by a quantity of heat This is done indirectly by a calorimetry procedure known as the method of mixtures If several substances at various temperatures are brought together the hotter substances lose heat and the colder substances gain heat until all the substances reach a common equilibrium temperature If the system is insu lated so that no heat is lost to or gained from the surround ings then by the conservation of energy the heat lost is equal to the heat gained In this experiment hot metal is added to water in a calorimeter cup and the mixture is stirred until the system is in thermal equilibrium The calorimeter insulates the system from losing heat Fig 17 1 By the conservation of energy the heat lost by the metal is equal to the heat gained by the water and cup and stirrer In equation form heat lost heat gained or AQ metal AO vitet
63. Example C 1 this would be E 5 93 0 29 The term gives a measure of the precision of the experimental value The accuracy of the mean value of a set of experi mental measurements 5 93 in the example above may be expressed in terms of percent error or percent difference The dispersion of an experimental measurements may be expressed by other means such as the standard deviation see Appendix D so the method should be specified when reporting www ATIBOOK ir APPENDIX D Standard Deviation and Method of Least Squares STANDARD DEVIATION To avoid the problem of negative deviations and absolute Then values it is statistically convenient to use the square of the deviation I2 The variance of a set of measurements is the aver g wae age of the squares of the deviations 1 2 0 26 0 06 0 05 0 01 0 15 ga N 5 0 33 ZR 2 OL di d ds dy The experimental value E is then commonly reported as eu po x2 65 x ras E x 0 5 93 0 33 i 1 i The standard deviation is used to describe the pre D 1 cision of the mean of a set of measurements For a nor mal distribution of random errors it can be statistically shown that the probability that an individual measurement will fall within 1 standard deviation of the mean which is assumed to be the true value is 68 Fig D 1 The The square root of the variance is called the standard deviation
64. F where F and F are the x and y components of F respectively That is the resultant can be resolved into these components Use half of an other sheet of graph paper for the graphical method Vectorresolution Givenaforce vector of F 0 300 g N at 60 resolve the vector into its x and y components and find the magnitudes of F and F by the following procedures a Graphical Draw a vector diagram to scale on the other half of the sheet of graph paper used in Procedure 4 with the component vectors see Fig 5 3b and measure the magnitudes of F and F Record the results in the data table b Analytical Compute the magnitudes of F and F see the Theory section Record the results in the data table c Experimental Clamp pulleys at 240 90 and 0 on the force table Place a total of 0 300 kg on the 240 pulley string using a weight hanger This force is then the equilibrant of F 0 300 g N at 60 since 60 180 240 which must be used on the force table rather than the force itself Add weights to the 0 and 90 hangers until the system is in equilibrium The 0 and 90 forces are then the F and F components respectively of F Record their magnitudes in the data table Vector addition IV Given the force vectors F 0 100 g N at 30 F 0 200 g N at 90 and F4 0 30 g N at 225 find the magnitude and direction of their resultant F F F F by the following pro
65. Measure the length of the pendulum L in meters from the center of rotation to the center of the bob Record it in the report SETTING UP DATA STUDIO 1 Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There are seven channels to choose from Digital Channels 1 2 3 and 4 are the small buttons on the left ana log Channels A B and C are the larger buttons on the right as shown in e CI Fig 14 3 3 Click on the Channel 1 button in the picture A win dow with a list of sensors will open 4 Choose the Rotary Motion Sensor from the list and press OK This information will be needed during the setup of Data Studio 5 The diagram now shows you the properties of the RMS sensor directly under the picture of the interface See CI Fig 14 3 6 Connect the sensor to Channels 1 and 2 of the inter face as shown on the computer screen 7 Adjust the properties of the RMS as follows First Measurements tab select Angular Position Chapters 1 and 2 and select the unit of measure to be degrees Also select Angular Velocity Channels 1 and 2 in rad s Rotary Motion Sensor tab set the Resolution to high 1440 divisions rotations and set the Linear Scale to Large Pulley Groove mPewMen emo aes e Measurements Measurements Rota Motion Sensor Visiblliy Name T Rotation Count
66. Motion Laboratory Report C Period of Oscillation RV DATA TABLE 3 Total suspended Total time Number of Average period T mass oscillations T m My m ma ms Calculations show work Slope of graph Computed spring constant k Percent difference of k s in B and C fr questions 1 Interpret the intercepts of the straight line for the spring elongation in the mg versus y graph of Part B 228 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 14 Simple Harmonic Motion Laboratory Report 2 Is the elastic property of the rubber band a good example of Hooke s law Explain 3 Draw a horizontal line through the y intercept of the straight line graph of Part B and form a triangle by drawing a vertical line through the last data point a Prove that the area of the triangle is the work done in stretching the spring Hint W 5 kx and area of triangle A 5 ab that is 5 the altitude a times the base b b From the graph compute the work done in stretching the spring 4 Interpret the x intercept of the straight line of the 7 versus m graph of Part C continued 229 www ATIBOOK ir EXPERIMENT 14 Simple Harmonic Motion Laboratory Report 5 For a mass oscillating on a spring at what positions do the a velocity and b acceleration of the mass have maximum values 6 What is the form of the equation of mo
67. Pm 61 145 Chlorine CI 17 35 453 Protactinium Pa 9 231 Chromium Cr 24 51 996 Radium Ra 88 226 Cobalt Co 27 58 9332 Radon Rn 86 222 Copper Cu 29 63 545 Rhenium Re 725 186 2 Curium Cm 96 247 Rhodium Rh 45 102 9055 Dysprosium Dy 66 162 50 Rubidium Rb 37 85 4678 Einsteinium Es 99 254 Ruthenium Ru 44 101 07 Erbium Er 68 167 26 Rutherfordium Rf 104 257 Europium Eu 63 151 96 Samarium Sm 62 150 4 Fermium Fm 100 253 Scandium Sc 21 44 9559 Fluorine F 9 18 9984 Selenium Se 34 78 96 Francium Fr 87 223 Silicon Si 14 28 086 Gadolinium Gd 64 157 25 Silver Ag 47 107 868 Gallium Ga 31 69 72 Sodium Na 11 22 9898 Germanium Ge 32 72 59 Strontium Sr 38 87 62 Gold Au 79 196 967 Sulfur S 16 32 06 Hafnium Hf 72 178 49 Tantalum Ta 73 180 9479 Hahnium Ha 105 260 Technetium Tc 43 99 Helium He 2 4 00260 Tellerium Te 52 127 60 Holmium Ho 67 164 9303 Terbium Tb 65 158 9254 Hydrogen H 1 1 0080 Thallium Tl 81 204 37 Indium In 49 114 82 Thorium Th 90 232 0381 Iodine I 53 126 9045 Thulium Tm 69 168 9342 Iridium Ir TI 192 22 Tin Sn 50 118 69 Tron Fe 26 55 847 Titanium Ti 22 47 90 Krypton Kr 36 83 80 Tungsten W 74 183 85 Lanthanium La 57 138 9055 Uranium U 92 238 029 Lawrencium Lr 103 257 Vanadium Vy 23 50 9414 Lead Pb 82 207 12 Xenon Xe 54 131 30 Lithium Li 3 6 941 Ytterbium Yb 70 173 04 Lutetium Lu 71 174 97 Yttrium Y 39 88 9059 Magnesium Mg 12 24 305 Zinc Zn 30 65 37 Manganese Mn 25 54 9380 Zirconium Zr 40 91 22 Mendelevium Md 101 256 www
68. STUDIO calibrate the sensor The procedures described here assume Note The force sensor needs to be calibrated before use Hii the Orge sensor Dao bapi property aM rated Refer to the user s manual for instructions on how to Additional blocks Force S sensor o v constant 1 Table Wooden block Motorized car CI Figure 10 1 The experimental setup A wooden block slides on a flat surface while being pulled by a motorized car that moves at a constant speed Additional blocks can be added as necessary on top of the wooden block so that the string is hori zontal when connected to the force sensor The force sensor rides on the motorized car As an alternative PASCO dynamic cars can be stacked on top of a friction block to achieve the same effect Reprinted courtesy of PASCO Scientific 167 www ATIBOOK ir 168 EXPERIMENT 10 Friction N Constant speed f a F mg CI Figure 10 2 Free body diagram of the sliding block The horizontal forces are F the tension on the string and f the friction from the surface The force sensor measures F At constant speed the horizontal force vectors are equal and opposite and F f The force sensor readings can be taken to be the friction as long as the block slides at constant speed 1 2 CI Figure 10 3 The Experiment Setup Window Open Data Studio and choose Create Experiment The Experiment Setup win
69. Signal Generator window will open See CI Fig 20 3 7 The default form of the signal generator function is a sine wave Change it to a triangle wave by selecting from the drop menu Set the amplitude to 5 00 V 9 Set the frequency to 0 500 Hz This will produce a tri angle wave with a period of 2 seconds Click on the Measurement and Sample Rate button on the Signal Generator window A list of measurements will open Choose to measure the output current and deselect all others Do not close the Signal Generator window Move it toward the bottom of the screen The Data list should now have two icons one for the voltage reading of the sensor and one for the output current of the source Create a graph by dragging the Voltage icon from the Data list and dropping it on the Graph icon in the Displays list A graph of voltage versus time will open The graph window will be called Graph 1 Drag the Output Current icon from the Data list and drop it on top of the x axis of the graph The time axis should change to a current axis Graph 1 is now a graph of voltage versus current o 10 11 12 13 14 www ATIBOOK ir 304 EXPERIMENT 20 Ohm s Law AB C Signal Generator E aesa Sangle Rate Pojk lt J Low 19 r Sensor Sampling Opton l Reduce sempe rate ty averages Eleve Sirge Fate Hi f Zero sensor atomaticaly on start 205 02 2tn
70. Spectrum Divided circle Wavelength 1 A Line Color reading 1 n H n 3 Hg n 4 H n 5 Hs n 6 Calculations Slope of Graph show work RV QUESTIONS R experimental Accepted value Percent error R 4 from graph Accepted value Percent error 1 Compute the value of the Rydberg constant from the Bohr theory and compare it with the accepted empirical value 454 Laboratory Report www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 31 Line Spectra and the Rydberg Constant 2 Why are only four lines seen in the Balmer series Transitions for n gt 6 also exist Justify your answer mathematically 3 As n becomes very large the wavelengths of the Balmer and other series approach a minimum wavelength or series limit Eq 31 1 What is the wavelength of the series limit for the Balmer series Laboratory Report 455 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s JEI EXPERIMENT 3 2 F The Transmission Diffraction Grating Measuring the Wavelengths of Light EH Single Slit and Double Slit Diffraction f Advance Study Assignment Read the experiment and answer the following questions 1 What is a diffraction grating Distinguish between the two types of gratings 2 What is the grating constant What would be the grating constant for a
71. Voltage sensor I I I I I p t Re Ri Voltage sensor CI Figure 23 6 Resistors connected in parallel Three different parallel circuits will be analyzed each time adding an extra branch to the circuit 9 Remove the fit information boxes and print the graph Label it Parallel Circuits and attach it to the laboratory report 10 Calculate the theoretical expected value of the equivalent resistance of each circuit Compare the theoretical values with the measured ones by taking a percent difference 11 Using the printout of the graph or the Smart Tool on the graph toolbar determine the maximum value of the voltage and the maximum value of the current for each run Report them in CI Data Table 3 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s E c EXPERIMENT 2 3 Resistances in Series and Parallel amp Laboratory Report A Measuring Resistance ED onm taste 1 Purpose To measure the actual resistance of each of the three resistors Slope Average Resistor measurements resistance R 2 3 1 R 2 3 1 R 2 3 Don t forget units continued 355 www A TIBOOK ir lt PE IR Ul Ml IE IN B Resistances in Series ED vata taste 2 Purpose To experimentally measure the equivalent resistance of series circuits 23 Resistances in Serie
72. a liquid To gain familiarity with a hydrometer measure the densities of water saltwater and alcohol and record in the Data Table for Part D Comment on their relative densities www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 8 Archimedes Principle Buoyancy and Density RWV Laboratory Report A Direct Proof of Archimedes Principle Type of metal Buoyant force in newtons Mass of metal m in air Weight of displaced water Mass of beaker m in newtons Mass of metal m Percent difference submerged in water Mass of beaker and displaced water m my Mass of displaced water m Calculations show work Don t forget units 275 continued www A TIBOOK ir EXPERIMENT 18 Archimedes Principle Buoyancy and Density Laboratory Report B Density of a Heavy Solid p gt Pw Calculations Specific gravity show work Density C Density of a Light Solid p lt py Mass of block in air Specific gravity Mass of block and sinker Density with only sinker submerged Mass of block and sinker with both submerged Calculations show work 276 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 18 Archimedes Principle Buoyancy and Density Laboratory Report D Density of a Liquid p Measured density of water Measured density of saltwater Measured density of alcohol Com
73. a row of slits Transmission gratings are ruled on glass and the unruled slit areas transmit incident light The transmission type grating is used in this experi ment Common laboratory gratings have 300 grooves per mm and 600 grooves per mm about 7500 grooves per in and 15 000 grooves per in and are pressed plastic replicas mounted on glass Glass originals are very expensive Diffraction consists of the bending or deviation of waves around sharp edges or corners The slits of a grating give rise to diffraction and the diffracted light interferes so as to set up interference patterns TI Fig 32 1 Complete constructive interference of the waves occurs when the phase or path difference is equal to one wavelength and the first order maximum occurs for dsin A where d is the grating constant or distance between the grating lines 0 is the angle the rays are diffracted from the incident direction and d sin 6 is the path difference between adjacent rays The grating constant is given by TI 32 1 d 1 N TI 32 2 where N is the number of lines or grooves per unit length usually per millimeter or per inch of the grating A second order maximum occurs for d sin 2A and so on so that in general 463 dsin n n 12 3 1132 3 where n is the order of the image maximum The inter ference is symmetric on either side of an undeviated and undiffracte
74. acceleration EQUIPMENT NEEDED Pulley preferably low inertia precision ball bearing type with support Two weight hangers and weights masses String Laboratory timer or stopwatch Meter stick Take a look at the apparatus shown in Fig 6 1a Consider how you could use it to experimentally investigate the validity of Newton s second law Note that the equation F rna has three independent variables and can be written in different ways m F a and a F m In order to find out how any one of the three variables affects motion it is essential to hold the other two constant From the figure and given equipment how could the acceleration a of the mass hangers be determined from direct mea surements Hint Think of a kinematic equation that includes the three variables In case you missed it the kinematic equation that applies to this situation is y v t at In this equation there is a condi tion on the acceleration What is it The apparatus shown in Fig 6 1a is called an Atwood machine and it allows for all of the variables of F e ma to be net controlled If the system with loaded masses is released from rest what quantity in the kinematic equation could be eliminated For this case solve the kinematic equation for the acceleration continued 83 www ATIBOOK ir EXPERIMENT 6 Experimental Planning Did you get 2y Here the meter stick and stopwatch come into play and the distance trave
75. all the components in place as shown in after the first minimum that is the first CI Fig 29 6 press the START button and slowly maximum rotate the analyzer through a one and a half turns 3 Determine by what angle the analyzer was Press the STOP button rotated in going from the first minimum to c Press the Scale to Fit button the leftmost button the first maximum on the graph toolbar to bring all the data onto e Case 2 Repeat for the angle between the first the graph screen then print the graph Attach the maximum and the second minimum graph to the laboratory report f Case 3 Repeat for the angle between the second minimum and the second maximum g Case 4 Repeat for the angle between the second maximum and the third minimum Light sensor Aperture disk Polarizers Rotary motion sensor Diode laser CI Figure 29 6 Order of components on the bench Light from the laser will pass a polarizer and then the analyzer before entering the light sensor www A TIBOOK ir Name Section Date Lab Partner s Pic EX P ERIM ENT 29 Malus s Law amp Laboratory Report ED vata taste 1 Purpose To investigate the relative orientations of polarizer and analyzer that produce minimum and maximum transmitted intensity Successive minima and maxima Total analyzer rotation between of intensity minimum and maximum Omin g Binal Case 1 Omin B oix Case 2 Omi
76. and crystal double refraction along with optical activity The CI pro cedure focuses on Malus s law and examines the intensity of light transmitted through a polarizer and an analyzer INTRODUCTION AND OBJECTIVES When speaking of polarized light Polaroid sunglasses usually come to mind as this is one of the most common applications of polarization However few people under stand how such sunglasses reduce glare Since the unaided human eye cannot distinguish between polarized light and unpolarized light we are not normally aware of the many instances of polarized light around us Bees on the other hand with their many faceted eyes can detect polarized light and use scattered polarized sunlight in navigating Although the unaided human eye cannot detect polar ized light with a little help polarization can be investigated experimentally This is the purpose of the experiment RV OBJECTIVES After performing this experiment and analyzing the data you should be able to 1 Explain what the polarization of light means 2 Describe several means by which light can be polarized 3 Explain some practical applications of polarized light d ossectives The purpose of the CI activity is to investigate the trans mission of light through two polarizer filters a polarizer and an analyzer as a function of the angle 0 between the planes of polarization A light sensor is used to measure the intensity of the transmitt
77. and down it is not a true nodal point Record this length L and the total suspended mass in the data table Since the length of two loops is equal to one wavelength L A Repeat Procedure 4 for consecutive standing wave patterns up to eight measured loops if possible The weight hanger by itself may supply too much ten sion for higher order patterns so it may have to be removed and smaller weight s suspended Compute the wavelength for each case It should become evident that in general A 2Ly N or Ly NA 2 where N is the number of loops in a given Ly Notice the similarity of the latter form of this equation to Eq 15 2 wherein the length L is the total vibrating length of the string Note that Eq 15 7 can be rewritten as n T 2 CAK 15 7a where fand u are constants It has the form of an equa tion of a straight line y mx b with x VF and b 0 Plot the experimental data on a graph of A versus F Draw the straight line that best fits the data and determine the slope of the line From this value and the previously determined value of u compute the average frequency f of the oscillations The string vibrator operates on 60 cycle ac cur rent The vibrating action is accomplished by means of an electromagnet operated by the input current The vibrator arm is attracted toward an electromag net during each half cycle or twice each cycle so the vibrating frequency is 2 X 60 120 Hz cy
78. and forth and notice the reversal of direction of the motion of the spectrum when the prism is rotated in one direction Focusing on the yellow line for mercury the brighter yellow line stop rotating the prism at the position of the reversal of motion of this line This sets the prism for minimum deviation for the yellow line see Experiment 30 which will be taken EXPERIMENT 31 Line Spectra and the Rydberg Constant 451 as an average for the spectrum The other lines have slightly different minimum deviations a Without disturbing the prism starting at the red end of the spectrum set the crosshairs of the telescope on the extreme red line and record the color and divided circle reading in the laboratory report Repeat this procedure for each spectral line in order Turn off the discharge tube as soon as possible to conserve the life of the tube b Find the wavelengths of the spectral lines for the discharge tube gas in Appendix A Table A8 and match them to the line readings c Using these data plot the wavelength A versus the divided circle reading 0 This calibrates the spectrometer and unknown wavelengths can be determined from divided circle readings from the calibration curve With the discharge tube power supply off replace the mercury or helium discharge tube with a hydrogen discharge tube Turn on the power supply and starting with the red line of the hydrogen spectrum determine the divided
79. and the differences among them 3 Describe what is meant by the exponential tempera ture coefficient of a thermistor EQUIPMENT NEEDED Slide wire Wheatstone bridge assembly with a 3 V battery and a single pole single throw switch Standard decade resistance box Copper coil and optional constantan or manganese coil Thermistor Immersion vessel and stirrer Thermometer Immersion heater and power source or Bunsen burner and stand or hot plate 2 sheets of Cartesian graph paper THEORY The change in resistance AR of a substance is propor tional to the change in temperature AT This change in resistance is commonly expressed in terms of the fractional change AR R where R is the initial resistance For many substances for example metals the change in resistance is to a good approximation a linear function of temperature 22 1 where the constant of proportionality is called the temperature coefficient of resistance and has the units of inverse temperature 1 C or SU For the change in temperature AT T T it is con venient to take the initial temperature T as 0 C and with AR R R Eq 22 1 can be written R R R aT o or R R R aT Ry aT 22 2 325 where R is then the resistance of the conductor at some temperature T C and R is the resistance at T 0 C The linearity of the temperature dependence is only approximate
80. and then in parallel An increasing voltage will be applied and the overall current in the circuit through the voltage source will be measured Rewriting Ohm s law as V IR notice that a plot of voltage in the y axis versus current in the x axis must result in a straight line with the slope equal to the overall resistance in the circuit V RI td y mx Using voltage and current sensors we will find the resistances of the circuits by measuring the slope of a voltage versus current plot L serine up pata stupio T Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There are seven channels to choose from and a signal gen erator Digital Channels 1 2 3 and 4 are the small buttons on the left analog Channels A B and C are the larger buttons on the right the signal generator is all the way to the right as shown in CI Fig 23 1 3 Click on the Channel A button in the picture A win dow with a list of sensors will open 4 Choose the Voltage Sensor from the list and press OK 5 Connect the sensor to Channel A of the interface as shown on the computer screen 6 The screen now shows you the properties of the Volt age Sensor directly under the picture of the interface Adjust the sample rate to 20 Hz 7 Click on the picture of the Signal Generator The Signal Generator window will open See CI Fig
81. angle 0 relative to the horizontal Your instructor will tell you how to do this Aim the projectile down an aisle or hallway being careful not to aim at anything or anybody Using a protractor to set the angles of projection fire the projectile at angles of 20 30 40 45 50 60 and 70 with two or three trials for each angle The projectile should be aimed so that it lands as close as possible to the same spot for the trials of a particular angle Station one or more lab partners at a safe distance near where the projectile strikes the floor They are to judge the average range of the two or three trials Measure the average range for each angle of projec tion and record the data in Data Table 3 Suggestion It is convenient to measure the dis tance from the gun to the position where the ball lands and to mark this position The range measurement then can be made relative to this measured mark in stead of from the starting point each time Also it is convenient to shoot toward a wall at the end of the hall or aisle or to lay a meter stick on the floor perpendicu larly to the line of flight in order to stop the ball from rolling Plot the range versus the angle of projection and draw a smooth curve that fits the data best As might be ex pected the points may be scattered widely because of the rather crude experimental procedure Even so you should be able to obtain a good idea of the angle for the maximum ra
82. assumption of no frictional forces acting on the particle In this experiment the simple harmonic motion of a pendulum will be investigated A simple pendulum consists of a mass called a bob suspended by a massless string from a point of support The pendulum swings in a plane The restoring force on a simple pendulum is the com ponent of its weight that tends to move the pendulum back to its equilibrium position As can be seen from e CI Fig 14 1 the magnitude of the force is CI 14 1 F mg sinO Note however that this force is not proportional to the angu lar displacement 0 of the pendulum as required for SHM v oN 7 mg cos 0 E mg iri mg CI Figure 14 1 Forces acting on a swinging pendulum The restoring force acting on a pendulum is the component mg sin of gravity which attempts to bring the pendulum back to the equilibrium position 231 but is proportional to the sin0 instead A pendulum can be approximated to be in SHM motion only if the angle 0 is small in which case sin 0 where 0 is in radians Thus F mg sin mg6 CI 14 2 Notice that in this approximation the force is directly pro portional to the displacement 6 As the pendulum swings kinetic energy is converted into potential energy as the pendulum rises This potential energy is converted back to kinetic energy as the pendu lum swings downward The kinetic and potential energies
83. better accuracy Explain 2 Complete the following sentences a When the unbalanced force increases total mass remaining constant the acceleration of the system b When the total mass that is auseleingi increases unbalanced force remaining constant the acceleration of the system 3 How can the value of g the acceleration due to gravity be detismined using an Atwood machine 4 Using the data in TI Data Table 2 constant total mass plot am versus m m for each Trial and draw a straight line that best fits the data Find the slope and intercept of the line and enter the values below Rewrite Eq TI 6 6 in slope intercept form y mx b and using the data in Trial 6 compute the slope and intercept Show calculations Compare and comment on your results From graph From Eq TI 6 6 Slope units units Intercept units units 95 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir C EX PER IM ENT 6 Newton s Second Law The Atwood Machine S courpment neevep Photogate Pulley System PASCO ME 6838 Smart Pulley Mass set that includes 1 g 2 g and 5 g weights Suggested PASCO ME 8967 2 mass hangers Clamps and support rods Graph paper A mory When an Atwood machine is unbalanced the masses move one ascending and the other descending See Fig TI 6 1 As the masses move the string causes the pulley to rotate With m and
84. circle reading for each spectral line with the crosshairs of the telescope positioned on the cen ter of the line Record in the laboratory report The red line is referred to as H in spectroscopic notation The other sequential lines are referred to as Hg etc with subscripts in Greek alphabetical order Determine the wavelengths of the hydrogen lines from the calibration curve and plot the reciprocal of the wavelength 1 A versus 1 7 Begin the abscissa scale with zero Draw the best straight line that fits the data points and determine the slope of the line Note that Eq 31 1 5 4 R 2 rR 4 m has the form of a straight line y mx b with the negative slope equal to the Rydberg constant Com pare the slope of the line with the accepted value of the Rydberg constant by computing the percent error Compare the intercept of this line with R 4 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 1 Line Spectra and the Rydberg Constant RV Laboratory Report Colors of the Continuous Spectrum DATATABLE 1 Mercury or Helium Spectrum Divided circle Wavelength Sequence of colors Color reading from Table A8 rd Don t forget units continued 453 www ATIBOOK ir EXPERIMENT 31 Line Spectra and the Rydberg Constant DATA TABLE 2 Hydrogen
85. cm X 3 4 cm X 4 10 cm Compute the volume of the block showing explicitly by underlining how doubtful figures are carried through the calculation and report the final answer with the correct number of significant figures Calculations Computed volume show work in powers of 10 notation units c In an experiment to determine the value of 7 a cylinder is measured to have an average value of 4 25 cm for its diameter and an average value of 13 39 cm for its circumfer ence What is the experimental value of 7 to the correct number of significant figures Calculations show work Experimental value of 7 units 16 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis Laboratory Report 3 Expressing Experimental Error a If the accepted value of 7 is 3 1416 what are the fractional error and the percent error of the experimental value found in 2 c Calculations show work Fractional error Percent error b In an experiment to measure the acceleration g due to gravity two values 9 96 m s and 9 72 m s are determined Find 1 the percent difference of the measurements 2 the percent error of each measurement and 3 the percent error of their mean Accepted value g 9 80 m s Calculations show work Percent difference Percent error of E Percent error of E Percent error of mean continued 17 www
86. data tape give 2 What precautions should be taken in using the apparatus What could happen if this is not done 3 What equation describes the instantaneous velocity of an object in free fall and what is the shape of the graph of the instantaneous velocity versus time continued 65 www ATIBOOK ir EM IPE IR TIME IN WA 4 Should the graph of instantaneous velocity versus time have a y axis intercept of zero Explain 5 Describe how the instantaneous velocity of an object in free fall can be calculated from displacement and time data 66 Advance Study Assignment www A TIBOOK ir T d EX PER M ENT 4 A Uniformly Accelerated Motion See the previous Introduction and Objectives AY EQUIPMENT NEEDED Free fall apparatus Meter stick RV THEORY Some free fall timer apparatuses are shown in e TI Fig 4 1A The free fall spark timer assembly consists of a metal object that falls freely between two wires with a tape strip of specially treated paper between the object and one of the wires The spark timer is a fast timing device that supplies a high voltage across the wires periodically at preset time intervals for example a frequency of 60 Hz or time interval of amp s since t 1 f The free fall appa ratus is equipped with an electromagnet that releases the metal object when the spark timer is activated A high voltage causes a spark to jump between two electrical conductors in close pro
87. deformation or displacement of the spring and x is its initial position The minus sign indicates that the force and displacement are in opposite directions For coil springs the constant k is called the spring or force constant The spring constant is sometimes called the stiffness constant because it gives an indication of the relative stiffness of a spring the greater the k the greater the stiffness As can be seen from TI Eq 14 1 k has units of N m or Ib in According to Hooke s law the elongation of a spring is directly proportional to the magnitude of the stretching force For example as illustrated in e TI Fig 14 1 if a spring has an initial length y and a suspended weight of mass m stretches the spring to a length y then in equilib rium the weight force is balanced by the spring force and F mg k y Yo Here y is used to indicate the vertical direction instead of x as in TI Eq 14 1 which is usually used to mean the hori zontal direction Similarly if another mass m is added and the spring is stretched to a length yp then The restoring spring force and the stretching force are equal in magnitude and opposite in direction Newton s third law 223 TI Figure 14 1 Hooke slaw An illustration in graphical form of spring elongation versus force The greater the force the greater the elongation F ky This Hooke s law relationship holds up to the elastic limit F 2mg Ky yo
88. depends on the mass of a falling object In other words does a heavier object fall faster than a lighter object What do your experimental results show 2 What is probably the greatest source of error in the experimental procedure B Linear Air Track 3 What are the major sources of error in this procedure 4 What would be the shapes of the curves for a graph of y versus t of the data in each experimental case How would you determine the value of the car s acceleration from a graph using only y and t values that is not computing v continued 57 www ATIBOOK ir EXPERIMENT 4 Uniformly Accelerated Motion 5 What is the physical significance of the slope of the graph for the case of the level air track 6 What is the maximum possible value of the slope of a v versus t curve for a car released from rest on an air track elevated at one end Describe the experimental setup in this case 58 Laboratory Report www A TIBOOK ir C I EX PERIMENT 4 Uniformly Accelerated Motion AY courment neeveo 1 collision or plunger cart Pasco Collision Cart ME 9454 or ME 9430 Any of the classic carts or the Pascars will work fine lfanaccessory Pasco ME 9491 1 dynamics track 1 rotary motion sensor RMS CI 6538 Brackets and pulley mounts 1 cart string bracket CI 6569 1 dynamics track mount accessory CI 6692 to mount the RMS to the track 1 RMS IDS adapter ME 6569 track pulley bracket String Optional Track end stop
89. effect compares the unknown resistance R with a standard resis tance R Should R R then R R The circuit diagram for a slide wire form of the Wheatstone bridge is shown in Fig 21 4 along with a photo of an actual bridge The line from a to d represents a wire and C is a contact key that slides along the wire so as to divide the wire into different length segments The resistances of the segments are proportional to their lengths so the resistance ratio may be expressed in terms of a length ratio 21 10 Equation 21 9 can then be written in terms of the length ratio Ee 2 R 21 10 This type of bridge is convenient since the length seg ments can be measured easily The resistances R and R of the length segments may be quite small relative to R and R because the bridge equation depends only on the ratio R R or L L This fact makes it possible to use a wire as one side of the bridge www ATIBOOK ir 314 Figure 21 5 Resistance measurement EXPERIMENT 21 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method a Circuit diagrams for experimental procedures for ammeter voltmeter methods of measuring resistance EXPERIMENTAL PROCEDURE A Ammeter Voltmeter Methods 1 Set up a circuit as shown in Fig 21 5a where R is a small known resistance and R is the rheostat How ever do not connect the wire to the positive side of the battery
90. effect on a the frequency of rotation f with r constant and b f and r when both are free to vary 3 Does the centripetal force acting on an object in uniform circular motion do work on the object Explain continued 153 www ATIBOOK ir EXPERIMENT 9 Centripetal Force 4 154 Figure 9 1 shows a student swinging a ball in a circle about his head Show that the rope cannot be exactly horizontal Hint Take the rope s tension force T to be at an angle below the horizontal and examine the components of T Use a diagram to illustrate Laboratory Report www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 10 Friction AY Advance Study Assignment Read the experiment and answer the following questions 1 State the three general empirical rules used to describe friction 2 What is the normal force and why is it used instead of the load 3 Why is it important to have the string parallel to the horizontal surface in the procedures where suspended weights are used 4 What is the coefficient of friction and in what units is it expressed Distinguish between u and up Which is generally greater 155 continued www A TIBOOK ir EXPERIMEN TF 10 Advance Study Assignment 5 Explain how graphs of weight versus normal force in Procedures A and B give the coefficients of friction Advance Study Assignment Read the experiment and answer the following question 1 Under
91. for the first 5 seconds He requests you plot the results on a distance versus time graph for a visual display Oh one other thing He wants to open his parachute when reaching 60 mi h At what time or between which seconds should he do this 3 Given three objects with same size and shape but different masses when dropped would the heaviest fall the fastest If so would this mean that the acceleration due to gravity depends on mass Or could there be another factor involved Hint Take a look at the opening sentence of this experimental planning 4 Suppose that the initial height of the object were measured from the top of the object at the release point to the floor How would this affect your experimental result for g that is would it be too high or too low Is this a random or a systematic error RV Advance Study Assignment Read the experiment and answer the following questions B Linear Air Track 1 How is the acceleration of a car traveling on an elevated air track related to a the angle of elevation b the height of elevation continued 49 www ATIBOOK ir EXPERIMENT 4 Advance Study Assignment What is the equation describing the instantaneous velocity of a car on an elevated air track and what is the shape of the graph of the instantaneous velocity versus time Will the graph of instantaneous velocity versus time have a y axis intercept of zero Explain Describe how the instantaneous velo
92. forget units continued 487 www ATIBOOK ir EXPERIMENT 33 Detection of Nuclear Radiation The Geiger Counter Laboratory Report C Inverse Square Relationship DATA TABLE 2 Purpose To determine the count rate versus distance from source Source to counter Count rate N ides los N distance r cpm g S Closest distance Farthest distance Calculations show work Slope of graph 488 Theoretical value Percent error www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 33 Detection of Nuclear Radiation The Geiger Counter Laboratory Report RV QUESTIONS 1 What is the average percent increase in the count rate over the voltage range of the Geiger tube plateau Obtain from a graph of the data 2 If a dead time and b background radiation corrections were taken into account how would each correction affect the graph of N versus V 3 Give possible reasons why the experimental result of N versus r is not exactly an inverse square relationship 4 A count rate of 8000 cpm is recorded at a distance of 5 0 cm from a point source What would be the observed count rate at a distance of 20 cm 489 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 4 Radioactive Half Life AY Advance Study Assignment
93. frictional losses and the theoretical mechanical advantage TMA which expresses the ideal nonfic tional case The relative amount of useful work done by a machine is expressed by the ratio of the useful work out put and the work input which is called the efficiency s Basically efficiency tells what you get out for what you put in The rest of the input is lost mainly to work done against friction In this experiment the AMAs TMAs and the effi ciencies of some simple machines will be experimentally determined to illustrate these concepts and to show the parameters on which the force multiplications of machines depend After performing the experiment and analyzing the data you should be able to do the following 1 Describe how machines do work for us 2 Distinguish between TMA and AMA 3 Explain how the TMAs can be measured for a an inclined plane b a lever and why the TMA gives a good approxi mation of the AMA c pulley s EQUIPMENT NEEDED Two single pulleys and two double or triple sheave pulleys Wheel and axle Fig 13 5 Two weight hangers slotted weights and single weight Spring scale calibrated in newtons Meter stick Vernier calipers String Tape The single pulleys are not really necessary as one sheave of the multiple pulleys can be used as a single pulley The single pulleys are convenient for instruction THEORY The actual mechanical advantage AMA of a
94. from the circuit and with the voltmeter measure and record the voltage drop across each resistor and across all three resistors as a group Remember a voltmeter is always connected in parallel or across a circuit element to measure its voltage drop Compare the experimentally measured values with the theoretically computed values by finding the percent error Use the theoretical values as the accepted values B Resistors in Parallel 8 Set up a parallel circuit with R Rj and R as in TI Fig 23 2a with the ammeter and voltmeter con nected as before in Procedure 3 Check the circuit arrangement by tracing the current from the source through the circuit to see that it divides into three parallel branches at the junction of the resistors and comes together again at the opposite junction Close the circuit after it has been checked and record the voltage and current readings in the labora tory report If using a variable power supply adjust the voltage if necessary Open the circuit after taking the reading www ATIBOOK ir 342 9 10 11 12 EXPERIMENT 23 Resistances in Series and Parallel Using the resistor values and the measured voltage compute a the equivalent resistance R of the cir cuit b the current supplied by the source and c the current through each resistor Show your calculations in the laboratory report Returning to the experimental circuit measure and record the volta
95. how close they are together The more precise a group of measurements the closer together they are However a large degree of precision does not necessarily imply accu racy as illustrated in Fig 1 3 Example 1 2 Two independent experiments give two sets of data with the expressed results and uncertain ties of 2 5 0 1 cm and 2 5 0 2 cm respectively The first result is more precise than the second because the spread in the first set of measurements is between 2 4 and 2 6 cm whereas the spread in the second set of measurements is between 2 3 and 2 7 cm That is the measurements of the first experi ment are less uncertain than those of the second Obtaining greater accuracy for an experimental value depends in general on minimizing systematic errors Obtaining greater precision for an experimental value depends on minimizing random errors C Least Count and Significant Figures In general there are exact numbers and measured numbers or quantities Factors such as the 100 used in calculating percentage and the 2 in 27rr are exact numbers Measured numbers as the name implies are those obtained from measurement instruments and generally involve some error or uncertainty In reporting experimentally measured values it is important to read instruments correctly The degree of uncertainty of a number read from a measurement instru ment depends on the quality of the instrument and the fineness of its measuring scale When
96. how the physical relationship and experimental data can be used to find other useful information for example the value of the acceleration due to gravity After performing this experiment and analyzing the data you should be able to do the following 1 Apply the scientific method to theoretical predictions to check their validity 2 Understand how physical parameters are varied so as to investigate theoretical predictions 3 Appreciate the use of approximations to facilitate experimental investigations and analyses EQUIPMENT NEEDED Meter stick Laboratory timer or stopwatch Protractor String Three or more pendulum bobs of different masses Pendulum clamp if available sheet of Cartesian graph paper THEORY A simple pendulum consists of a bob a mass attached to a string that is fastened such that the pendulum assembly can swing or oscillate freely in a plane Fig 3 1 For a simple or ideal pendulum all the mass is considered to be concentrated at a point at the center of mass of the bob Some of the physical properties or parameters of a simple pendulum are 1 the length L of the pendulum 2 the mass m of the pendulum bob 3 the angular distance 0 through which the pendulum swings and 4 the period T of the pendulum which is the time it takes for the pendulum to swing through one complete oscillation for example from A to B and back to A in Fig 3 1 From experience or preli
97. hy can be measured directly with a meter stick Solve Equation 4 for V 8 Recall that the velocity V needed to be determined to find v in Eq 1 Your last result gives V in terms of measurable quantities Substitute your expression for V into Eq 1 and solve for v 128 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT amp Advance Study Assignment s v now expressed in terms of known and measurable quantities It should be and this is the theory of how the projectile initial velocity can be determined experimentally using the ballistic pendulum RV Advance Study Assignment Read the experiment and answer the following questions A The Ballistic Pendulum 1 In determining the magnitude of the initial velocity of the ballistic pendulum projectile what conservation laws are involved and in which parts of the procedure 2 Why is it justified to say that the momentum in the horizontal direction is conserved over the collision interval Is momentum conserved before and after the collision Explain 3 Why are the heights measured to the center of mass of the pendulum ball system continued 129 www ATIBOOK ir EXPERIMENT amp Advance Study Assignment B Determination of the Initial Velocity of a Projectile from Range Fall Measurements 4 After the horizontal projectile leaves the gun what are the accelerations in the x and y directions 5 How is the location where the ball strikes t
98. inherent uncertainty or doubtfulness because of the estimated figure However the greater the number of significant figures the greater the reliability of the measurement the number represents For example the length of an object may be read as 3 65 cm three significant figures on one instrument scale and as 3 5605 cm five significant figures on another The latter reading is from an instrument with a finer scale why and gives more information and reliability Zeros and the decimal point must be properly dealt with in determining the number of significant figures in a result For example how many significant figures does 0 0543 m have What about 209 4 m and 2705 0 m In such cases the following rules are generally used to deter mine significance 1 Zeros at the beginning of a number are not significant They merely locate the decimal point For example 0 0543 m has three significant figures 5 4 and 3 2 Zeros within a number are significant For example 209 4 m has four significant figures 2 0 9 and 4 3 Zeros at the end of a number after the decimal point are significant For example 2705 0 has five significant figures 2 7 0 5 and 0 Some confusion may arise with whole numbers that have one or more zeros at the end without a decimal point Consider for example 300 kg where the zeros called trailing zeros may or may not be significant In such cases it is not clear which zeros serve only to locate
99. is equal in magnitude to the load N mg in TI Fig 10 1 and N mg cos 0 in TI Fig 10 3 which avoids any con fusion between weight and load With f N written in equation form f uN or TI 10 1 H ad N where the Greek letter mu 2 is a unitless constant of proportionality called the coefficient of friction Why does u have no units When a force F is applied to the block parallel to the surface and no motion occurs then the applied force is balanced by an opposite force of static friction 159 TI Fig 10 1b F f ma 0 As the magnitude of the applied force is increased f increases to a maxi mum value given by see TI Fig 10 1c TI 10 2 Ssa Z UN static friction where p is the coefficient of static friction The maximum force of static friction is experimentally ap proximated by the smallest force applied parallel to the surface that will just set the block into motion At the instant the applied force F becomes greater than f MN however slightly the block is set into motion and the motion is opposed by the force of ki netic sliding friction f TI Fig 10 1d and fe uN TI 10 3 kinetic friction where w is the coefficient of kinetic sliding friction The unbalanced force causes the block to accelerate F f ma However if the applied force is reduced so that the block moves with a uniform velocity a
100. mass of cord the data in the TI Trial Data Table the third car be m3 4 Compute the Af s for each trial and calculate the percent difference for each trial set From the data decide which timing method should be used on the basis of consistency or precision 2 Mark off two equal and convenient lengths for example or 1 m on both sides of the center po sition of the air track Make full use of the length of the track but leave some space near the ends of the track Place the four tape reference marks at the lower edges of the track so as not to interfere with the car motion Do not mark the air track surface itself with tape or anything else CASE 1 COLLISION BETWEEN Two CARS OF NEARLY EQUAL Mass WITH ONE INITIALLY AT REST 5 With one of the cars m5 of nearly equal mass sta tionary at the center position of the air track start the other car m moving toward the stationary car See TI Fig 7 1 It may be more convenient to start m moving away from m and take measurements as m returns from rebounding from the end of the track A trial run should show that m remains at rest or nearly at rest after collision and that m is in motion Determine the time it takes for m to travel be tween the reference marks as it approaches m and the time it takes for m to travel between the other 3 Time trials By measuring the time interval Ar it takes a car to move the reference mark length d one can determine the magnitu
101. may be jolted off the hangers by the impact on hitting the floor It may be helpful to place a shock absorbing pad on the floor Also one lab partner should attend to the upper weight to pre vent it or some of it from falling Take turns at each task pens ee 1 Measure the frictional mass to a precision of 5 g Fine adjustment of the descending mass may be made by using small custom masses paper clips as needed These paper clips can be attached to the cord just above the m hanger Good precision is necessary for good results because the frictional force is com parable in magnitude to the accelerating force Small errors in the frictional masses may create large experi mental errors www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s T EX PERIMENT 6 Newton s Second Law The Atwood Machine RV Laboratory Report AY DATA TABLE 1 Purpose To investigate a F m by holding F constant If not considering pulley inertia and friction ignore columns and m and m symbols Trial ma Descending mass My Ascending mass m Distance of travel yC 2 Run 1 Time of travel Run 2 t Run 3 Average Measured acceleration a 2y t Total mass m m Meg Measured frictional mass m m My Net force m m m g Theoretical accelerati
102. minima by dividing the previous distance by 2 Record the result in CI Data Table 1 11 Repeat the measurements for the second the third and if possible the fourth order minima Use the magnifier button to enlarge the parts of the graph as needed 12 Calculate sin 0 for each case using the derived for mula from the small angle approximation See CI Data Table 1 for the formula Enter the values in both CI Data Tables 1 and 2 13 To check how well the observed pattern matches the theory use the known wavelength of the light and the known width of the slit to calculate the theoretical value of sin 0 for each case Compare the theory to the experiment by taking percent differences Record all results in CI Data Table 1 14 To demonstrate that the experimental data can also be used to find the wavelength of the light use the data in CI Data Table 2 with CI Eq 32 1 to calculate the wavelength of the light for each case then find an average Compare the average to the expected value by taking a percent error 15 Cancel all zooms and fix up the graph window so that all data collected can be seen Print the graph and la bel each minimum on both sides of the center with the appropriate m value Title this graph Graph 1 Single Slit Pattern 0 04 mm If no printer is available make a careful sketch of the graph paying attention to the location of the minima along the hori zontal axis Attach the graph to the laborat
103. of f length L Mg e m L gt 100 cm Figure 12 5 Equilibrium A meter stick in equilibrium with one suspended mass See text for description in position helps Move the meter stick in the support clamp until the system is in equilibrium This case is analogous to the solitary seesaw sitting on one side of a balanced seesaw with no one on the other side Record the support position x in Data Table 2 Since the meter stick is in balance static equi librium the point of support must be at the center of gravity of the system that is the torques clockwise and counterclockwise on either side of the meter stick must be equal But where is the mass or force on the side of the meter stick opposite the suspended mass The balancing torque must be due to the mass of length L of the meter stick Fig 12 5 To investi gate this a Using the total mass m of the meter stick mea sured previously as m with a moment arm r see the diagram in Data Table 2 compute the counterclockwise and clockwise torques and compare them by computing the percent differ ence Record it in Data Table 2 b Now the masses of the lengths of meter stick will be taken into account Compute the average lin ear mass density of the meter stick see Theory Section B and record it in the data table If we assume that the mass of the meter stick is uniformly distributed the center of mass or center of gravity of the length o
104. of your graph 5 What physical quantity of the system is represented by the slope of the force versus acceleration graph How well does it match the experimental setup 6 From the results was there a good agreement between the experimental acceleration and the theoretical expected acceleration What causes the difference Discuss sources of experimental uncertainty for this experiment 102 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 7 Conservation of Linear Momentum RV Advance Study Assignment Read the experiment and answer the following questions 1 What is meant when we say that a quantity such as linear momentum is conserved 2 What is the condition for the conservation of linear momentum of a system 3 Show that Newton s second law can be written in the form F Ap At 4 Is the conservation of linear momentum consistent with Newton s first and third laws of motion Explain 103 continued www A TIBOOK ir EXPERIMEN Y 7 5 In a system of particles for which the total linear momentum is conserved is the linear momentum of the individual particles constant Explain 6 Suppose that a particle of mass m approaches a stationary mass m and that m gt gt mj What would you expect to happen on collision Advance Study Assignment Read the experiment and answer the following questions 1 What mechanism will be used to make the collision between the ca
105. or correct them B Accuracy and Precision Accuracy and precision are commonly used synonymously but in experimental measurements there is an important distinction The accuracy of a measurement signifies how close it comes to the true or accepted value that is how nearly correct it is Example 1 1 Two independent measurement results using the diameter d and circumference c of a circle in the determination of the value of 7 are 3 140 and 3 143 Recall that m c d The second result is F 21 6 C Error TS b Length measurement Figure 1 2 Personalerror Examples of personal error due to parallax in reading a a thermometer and b a meter stick Readings may systematically be made either too high or too low www ATIBOOK ir EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis 5 a Good precision but poor accuracy b Poor precision and poor accuracy amp c Good precision and good accuracy Figure 1 3 Accuracy and precision The true value in this analogy is the bull s eye The degree of scattering is an indication of precision the closer together a dart grouping the greater the precision A group or symmetric grouping with an average close to the true value represents accuracy more accurate than the first because the true value of ar to four figures is 3 142 Precision refers to the agreement among repeated measurements that is the spread of the measurements or
106. pL 0 50 g cm 16 cm 8 0 g www A TIBOOK ir 196 EXPERIMENT 12 Torques Equilibrium and Center of Gravity EXPERIMENTAL PROCEDURE Here the equilibrium conditions will be determined by the summing of torques or moments of force hence the term moments of force method A Apparatus with Support Point at Center of Gravity 1 A general experimental setup is illustrated in Fig 12 4 where the masses or weights are suspended by clamp weight hangers The hooked masses may also be sus pended from small loops of string which can be slid easily along the meter stick The string allows the position of a mass to be read easily and may be held in place by a small piece of masking tape 4 a Determine the mass of the meter stick with out any clamps and record it in the laboratory report b Weights may be suspended by loops of string or clamps with weight hangers The string method is simpler however if you choose or are instructed to use weight hangers weigh the three clamps to gether on a laboratory balance and compute the average mass of a clamp Record it in the labora tory report 2 With a knife edge clamp on the meter stick near its center place the meter stick without any suspended weights on the support stand Make certain that the knife edges are on the support stand The tightening screw head on the clamp will be down Adjust the meter stick through the clamp until the stick is balanced on the stand
107. performing this experiment and analyzing the data you should be able to 1 Explain what is meant by the half life of a radioactive isotope 2 Distinguish between radioactive half life and time constant 3 Describe how the half life of a short lived radioactive isotope can be measured EQUIPMENT NEEDED Geiger counter rate meter with clip mount or scaler type with tube mount Cesium 137 Barium 137m Minigenerator with solution Laboratory timer or stopwatch Disposable planchet small metal cuplike container to hold radioactive sample 2 sheets of Cartesian graph paper or optional 1 sheet of Cartesian and 1 sheet of semi log graph paper 3 cycle THEORY The activity of a radioactive isotope is proportional to the quantity of isotope present and the radioactive decay pro cess is described by an exponential function N Ne Ne 34 1 where N is the number of nuclei present at time f N is the original number of nuclei present at t 0 A is the de cay constant of the process and the time constant 7 1 A The variable N can also represent the activity cpm of an isotope sample The half life is the time it takes for the number of nuclei present or activity to decrease by one half N N 2 Hence N 1 hyp T N e 12 Because g 0699 1 2 by comparison 0 693 hn and 0 693 tn 0 6937 EE 34 2 Thus the half life can be computed if t
108. provided determine the periods of a pendulum with each mass as the bob keeping length L and the small angle of oscillation constant Record your results in Data Table 2 and draw a conclusion from the data 4 Experimentally investigate the relationship between the length and period of the pendulum Using four dif ferent lengths such as 0 20 0 40 0 60 and 0 80 m determine the average period of a pendulum of each length keeping mass and the small angle of oscilla tion constant Record the data in Data Table 3 www ATIBOOK ir EXPERIMENT 3 The Scientific Method The Simple Pendulum 41 5 Compute the theoretical period for each pendulum length Eq 3 2 and enter the results in Data Table 3 g 9 80 m s 980 cm s Compute the percent error between the experimen tal and the theoretical values of the period for each pendulum length and record in Data Table 3 Draw conclusions about the validity or applicability of Eq 3 2 The object of the preceding experimental procedures was to determine the validity or applicability of Eq 3 2 that is whether the experimental results agree with the theoretical predictions as required by the scientific method Once found acceptable a theoretical expression can then be used to determine experimentally other quantities occurring in the expression For example Eq 3 2 provides a means for experimentally determining g the acceleration due to gravity by measur
109. s 1 year 365 days 8 76 X 10 h 5 26 X 10 min 3 16 X 10 s 360 277 rad 180 s rad 1 rad 57 3 90 7 2 rad 60 7 3 rad 0 0175 rad 45 7 4 rad 30 7 6 rad 1 m s 3 6 km h 3 28 ft s 2 24 mi h 1 km h 0 278 m s 0 621 mi h 0 911 ft s 1 ft s 0 682 mi h 0 305 m s 1 10 km h 1 mi h 1 467 ft s 1 609 km h 0 447 m s 60 mi h 88 ft s 1 newton N 10 dynes 0 225 Ib 1 lb 4 45 N Equivalent weight of 1 kg mass on the Earth s surface 2 2 lb 9 8 N 1 Pa N m 1 45 x 10 Ib in 7 4 X 1073 torr mm Hg 1 tor mm Hg 133 Pa N m 0 02 1b in l atm 14 7 lb in 1 013 X 10 N m Pa 30 in Hg 76 cm Hg 1 bar 10 N m Pa 1 millibar 10 N m Pa 1J 10 ergs 0 738 ft lb 0 239 cal 9 48 X 10 Btu 624 X 105 eV 1 kcal 4186 J 3 968 Btu 1 Btu 1055 J 778 ft lb 0 252 kcal 1 cal 4 186 J 3 97 10 Btu 3 09 ft lb 1 ft lb 1 356 J 1 29 X 10 Btu leV 1 60 x 10 J 1 W 0 738 ft Ib s 1 34 X 10 hp 3 41 Btu h 1 ft Ib s 1 36 W 1 82 X 10 hp 1 hp 550 ft Ib s 745 7 W 2545 Btu h 1u 1 66 x 1077 kg lt gt 931 MeV 1 electron mass 9 11 X 10 kg 5 49 x 10 u 0 511 MeV 1 proton mass 1 672 X 107 kg 1 00728 u 938 3 MeV 1 neutron mass 1 674 x 107 kg 1 00867 u lt gt 939 6 MeV www ATIBOOK ir TABLE B4 Trigonometric Relationships APPENDIX B Mathematical and Physical Constants
110. seen directly from Fig 5 2 y 120 Why Using the law of cosines Eq 5 1 R A B 2AB cos y 2 45 N 1 47 N 2 2 45 N 1 47 N cos 120 6 00 N 2 16 N 2 3 60 N 0 500 11 76 N and taking the square root R 343N The directional angle 0 may be found using the law of sines Eq 5 2 eee B sin y R _ 1 47 N sin 120 si 21 8 3 43 N Remember that this is the angle between vectors R and A Note that the results are the same as in Example 5 1 to two significant figures Value obtained by calculator or from trig table with cos 120 cos 180 120 cos60 using the trigonometric identity cos A B cosAcos B sinA sin B www ATIBOOK ir EXPERIMENT 5 The Addition and Resolution of Vectors The Force Table 77 COMPONENT METHOD If two vectors A and B are at right 90 angles Fig 5 32 then the magnitude of their resultant is given by the Pythagorean theorem R NV A B the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the legs of the triangle Notice that the law of cosines reduces to this formula with y 90 because cos 90 0 The angle of orientation is given by tan 0 B A or 0 tan B A By the inverse process a vector may be resolved into x and y components Fig 5 3b That is the vector R is the resul tant of R and R and R R R where R Rcos 0 and R R
111. should be drawn parallel to the shorter edge of the page and about 3 to 4 cm from that edge Make a mark near the center of the line and place the candle on the mark Optical density does not correlate directly with mass density In some instances a material with a greater optical density than another may have a lower mass density www ATIBOOK ir Glass plate ieee gm mage 1 gt Position 1 p A Position 2 Candle line Center line Figure 27 4 Glass plate as a mirror The arrangement for the experimental procedure using a glass plate as a mirror See text for description Images are displaced for illustration Put the glass plate near the center of the paper as shown in the figure With the length of the plate paral lel to the candle line draw a line along the edge of the glass plate side toward the candle Light the candle Caution Take care not to burn yourself during the experimental procedure Looking directly over the candle with your eye as in position 1 in Fig 27 4 you will observe an image of the candle image 1 in the glass plate The glass plate reflects light and serves as a mirror Observing should be done with only one eye open 2 Observing the top of the flame from a side position position 2 in Fig 27 4 you will see a double image one nearer than the other Can you explain why Place a pin in the pin board near the glass plate so that it is aligned in the line of sight
112. sin 0 The magnitude of Ris given by R VR R 5 3 and ES t 5 4 an 0 R 5 4 or R 0 tan 2 R resultant magnitude and angle a R R cos 0 Ry R sin 0 Rz VR Ry 0 tan MRR X b Figure 5 3 Vector resultant and components a The vec tor addition of A and B gives the resultant R b A vector such as R can be resolved into x and y rectangular com ponents R and R respectively The vector sum of any number of vectors can be obtained by using the component method This is conve niently done by having all the vectors originate from the origin and resolving each into x and y components as shown in Fig 5 4 for R A t B C The procedure is to add vectorially all of the x com ponents together and all of the y components together The R and R resultants are then added together to get the total resultant R To illustrate this for the vectors in Fig 5 4 R A B C 6 0 cos 60 N 0 10 cos 30 N 53 7N A B C 6 0 sin 60 N 5 0N 10 sin 30 N 5 2N R y where the component directions are indicated by the posi tive and negative signs arbitrary units Note that B has no x component and that C and C are in the negative x and y directions as indicated by the minus signs Then the mag nitude of R is Eq 5 3 R VR R V 5 71 N 5 2 N 7 7N and by Eq 5 4 R AN tan n 42
113. so as to give weight forces of F F 0 200 g N in these directions The weight hangers usually have masses of 50 g or 0 050 kg Using a third pulley and weights determine the magnitude and direction of the equilibrant force that maintains the central ring centered in equilibrium around the center pin Record the magnitude and direction of the resultant of the two forces in the data table Remember the resul tant has the same magnitude as the equilibrant but is in the opposite direction Note The string knots on the central ring should be of a nontightening variety so that the strings will slip freely on the ring and allow the strings to pull directly away from the center Pull ing the center ring straight up a short distance and releasing it helps adjust the friction in the pulleys as the ring vibrates up and down so that it can settle into an equilibrium position involving only the ap plied forces When the forces are balanced the pin may be carefully removed to see whether the ring is centered on the central hole Vector addition II Repeat Procedure 2 for F 0 200 g N at 20 and F 0 150 g N at 80 Use the other half of the sheet of graph paper used in Pro cedure 2 a for the graphical analysis Be careful in the analytical analysis Can you use tan 0 F F in this case Vector addition III Repeat Procedure 2 with F F 0 200 g N at 0 and F F 0 150 g N at 90 In this case F F
114. so that the galvanometer registers no current Then points b and c in the circuit are at the same potential current 7 flows through both R and R and current J flows through both R and R Figure 21 3 Wheatstone bridge circuit diagram See text for description www ATIBOOK ir EXPERIMENT 21 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method 313 Figure 21 4 Slide wire Wheatstone bridge a Circuit diagram for resistance measurements The resistances R and R are varied by sliding the contact C along the wire The galvanometer G is used to indicate when the bridge is balanced b The contact slides over the wire on a meter stick When contact is made the lengths L and L on either side of C are easily read Photo Courtesy of Sargent Welch Also the voltage drop V across R is equal to the voltage drop across Rj Vac for a zero galvanometer deflection Vas Vac Similarly Voa Vea 21 7 Why Writing these equations in terms of currents and resistances by Ohm s law TR hR 21 8 IR L R Then dividing one equation by the other and solving for R yields r RR 21 9 c R 21 9 Hence when the bridge is balanced the unknown resis tance R can be found in terms of the standard resistance R and the ratio R R Notice that the difficulties of the ammeter voltmeter methods are eliminated The Wheatstone bridge in
115. spanner wrench Do not attempt to do this without your instructor s permission or supervision D Density The density p of a substance is defined as the mass m per unit volume V that is p m V Thus the densities of substances or materials provide comparative measures of the amounts of matter in a particular unit space Note that there are two variables in density mass and volume Hence densities can be affected by the masses of atoms and or by their compactness volume As can be seen from the defining equation p m V the SI units of density are kilogram per cubic meter kg m However measurements are commonly made in the smaller metric units of grams per cubic centimeter g cm which can easily be converted to standard units Density may be determined experimentally by measur ing the mass and volume of a sample of a substance and cal culating the ratio m V The volume of regularly shaped objects may be calculated from length measurements For example Rectangle V IXwXh length X width X height Cylinder V AI 7 al circular cross sectional area A mr where r is the radius and is the length of the cylinder In the British fps foot pound second system density is expressed in terms of weight rather than mass For example the weight density of water is 62 4 Ib ft Figure 2 6 Density mass and volume The marble and the Styrofoam ball have equal masses but dif
116. strikes the paper the indentation mark will enable you to determine the range of the projectile Also mark the position of the appa ratus on the table for example using a piece of tape as a reference It is important that the gun be fired from the same position each time Shoot the ball five times hitting the paper and mea sure the horizontal distance or range x the ball travels for each trial see Fig 8 3 If faint indentation marks cannot be found on the paper cover it with a sheet of carbon paper carbon side down The ball will then make a carbon mark on the paper on impact Record the measurements in Data Table 2 and find the average range The height y is measured from the bottom of the ball as it rests on the gun to the floor Measure this distance and record in the data table Using Eq 8 7 compute the magnitude of the initial velocity of the ball g 9 80 m s 980 cm s Compare this to the velocity determined in Part A and compute the percent difference Dependence of Projectile Range on the Angle of Projection With the ballistic pendulum apparatus on the floor with pendulum removed elevate the front end so that The range will be measured from the floor position directly below the center of the ball just as it leaves the gun to the marks on the paper on the floor The floor location is determined by putting the ball on the gun without loading the spring 12 13 it can be fired at an
117. swing platform or single beam double pan balance with swing platform and set of weights Overflow can or graduated cylinder and eye dropper Two beakers Metal cylinder irregularly shaped metal object or metal sinker Waxed block of wood Saltwater solution and alcohol String Hydrometer and cylinder THEORY When placed in a fluid an object either floats or sinks This is most commonly observed in liquids particularly water in which light objects float and heavy objects sink But the same effect occurs for gases A falling object is sinking in the atmosphere whereas other objects float Fig 18 1 Objects float because they are buoyant or are buoyed up That is when submerged there must be an upward force that is greater than the downward force of the object s Figure 18 1 Gas buoyancy Archimedes principle applies to fluids liquids or gases Here a helium filled blimp floats in air Bill Aron PhotoEdit www ATIBOOK ir 272 EXPERIMENT 18 Archimedes Principle Buoyancy and Density Ap pg ha hj Figure 18 2 Buoyancy A buoyant force arises from the difference in pressure at different depths The pressure at the bottom of the submerged block p is greater than that at the top pj so there is a buoyant force directed upward the arrow is shifted for clarity weight and on release the object will be buoyed up and float When floating the upward buoyant force i
118. that the ring is centered around the central pin The balancing force is not the resultant R but rather the equilibrant E or the force that balances the other forces and holds the ring in equilibrium The equilibrant is the vector force of equal magni tude but in the opposite direction to the resultant that is R E See Fig 5 6 For example if an equilibrant has a magnitude of 0 30 g N in a direction of 225 on the circular scale the resultant of the forces has a magnitude of 0 30 g N in the opposite direction 225 180 45 It should be evident that the resultant cannot be determined directly from the force table Why Figure 5 5 Force tables Various types of force tables The table in c may be used vertically for demonstration b or horizontally in the laboratory Photos Courtesy of Sargent Welch The magnitude of the weight force vectors is in general given in the form R mg 0 150 g N for example where it is understood that the mass is in kilograms and g is the acceleration due to gravity It is conve nient to leave g in symbolic form so as to avoid numerical calculations until necessary This is similar to carrying along 7 in symbolic form in equations Also note that the masses of the laboratory weights usually have values stamped in grams Don t forget to change grams to kilograms when working in the SI for example 150 g 0 150 kg www ATIBOOK ir EXPERIMENT 5 The Addi
119. the decimal point and which are actually part of the measure ment and hence significant That is if the first zero from the left 300 kg is the estimated digit in the measurement then only two digits are reliably known and there are only two significant figures Similarly if the last zero is the estimated digit 300 kg then there are three significant figures This ambiguity is be removed by using scientific powers of 10 notation 3 0 X 10 kg has two significant figures 3 00 X 10 kg has three significant figures This procedure is also helpful in expressing the significant figures in large numbers For example sup pose that the average distance from Earth to the Sun 93 000 000 miles is known to only four significant fig ures This is easily expressed in powers of 10 notation 9 300 X 107 mi D Computations with Measured Values Calculations are often performed with measured val ues and error and uncertainty are propagated by the mathematical operations for example multiplication or division That is errors are carried through to the results by the mathematical operations The error can be better expressed by statistical meth ods however a widely used procedure for estimating the uncertainty of a mathematical result involves the use of significant figures The number of significant figures in a measured value gives an indication of the uncertainty or reliability of a measurement Hence you might exp
120. the known wavelength of the light and the known separation of the slits to calculate the theoret ical value of sin 0 for each case Compare the theory to the experiment by taking percent differences Re cord all results in CI Data Table 3 To demonstrate that this experimental data can also be used to find the wavelength of the light use the EXPERIMENT 32 Single Slit and Double Slit Diffraction 13 C 1 2 475 data in CI Data Table 4 to calculate the wavelength of the light for each case then find an average Compare the average to the expected value by taking a percent error Cancel all zooms and fix up the graph window so that all data collected can be seen Print the graph and label each maximum on both sides of the center with the appropriate n value Title this graph Graph 2 Double Slit Pattern d 0 25 mm w 0 04 mm If no printer is available make a careful sketch of the graph paying attention to the location of the maxima along the horizontal axis Attach the graph to the lab oratory report Comparing Single Slit Pattern to Double Slit Pattern Change the double slit set to a set with slit separa tion 0 25 mm and slit width 0 08 mm Collect data as before and print the graph Label on the graph the maxima with their appropriate n values Title this graph Graph 3 Double Slit Pattern d 0 25 mm w 0 08 mm Repeat with the double slit set of slit separation 0 50 mm and slit w
121. the ordinate Y axis so that the curve for each absorber occupies most of the graph paper Determine the range of beta absorption for each absorber in sheet units from the graph and record Multiply each range in sheet units by the respec EXPERIMENT 35 The Absorption of Nuclear Radiation 503 tive average sheet thickness to determine the range in length units B Absorption of Gamma Radiation 8 10 11 12 Using the result of the range of beta absorption in alu minum from Procedure 7 place in front of the probe the minimum number of sheets of aluminum that will completely absorb the beta radiation Then move the source toward the probe until the intensity observed on the Geiger counter is 700 cpm to 800 cpm Record this intensity 7 in Data Table 3 The Observed intensity is then almost solely due to gamma radiation Why Leaving the aluminum sheet s in place insert lead sheets one at a time between the aluminum sheets and the source Measure and record the count rate after each sheet is inserted Be careful not to move the source Insert a total of 10 sheets of lead After the sixth sheet two sheets may be inserted at a time Remove all the sheets Remove the source several meters across the room from the probe and measure the background radiation intensity J over a 4 min to 5 min interval See Experiment 33 for a description of the procedure if necessary Subtract the background count rate from
122. thermal coefficient of linear expansion with units of inverse temperature that is 1 C Note that with a temperature decrease and a contraction AL would be negative or a negative expansion As Eq 16 1 shows aris the fractional change in length per degree temperature change AL L This thermal To help understand what is meant by fractional change consider a money analogy If you have 1 00 in the bank and get 5 interest then the fractional change increase in your money is A 5 cents 100 cents 1 20 0 050 or 5 0 www A TIBOOK ir 252 EXPERIMENT 16 The Thermal Coefficient of Linear Expansion oC beu S 3 S S x Kes ws as iE Cr ed lt S a 9 9 9 9 449 Qs 6 6 6 e 9 o o Y Y Y Y 4 4 4 4 Y Y Y Y e 0 o Y Y T Y 4 4 4 4 e 0 0 o b Figure 16 1 A springy solid a The elastic nature of interatomic forces is indicated by simplistically representing them as springs which like the forces resist deformation b Heat causes the molecules to vibrate with greater amplitudes in the lattice thereby increasing the volume of the solid right The arrows represent the molecular bonds and the drawing is obvi ously not to scale Shipman Wilson and Todd An Introduction to Physical Science Twelfth Edition Copyright 2008 by Houghton Mifflin Company Reprinted with p
123. three dimensions the path is along an equipotential surface An electric field may be mapped experimentally by determining either the field lines of force or the equipo tential lines Static electric fields are difficult to measure and field lines are more easily determined by measuring small electric currents flow of charges maintained in a conducting medium between charge configurations in the form of metal electrodes The steady state electric field lines closely resemble the static field that a like configuration of static charges would produce The current is measured in terms of the voltage potential difference by a high resistance voltme ter or multimeter or VTVM In other instances equipotentials are determined and hence the field lines using a simple galvanometer as a detector When no current flows between two probe points as indicated by a zero deflection on the galvanometer there is no potential difference between the points AV 0 and the points are on an equipotential B Magnetic Field Analogous to an electric field a magnetic field B was originally defined as the magnetic force per unit pole The direction of the force at a particular location is that of the force experienced by a north magnetic pole Just as the electric field may be mapped around an electric charge magnetic lines of force may be mapped around a magnet A single magnetic pole or magnetic monopole has never been observed so th
124. to the kinetic energy of the system just after collision friction of the support is considered negligible Hence x m M V m Mgh 8 2 kinetic energy change in just after collision potential energy Solving Eq 8 2 for V V V2gh 8 3 Substituting this expression into Eq 8 1 and solving for Y yields Vy m V2gh 8 4 intial speed Hence by measuring m M and h the initial velocity of the projectile can be computed www ATIBOOK ir EXPERIMENT 8 Projectile Motion The Ballistic Pendulum 133 X peM Vo oe M ri i hy hy ee Before After Figure 8 2 Ballistic pendulum action Ideally the horizon tal linear momentum is conserved during collision After collision work is done against gravity and kinetic energy is converted into potential energy Rotational consider ations neglected B Determination of the Initial Speed of a Horizontal Projectile from Range Fall Measurements If a projectile is projected horizontally with an initial veloc ity of magnitude v from a height of y it will describe an arc as illustrated in Fig 8 3 The projectile will travel a horizontal distance x called the range while falling a vertical distance y The initial vertical velocity is zero v 0 and the acceleration in the y direction is the acceleration due to grav ity a g There is no horizontal acceleration a 0 hence the comp
125. trials in TI Data Table 1 Repeat this procedure for the other two objects 3 Compute the acceleration g due to gravity from using the times of fall Find the average mean value Note The results obtained by this procedure may have very poor accuracy and precision Why B Linear Air Track 4 The air track should be set up and leveled by the in structor or laboratory assistant Do not attempt to make any adjustments to the air track Ask your instructor for assistance if you need it www A TIBOOK ir 54 EXPERIMENT 4 Uniformly Accelerated Motion 5 Turn on the air supply and place the car in motion by applying a small force on the car in a direction parallel to the air track Do not attempt to move the car on the air track if the air supply is not turned on Use the same small force for each trial for example by compressing a spring attached to the car Using laboratory timers or stopwatches determine the times required for the car to travel several convenient distances such as 0 20 m 0 40 m 0 50 m 0 75 m and so on Record the times and distances in TI Data Table 2 Several students should work together each with a timer taking a time reading as the car passes his or her assigned distance mark Make several practice trials before taking actual data Remember that the distances are length intervals and need not be mea sured from the end of the air track Make use of as much of the air track as is conven
126. until the instructor has checked it Record the value of R in the first of the spaces provided for this purpose in Part A of the laboratory report Most common meters have three scale connec tions with a binding post common to all three scales It is good practice initially to make connections to the largest scale This prevents the instruments from being pegged and possibly damaged should the magnitudes of the current and voltage exceed the smaller scales limits The scale setting may be changed for greater sen sitivity by moving the connection to a lower scale after the general magnitude of a measurement is known Also attention should be given to the proper polarity and Otherwise the meter will be pegged in the opposite direction Connect to and to However do not activate the circuit until your laboratory instructor has checked it The current in the circuit is varied by varying the rheostat resistance R Activate the circuit and take three different readings of the ammeter and voltmeter for three different currents Adjust R so that the three currents differ as much as possible Record the data in Data Table 1 and deactivate the circuit after each of the three readings until the rheostat is set for the next reading Also record the resistance of the voltmeter The resistance of the meter will be found on the meter face or will be supplied by the instructor The voltmeter re sistance is c
127. where the forces are F m g The lever arms are mea sured from the 50 cm position of the meter stick which is the pivot point or the location of the axis of rotation The official abbreviation for gram is g and the commonly used symbol for acceleration due to gravity is g The gravity g is written in italics and the gram g is not Look closely to avoid confusion www ATIBOOK ir EXPERIMENT 12 Torques Equilibrium and Center of Gravity 195 In general r 50 cm xj where x is the centimeter location of a mass Hence m g 50 cm 10cm mg 50 cm 40 cm m3g 60 cm 50 cm magr and canceling the g s m 40 cm m 10 cm m3 10 cm mar Then putting in the mass values 50 g 40 cm 100 g 10 cm 50 g 10 cm 100 g ry and solving for r4 _ 2500g cm 100g Hence for rotational equilibrium m is 25 cm from the support position axis of rotation or at the 75 cm position on the meter stick measured from the zero end Here it is assumed that the meter stick is uniform uni form mass distribution so that the torques caused by the masses of the portions of the meter stick are the same on both sides of the support and therefore cancel T4 25cm B Center of Gravity and Center of Mass The gravitational torques due to individual mass par ticles of a rigid body define what is known as the body s center of gravity The center of gravity is the balance point the poi
128. with constant speeds will be used so that only the relation in input i the a pains iini ship between work and changes in gravitational potential In an ideal conservative system mechanical energy i n pe wae oe eee a is transferred back and forth between kinetic energy and P E P TOME AME data you should be able to potential energy In such a system the sum of the kinetic and potential energies is constant as expressed by the law 1 Explain how work and energy are related of conservation of mechanical energy However in actual 2 Describe how frictional work can be determined systems friction is always present and these systems are experimentally using either force distance or energy nonconservative That is some energy is lost as a result of considerations the work done against frictional forces Even so the total 3 Better appreciate the nonconservative aspects of real energy is conserved conservation of total energy The situations and the difference between the conservation total energy is there in some form of mechanical energy and the conservation of total In this experiment the conservation of energy will be energy used to study the relationship between work and energy in EQUIPMENT NEEDED String Inclined plane with a low friction pulley and Hall s i aid e canas ca Protractor if plane not so equipped Weight hanger and slotted weights dcc LL THEORY and A Work of Friction Force Distance Method f m 11 1 mg mg s
129. with the front or nearer image of the candle image 2 in Fig 27 4 double image not shown in figure Place another pin closer to you or to the edge of the paper so that both pins and the candle image are aligned Mark the locations of the pins Repeat this procedure viewing from a position on the other side of the candle 3 Remove the equipment from the paper Draw straight lines through the pair of pin points extending from the candle line through the glass plate line Extend the candle line if necessary The lines will intersect on the opposite side of the plate line at the location of the candle image Draw lines from the actual candle position or mark to the points of intersection of the previously drawn lines and the plate line These lines from the candle mark to the glass plate line and back to the Observation positions are ray tracings of light rays 4 Draw normal lines to the glass plate line at the points of intersection of the ray lines Label and measure the angles of incidence 0 and reflection 6 Record the data in the laboratory report Also measure the perpendicular distances from the glass plate line to the candle mark the object EXPERIMENT 27 Reflection and Refraction 397 distance d and to the candle image position the image distance dj Compute the percent differ ences of the quantities as indicated in the labora tory report PLANE MIRROR 5 a Place the mirror near the center of a sheet of
130. www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 1 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method RW Laboratory Report A Ammeter Voltmeter Methods DATA TABLE 1 Accepted value of R Purpose To measure resistance values DATA TABLE 2 Voltmeter resistance R Purpose To measure resistance values Rheostat Current Voltage V Resistance R Rheostat Current Voltage V R V I setting Ry 6 o C setting Rj o C C 1 1 2 2 3 3 Average R Average R Calculations show work Percent error of R Don t forget units Percent error of R Ammeter resistance R continued www ATIBOOK ir EXPERIMEN T 24 DATA TABLE 3 Purpose To measure resistance values Voltmeter resistance R The Measurement of Resistance Laboratory Report Accepted value of R DATA TABLE 4 Purpose To measure resistance values Rheostat Current Voltage V Resistance R Rheostat Current Voltage V R VII setting Ry C C6 3 setting Ry C C6 2 C6 2 1 1 2 2 3 3 Average R Average R Percent error of R Percent error of R Ammeter resistance R Calculations show work 318 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 21 T
131. 0 then F fk WN Usually for a given pair of surfaces ju lt pu That is it takes more force to overcome static friction get an object moving than to overcome kinetic friction keep it moving Both coefficients may be greater than 1 but they are usually less than 1 The actual values depend on the nature and roughness of the surfaces These conditions on f are sometimes written f uN that is f is less than or equal to the maximum value of u N As the applied force is increased f increases and there is no motion until finax is reached www ATIBOOK ir 160 EXPERIMENT 10 Friction b d TI Figure 10 1 Friction The applied force is balanced by the force of static friction f a c and F f ma 0 As the applied force increases so does the force of static friction until a maximum value is reached fnax MN A slightly greater force d sets the block into motion F f ma with the applied force being opposed by the force of kinetic friction fy RV EXPERIMENTAL PROCEDURE A Determination of u 1 Determine the mass of the wooden block on a labora tory balance and record it in the laboratory report Clean the surfaces of the board and block so they are free from dust and other contaminants Place the board with the pulley near the edge of the table so that the pulley projects over the table s edge TI Fig 10 2 Attach one end of a length of string to the wooden block and th
132. 0 rotation occur and only this wavelength color of light will be transmitted As a result of nonuni form crystal thickness a colored pattern is observed when the crystal is viewed through crossed polarizers F Optical Stress Analysis An important application of polarized light is optical stress analysis of transparent materials Glasses and plastics are usually optically isotropic If polarized light is transmitted through an isotropic material and viewed with a crossed polarizer the transmitted light intensity is minimal However when many materials are mechanically stressed they become optically anisotropic indices of refraction vary with direction and the polarization of the transmitted polarized light is affected Areas of strain may then be identified and studied through an analyzer e TI Fig 29 7 For example improperly annealed glass may have internal stresses and strains that may later give rise to cracks G Liquid Crystal Displays LCDs LCDs or liquid crystal displays are now commonly used in wristwatches hand calculators and even gas pumps A liquid crystal is a liquid in which the molecules have some order or crystalline nature Liquid crystals used in LCDs Crystal Analyzer Outgoing polarization direction 90 rotation TI Figure 29 6 Optical activity Certain substances have the property of being able to rotate the plane of polarization of a beam of linearly polarized light through 90
133. 0 on the x axis CI Fig 7 5 shows what the screen should look like after all setup is complete The size of the graph window can be maximized so that you can observe the plots better g EXPERIMENTAL PROCEDURE The complete experimental setup is shown in CI Fig 7 6 Each car is connected to its own sensor and pulley system one on each side of the track Here are the instructions for setting up the carts 1 Place Cars 1 and 2 with the cart string brackets at tached on the track with the magnetic sides facing each other The cart string brackets may need reposi tioning so that they face the outside of the track as shown in CI Fig 7 6 Install a rotary motion sensor RMS on each side of the track with the pulleys facing the inside of the track On the opposite side of the track install the RMS IDS adapters small pulleys See CI Fig 7 7 for reference www A TIBOOK ir EXPERIMENT 7 Conservation of Linear Momentum 119 4 DataStudio 3 x Fie Edt Experiment Window Display Heb lr Surmary zetu Start UB EJ Calculate Curve it fA Graph 1 Velocity Ch 1 amp 2 m s i Velocity Ch 3 amp 4 m z z Eg TotalP mt v1 mz v2 Ei TotalkE 0 5 mi vl 2 C5 3 21 VSAA No Data T 7 8 9 1 Valocity Zh 3 amp 4 No Data un ui e b REG m 6 tT 5 10 Time s H Displays ai Digits fae FFI 3 Graph TotalP No Data
134. 0 x 10 Tron cast 9 0 x 10 wrought 19 0 x 10 Steel 19 2 x 10 TABLE A3 Coefficients of Linear Thermal Expansion Substance dC Aluminum 24 0 x 1076 Brass 18 8 X 10 Copper 16 8 x 1075 Glass window 8 5 x 1076 Pyrex 3 3 x 1075 Iron 11 4 x 1075 Lead 29 4 x 1075 Nickel 12 8 x 1079 Silver 18 8 x 1076 Steel 13 4 x 1079 Tin 26 9 x 1075 Zinc 26 4 X 1076 511 www ATIBOOK ir 512 APPENDIX A Material Properties TABLE A4 Specific Heats Substance kcal kg C or cal g C J kg C Aluminum 0 22 92 Brass 0 092 385 Copper 0 093 389 Glass 0 16 670 Iron 0 11 460 Lead 0 031 130 Mercury 0 033 138 Nickel 0 11 460 Silver 0 056 234 Steel 0 11 460 Tin 0 054 226 Water 1 00 4186 Zinc 0 093 389 TaBLE A5 Color Code for Resistors Composition Type ohms Q Bands A and B Band C Band D Resistance Significant tolerance Color figure Color Multiplier Color percent Black 0 Black 1 Silver 10 Brown 1 Brown 10 Gold 5 Red 2 Red 100 Red Ru Orange 3 Orange 1 000 Yellow 4 Yellow 10 000 Green 5 Green 100 000 Blue 6 Blue 1 000 000 Purple violet 7 Gray 8 Silver 0 01 White 9 Gold 0 1 A B D S First significant figure Tolerance Second significant figure Multiplier For example if the bands on a resistor are red A black B orange C the resistance is 20 X 1000 20 000 Q or 20 kO www ATIBOOK ir TABLE A6 Resistivities and Temperature Coefficients
135. 10 2 C2 N m 4n X 107 1 26 X 10 T M A 6 378 X 106 m 3963 mi 6 357 X 106 m 3950 mi 6 4 X 10 km for general calculations 6 0 X 10 kg 7 4 X 1022 kg g mass of Earth 2 0 X 10 kg 1 5 X 108 km 93 X 10 mi 3 8 X 10 km 2 4 X 10 mi 3500 km 2160 mi 1 4 x 106 km 864 000 mi www ATIBOOK ir PHYSICS LABORATORY EXPERIMENTS eventh Edition JERRY D WILSON CECILIA A HERNANDEZ HALL American River College amp e BROOKS COLE CENGAGE Learning e BROOKS COLE CENGAGE Learning Physics Laboratory Experiments Seventh Edition Jerry D Wilson Cecilia A Hern ndez Hall Publisher Mary Finch Development Editor Brandi Kirksey Editorial Assistant Joshua Duncan Senior Media Editor Rebecca Berardy Schwartz Marketing Manager Nicole Mollica Marketing Coordinator Kevin Carroll Marketing Communications Manager Belinda Krohmer Associate Content Project Manager Jill Clark Art Director Cate Barr Senior Print Buyer Diane Gibbons Production Service Pre Press PMG Senior Photo Editor Jennifer Meyer Dare Photo Researcher Pre Press PMG Cover Designer Hannah Wellman Cover Image A teacher adjusting a scientific instrument O Veer Incorporated Compositor Pre Press PMG 2010 2005 Brooks Cole Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced transmitted stored or used in any form or by any means gr
136. 12 Assemble a pulley system as illustrated in Fig 13 3b and repeat Procedures 9 through 11 for this case Don t forget to include the mass of the movable pulley as part of the load since it too is being raised 13 Assemble a pulley system as illustrated in Fig 13 4a or b and repeat Procedures 9 through 11 D Wheel and Axle 14 Using the vernier calipers determine the radii of the wheel largest diameter and of the larger and smaller axles The wheel and axle apparatus commonly used has three sizes 15 16 17 Fixing and wrapping strings around the wheel and axle set up the apparatus with weight hangers and enough weights on the input force weight hanger so that it descends with a slow uniform speed Start with the larger diameter axle if your wheel and axle has multiple axles Record the masses of the applied force and the load in Data Table 4 Calculate the AMA TMA and efficiency e for this case Repeat Procedures 15 and 16 with the load suspended from the smaller axle if your wheel and axle has multiple axles www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 1 3 Simple Machines Mechanical Advantage RV Laboratory Report A Inclined Planes DATA TABLE 1 0 TMA 5 10 15 20 25 30 35 40 45 Comment on graph Comm
137. 134 EXPERIMENT 8 Projectile Motion The Ballistic Pendulum But using the trigonometric identity 2 sin0cos0 sin 26 we find that the range or maximum distance in the x direction is v sin 20 R EE XN 8 11 range From Eq 8 11 it can be seen that the range of the pro jectile depends on the angle of projection 0 The maximum range Rmax occurs when sin 20 1 Since sin 90 1 by comparison 20 90 or 0 45 Hence a projectile has a maximum range for 0 45 and R 9s S 8 12 max maximum range 0 45 which provides another convenient method to determine experimentally the initial speed of a projectile Note This development neglects air resistance but the equations give the range to a good approximation for rela tively small initial speeds and short projectile paths Why EXPERIMENTAL PROCEDURE Caution With projectiles involved it is recommended that safety glasses be worn during all procedures A The Ballistic Pendulum 1 Obtain the projectile ball which may be in the pen dulum bob Note When removing the ball from the pendulum bob of some types of ballistic pendula be sure to push up on the spring catch that holds the ball in the pendulum so as not to damage it Place the projectile ball on the ball rod of the spring gun and cock the gun by pushing on the ball Both ball and rod may move backward or the ball may slip over the rod depending on the
138. 2 2 Substituting Eqs 30 3 and 30 5 into Snell s law Eq 30 1 yields Eq 30 2 0 0 5 30 5 EXPERIMENTAL PROCEDURE 1 Two types of prism spectrometers are shown in e Fig 30 3 one of which is an adapted force table see Experiment 5 The four basic parts of a spec trometer are the a collimator and slit assembly b prism c telescope and d divided circle The collimator is a tube with a slit of adjust able width at one end and a converging lens at the other Light from a light source enters the collimator The length of the collimator tube is made equal to the focal length of the lens so as to make the rays of the emerging light beam parallel The prism deviates and disperses the beam into a spectrum The objective lens of the telescope converges the beam and produces an image of the slit which is viewed through the telescope eyepiece The eyepiece is fitted with cross hairs which may be fixed on a a Figure 30 3 Prism spectrometer a Simple spectrometer The prism rests on a graduated divided circle used for angle measurements Light directed into the collimator tube on the left is refracted by the prism to the adjustable telescope on the right b Advanced spectrometer The collimator has a built in light source and the angular measurement scale has a vernier scale that can be read to 1 minute of arc Fisher Scientific Company LLC Some procedures may not apply to the force tabl
139. 2 Law of reflection The angle 6 between the incident ray and the normal to the surface is equal to the angle 0 between the reflected ray and the normal that is 0 0 Only a single ray is shown The object distance d is also equal to the image distance d for a plane mirror Normal Medium 1 Figure 27 3 Refraction of two parallel rays When medium 2 is more optically dense than medium 1 then v lt v and the rays are bent toward the normal as shown here If v gt v the rays are bent away from the normal as though the ray arrows were reversed in the reverse ray tracing here From the geometry of Fig 27 3 where d is the dis tance between the parallel rays at the boundary we have Vit Vot sin and sin0 d or sin vy A 27 1 sinf v where the ratio of the velocities n is called the relative index of refraction Equation 27 1 is known as Snell s law If v lt v as in Fig 27 3 the rays are bent toward the normal in the second medium And if v gt v4 the rays are bent away from the normal for example reversed rays in Fig 27 2 with medium 2 taken as medium 1 For light traveling initially in vacuum or approxi mately for light traveling initially in air the relative index of refraction is called the absolute index of refraction or simply the index of refraction and n 27 2 y where c is the speed of light in vacuum and v is the speed of l
140. 3 rise Sweep time div Exp time constant Computed RC Percent error Case 1 RC Case 2 RC Case 3 R4C Calculations show work Slope of the 7 versus R plot Percent difference between slope and C Don t forget units continued 383 www A TIBOOK ir EXPERIMENT 26 TheRC Time Constant Electronic Timing Laboratory Report RV DATA TABLE 2 Purpose To determine the effect of C on the time constant Divisions R C for 0 63 Sweep Exp time Computed Percent rise time div constant RC error Case 4 Case 5 Slope of the 7 versus C plot Percent difference between slope and R Experimental RC time constant Capacitance C Computed R Marked value of R Percent error 384 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 26 TheRC Time Constant Electronic Timing Laboratory Report RV QUESTIONS 1 Judging on the basis of your experimental results under what conditions are the charging times of different RC circuits the same 2 In the form V V 1 e the 7 RC in the exponential must have units of time Why Show that this is the case 3 How could the value of an unknown capacitance be determined using the experimental procedures Show explicitly by assuming a value for an experimentally determined time constant 385 www A
141. 4 Uniformly Accelerated Motion RW Laboratory Report A Object in Free Fall RV DATA TABLE 1 Purpose To determine g experimentally and check mass dependence y m Time of fall t Calculated g Trial 1 2 3 4 Average mean value m Time of fall t Calculated g Trial 1 2 3 4 Average mean value m3 Time of fall t Calculated g Trial 1 2 3 4 Average mean value Calculations show work attach page to report 55 continued www ATIBOOK ir EXPERIMENT 4 Uniformly Accelerated Motion Laboratory Report B Linear Air Track RV DATA TABLE 2 Purpose To determine g experimentally Distances 1 Time 5 1 Level air track 2 3 Average Computed v 2 Time 5 1 Elevated air track 2 hy 3 Average Computed v 3 Timet 1 Elevated air track 2 hy 3 Average Computed v Calculations show work Length of air track L 1 Experimental values of g Percent error 1 computed from data 1 Slopes of graphs 1 5 2 e 2 S S oo 3a 56 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 4 Uniformly Accelerated Motion Laboratory Report RV QUESTIONS A Object in Free Fall 1 Objects of different mass were used to see whether the acceleration due to gravity
142. 4 4 When this general expression is applied to a resistance R for which V IR Ohm s law the expanded energy or work in Eq 24 4 can be written t W IVt P Rt id 24 5 The electrical energy expended is manifested as heat energy and is commonly called joule heat or R losses I R being the power or energy expended per time W t PRit PR Equation 24 5 shows how the joule heat varies with resistance 1 For a constant current J the joule heat is directly proportional to the resistance I R 2 For a constant voltage V the joule heat is inversely proportional to the resistance V R The energy expended in an electrical circuit as given by Eq 24 5 has the unit of joule J The relationship www A TIBOOK ir 362 EXPERIMENT 24 Joule Heat 12 V de power supply or storage battery Immersion heater a Figure 24 1 Joule heat determination a The circuit diagram for the experimental procedure to measure joule heat See text for description b An electric calorimeter Photo Courtesy of Sargent Welch conversion factor between joules and heat units in calories was established by James Joule from mechanical considerations the mechanical equivalent of heat You may have learned that in his mechanical experi ment Joule had a descending weight turn a paddle wheel in a liquid He then correlated the mechanical gravitational potential energy lost by the descending w
143. 6 1 Taking the more massive hanger 715 to be moving in the positive direction the unbalanced or net force is Fret mg mg m m g TI 6 1 where the friction and inertia of the pulley are neglected By Newton s second law TI 6 2 Fe ma m m a where m m m is the total mass of the moving sys tem Then equating Eqs TI6 1 and TI6 2 m m g m m a and solving for a Fii a M total m m g m my TI 6 3 acceleration theoretical Optional In the experimental arrangement there may be an appreciable frictional force f associated with the pulley that opposes the motion Also the pulley has inertia In an attempt to take this inertia into account an equivalent mass m may be added to the total mass in cal culations not physically added in the experiment Hence for better accuracy the equation for the acceleration of the system should be modified as follows F f m m maa m m g f m m Meg a 89 or oe m m g a TI 6 4 m m Meg If the masses of the Atwood machine move with a constant speed the magnitude a of the acceleration of the system is zero and E m m g f m m Meg a Solving for f and equating to mg with f m 8 f m m g mg TI 6 5 uniform speed which provides a method for determining the magnitude of th
144. 6B Proper graphing An example of a properly labeled and plotted graph See text for description www ATIBOOK ir EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis 11 TABLE 1 1 Data for Figure 1 7 Mass kg Period s d 0 025 1 9 az 0 40 0 050 2 7 nn 0 30 0 10 3 8 0 25 0 15 4 6 0 28 0 20 5 4 ete 0 18 0 25 6 0 n 0 15 in Fig 1 6B with an approximately equal number of points on each side of the line gives a line of best fit In cases where several determinations of each experi mental quantity are made the average value is plotted and the mean deviation or the standard deviation may be plotted as error bars For example the data for the period of a mass oscillating on a spring given in Table 1 1 are plotted in Fig 1 7 period T versus mass m The d is the mean deviation shown here for an illustration of error bars See Appendix C A smooth line is drawn so as to pass within the error bars Your instructor may want to explain the use of a French curve at this point Graphs should have the following elements see Fig 1 7 1 Each axis labeled with the quantity plotted 2 The units of the quantities plotted 3 The title of the graph on the graph paper commonly listed as the y coordinate versus the x coordinate 4 Your name and the date STRAIGHT LINE GRAPHS Two quantities x and y are often linearly related that is there is an algebraic relationship of the form y mx b
145. 75 www ATIBOOK ir EXPERT MIE IN TF i 7 Experimental Planning A common experimental setup is shown in GL Fig 11 1 for a car moving up an inclined plane at a constant speed pulled by a descending mass suspended over a pulley Free body diagrams for the forces acting on each object are also shown 1 Write an equation for the sum of the forces acting on the car parallel to the plane and also for the sum of the forces acting on the descending mass Note that the car and descending mass both move with constant velocities 2 If the mass of the connecting string is small compared to the other masses F and T will be approximately equal Use this result to combine the equations and solve for the force of friction fin terms of the masses and angle Did your result include a sin term Check with a classmate or the instructor to verify your result 3 Now consider the case of the car moving down the plane with a constant speed pulling a smaller mass upward Draw the free body diagrams and repeat the process used above to obtain an expression for fin this case Use m for the ascending mass How does this result compare to the previous one Note that W fd applies in both cases of the block moving up and down the plane where d is the distance the block moves 176 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 11 Experimental Planning 4 Examine your equations for f and determine what experimental quantities n
146. ATIBOOK ir APPENDIX B TABLE B1 Metric Prefixes Mathematical and Physical Constants Multiple Name Abbreviation 1 000 000 000 000 000 000 10 8 exa E 1 000 000 000 000 000 105 peta P 1 000 000 000 000 10 tera T 1 000 000 000 10 giga G 1 000 000 106 mega M 1 000 10 kilo k 100 10 hecto h 10 10 deka da 1 1 0 1 107 deci d 0 01 10 centi c 0 001 10 milli m 0 000001 1076 micro H 0 000000001 10 nano n 0 000000000001 10 pico p 0 000000000000001 107 P femto f 0 000000000000000001 10715 atto a TABLE B2 Physical Constants Acceleration due to gravity Universal gravitational constant Electron charge Speed of light Boltzmann s constant Planck s constant Electron rest mass Proton rest mass Neutron rest mass Coulomb s law constant Permittivity of free space Permeability of free space Astronomical and Earth data Radius of the Earth equatorial polar average Mass of the Earth the Moon the Sun Average distance of the Earth from the Sun Average distance of the Moon from the Earth Diameter of the Moon Diameter of the Sun Q e a S 9 8 m s 980 cm s 32 2 ft s N m 6 67 X 100 7 g 1 60 x 107 C 3 0 X 105 m s 3 0 x 10 cm s 1 86 X 10 mi s 1 38 x 10 2 J K 6 63 X 10 7 J s 4 14 X 10 eV s h 2a 1 05 x 1077 J s 6 58 x 107 6 eV s 9 11 X 10 kg 5 49 x 10 u amp 0 511 MeV 1 672 X 107 kg 1 00783 u 938 3 MeV 1 674 X 107 kg 1 00867 u 939 1 MeV 1 4a
147. ATIBOOK ir Name Section Date Lab Partner s Tita EX PERIMENT 2 3 Resistances in Series and Parallel RW Laboratory Report Resistor values R R4 R R A Resistors in Series Calculations Source voltage V show work Equivalent resistance R Current J Voltage drops across resistors V V V3 Don t forget units continued 343 www ATIBOOK ir EXPERIMENT 22 Resistances in Series and Parallel Laboratory Report Experimental measurements Percent error I I Vi L V5 I V3 V V V3 V across resistors as a group B Resistors in Parallel Calculations Source voltage V show work Equivalent resistance R Current 7 Current through resistors J h I Experimental measurements Percent error I Vi I V h V3 I L h h 344 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 23 Resistances in Series and Parallel Laboratory Report Optional Procedure Calculations Source voltage V show work Equivalent resistance R Current J Current through resistors J I I Experimental measurements Percent error I Vi I V3 I V I continued 345 www ATIBOOK ir EXPERIMENT 22 Resistances in Series and Parallel Laboratory Report C Resistors in Series Parallel Calculations Source voltage V show work
148. B the vectors are placed head to tail or tip to tail that is the head of A and the tail of B Fig 5 1a Vector arrows may be moved around as long as they remain pointed in the same direction Then drawing a vector from the tail of A to the head of B gives the vector R and completes the triangle R is the resultant or vector sum of A B in other words by vector addition R A B 75 analytical The chief methods of these will be described and the addition of force vectors will be investigated The results of graphical and analytical methods will be com pared with the experimental results obtained from a force table The experimental arrangements of forces vectors will physically illustrate the principles of the methods of vector addition After performing this experiment and analyzing the data you should be able to do the following 1 Add a set of vectors graphically to find the resultant 2 Adda set of vectors analytically to find the resultant 3 Appreciate the difference in convenience between using graphical and using analytical methods of vector addition Vectors will be indicated by bold face roman letters String Protractor Ruler Level 3 sheets of Cartesian graph paper The magnitude of R is proportional to the length of the vector arrow and the direction of R may be specified as being at an angle 0 relative to A POLYGON METHOD If more than two vectors are added the head t
149. Because we take the average of the squares of the devia tions and then the square root the standard deviation is sometimes called the root mean square deviation or simply the root mean square Notice that always has the same units as x and that it is always positive Example D 1 What is the standard deviation of the set of numbers given in Example 1 6 in Experiment 1 Solution First find the square of the deviation of each of the numbers Noraber of measurements dl 5 42 5 93 0 26 d 6 18 5 93 0 06 di 5 70 5 93 0 05 d 6 01 5 93 0 01 d2 6 32 5 93 0 15 Figure D 1 See text for description For a small number of measurements it can be statistically shown that a better value of the standard deviation is given by o V 1 N 1 Sd This normal or Gaussian distribution is represented by a bell shaped curve Fig D 1 That is the scatter or dispersion of the measurements where N is replaced by N 1 Your instructor maywant you to use this is assumed to be symmetric about the true value of a quantity form of the standard deviation 521 www ATIBOOK ir 522 APPENDIX D Standard Deviation and Method of Least Squares probability of a measurement falling within 2 standard deviations is 95 METHOD OF LEAST SQUARES Let y m x b be the predicted equation of the best fitting straight line for a set of data The vertical dev
150. By measuring the velocities of cars of the same and different masses before and after collision the total momentum of a system can be determined and the conservation of linear momentum investigated RV OBJECTIVES After performing this experiment and analyzing the data you should be able to do the following 1 Explain when linear momentum is conserved and what this means in terms of force and motion 2 Apply the conservation of linear momentum to a system 3 Describe two body collisions in terms of the conser vation of linear momentum B OBJECTIVES Understand that momentum is conserved for both elastic and inelastic collisions 2 Distinguish between elastic and inelastic collisions in terms of the conservation of kinetic energy 105 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir T E X P E R J IMENT 7 Conservation of Linear Momentum RV EQUIPMENT NEEDED e Air track Three cars two of similar mass Four laboratory timers or stopwatches Laboratory balance Masking tape Meter stick if no length scale on air track Velcro optional f electronic photogates timers and computer assisted data analysis are available your instructor will give you instruction on their use RV THEORY The linear momentum p of a particle or object is defined as TI 7 1 p my where m is the mass of the object and v its velocity Since velocity is a
151. C circuits See text for description www ATIBOOK ir EXPERIMENT 26 The RC Time Constant Electronic Timing 381 Open the circuit and repeat Procedures 3 and 4 with R R 5 KQ and R R 20 KQ Record in TI Data Table 2 On a Cartesian graph plot the experimental 7 versus R Determine the slope of the straight line that best fits the data To what does the value of the slope correspond Replace R with R 10 kQ and repeat Procedures 3 and 4 with C C 0 05 uF and C C 02 uF On a Cartesian graph plot the experimental 7 versus C You should have three data points for 7 with Rj 10 Why Determine the slope of the straight line that best fits the data To what does the value of the slope correspond Compute the time constants for each of the RC combi nations using the known R and C values and compare with the experimentally determined values by finding the percent errors Optional Use your knowledge gained in this experi ment to determine experimentally the value of the un known resistor Remove the masking tape after doing so and compute the percent error www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date ETX PIETRI Lab Partner s f T1 MENT The RC Time Constant Electronic Timing RWV Laboratory Report RV DATA TABLE 1 Purpose To determine the effect of R on the time constant Divisions for 0 6
152. E zr E Percent difference X 100 1 3 E E 2 Dividing by the average or mean value of the experi mental values is logical because there is no way of decid ing which of the two results is better Example 1 5 What is the percent difference between two measured values of 4 6 cm and 5 0 cm Solution With E 4 6 cm and E 5 0 cm m E E Percent difference X 100 E E 2 Although percent error is generally defined using the absolute difference IE Al some instructors prefer to use E A which results in positive or negative percent errors for example 0 6 in Example 1 4 In the case of a series of measurements and computed percent errors this gives an indication of systematic error Percent diff 5 0 4 6 x 100 ercen IHlIerence 5 0 4 6 2 04 s 1009 8 48 a As in the case of percent error when the percent difference is large it is advisable to check the experiment for errors and possibly make more measurements In many instances there will be more than two mea surement values When there are three or more measurements the percent difference is found by dividing the absolute value of the difference of the extreme values that is the values with greatest difference by the average or mean value of all the measurements AVERAGE MEAN VALUE Most experimental measurements are repeated se
153. E INITIALLY AT REST 21 Switch the cars on the track so that their magnetic ends are facing away from each other The easiest way to do this without altering the strings is to unscrew the cart string brackets from the carts but not from the strings The cars can then be switched under the brackets and the brackets reinstalled 22 Place a small piece of clay on the colliding end of both cars Note Velcro strips and sticky masking tape also work well for this Some PASCO carts already come with Velcro strips attached 23 Set Car 2 somewhere on the middle of the track at rest 24 Set Car 1 all the way to the end of the track 25 Press the START button and then give Car 1 a good push toward Car 2 26 Press the STOP button after the collision before the cars reach the end of the track and bounce The cars must stick together after the collision Several practice runs and the help of a partner may be needed to get the hang of it 27 Repeat steps 10 to 20 for this set of data but enter the results in CI Data Table 2 Some PASCO carts have magnets on both ends These won t work A new set of carts with no magnets plunger carts will be needed which means new masses must be measured and entered in the calculator if this is the case www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s C I E XPERIMENT 7 Conservation of Linear Momentum amp
154. E of the pendulum at any time f with matching time axes 19 It is not necessary to be able to see both graph windows at the same time but they can be moved around the screen so that both are visible Their sizes may also be adjusted so that when they are active they occupy the full screen individually It is easy to change from view ing one to viewing the other by clicking on the particular graph to bring it to the front CI Fig 14 6 shows what the screen will look like after all the setup is finished a EXPERIMENTAL PROCEDURE 1 Put the rotary motion sensor on a support rod Install the mass on the light rod and then install the pendulum on the front screw of the rotary motion sensor A diagram of the equipment setup is shown in e CI Fig 14 7 m laix gr Sumenary Seip gt Sta 00 00 0 gg Colzviste IA Graph 1 d vods ation C TET eg El amp al waa Fa z wl Al jd Zi amp Data gt x i J wi Angular Velocity Ch 122 rad s KEz05 M v2 B v2 L7 smscth 5 w B PE M 7981 L L cos smo Angular Positice d lt 0 0920 iB Graph 2 0 2022 x BS s aj ia i 7 Fo wl AL EL o oe 7 x ic A Histogram Meter o Scope SX Seund Ar alyzer Q Seund Crestor Table E Workbook Anguiss Positio CI Figure 14 6 Data Studio setup Graph displays are generated for angular position kinetic energy and potential energy The individual graph windows can be viewed together
155. EAR SAFETY RULES Radioactive sources will be used in the next few experi ments Some sources are solids and are encapsulated to prevent contact However liquid sources may also be used and transferred during an experiment Some general safety precautions for the use of radioactive materials follow 1 Radioactive materials should be used only by or under the supervision of a person properly informed about the nature of the material 2 Care should be taken to avoid unnecessary handling or contact with the skin 3 Mouth pipetting is strictly prohibited 4 Eating drinking and smoking should not be permitted in any area where radioactive materials are being used 5 6 Protective gloves or forceps should be used when the material is handled or transferred All persons working with radioactive material should thoroughly wash their hands immediately afterward When not in use radioactive materials should be stored in an appropriately labeled container and in a place of limited access Should an accident occur particularly if it involves radioactive materials it should be reported immedi ately to the laboratory instructor If you are pregnant make your instructor aware of this and do not go to the laboratory 482 www A TIBOOK ir EX PE Rl MENT 3 3 Detection of Nuclear Radiation The Geiger Counter INTRODUCTION AND OBJECTIVES Nuclear radiations alpha beta and gamma rays or par
156. Experiment A See your textbook for modern theories of friction between two surfaces 173 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s FA EX PERIMENT 1 1 Work and Energy 2 Wa mig F w F f GL Figure 11 1 Going up Work and energy considerations for Experimental Planning faj Experimental Planning Work and energy are intimately related like heat and temperature By doing work on an object it can gain energy Conversely when energy is expended work may be done This experiment demonstrates the work energy relationship in the context of work done by friction The work W done by a constant force F acting on an object and moving it through a parallel displacement d is given by the product of their magnitudes W Fd a scalar quantity Work then involves a force acting on an object and moving it through a distance However the constant force may not be acting parallel to the displacement In this case the magnitude of the component of the force parallel to the displacement is F cos0 where 6 is the angle between the force and displacement vectors So in general W F cos0 d which is commonly written W Fd cos0 GL 11 1 In the case of friction W f d where fis the force of friction assumed to be constant Explain why there is a sign in this equation Consider the value of the angle 0 continued 1
157. F Zero senno tomsiz on start rd T Reverse tori of a songes CI Figure 6 1 The Experiment Setup window The seven available channels are numbered through 4 and A B or C The Smart Pulley is connected to Channel 1 of the Science Workshop Interface Reprinted courtesy of PASCO Scientific LH Display an Digits A FFT j Histogram Meter Scope m Tabie E Workbook Velocity Ch 1 No Date CI Figure 6 2 Data Studio setup A graph of velocity versus time was created by dragging the Velocity icon from the data list and dropping it on the Graph icon in the displays list below In this picture the graph window has been resized to occupy most of the screen Reprinted courtesy of PASCO Scientific a EXPERIMENTAL PROCEDURE A Varying the Total Mass Unbalanced Force Constant 1 Set up the Atwood machine using the Photogate Pulley System Smart Pulley instead of a conven tional pulley The ascending mass should begin close to but not touching the floor The descending mass will start at the top CI Fig 6 3 shows the experi mental setup Make the string long enough and install the pulley high enough so that the masses can move at least half a meter If using the PASCO ME 8967 mass and hanger set be gin by placing 50 g on each hanger This added weight will prevent the system from moving too fast and data collection will be easier If you are using a conventional
158. Geomet ric analysis give equations for the positions of single slit dark fringes and double slit bright fringes The CI portion of this experiment investigates these fringe relationships After performing this experiment and analyzing the data you should be able to 1 Verify that the positions of the minima in a diffraction pattern match the positions predicted by theory 2 Use a diffraction and interference pattern to determine the wavelength of light 3 Compare the patterns formed by single slits to those formed by double slits 4 Investigate the effects of changing slit width and slit separation 461 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir T J EX PER M ENT 3 2 The Transmission Diffraction Grating Measuring the Wavelengths of Light RV EQUIPMENT NEEDED Spectrometer Diffraction grating and holder Mercury discharge tube Power supply for discharge tube ncandescent light source Instructor s note If a spectrometer is not available an alternative inexpensive method is described in the Instructor s Manual RV THEORY A diffraction grating consists of a piece of metal or glass with a very large number of evenly spaced parallel lines or grooves This gives two types of gratings reflection gratings and transmission gratings Reflection gratings are ruled on polished metal sur faces light is reflected from the unruled areas which act as
159. Hence the blue sky light we see is partially polar ized even though we can t visually detect it without a little help E Optical Activity Certain substances have the property of being able to rotate the plane of polarization of a beam of polarized light This rotation called optical activity is exhibited by crystalline mica quartz some sugars and many long chain molecu lar polymers The principle is illustrated for an optically active crystal in e TI Fig 29 6 Notice that the crystal essentially changes the direc tion of one of the vector components of the polarized light along one of its optical axes The vector resultant is then rotated 90 to the polarization plane of the incoming light and transmitted through the crossed analyzer which would not be the case without rotation After Lord Rayleigh 1842 1919 the British physicist who described the effect Incident unpolarized Polarizer light Incoming polarization direction In traveling through the crystal the components travel at different speeds Suppose the thickness of the crystal is such that the vertical component gains or falls behind by one half wavelength compared with the horizontal component The effect is a reversed vertical component and a 90 rota tion of the plane of polarization as shown in the figure Only for this particular wavelength of light and this particular crystal thickness or an appropriate multiple thereof will a 9
160. Hint See resistivity in your textbook 5 Do heating appliances such as hair dryers and toasters have high resistance or low resistance elements Explain 366 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 5 The RC Time Constant Manual Timing RW Advance Study Assignment Read the experiment and answer the following questions 1 What is an RC time constant 2 What must the unit s of an RC time constant be Show this explicitly Hint Q CV and V IR 3 When an RC series circuit is connected to a dc source what is the voltage on a capacitor after one time constant when a charging from zero voltage and b discharging from a fully charged condition 4 If the resistance in a capacitor circuit is increased does the charging time of the capacitor increase or decrease Explain 367 continued www ATIBOOK ir EXPERIMENT 25 Advance Study Assignment 5 Can the voltage across a capacitor be measured with a common voltmeter Explain 368 www A TIBOOK ir EX P E Rl ENT 2 5 The RC Time Constant Manual Timing INTRODUCTION AND OBJECTIVES When a capacitor is connected to a dc power supply or battery charge builds up on the capacitor plates and the potential difference or voltage across the plates increases until it equals the voltage of the source At any time the charge Q of the capacitor is related to the voltage across the capacitor plates by Q CV w
161. I Fig 23 3 To find the equivalent resistance of this series parallel circuit one first collapses the parallel branch into a single equiva lent resistance which is given by TI Eq 23 7 This equiva lent resistance is in series with R and the total equivalent resistance R of the circuit is R R Rp AY EXPERIMENTAL PROCEDURE 1 Examine the resistors The colored bands conform to a color code that gives the value of a resistor Look up the color code in Appendix A Table A5 read the value of each resistor and record in the laboratory report Designate the smallest resistance as R and consecutively larger values as R5 R3 and R4 2 In the following procedures you will be asked to com pute theoretically various quantities for a given circuit arrangement The quantities are then determined by actual circuit measurements and the calculated and experimental results are compared Before initially activating each circuit arrangement have the circuit checked by the instructor unless otherwise instructed A Resistors in Series 3 Set up a series circuit with R Ry and R3 as in TI Fig 23 1a with a switch and ammeter in the circuit next to the voltage source A convenient way to check a circuit to see whether it is properly connected is to trace the path of the current with your finger through the circuit Do this making sure that the current goes EXPERIMENT 23 Resistances in Series and Parallel 341 through eac
162. If the horizontal distance from the starting point to the point where the trace reaches 63 of the maximum voltage V as shown in TI Fig 26 1 is 6 5 divisions 1 division 1 cm the time for 6 5 horizontal divisions is equal to one time con stant 7 With the SWEEP TIME DIV set at 5 ms div the value of the RC time constant would be 6 5 div x 5 ms div 32 5 ms RV EXPERIMENTAL PROCEDURE 1 Turn on the oscilloscope and function generator Set the function generator frequency to 100 Hz and the wave amplitude near maximum Connect the square wave output of the function generator directly to the vertical input terminals of the oscilloscope Set the oscilloscope as follows Note Different oscilloscopes differ somewhat in the names and loca tions of controls Vertical CH A DC VOLTS DIV 0 5 MODE CH A POSITION Center Trace CH B GND Horizontal TIME DIV 2 mSEC POSITION Center the trace Triggering LEVEL 12 00 position COU PLING SYNC AC SLOW SOURCE INT SLOPE The Vertical VOLTS DIV and Horizontal TIME DIV will be used here Check that the small red knobs in the center of the VOLTS DIV and TIME DIV controls are in the cali brated position Adjust the FOCUS and INTENSITY controls for a sharp clear trace Caution Intensity should be kept low to protect the phosphor on the screen If time permits experiment with the controls to see how they affect the display Obtain a stationary trace of one or two cycles of the squ
163. K ir EXPERIMEN TF 2 1 Advance Study Assignment B Wheatstone Bridge Method 4 Why is the Wheatstone bridge called a null instrument 5 When the galvanometer in a Wheatstone bridge circuit shows no deflection why are the voltages across opposite branches on each side of the galvanometer necessarily equal 6 For a slide wire Wheatstone bridge why should the sliding key not be moved with the key depressed 310 www A TIBOOK ir EX PE RI M ENT 2 1 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method INTRODUCTION AND OBJECTIVES The magnitude of a resistance can be measured by several methods One common method is to measure the voltage drop V across a resistance in a circuit with a voltmeter and the current through the resistance with an ammeter By Ohm s law then R V I However the ratio of the mea sured voltage and current does not give an exact value of the resistance because of the resistances of the meters This problem is eliminated when one measures a re sistance or more properly compares a resistance with a standard resistance in a Wheatstone bridge circuit named after the British physicist Sir Charles Wheatstone 1802 1875 In this experiment the ammeter voltmeter and the Wheatstone bridge methods of measuring resistances will be investigated EQUIPMENT NEEDED A AMMETER VOLTMETER METHODS Ammeter 0 A to 0 5 A Voltmeter 0 V to 3 V Rhe
164. L PROCEDURE 1 Setup a simple pendulum arrangement If a pendulum clamp is not available the string may be tied around something such as a lab stand arm Make sure that the string is secure and does not slip on the arm 2 Experimentally investigate the small angle approxi mation Eq 3 2 and the theoretical prediction Eq 3 1 that the period increases with larger angles Do this by determining the pendulum period for the several angles listed in Data Table 1 keeping the length and mass of the pendulum constant Measure the angles with a protractor Note 0 is the initial angular distance of the bob before release Rather than timing only one oscillation time several four or five and determine the average period Timing is generally more accurate if you start the pendulum oscillating before the timing begins Also it is usually best to take the timing reference point as the lowest point of the swing Measure and record the pendulum length The length should be measured to the center of the pendu Ium bob Why Compute the percent error of the period for each angle 0 using Eq 3 2 to calculate the theoretical value In this case do not use the absolute difference so that each percent error will have a sign or Further analysis will be done in the Questions section Proceed to the next step 3 Experimentally investigate whether the period is independent of the mass of the pendulum bob Using the three masses
165. Laboratory Report f Compute the percent error of the experimental value of g determined from the graph in part e Accepted value g 9 8 m s Calculations show work Percent error g The relationship of the applied force F and the displacement x of a spring has the gen eral form F kx where the constant k is called the spring constant and is a measure of the stiffness of the spring Notice that this equation has the form of a straight line Find the value of the spring constant k of the spring used in determining the experi mental data plotted in the Fig 1 6B graph Note Because k F x the units of k in the graph are N m Calculations show work Value of spring constant of spring in Fig 1 6B graph units h The general relationship of the period of oscillation T of a mass m suspended on a spring is T 27r V m k where k is the spring constant Replot the data in Fig 1 7 so as to obtain a straight line graph and determine the value of the spring constant used in the experiment Hint Square both sides of the equation and plot in a manner similar to that used in part e Show the final form of the equation and calculations Calculations show work Value of spring constant of spring in Fig 1 7 units The data in sections g and h above were for the same spring Compute the percent difference for the values of the spring constants obtained in each section continued 19 www
166. Laboratory Report CASE 1 ELASTIC COLLISION BETWEEN Two CARS OF NEARLY EQUAL Mass WITH ONE INITIALLY AT REST Car 1 m Car 2 m Collision started at t Total collision time At f t Collision ended at t ED omame Purpose To analyze an elastic collision between two objects of nearly identical mass Just before the Just after the collision collision Changes Velocity of Car 1 m Ay Velocity of Car 2 V5 Av Total momentum Proa AP Total kinetic energy Kroui AK Don t forget units 123 continued www ATIBOOK ir EXPERIMENT 7 Conservation of Linear Momentum CASE 2 INELASTIC COLLISION BETWEEN Two CARS OF NEARLY EQUAL Mass WITH ONE INITIALLY AT REST Car 1 m Car 2 m Collision started at t Total collision time At f f Laboratory Report Collision ended at t ED orate Purpose To analyze an inelastic collision between two objects of nearly identical mass Just before the Just after the collision collision Changes Velocity of Car 1 Vi Ay Velocity of Car 2 V2 Av Total momentum Pu AP Total kinetic energy Koa AK 124 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 7 Conservation of Linear Momentum Laboratory Report ED auestions 1 How well do the results support the law of conservation of momentum considering th
167. Maximum intensity One half intensity Minimum intensity Calculation of angle for one half intensity 2 Three polarizers Explanation Sketch continued 429 www ATIBOOK ir EXPERIMENT 29 Polarized Light Laboratory Report B Polarization by Reflection and Refraction 3 Polarization angle calculation 4 a Observations on reflected light b Observations on transmitted refracted light C Polarization by Crystal Double Refraction Observations 430 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 29 Polarized Light Laboratory Report D Optical Activity Observations RV QUESTIONS 1 In the polarization of light by reflection with a transparent material would it be possible to have an optimum polarization angle 6 less than 45 Justify your answer Hint Consider the definition of the index of refraction 2 Ata sale of polarizing sunglasses there is a half price special on some glasses with lenses that have a horizontal polarization direction Would you buy them If not why not continued 431 www A TIBOOK ir EXPERIMENT 29 Polarized Light Laboratory Report 3 In the procedure using microscope slides why was the polarization of the transmitted light more observable with an increasing number of slides 4 The light coming from a liquid crystal display LCD as on a watch or calculator is polarized How could you conveniently show this to be the case
168. Optional Consider a long whip antenna of the type used on some automobiles for CB radios Show that the natural frequencies of oscillation for the antenna are f mv 4L where m 1 3 5 vis the wave speed and L is the length of the antenna Hint The boundary conditions are a node and an antinode 247 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 6 The Thermal Coefficient of Linear Expansion RV Advance Study Assignment Read the experiment and answer the following questions 1 What is the cause of thermal expansion on the molecular level 2 Distinguish between linear expansion and isotropic expansion 3 How is the thermal coefficient of linear expansion determined experimentally 4 What are the units of the thermal coefficient of linear expansion 249 continued www A TIBOOK ir EXPERIMEN TF 16 Advance Study Assignment 5 What is meant by the fractional change in length 250 www A TIBOOK ir EXPERI ENT 1 6 The Thermal Coefficient of Linear Expansion INTRODUCTION AND OBJECTIVES With few exceptions solids increase in size or dimensions as the temperature increases Although this effect is rela tively small it is very important in applications involving materials that undergo heating and cooling Unless these changes are taken into account material and structural damage can result for ex
169. Physics Laboratory Experiments Seventh Edition Jerry D Wilson Cecilia A Hernandez Hall Metric Prefixes Multiple Name Abbreviation 1 000 000 000 000 000 000 1038 exa E 1 000 000 000 000 000 1055 peta P 1 000 000 000 000 1022 tera T 1 000 000 000 10 giga G 1 000 000 106 mega M 103 kilo k 10 hecto h 10 deka da 107 deci d 102 centi c 103 milli m 0 000001 10 micro m 0 000000001 10 nano n 0 000000000001 10 2 pico p 0 000000000000001 1075 femto f 0 000000000000000001 10 18 atto a Physical Constants Acceleration due to gravity Universal gravitational constant Electron charge Speed of light Boltzmann s constant Planck s constant Electron rest mass Proton rest mass Neutron rest mass Coulomb s law constant Permittivity of free space Permeability of free space Astronomical and Earth data Radius of the Earth equatorial polar average Mass of the Earth the Moon the Sun Average distance of the Earth from the Sun Average distance of the Moon from the Earth Diameter of the Moon Diameter of the Sun 9 8 m s 980 cm s 32 2 ft s 2 667 x 19 1 NE kg 1 60 x 10 C 3 0 X 108 m s 3 0 X 10 cm s 1 86 X 10 mi s 1 38 x 1073 J K 6 63 X 1074 J s 4 14 X10 P eV s h 2n 1 05 X 104 J s 6 58 X 10 16 eV s 9 11 X 102 kg 5 49 x 1074 u amp 0 511 MeV 1 673 x 107 kg 1 0078 u lt 938 3 MeV 1 675 x 107 kg 1 00867 u lt gt 939 3 MeV l 4ne 9 0 x 10 N m C 8 85 X
170. Predicted Order of from from center Yn nA Percent or sing sind i minimum nton ton L d difference n i n 2 n 3 n 4 n 5 n 6 ED omame Purpose To determine the wavelength of light using a double slit interference pattern Calculated Order of Ym Calculated m sin minimum L n 1 n 2 n 3 n 4 Average Percent error Be sure to attach a copy of the graph to the report C Comparing Single Slit Pattern to Double Slit Pattern Attach the graphs to the report Don t forget to label them appropriately so that it is easy to distinguish between them 478 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 3 2 JSingle Slit and Double Slit Diffraction Laboratory Report Rd ouestons 1 Comparison between Graphs 1 and 2 a What parameters of the experiment were kept constant in producing Graphs 1 and 2 What parameters were changed b Compare the locations of the first minima of diffraction m 1 and m 1 on Graph 1 to the same positions along the x axis on Graph 2 Are the positions also minima in Graph 2 c In Graph 2 how many interference fringes bright are in between the locations of m and m 1 of the single slit pattern 2 Comparison between Graphs 2 and 3 a What parameters of the experiment were kept constant in producing Graphs 2 and 3 What parameters were changed b Desc
171. RC circuit A capacitor and a resistor are connected in series to a voltage source 387 The capacitor is fully charged when V V which theoret ically requires an infinite amount of time t In prac tice however it is said the capacitor is fully charged if we wait long enough But how long is long enough Let s say until the voltage across the capacitor is 99 996 of the voltage of the source The time it takes for this to happen can be calculated as follows V VW e 0 999 V V 1 e 0 999 1 e e 0 999 e 0 001 t n 0 001 T Thus the time needed is t r In 0 001 6 97 77 CI 26 4 For experimental purposes for a time of about seven time constants the capacitor is considered to be fully charged Another time that is of special interest is the time con stant itself Notice that at a time t 7 RC one time constant after starting the charging process the voltage across the capacitor has increased to 63 of the voltage of the source as shown here V WW et W e x quu CI 26 5 0 63V Notice that if you experimentally find at what time the voltage is 63 of the maximum you are finding the time constant of the circuit In this experiment the voltage source will be a sig nal generator that will produce a positive square wave www A TIBOOK ir 388 EXPERIMENT 26 The RC Time Constant Electronic Timing
172. T Conclusion error Experimental Theoretical Value of g from experimental data slope of graph units Percent error RV QUESTIONS 1 It was suggested that you measure the time for several periods and determine the average period rather than timing only one period a What are the advantages of this method b How and why would the result be affected if a very large number of periods were timed 44 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 3 The Scientific Method The Simple Pendulum Laboratory Report 2 In general the results of Procedure 2 may not have shown clear cut evidence that the period increases as dramatically with the angle as Eq 3 1 might suggest To understand why write Eq 3 1 as Te a8 9 4 0 T T 1 T sin sin 4 2 64 2 L and compute T in terms of T her T s for angles of 5 20 and 60 Comment on the theoretical predictions and experimental accuracy in relation to your results in Data Table 1 3 Is air resistance or friction a systematic or a random source of error Would it cause the period to be larger or smaller than the theoretical value Hint Consider what would happen if the air resistance were much greater for example as though the pendulum were swinging in a liquid 4 Thomas Jefferson once suggested that the period of a simple pendulum be used to define the standard unit of length W
173. TI 6 3 development SETTING UP DATA STUDIO 1 Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There are seven channels to choose from Digital channels 1 2 3 and 4 are the small buttons on the left analog channels A B and C are the larger buttons on the right as shown in CI Fig 6 1 3 Click on the Channel 1 button in the picture A win dow with a list of sensors will open 4 Choose the Smart Pulley from the list and press OK 97 5 Connect the sensor to the interface as shown on the computer screen 6 The Data list on the left of the screen should now have one icon for velocity 7 Create a graph by dragging the velocity data icon from the data list and dropping it on top of the graph icon of the displays list A graph of velocity versus time will open The window will be called Graph 1 8 e CI Fig 6 2 shows what the screen should look like once the setup is complete www A TIBOOK ir 98 EXPERIMENT 6 Newton s Second Law The Atwood Machine Measuemerts Measremeris Constants Visibility Name Unit of Measure T State Chi Vaan v T Spoke Timer Ch 1 ko oJ T Postion Ch 1 b fV Velochy Ch 1 be T Acceleration Ch 1 FOE T Angus Postion Ch 1 5 x r Sample Rate is ite r Sensor Samping Options T Reduce suole rote ty aveaagra pope EXective SerpleRete Hr
174. TIBOOK ir This page intentionally left blank www A TIBOOK ir C I ESXUPAE R M ENT 2 6 The RC Time Constant Electronic Timing S courment neevep This activity is designed for the Science Workshop 750 Interface which has a built in function generator 1000 0 resistor e 330 uF capacitor e Voltage sensor PASCO CI 6503 e Cables and alligator clips e Multimeter that can measure resistance and capacitance Second resistor of different value ED teory A Charging a Capacitor e CI Fig 26 1 shows a series RC circuit a resistor connected in series with a capacitor and a power source of voltage V As soon as the voltage source is turned on the capaci tor starts charging As the charge in the capacitor increases exponentially with time so does the voltage across its plates The voltage across the capacitor at any time f is given by V V eo CI 26 1 The quantity RC is called the time constant 7 of the circuit that is T RC CI 26 2 With the resistance measured in ohms and the capaci tance in farads it is easy to show that the time constant has units of seconds See Question 1 In terms of the time constant CI Eq 26 1 can be written as V WW e CI 26 3 The voltage across the capacitor will increase exponen tially with time until it matches the voltage of the source Resistor Voltage Source Capacitor CI Figure 26 1 A series
175. To analyze m m case with v 0 Trial Before collision After collision My P Percent 7J diff Don t forget units 111 continued www ATIBOOK ir EXPERIMEN Y 7 RV DATA TABLE 2 Purpose To analyze m gt m case with v 0 Conservation of Linear Momentum Laboratory Report Before collision After collision m n n4 Trial Total Total Percent At Vi momentum At Vi Pi At V3 P3 momentum diff 6 6 lt SEIEN 2 1 2 3 AY DATA TABLE 3 Purpose To analyze the m m case initial motions in opposite directions Before collision m m Total Trial At Vi Di At Vo P momentum L C 1 2 3 After collision m m Total Percent Trial At vi Pi Ab v Pa momentum diff C 2 C 6 C 1 2 3 112 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 7 Conservation of Linear Momentum Laboratory Report RV QUESTIONS 1 Do the results of the experiment support the conservation of linear momentum Consider possible sources of error 2 Was it necessary to have equal length intervals in the experiment to investigate properly the conservation of momentum Explain 3 In Cases 1 and 2 one of the cars was initially at rest so it must have r
176. URE A Metal Conductor s 1 Set up the circuit as in Fig 22 1 with the copper coil in the container of water near room temperature and the heating arrangement for the water immersion heater or other heat source Place the thermometer in the water Have the instructor check your setup Standard resistor Material specimen Figure 22 1 Temperature dependence of resistance The circuit diagram for the experimental procedure to mea sure the temperature dependence of resistance See text for description 2 After your setup has been checked close the switch and balance the bridge circuit to measure the re sistance R of the coil at the initial water tempera ture The value of the standard resistance R should be selected so that the bridge is balanced with the contact key C as near the center of the slide wire as possible Then with L Ly it follows that R R Eq 22 5 Record in Data Table 1 the initial temperature of the water the magnitude of R and the lengths of the wire segments of the bridge 3 Slowly raise the temperature of the water by about 10 C Stir the water while heating and discontinue heating when the temperature is about 2 C below the de sired temperature Continue stirring until a maximum steady temperature is reached Balance the bridge and record the measurements Adjust R if necessary Record the measurements of temperature and bridge length in the data table 4 Repeat Procedure
177. Waves in a String Laboratory Report Calculations show work fr questions 1 The length L is not the wavelength of the fundamental frequency of the string a With the tension equal to F to which natural frequency does the wavelength equal to L correspond b What tension in the string would be required to produce a standing wave with a wavelength equal to L Hint Use Eq 15 7 2 Theoretically the vibrator frequency is 120 Hz However sometimes the vibrator resonates with the string at a subharmonic of 60 Hz a If this were the case in all instances how would it affect the slope of the graph 246 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 15 Standing Waves in a String Laboratory Report b If you have some scattered data points far from the straight line on your graph analyze the data for these points using Eq 15 7 to determine the frequency 3 How many normal modes of oscillation or natural frequencies does each of the following have a a simple pendulum b a clothes line and c a mass oscillating on a spring 4 Stringed musical instruments such as violins and guitars use stretched strings Explain a how tightening and loosening the strings tunes them to their designated tone pitch or frequency b why the strings of lower tones are thicker or heavier c why notes of higher pitch or frequency are produced when the fingers are placed on the strings 5
178. XPERIMENT 4 Uniformly Accelerated Motion 61 10 velocities in CI Data Table 2 and calculate by how much the velocity increases as the times double triple etc Use the Fit Tool to determine the slope of the veloc ity graph The fit tool is on the graph toolbar it is a drop menu called Fit Choose a Linear Fit for your graph Report the slope in CI Data Table 2 What is the slope of a velocity versus time plot measuring Hint Think of the units www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s C 1 EXPERIMENT 4 Uniformly Accelerated Motion amp Laboratory Report ED ona Purpose To investigate a position function that is proportional to the square of the time How many times larger is x than x4 Time Position x X fi X h X2 tz X3 t4 X4 ED orate Purpose To investigate a velocity function that is proportional to the time How many times larger is v than v Time Velocity v Vy f v bh Vo ty V3 ts V4 Slope of the graph Don t forget units 63 units continued www A TIBOOK ir EXPERIMENT 4 Uniformly Accelerated Motion Laboratory Report SJ questions 1 In CI Data Table 1 you measured the position of the car at different times When the time doubled did the distance from the origin double also When the time tripled did the di
179. a ball on a rope around one s head the centripetal force F ma is supplied by the person and transmitted through the rope Tony Freeman PhotoEdit where m is the mass of the object In terms of distance and time the orbital speed v is given by v 2ar T where 27r is the circumference of the circular orbit of radius r and T is the period Notice that Eq 9 2 describes the centripetal force act ing on an object in uniform circular motion in terms of the properties of the motion and orbit It is equal to the ex pression of a physical force that actually supplies the cen tripetal action For example in the case of a satellite in uniform circular motion around the Earth the centripetal force is supplied by gravity which is generally expressed F Gmym r and F F Similarly for an object be ing held in uniform circular motion by the tension force of a string the tension force F is equal to Eq 9 2 that is F mv r The centripetal force given by Eq 9 2 can also be ex pressed in terms of the angular speed w or frequency f of rotation using the expressions v rw and w 2f F ii mer mro r r and F mr 2af 4v mrf 9 3 Technically it is the component of F directed toward the center of the circular orbit The rope cannot be exactly horizontal See Question 4 at the end of the experiment where w is in radians per second and f is in hertz Hz 1 s or cycles per second
180. a of contact the more friction This would seem to contradict rule 1 2 However the actual contact area of the surfaces should depend on the force that presses the surfaces together or the load Increasing this force should increase the amount of contact of the irregularities between the surfaces and hence the friction Rule 2 then seems logical 3 Is it consistent that the friction between a sliding object and a surface be independent of the slid ing speed It would seem that the rate at which the 157 surface irregularities meet which is dependent on the sliding speed should have some effect With such thoughts in mind in this experiment the validity of the foregoing empirical rules will be investi gated Experimentally you might find that they are very general and at best approximations when applied to dif ferent materials and different situations RV OBJECTIVES After performing the experiment and analyzing the data you should be able to do the following 1 Comment on the validity of the empirical rules of friction 2 Describe how coefficients of friction are determined experimentally 3 Tell why the normal reaction force of a surface on an object is used to determine the frictional force rather than the weight of the object ED osusectives 1 Verify that friction is proportional to the normal force 2 Indicate whether or not friction is independent of slid ing speed www A TIBOOK ir This pa
181. al results in determining the percent error Attach these results to the laboratory report www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 4 Joule Heat RW Laboratory Report Mass Material Specific heat Calorimeter cup Immersion coil Calorimeter cup and water Water DATA TABLE Purpose To determine the mechanical equivalent of heat Time Voltage V Current Temperature C C 2 C C 0 Ti T Calculations Average voltage show work Average current Electrical energy expended Heat energy gained Ratio of results Percent error Don t forget units continued 365 www ATIBOOK ir EXPERIMENT 24 _ Joule Heat Laboratory Report RV QUESTIONS 1 What are the major sources of error in the experiment Why should the initial temperature of the water be several degrees below room temperature 2 Why was it necessary to make adjustments to maintain a constant current in the circuit 3 If the cost of electricity is 12 cents per kWh what was the cost of the electricity used in performing the experiment 4 a Circular metal wires in electrical circuits may have different cross sectional areas different diameters and different lengths For a given applied voltage how would the joule heat vary with these parameters b Would the wire material make a difference
182. al applications Fig 13 4b F Wp mg F m Mg a b Figure 13 4 Pulley arrangement with double movable pulleys a The pulleys may be arranged in tandem or b have a common axis for compactness www A TIBOOK ir 212 EXPERIMENT 13 Simple Machines Mechanical Advantage D Wheel and Axle The combination of a wheel and axle has many practi cal applications For example when you open a door by turning a doorknob you are using a wheel and axle This simple machine consists of a wheel fixed to a shaft or axle with the same axis of rotation 6 Fig 13 5a Essentially it is equivalent to a lever with unequal lever arms A force F applied tangentially to the wheel with a radius R can lift a load w F by means of a string or rope wrapped around the axle radius r The AMA of the wheel and axle is F w AMA 13 10 F F wheel and axle In one revolution the input force acts through a distance 27R and the output force through a distance of 2zr For the ideal nonfictional case Fid F 27R Fd w 2arr and the TMA is d R TMA 13 11 d r o wheel and axle A practical application of a wheel and axle is shown in Fig 13 5b along with an experimental setup In measuring the force to determine the AMA of a wheel and axle it is convenient to use the static equi librium case as for the pulley system in Section C of the experimental procedures EXPERIMENTAL PROCEDURE A
183. al force be experimentally determined and how is it used in the calculations 5 What is measured in the experiment and how is this used to compute the acceleration of the system Advance Study Assignment Read the experiment and answer the following questions 1 When the Atwood machine is moving what is the shape of a velocity versus time plot for the motion Why 2 The photogate will measure the tangential speed of the pulley Why is this speed the same as the speed of the ascending and descending masses 86 www ATIBOOK ir EX PER J MENT 6 Newton s Second Law The Atwood Machine OVERVIEW Experiment 6 examines Newton s second law using the Atwood machine by TI procedures and or CI procedures Both procedures apply the second law by 1 varying the total mass while keeping the unbalanced force constant and 2 varying the unbalanced force while keeping the total mass constant The TI procedure determines the accelerations of the system using distance time measurements In the CI pro cedure speed time measurements are used by electroni cally observing the motion of the pulley INTRODUCTION AND OBJECTIVES Newton s second law of motion states that the accelera tion a of an object or system is directly proportional to the vector sum of the forces acting on the object the unbal anced or net force F e XF and inversely proportional to the total mass m of the system a F e m In equation fo
184. alance determine the mass of the car m and record it in the laboratory report 2 Arrange the inclined plane and the car as shown in Fig 11 3 with an angle of incline of 0 30 Make certain that the pulley is adjusted so that the string at tached to the car is parallel to the plane Should the car accelerate up the plane by the weight of the weight hanger alone place some weights in the car so that the car is initially stationary Then add the additional mass to that of the car in Data Table 1 3 Add enough weights to the weight hanger so that the car moves up the incline with a slow uniform speed when the car is given a slight tap Record the total sus pended mass in Data Table 1 4 With the car positioned near the bottom of the incline mark the position of the car s front wheels and give the car a slight tap to set it into motion Stop the car near the top of the plane after it moves up the plane with a constant speed and measure the distance d it moved up the plane as determined by the stopped posi tion of the car s front wheels Or measure the height h www ATIBOOK ir a Figure 11 3 Types of inclined planes Sargent Welch the weight hanger descends This corresponds to the situation in Fig 11 1 The lengths d and A are the same Record this length in Data Table 1 as d With the car near the top of the plane remove enough weights from the weight hanger so that the car rolls down the inclined plane w
185. allel ray and is not needed to locate the tip of the image The focal ray is often omitted as the chief and parallel rays locate To help remember the difference note that a concave mirror is recessed as though one were looking into a cave www ATIBOOK ir 406 EXPERIMENT 28 Spherical Mirrors and Lenses a4 a Concave mirror Mirror surface b Convex mirror Figure 28 2 Mirror ray diagrams Examples of the ray diagram method for determining the image characteristics for a a concave or converging spherical mirror and b a convex or diverging spherical mirror the image However the focal ray can be helpful when the object is inside the center of curvature For a convex mirror the chief and parallel rays appear to go through C and F as illustrated in Fig 28 2b A concave mirror is called a converging mirror be cause rays parallel to the optic axis converge at the focal point Similarly a convex mirror is called a diverging mirror because the rays parallel to the optic axis appear to diverge from the focal point If the image is formed on the same side of the mirror as the object the image is said to be a real image In this case the light rays converge and are concentrated and an image can be observed on a screen placed at the image distance An image that is formed behind or inside the mirror is called a virtual image Here the rays appear to diverge from the image and no i
186. ally measured values to accepted theoretical or measured values Even so you will experience the excitement of the scientific method Imagine that you are the first person to perform an experiment to test a scientific theory GENERAL LABORATORY PROCEDURES Safety The most important thing in the laboratory is your safety and that of others Experiments are designed to be done safely but proper caution should always be exercised A potential danger comes from a lack of knowledge of the equipment and procedures Upon entering the physics lab at the beginning of the lab period you will probably find the equipment for an experiment on the laboratory table Restrain your curiosity and do not play with the equipment You may hurt yourself and or the equipment A good general rule is ix Do not touch or turn on laboratory equipment until it has been explained and permission has been given by the instructor Also certain items used in various experiments can be particularly dangerous for example hot objects electricity mercury lamps and radioactive sources In some instances such as with hot objects and electricity basic common sense and knowledge are required However in other instances such as with mercury lamps and radioactive sources you may not be aware of the possible dangers Mercury lamps may emit ultraviolet radiation that can be harmful to your eyes Consequently some sources need to be properly shielded Some radio ac
187. ample a piston may become too tight in its cylinder a rivet could loosen or a bridge girder could produce damaging stress The expansion properties of a material depend on its internal makeup and structure Macroscopically the ther mal expansion is expressed in terms of temperature coef ficients of expansion which are experimental quantities that represent the change in the dimensions of a material per degree of temperature change In this experiment the thermal expansion of some metals will be investigated and their temperature coefficients of linear expansion determined After performing this experiment and analyzing the data you should be able to 1 Tell how the thermal coefficient of linear expansion describes such expansion 2 Explain how the thermal coefficient of linear expan sion is measured and give an order of magnitude of its values for metals 3 Describe and give examples of how thermal expan sion considerations are important in applications of materials EQUIPMENT NEEDED Linear expansion apparatus and accessories Steam generator and stand Bunsen burner and striker or electric hot plate Rubber tubing Beaker Meter stick Thermometer 0 C to 110 C Two or three kinds of metal rods for example iron and aluminum THEORY Changes in the dimensions and volumes of materials are common effects The thermal expansion of gases is very obvious and is generally described by gas
188. anced 6 In using the equations to determine the temperature dependence of resistance what temperature scale is used 324 www A TIBOOK ir EX PE RI ENT 2 2 The Temperature Dependence of Resistance INTRODUCTION AND OBJECTIVES The electrical resistance of all substances varies somewhat with temperature For pure metals and most alloys the re sistance increases with increasing temperature However for some substances such as carbon and many electrolytes conducting solutions the resistance decreases with in creasing temperature Then too for some special alloys for example constantan 55 Cu 4596 Ni the resistance is virtually independent of temperature over a limited range The temperature dependence of resistance for a sub stance is commonly expressed in terms of its temperature coefficient of resistance which is the fractional change in the resistance per degree change in temperature For many electrical applications it is important to know tempera ture coefficients and to take into account the temperature dependence of resistances In this experiment this temper ature dependence will be investigated and the temperature coefficients of some materials determined After performing this experiment and analyzing the data you should be able to 1 Explain how the resistances of common metallic con ductors vary with temperature 2 Discuss the temperature coefficient of resistance for various materials
189. and hence the TMA The efficiency 2 of a machine is defined as the ratio of its work output and its work input and work output W Fd F F AMA 134 WERE Fa 4A IMA S The efficiency is often expressed as a percentage Because of friction AMA lt TMA and the efficiency is always less than 1 or 100 The efficiency tells what part of the work input goes into useful work output Useful work output W e work input W for example if e 0 7 or 70 then 70 of the work in put is used by the machine to do useful work The rest of the work input 0 3 or 30 is lost to friction A Inclined Plane The theory of the inclined plane 6 GL Fig 13 1 was pre sented in the TI Experimental Planning with the result iN OR NN 13 5 F d sin 7 inclined plane B Lever The Zever is a very efficient simple machine It consists of a rigid bar that is pivoted to rotate about a point or line called the fulcrum Fig 13 2 The input force F com monly called the effort is applied to the end of the lever to maintain or lift a load w The input force F must be equal to static case Fig 13 2a or greater than the weight of the load when lifted Fig 13 2b The input and output lever arms L and L are the distances from the fulcrum to the effort F and from the fulcrum to the load F respectively The theoretical mechanical advantage TMA of a lever can be calculated from work considerations
190. and can be read ily measured However the magnitude of the centripetal force IM ENT 9 can also be determined from other experimental parameters for example the frequency of rotation of the object mass and radius of orbit Centripetal force will be experimentally investigated by measuring these parameters and comparing the calculated results with the direct measurement of the spring force which mechanically supplies the center seeking centripetal force After performing the experiment and analyzing the data you should be able to do the following 1 Explain why a centripetal force is necessary for circu lar motion 2 Describe how the magnitude of the centripetal force for uniform circular motion may be determined from motional parameters 3 Summarize what determines the magnitude of the cen tripetal force necessary to keep an object in uniform circular motion EQUIPMENT NEEDED A Manual Centripetal Force Apparatus Laboratory timer or stopwatch Meter stick Weight hanger and slotted weights String Laboratory balance Safety glasses B Centripetal Force Apparatus with Variable Speed Rotor and Counter Laboratory timer or stopwatch Weight hanger and slotted weights Vernier caliper Support rod and clamp String Safety glasses THEORY An object in uniform circular motion requires a centrip etal or center seeking force to hold it in orbit For ex ample when one swings a ball on a rope
191. and suspend a weight hanger from the rubber band Add an appropriate weight to the weight hanger for example 100 300 g and record the total suspended weight mg in TI Data Table 1 Fix a meter stick vertically alongside the weight hanger and note the position of the bottom of the weight hanger on the meter stick Record this as y in the data table www ATIBOOK ir EXPERIMENT 14 Simple Harmonic Motion 225 2 Add appropriate weights for example 100 g to the weight hanger one at a time and record the total sus pended weight and the position of the bottom of the weight hanger on the meter stick after each elongation yo y3 etc The weights should be small enough so that seven or eight weights can be added without over stretching the rubber band 3 Plot the total suspended weight force versus elonga tion position mg versus y and draw a smooth curve that best fits the data points B Spring Elongation 4 Repeat Procedures 1 and 2 for a coil spring and record the results in TI Data Table 2 Choose appropriate mass increments for the spring stiffness A commer cially available Hooke s law apparatus is shown in e TI Fig 14 3 5 Plot mg versus y on the same sheet of graph paper used in Procedure 3 double label axes if necessary and draw a straight line that best fits the data Determine the slope of the line the spring constant k and record it in the data table Answer TI Questions 1 through 3 following
192. aphic electronic or mechanical including but not limited to photocopying recording scanning digitizing taping Web distribution information networks or information storage and retrieval systems except as permitted under Section 107 or 108 of the 1976 United States Copyright Act without the prior written permission of the publisher For product information and technology assistance contact us at Cengage Learning Customer amp Sales Support 1 800 354 9706 For permission to use material from this text or product submit all requests online at www cengage com permissions Further permissions questions can be emailed to permissionrequest cengage com Library of Congress Control Number 2009927944 ISBN 13 978 0 547 22748 1 ISBN 10 0 547 22748 5 Brooks Cole 20 Channel Center Street Boston MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe including Singapore the United Kingdom Australia Mexico Brazil and Japan Locate your local office at international cengage com region Cengage Learning products are represented in Canada by Nelson Education Ltd For your course and learning solutions visit www cengage com Purchase any of our products at your local college store or at our preferred online store www ichapters com Printed in the United States of America 1234567 1312111009 www A TIBOOK ir What is the meaning of it all Mr Holmes A
193. arallel circuit 358 www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 4 Joule Heat Ay Advance Study Assignment Read the experiment and answer the following questions 1 Explain a joule heat and b 7 R losses 2 What is the difference between joule heat and power 3 Given two different resistances how does the total joule heat vary if they are connected to a battery of fixed voltage V a in series and b in parallel 359 continued www A TIBOOK ir EXPERIMENT 24 Advance Study Assignment 4 In the experiment why isn t the final temperature of the system read at the same time that the power supply is unplugged and the timer stopped 5 Suppose that oil were used in the experiment instead of water Would a the joule heat and b the temperature rise be the same Explain 360 www A TIBOOK ir EX Pek Joule Heat INTRODUCTION AND OBJECTIVES Whenever there is an electrical current in a conductor some electrical energy is converted into heat energy For a given current J the energy conversion is greater in a conductor of greater resistance This is analogous to the conversion of mechanical energy into heat energy due to frictional resistance The heat generated or power dissipated in an electrical circuit is commonly referred to as joule heat after James Prescott Joule 1818 1889 the English scientist who investigated the conversion of electrical energy into
194. are wave pattern on the screen Adjust the verti cal VOLTS DIV and the function generator amplitude until the pattern is exactly 8 divisions high This is about 8 cm high If V is 8 divisions the 5 division horizontal line will be very close to the 0 63V criterion for measuring the time constant since 5 8 0 625 actually 0 625V 2 Then set up the circuit as shown in e TI Fig 26 3 with R R 10 KQ and C C 0 1 uF Have the instructor check the circuit before attaching the final lead to the oscilloscope 3 Close the oscilloscope circuit by connecting the wire to the circuit and note the pattern Carefully adjust the trigger controls so that the curve starts upward at the left end of the trace The exponential rise time can be observed in greater detail by increasing the sweep rate decreasing the TIME DIV Adjust the time TIME DIV until the rising curve extends well across the screen Be sure that the vari able TIME DIV remains in the calibrated position 4 With the total pattern 8 divisions high the time con stant is represented by the horizontal distance from the point where the trace starts to move up to the point where it crosses the horizontal line 5 divisions up The time is found by multiplying the horizontal distance by the TIME DIV setting see TI Example 26 1 Re cord in TI Data Table 1 Signal generator TI Figure 26 3 RC circuit Circuit diagram for the experimental procedure for studying R
195. ased in the vicinity of a stationary positive source charge it would move along a line of force in the direction indicated away from the source charge A negative charge would move along the line of force in the opposite direction Once the electric field for a particular charge configuration is known we tend to neglect the charge configuration itself since the effect of the con figuration is given by the field Since a free charge moves in an electric field by the action of the electric force work W Fd is done by the field in moving charges from one point to another for example from A to B in Fig 19 1b To move a positive charge from B to A would require work supplied by an external force to move the charge against the electric field force The work W per charge q in moving the charge between two points in an electric field is called the potential difference AV between the points NM MEE Md 19 3 do It can be shown that the potential at a particular point a distance r from the source charge q is V kq r See your textbook If a charge is moved along a path at right angles or perpendicular to the field lines no work is done W 0 since there is no force component along the path Then along such a path dashed line paths in Fig 19 1b AV Vg Vc W q 0 and Vc Vz Hence the potential is constant along paths perpendicular to the field lines Such paths are called equipotentials In
196. ass of the displaced water m If the can does not fit on the balance platform first suspend and immerse the object in the full overflow can and catch the over flow in the beaker and find m Then attach the sample to the balance arm and suspend it in a beaker of water that will fit on the balance platform to find m Balance arm Overflow can Beaker Figure 18 3 Archimedes principle The arrangement for proving Archimedes principle The weight of the dis placed liquid that overflows into the beaker is equal to the reduction in weight of the metal sample when it is sub merged which is equal to the buoyant force You may use an alternative method if no overflow can is available Attach a string to the sample and place it in a graduated cylinder Fill the cylinder with water until the sample is completely submerged Add water with an eyedropper until the water level is at a specific reference mark on the cyl inder for example 35 mL Remove the sample shaking any drops of wa ter back into the cylinder and weigh the cylinder and water m Refill the cylinder to the reference mark and weigh it again m mj The mass of the overflow water is then the difference between these measurements www ATIBOOK ir 274 3 EXPERIMENT 18 Archimedes Principle Buoyancy and Density The buoyant force is then the difference between the object s true weight and its submerged weight F mg mg According to Archim
197. ass on a platform balance Fig 2 1a On a beam balance the riders on the beams are used to balance the unknown mass on the platform Fig 2 1b The common laboratory beam balance is calibrated in grams In this case the least count is 0 1 g and a reading can be estimated to 0 01 g See Experiment 1 for a review of least count The official abbreviation of the gram unit is g roman The standard symbol for acceleration due to gravity is g italic where weight is given by mg which is not to be confused with mg for milligram Look closely so as to avoid confusion with these symbols 23 Before making a mass determination a balance should be checked without a mass to make sure the scale is zeroed reads zero Adjustments can be made by various means on different scales Balances with digital readouts are common Fig 2 1c These have the advantages of accuracy and ease of operation However electronic balances are much more delicate Fig 2 1d The mass value is displayed automatically and the accuracy or number of significant figures depends on the particular balance Some electronic balances have autocalibration and other have a keypad for calibration by the user Most electronic balances are zeroed by pressing a tare button This has the advantage that one can place an empty dish on the balance before pressing the tare button and then when the material is added to the dish the balance displays the mass of the conte
198. ass plate 402 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 8 Spherical Mirrors and Lenses fri Advance Study Assignment Read the experiment and answer the following questions 1 Distinguish between concave and convex spherical mirrors 2 What is the difference between a real image and a virtual image 3 Distinguish between diverging and converging lenses 4 What does the word focal mean with regard to the focal point of spherical mirrors and lenses 403 continued www ATIBOOK ir EXPERIMENT 2868 Advance Study Assignment 5 If an object is placed 15 cm in front of a concave mirror with a radius of curvature of 20 cm what are the image characteristics Show your work 404 www A TIBOOK ir EX PE RI ENT 2 8 Spherical Mirrors and Lenses INTRODUCTION AND OBJECTIVES Mirrors and lenses are familiar objects that are used daily The most common mirror is a plane mirror the type we look into every morning to see our image Spherical mirrors also have many common applications For exam ple convex spherical mirrors are used in stores to monitor aisles and merchandise and concave spherical mirrors are used as flashlight reflectors and as cosmetic mirrors that magnify Mirrors reflect light whereas lenses transmit light Spherical lenses are used to cause light rays to converge and hence focus them biconvex spherical lenses and to cause light rays to diverge biconca
199. at does not generate or supply a voltage acts as a resistance in the circuit This is true for the connecting wires the ammeter and the volt meter However the metallic connecting wires and the ammeter have negligibly small resistances so they do not greatly affect the current A voltmeter has a high resistance so there is little current through the voltmeter Hence to good approxima tions the ammeter registers the current in the resistor and the voltmeter reads the voltage drop across the resistance These approximations are adequate for most practical applications Applying Ohm s law to the portion of the circuit with R only V IR TI 20 3 S where V and J are the voltmeter and ammeter readings respectively Notice that the same current J flows through the rheostat R and the resistance R The voltage drop across R is then V IR TI 20 4 To apply Ohm s law to the entire circuit we use the fact that the applied voltage rise or the terminal voltage V of the voltage source must equal the voltage drops of the components around the circuit Then V V V or V IR IR KR R TI20 5 From TI Eq 20 5 it can be seen that for a constant R the current through this resistance and hence its voltage drop V can be varied by varying the rheostat resistance Ry The terminal voltage V is constant Similarly when R is varied the vo
200. at only two decimal places are shown Wait until data are collected to adjust this There have to be data on the display before any change can be noticed 12 CI Figure 10 4 shows what the screen will look like after the setup is complete and data are taken g EXPERIMENTAL PROCEDURE A The Effect of the Load 1 Measure the mass of the wooden block and of any other block or car that will be placed on top of it to add height as illustrated in CI Fig 10 1 Record the total mass in Trial 1 of CI Data Table 1 The force sensor is connected to analog channel A The sample rate is set to 200 Hz www ATIBOOK ir Fl Edt Doemer Wndow Depay Hap FF Snare x Soup gt so EBREEMD ec E amp Force Ch A N A Run fl EXPERIMENT 10 Friction A Forte ChA Runs Force amp Sound Analyzer A Sound Crestor E Table workbook 1 431 Sample Rale aah sf flowing zi r Sensor Sampling Options F Redxce sence rte by meten je Elechve Seercts Rale f Hr Zero erao a sors icy on stor Zero Sern F Reverse opo af sevoler 169 CI Figure 10 4 Data Studio setup A digits display will show the force reading of the sensor Once data are collected the size of the display window is adjusted to show two decimal places Data displayed using Data Studio Software Reprinted courtesy of PASCO Scientific 2 Set up the equipment as shown in CI Fig 10 1 It is important that the string connec
201. ate a graph by dragging the position data icon from the data list and dropping it on top of the graph icon of the displays list A graph of position versus time will open in a window called Graph 1 9 Now drag the velocity data icon and drop it some where in the middle of the graph The graph display will split into two graphs one of position the other of velocity as shown in e CI Fig 4 3 HB EXPERIMENTAL PROCEDURE WARNING Be careful not to touch the fan blades while they are spinning 1 2 Turn the fan on but hold on to the car so that it does not yet move Have a partner press the START button Let go of the car Your partner must press the STOP button before the car reaches the end of the track to prevent data being taken of collisions and rebounds with pulleys or end stops You may need to do a few practice runs to become familiar with the procedure Note If the graphs show negative values reverse the fan so that it is facing in the opposite direction and start again from the opposite side of the track Carefully turn off the fan You should have two graphs on the screen Use the Scale to fit button on the graph toolbar to display the data clearly Notice that the graph of position versus time is a smooth parabola The graph of velocity ver sus time is a straight line Click anywhere on the position versus time graph to make it active Use the Smart Tool a button on the graph toolbar labeled
202. attery TI CI 3 Consider resistors connected in parallel a How are the voltage drops across the individual resistors related to the voltage supplied by the battery b How are the currents through the individual resistors related to the current supplied by the battery 335 continued www ATIBOOK ir EXPERIMENT 22 Advance Study Assignment TI 4 Give draw and explain an analogy to liquid flow for the series parallel circuit in Part C of the experiment CI 4 Ina plot of voltage versus current what physical quantity is represented by the slope of the graph TI 5 How would the current divide in a parallel branch of a circuit containing two resistors R and R if a R R and b R 4R 336 www A TIBOOK ir EX PE RI J ENT 2 3 Resistances in Series and Parallel OVERVIEW Experiment 23 examines resistances in parallel and series combinations with both TI and CI procedures In the TI procedure the resistances are measured using a voltmeter and ammeter In the CI procedure measurements are made with a voltage and current sensor and graphs of V versus 7 are plotted from which the resistances are given by the slopes INTRODUCTION AND OBJECTIVES The components of simple circuits are connected in series and or parallel arrangements Each component may be rep resented as a resistance to the current in the circuit In com puting the voltage and current requirements of the circuit or part of th
203. awing a single vertical line from top to bottom of the page crossing time f Use the Smart Tools to find the time t that corre sponds to the moment just after the collision ended Report the value of t in the laboratory report Hint The collision does not end at the same time as when it started look carefully Again think of what the cars were doing right after the collision In the graph printout mark the time f in all graphs by drawing a single vertical line from top to bottom of the page crossing time fj The two vertical lines now separate the before collision from the after collision moments Determine how long in time the collision lasted Use the Smart Tool to determine at time f the velocity of Car 1 the velocity of Car 2 the total momentum of the system the total kinetic energy of the system Enter the results in CI Data Table 1 EXPERIMENT 7 Conservation of Linear Momentum 121 19 Use the Smart Tool to determine at time fy the velocity of Car 1 the velocity of Car 2 the total momentum of the system the total kinetic energy of the system Enter the results in CI Data Table 1 20 Calculate the change in velocity of each car the change in momentum of each car the change in the total momentum of the system and the change in the total kinetic energy of the system Enter the results in CI Data Table 1 CASE 2 INELASTIC COLLISION BETWEEN Two CARS OF NEARLY EQUAL Mass WITH ON
204. axis X is called the abscissa and the vertical axis Y the ordinate The location of a point on the graph is defined by its coordi nates x and y written x y referenced to the origin O the intersection of the X and Y axes When plotting data choose axis scales that are easy to plot and read The graph in Fig 1 6A shows an example of scales that are too small This bunches up the data mak ing the graph too small and the major horizontal scale values make it difficult to read intermediate values Also the dots or data points should not be connected Choose scales so that most of the graph paper is used The graph in Fig 1 6B shows data plotted with more appropriate scales Also note in Fig 1 6A that scale units on the axes are not given For example you don t know whether the units of displacement are feet meters kilometers or whatever Scale units should always be included as in Fig 1 6B It is also acceptable and saves time to use standard unit abbre viations such as N for newton and m for meter This will be done on subsequent graphs With the data points plotted draw a smooth line described by the data points Smooth means that the line does not have to pass exactly through each point but connects the general areas of significance of the data points not connecting the data points as in Fig 1 6A The graph As a general rule it is convenient to choose the unit of the first major scale division to th
205. be a straight line if the gamma radiation contained gamma rays of two different energies Explain 4 The mass absorption coefficient of iron is 0 058 for 1 24 MeV gamma rays What percentage if any of the beam of such gamma rays is transmitted through an iron plate 3 cm thick ppe 7 86 g cm Laboratory Report 509 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir APPENDIX A Material Properties TABLE A1 Densities of Materials Substance g cm kg m Solids Aluminum 2 7 2 7 X 10 Brass 8 4 8 4 x 10 Copper 8 9 8 9 x 10 Glass crown 2 5 27 2 5 2 7 X 10 flint 3 0 3 6 3 0 3 6 X 10 Gold 19 3 19 3 X 10 Iron and steel general 7 88 7 88 X 10 Lead 11 3 11 3 X 10 Nickel 8 8 8 8 x 10 Silver 10 5 10 5 x 10 Wood oak 0 60 0 90 0 60 0 90 x 10 pine 0 35 0 50 0 35 0 50 x 10 Zinc 7 1 7 1 x 10 Liquids Alcohol ethyl 0 79 0 79 x 10 methyl 0 81 0 81 x 10 Carbon tetra 1 60 1 60 x 10 chloride Gasoline 0 68 0 75 0 68 0 75 X 10 Glycerine 1 26 1 26 x 10 Mercury 13 6 13 6 x 10 Turpentine 0 87 0 87 x 10 Water 1 00 1 00 x 10 Gases at STP Air 0 001293 0 001293 x 10 Carbon dioxide 0 001975 0 001975 x 10 Helium 0 000179 0 000179 x 10 Hydrogen 0 000089 0 000089 x 10 Nitrogen 0 000125 0 000125 x 10 Oxygen 0 00143 0 00143 x 10 TABLE A2 Young s Modulus for Some Metals Metals N m Aluminum 6 5 x 10 Brass 9 0 x 10 Copper 12
206. bes Conducting sheets with grids Conducting paint Connecting wires 1 5 V battery or 10 V dc source Galvanometer or high resistance voltmeter or multimeter or vacuum tube voltmeter VTVM with two point contact field probe Single throw switch 3 sheets of Cartesian graph paper B Magnetic Field 2 bar magnets and 1 horseshoe magnet ron filings 3 sheets of paper or overhead transparency material Small compass 3 sheets of Cartesian graph paper or regular paper Leads from the dc input of an oscilloscope work nicely THEORY A Electric Field The magnitude of the electrostatic force between two point charges q and q is given by Coulomb s law _ Kqiq 19 1 p F where r is the distance between the charges and the con stant k 9 0 X 10 N m C The direction of the force on a charge may be determined by the law of charges or charge force law Like charges repel and unlike charges attract The magnitude E of the electric field E is defined as the electrical force per unit charge or E F q N C By convention the electric field is determined by using a 283 positive test charge q In the case of the electric field asso ciated with a single source charge q the magnitude of the electric field a distance r away from the charge is F kqq _ kq E 19 2 Io Io r E electric field The direction of the electric field may be determined by the law of c
207. bjects and record in Data Table 4 Determine the volume of the irregularly shaped metal object by the method described in Theory section D Record the volume in Data Table 4 Using a laboratory balance determine the mass of each object and record the results in Data Table 4 Calculate the density of the material of each object and find the percent error of each experimental result Accepted density values are given in Appendix A Table A1 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 Measurement Instruments Mass Volume and Density RWV Laboratory Report A Least Count of an Instrument Scale DATA TABLE 1 Purpose To practice determining least count and estimated fraction of least count Instrument Least count Estimated fraction Meter stick Vernier caliper Micrometer caliper Balance Graduated cylinder Calculations show work Don t forget units 29 continued www ATIBOOK ir EXPERIMENT 2 Measurement Instruments Mass Volume and Density B Thickness Measurements DATA TABLE 2 Zero reading Micrometer Caliper Purpose To practice using calipers Indicate units in the parentheses Laboratory Report Thickness of single Reading pace Thickness of pages Average page thickness C excluding covers Thickness of manual Average Actual number of pag
208. ble Spectral Lines of Some Elements Wavelength Relative Element nm Color intensity Helium 388 9 Violet 1000 396 5 near Violet 50 402 6 near Violet 70 438 8 Blue violet 30 447 1 Dark blue 100 471 3 Blue 40 492 2 Blue green 50 501 5 Green 100 587 6 Yellow 1000 667 8 Red 100 706 5 Red 70 Mercury 404 7 Violet 300 407 8 Violet 150 435 8 Blue 500 491 6 Blue green 50 546 1 Green 2000 577 0 Yellow 200 579 0 Yellow 1000 690 7 Red 125 Sodium 449 4 Blue 60 449 8 Blue 70 466 5 Blue 80 466 9 Blue 200 498 3 Green 200 514 9 Green 400 515 3 Green 600 567 0 Green 100 567 5 Green 150 568 3 Green 80 568 8 Green 300 589 0 Yellow orange 9000 589 6 Yellow orange 5000 615 4 Orange 500 616 1 Orange 500 Wavelengths of various colors General Color Representative nm ranges nm Red 650 0 647 0 700 0 Orange 600 0 584 0 647 0 Yellow 580 0 575 0 585 0 Green 520 0 491 2 575 0 Blue 470 0 424 0 491 2 Violet 410 0 400 0 420 0 Visible spectrum 400 0 700 0 nm www ATIBOOK ir TaBLE A9 Radioisotopes APPENDIX A Material Properties Principal Radiations MeV Isotope Half life Alpha Beta Gamma Barium 133 10 4 years 0 356 Bismuth 210 5 01 days 4 654 4 691 1 161 Carbon 14 5730 years 0 156 Cesium 137 30 1 years 0 512 1 173 Barium 137m 2 6 min 0 662 Cobalt 60 5 26 years 0 315 Iodine 131 8 07 days 0 606 Lead 210 22 3 years 0 017 0 061 0 0465 Manganese 54 312 5 days 0 835 Phosphorus 32 14 3 days 1 710 Poloni
209. but Eq 22 2 can be used over moderate temperature ranges for all but the most accurate work In contrast to pure metals which have positive tem perature coefficients of resistance increase in resistance with increase in temperature some materials have nega tive temperature coefficients decrease in resistance with an increase in temperature Carbon is an example and negative temperature coefficients of resistance generally occur in materials of intermediate conductivity or semi conducting materials Carbon has a relatively small negative temperature coefficient of resistance compared to other semiconduct ing materials Such materials with large negative tem perature coefficients are used in commercial components called thermistors A thermistor is a thermally sensitive resistor made of semiconducting materials such as oxides of manganese nickel and cobalt Because of relatively large negative temperature coefficients thermistors are very sensitive to small temper ature changes and are used for temperature measurements www ATIBOOK ir 326 EXPERIMENT 22 The Temperature Dependence of Resistance in a variety of temperature sensing applications such as for voltage regulation and time delay switches Unlike common metal conductors for a thermistor the change of resistance with a change of temperature is nonlinear and the o in Eq 22 1 is not constant The tem perature dependence of a thermistor is given by an expo ne
210. c Method The Simple Pendulum INTRODUCTION AND OBJECTIVES The laboratory is a place for the investigation of physical phenomena and principles In the process new discoveries may be made and technology advanced In some instances while trying to invent things in the laboratory scientists make various investigations at random This might be called the trial and error approach Edison s invention of the lightbulb is an example He kept trying until he found something that worked a car bonized thread for a filament Today the physics labora tory is used in general to apply what is called the scientific method No theory or model of nature is valid unless its predictions are in agreement with experimental results Rather than applying the somewhat haphazard trial and error approach scientists try to predict physical phenomena theoretically and then test the theories against planned experiments in the laboratory If repeated experimental results agree with the theoretical predictions the theory is considered to be valid and an accurate description of certain physical phenomena until some other results demonstrate otherwise To illustrate the scientific method in this experiment a theoretical expression or equation that describes the behavior of a simple pendulum is given The validity of this relationship will then be tested experimentally In the process you will learn what variables influence the period of a simple pendulum and
211. ccuracy or precision Explain 4 Distinguish between positive and negative zero errors and how corrections are made for such errors For what kind of error does a zero correction correct continued 21 www ATIBOOK ir 22 SPER IM EN 1 2 Advance Study Assignment What is the purpose of the ratchet mechanism on a micrometer caliper Explain how readings from 0 00 through 1 00 mm are obtained from the micrometer thim ble scale when it is calibrated only from 0 00 through 0 50 mm If the density of one object is greater than that of another what does this indicate Do the sizes of the objects affect their densities Explain Explain how the volume of a heavy irregularly shaped object may be determined experimentally Are there any limitations www A TIBOOK ir EX PER MENT 2 Measurement Instruments Mass Volume and Density INTRODUCTION AND OBJECTIVES Common laboratory measurements involve the determi nation of the fundamental properties of mass and length Most people are familiar with the use of scales and rulers or meter sticks However for more accurate and precise measurements laboratory balances and vernier calipers or micrometer calipers are often used particularly in mea surements involving small objects In this initial experiment on measurement you will learn how to use these instruments and what advantages they offer Density the ratio of mass to volume will also be considered an
212. ce Ice Safety glasses Strainer THEORY The change in temperature AT of a substance is pro portional to the amount of heat AQ added or removed from it AQ AT In equation form we may write AQ CAT where the constant of proportionality C is called the heat capacity of the substance However the amount of heat required to change the temperature of an object is also proportional to the mass of the object Hence it is convenient to define a specific heat capacity or simply specific heat c 17 1 E m 17 2 Cc 261 which is the heat capacity per unit mass of a substance Thus Eq 17 1 becomes AQ mcAT and 17 3 specific heat The specific heat is then the amount of heat required to change the temperature of 1 g of a substance C The calorie cal unit of heat is defined as the amount of heat required to raise the temperature of 1 g of water 1 C By definition then water has a specific heat of 1 cal g C AQ 1 cal mAT 1gXl C A kilocalorie kcal is the unit of heat defined as the amount of heat required to raise the temperature of 1 kg of water by 1 C In these units water has a specific heat of 1 kcal kg C or in SI units 4 18 X 103 J kg C Your instructor may recommend that you use one of these units cal g C C www A TIBOOK ir 262 EXPERIMENT 17 Specific Heats of Metals UE IC REPE Figure 17 1
213. ce has the same rise time as though it were charging and discharging It should be noted that the high point on the charging curve and the low point on the decay curve in Fig 26 2 are not V V and V 0 respectively since it takes infinite times for the capacitor to charge and discharge to these values However if the time constant is several times smaller than one half the period T of the square wave T f then to a good approximation the high and low points of the curve may be taken to correspond to V V and V 0 respectively www ATIBOOK ir 380 EXPERIMENT 26 The RC Time Constant Electronic Timing y ame charge Hu zd TI Figure 26 2 Charging and discharging When a square wave signal is applied to a capacitor in an RC circuit the capacitor periodically charges and discharges as shown here on a voltage versus time graph setting of 5 ms div Then the time for these two cycles is time ST div X div 5 ms div X 6 66 div 33 3 ms so the time for one cycle or the period of the wave is T 33 3 ms 2 16 7 ms What is the frequency of the wave The time constant of an RC circuit can be determined from a stationary oscilloscope pattern of the capacitor volt age versus time This is done by finding the horizontal dis tance time needed for the trace to reach 0 63V On an oscilloscope time is measured as a horizontal distance The scale is set by the knob marked SWEEP TIME DIV TI Example 26 1
214. ce the broom on one finger and you can try this at home Is the balance point in the middle or closer to one end Now suppose that the broom is cut into two pieces at the balance point How would the masses of the two pieces compare Are they the same or different and if different which piece would have a larger mass This situation can be modeled with the equipment for this experiment and you will be able to verify your answer or change your mind as appropriate Given the following equipment Meter stick and support stand String and one knife edge clamp or two knife edge clamps one with wire loop Laboratory balance Mass hanger and assorted masses 5 g 10 g 20 g 50 g 100 g continued 189 www ATIBOOK ir EXPERIMEN TF 12 Experimental Planning Set up an analogous situation to the balanced broomstick see GL Fig 12 1 Let s say the broomstick balanced at a point 1 3 of the distance from the bottom of the broom You can adjust the mass m in GL Fig 12 1 to get the balance point in the same relative position at the 33 cm mark on the meter stick Now instead of cutting the meter stick we will do some physics and predict what the mass of each piece would be if we cut the meter stick at the balance point The shorter piece would have a mass of m plus the mass of 33 cm of meter stick If the meter stick is uniform then 33 cm of the meter stick will have 33 100 or 3396 of the total mass of the meter stick If y
215. cedures a Graphical Use the polygon method b Analytical Use the component method c Experimental Use the force table Record the results in the data table Vector addition V Instructor s choice optional Your instructor will give you a set of vectors to add Record the results in the data table as you did for previous procedures www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 5 The Addition and Resolution of Vectors The Force Table RWV Laboratory Report Note Attach graphical analyses to Laboratory Report DATA TABLE Purpose To analyze results of different methods of vector addition Resultant R magnitude and direction Forces Graphical Analytical Experimental m F 0 200 g N 0 30 Vector addition I F 0 200 g N 6 120 o F 0 200 N 0 20 Vector addition II F 0 150 g N 6 80 m F F 0 2000 N 0 0 Vector addition III F F 0 150 N 6 90 F F F Vector resolution F 0 300 N 0 60 F F F F 0 100 g N 0 30 Vector addition IV F 0 200 g N 0 90 F 0 300 g N 0 225 Vector addition V Show analytical calculations below Calculation attach additional sheet if necessary Don t forget units ES 81 www ATIBOOK ir EXPERIMENT 5 The Addition and Resolution of Vectors The F
216. cent error from R B Nonohmic Component Don t forget to attach the graph to the laboratory report ED auestions 1 The graph of voltage versus current for the nonohmic resistor was not a straight line Describe what happened to the current as the voltage increased compared to what happened for the ohmic resistor 2 Why does the graph for the nonohmic resistor loop Hint What happens to the lightbulb filament as the current increases Don t forget units continued 307 www A TIBOOK ir EXPERIMENT 20 _ Ohm s Law Laboratory Report 3 Describe what is happening to the resistance of the lightbulb as the voltage increases Hint Look at the graph in segments and treat each segment as though it were a straight line with slope equal to the resistance 308 www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 1 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method AY Advance Study Assignment Read the experiment and answer the following questions A Ammeter Voltmeter Method 1 When one is measuring a resistance with an ammeter and voltmeter is the resistance given exactly by R V I Explain 2 Comment on the relative magnitudes of the resistances of an ammeter and a voltmeter 3 Is a an ammeter and b a voltmeter connected in series or parallel with a circuit component a resistance Explain continued 309 www ATIBOO
217. city of a car traveling on an elevated air track can be calculated from displacement and time data Advance Study Assignment 1 What precautions need to be taken when working with a fan propelled car 2 For an object moving with constant acceleration what will be the shape of a graph of 50 position versus time What will be the shape of a graph of velocity versus time www A TIBOOK ir EX PER d MENT 4 Uniformly Accelerated Motion OVERVIEW TI CI Experiment 4 examines uniformly accelerated motion using complementary TI and CI approaches The TI procedures investigate the accelerations of 1 an object in free fall and 2 a car on a linear air track for both horizontal and inclined motions The CI procedures extend the investigation by consid ering not only the linear relationship for uniformly accel erated motion v at but also the parabolic relationship x jat This is done using a fan car and a rotary motion sensor INTRODUCTION AND OBJECTIVES TI Cl An important case in kinematics is that of an object in uni formly accelerated motion one having a uniform or con stant acceleration Probably the most common example is a falling object near the surface of the Earth An object falling solely under the influence of gravity is said to be in free fall and that object falls with an acceleration g the acceleration due to gravity Near the Earth s surface the acceleration due to gravi
218. ck with the series of C Dependences of u optional added masses as in the previous procedure for the hor izontal board and record in TI Data Table 3 It may be helpful to tape the masses to the block 14 Use the inclined plane method to investigate the dependence of u on area material velocity rolling and lubrication The experimental setups are described in TI Data Table 4 Answer the questions listed after 12 Using a calculator find the tangents of the 0 angles ea dainqable and record Compute the average of these values and the average of the ratios h L These averages should be similar Why 13 Compare the average value of tan 0 with the value of pa found in the procedure for the horizontal board It can be shown theoretically that tan 0 ju in this case Compute the percent difference of the experi This experimental procedure and modifications were suggested by mental values Professor I L Fischer Bergen Community College New Jersey www ATIBOOK ir Name Section Date Lab Partner s T EX PERIMENT 10 Friction RW Laboratory Report Note Attach graphs to laboratory report Mass of block m A Determination of u RV DATA TABLE 1 Purpose To investigate f uN where N depends on m mw by measuring u on a level plane see TI Fig 10 2 My 0 N m My g f F Mg It is convenient to express the force in terms of mg where
219. cles per second Using this as the accepted value of the vi brational frequency compute the percent error of the experimentally determined value f you have some scattered data points far from the straight line see Question 2 www ATIBOOK ir 244 EXPERIMENT15 Standing Waves in a String b Figure 15 3 Standing wave apparatus a A string vibrator oscillates the string Different standing waves are produced by varying the tension in the string b A dual string vibrator Different tensions produce different normal modes Photos Courtesy of Sargent Welch www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 175 Standing Waves in a String RWV Laboratory Report Mass of string Total length of string L Linear mass density u Length of string between vibrator and pulley L DATA TABLE Purpose To determine the frequency of oscillation from normal modes Number of loops Suspended Measured length 2 measured mass Tension force F Ly for N loops Wavelength A VF N C C C C 3 F L 5 F Ls 6 Fs Le 8 F Lg For convenience the tension weight force may be expressed in terms of g that is if m 0 10 kg then F mg 0 10 g N Calculations Slope of graph show work Computed frequency f Accepted frequency Percent error Don t forget units continued 245 www ATIBOOK ir EXPERIMENT 15 Standing
220. coil or thermometer When the ice has melted measure and record the equilibrium tem perature 7 This should be 5 C to 8 C below room temperature Then plug in the power supply and at the same time start the stopwatch or laboratory timer Immedi ately read and record the initial ammeter and voltme ter readings As time goes on keep the current as constant as possible by varying the rheostat and or the power supply Record the voltage and the current every minute Stir the water frequently EXPERIMENT 24 Joule Heat 363 When the temperature of the water and calorimeter system is 10 C to 15 C above the initial temperature simultaneously unplug the power supply and stop the timer at the time of a particular minute interval read ing Continue stirring until a maximum temperature is reached and record this temperature T Compute the electrical energy expended in the coil in joules from the electrical and time readings Use the average value of the voltage readings as the effective voltage across the coil a Compute the heat energy in calories gained by the calorimeter system b Then take the ratio of the electrical and heat energy results to find the electrical equivalent of heat J cal or J kcal Compare this to the value of the mechanical equivalent of heat by comput ing the percent error If time permits ask your instructor repeat the exper iment and use the average value of the experiment
221. collide while passing each 10 11 12 13 14 other try making the strings longer and pressing STOP just before they collide A straight line graph should have appeared on the screen To see it better press the Scale to Fit button on the graph toolbar It is the leftmost button of the toolbar On the graph toolbar there is also a drop menu called Fit Choose to do a Linear Fit for the graph A box will pop up with information about the fit Make a note of the slope of the line This is the measured experimental acceleration Enter it in CI Data Table 1 Clear the fit information by going to the Fit menu and deselecting the linear fit Trial 2 Add 10 g to each hanger The descending mass should still have the 5 g unbalance Note that this increases the overall total mass of the system but keeps the unbalanced force the same Repeat the data collection process and enter the data in CI Data Table 1 Trials 3 and 4 Repeat two more times each time add ing an extra 10 g to each hanger Clear the graph window of all fit information and then print the graph Label each of the plots with the total mass of the system corresponding to each trial Paste the graph to the laboratory report Calculate the net unbalanced force in newtons Calculate the theoretical acceleration for each trial using Eq CI 6 1 Compare the theoretical value with the experimental value by taking a percent error B Varyi
222. conservation of energy 2 The following diagram illustrates three different positions of the pendulum as it moves in simple harmonic motion The angular displacement has been exaggerated for illustration purposes Label in the diagram which position corresponds to maximum KE which to maximum PE which to minimum KE and which to minimum PE 3 Was the amplitude of the pendulum constant Explain 4 The period of a simple pendulum in SHM is given by T 2n Use the measured length of the pendulum to calculate its period using this formula Then compare to the period you determined from the graph Discuss what causes the percent error 5 Optional Exercise Create a new calculation in the calculator window that will determine the total energy of the pendulum That is calculate KE PE Then plot the total energy as a function of time Was the total energy constant Explain 238 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 15 Standing Waves in a String fi Advance Study Assignment Read the experiment and answer the following questions 1 How is wave speed related to frequency and wavelength How is the period of oscillation related to wave speed 2 What is a standing wave and what are nodes and antinodes 3 What are normal modes 239 continued www A TIBOOK ir EXPERIMEN TF 15 Advance Study Assignment 4 How does the wavelength of a standing wave in a vibrating string vary w
223. crometer screw until it just makes contact with the rod Avoid mechanical backlash and electrical spark gap ionization see below by al ways turning the screw toward the rod just before read ing Do not force the screw Record the micrometer setting Do this three times and take the average as the initial setting As soon as the initial micrometer reading is taken read and record the initial temperature T The linear expansion apparatus may be equipped thermometer in the steam jacket should just touch the metal rod Allow steam to pass through the jacket until the thermometer reading stabilizes several minutes When equilibrium has been reached record the ther mometer reading Then carefully advance the mi crometer screw until it touches the end of the rod and record the micrometer setting Do this three times and take the average of the micrometer readings un less contact is indicated by electrical circuit Turn off the heat source with an electrical circuit that uses a bell light or 5 Repeat Procedures 3 and 4 for the other metal rods voltmeter to indicate when contact is made The Caution Be careful not to burn yourself with the 4 averaging process is unnecessary in this case condensed hot water in the steam jacket or the hot rod when you remove it Take proper precautions Turn the micrometer screw back from the end of the rod several millimeters to allow for the thermal 6 Compute AL and AT and find the coeffici
224. ct Whether an object will float or sink can be shown mathematically as follows The weight of an object is w M Z P amp V where V is the volume of the object and p m V Similarly the weight of the fluid displaced by the object or the buoyant force is Fp w mg pigV If the object is completely submersed in the fluid then V Vp and dividing one equation by the other yields F Wo ae pe E r 18 1 Wo Po o Hence whether the buoyant force F or the weight of the object w is greater depends on the densities and 1 An object will float in a fluid if the density of the object po is less than the density of the fluid p that is p lt pg 2 An object will sink if the object s density is greater than that of the fluid p gt py 3 An object will float in equilibrium at any submerged depth where it is placed if its density is equal to that of the fluid p pz SPECIFIC GRAVITY AND DENSITY Specific gravity will be used in the study and determination of density The specific gravity of a solid or liquid is defined as the ratio of the weight of a given volume of the substance w to the weight of an equal volume of water w Ws specific gravity sp gr a weight of a substance of given volume 18 2 weight of an equal volume of water where the subscripts s and w refer to the substance and water respectively Specific gravity is a density type desig
225. d 5 25 cm and c 16 38 cm c 1638 ce ee 19 d 305 c Td Or T It should be noted that percent error only gives a measure of experi mental error or uncertainty when the accepted or standard value is highly accurate If an accepted value itself has a large degree of uncertainty then the percent error does not give a measure of experimental uncertainty www ATIBOOK ir 8 EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis Then 3 12 and A 3 14 so E Al A _ 342 344l ies i 3 14 0 02 2X 0 314 100 0 6 Percent error x 100 Note To avoid rounding errors the preferred order of operations is addition and subtraction before multiplica tion and division If the uncertainty in experimentally measured values as expressed by the percent error is large you should check for possible sources of error If found additional measure ments should then be made to reduce the uncertainty Your instructor may wish to set a maximum percent error for experimental results PERCENT DIFFERENCE It is sometimes instructive to compare the results of two measurements when there is no known or accepted value The comparison is expressed as a percent difference which is the ratio of the absolute difference between the experimental values E and E and the average or mean value of the two results expressed as a percent absolute difference Percent difference X 100 average or E
226. d laboratory experience has revised this manual He retained the general format of the previous edition For each experi ment there are 1 Comments and Hints 2 Answers to post Experiment Questions and 3 Post lab Quiz Ques tions completion and multiple choice with answers and essay The Instructor s Resource Manual also includes laboratory safety references lists of scientific equipment suppliers and physics software suppliers and graph paper copy masters Of course the publication of this manual would not have been possible without a great deal of help Profes sor Hernandez and I would like to thank the people at PASCO in particular Paul A Stokstad Dave Griffith and Jon and Ann Hanks for their support and help We thank Fred B Otto for his in depth review of the experi ments Thanks also goes to Professor Jerry R O Connor of San Antonio College who reviewed and made helpful suggestions for the Guided Learning feature We are grateful to Mary Finch publisher Brandi Kirksey associ ate developmental editor Joshua Duncan editorial assis tant Jill Clark associate content project manager Nicole Mollica marketing manager and to Suganya Selvaraj at Pre Press PMG We both hope that you will find the seventh edition of Physics Laboratory Experiments helpful and educational And we urge anyone student or instructor to pass on to us any suggestions that you might have for improvement Jerry D Wilson Eme
227. d osin mA m 1 2 3 CI 32 the next bright band After that the centers of other dark condition for dark fringes bands are designated m 2 m 3 and so on Tradition ally positive and negative numbers are used to distinguish one side from the other where o is the width of the slit A is the wavelength of the light and 0 is the angle to the center of a particular band minimum designated by m 1 2 3 The m number is called the order number and the bands are referred to as approximation tanO sin0 y L for the first order first order second order third order and so on minimum we can in general write CI Eq 32 1 as Note the geometry in CI Fig 32 2 where tan0 y L Experimentally y amp L and using the small angle miN Ya m 1 2 3 CI 32 2 CI Eq 32 1 is sometimes written w sinf m m 1 2 3 where the plus and minus numbers are used to indicate dark bands on opposite sides of the central maximum small angles only 471 www A TIBOOK ir 472 EXPERIMENT 32 Single Slit and Double Slit Diffraction d Central EE a maximum m 1 CI Figure 32 2 Geometry of the single slit diffraction pattern The first order minimum m 1 is at a distance y from the central maximum In experimental conditions L is much larger than w and y L gt y where y is the distance between the center of the central maximum and the ce
228. d R3 2 Connect R to the output source of the 750 Interface using cables and alligator clips if needed A circuit diagram for this setup is shown in CI Fig 23 4 3 Put alligator clips on the prongs of the voltage sen sor and connect the voltage sensor across the resistor Make sure that the positive of the voltage sensor red lead is connected to the positive lead of the resistor 4 Press the START button Data collection will stop automatically after 4 5 seconds 5 Press the Scale to Fit button on the graph toolbar The Scale to Fit button is the leftmost button on the graph toolbar This will scale all data to fit the full screen Output current P Signal ey Resistor Q Voltage generator sensor output voltage CI Figure 23 4 The experimental setup A single resistor is connected to the source with the voltage sensor connected across the resistor The positive red lead of the voltage sensor must connect to the positive lead of the resistor 6 Use the Fit menu on the graph toolbar to do a Linear Fit of the data A box with information about the fit will appear Report the slope of the line in CI Data Table 1 as the value of R Do not forget units 7 Repeat the experiment two more times and determine an average value for R www ATIBOOK ir 352 8 9 EXPERIMENT 23 Resistances in Series and Parallel Repeat the process individually with R and R If the graph window gets too c
229. d central maximum of the slit image so the angle between symmetric image orders is 20 e TI Fig 32 2 In practice only the first few orders are easily observed with the number of orders depending on the grating constant If the incident light is other than monochromatic each order corresponds to a spectrum That is the grating spreads the light out into a spectrum As can be seen from TI Eq 32 1 since d is constant each wavelength color deviates by a slightly different angle so that the component wavelengths are separated into a spectrum Each diffraction order in this case corre sponds to a spectrum order The colorful displays seen on compact disks CDs result from diffraction n 2 71 Central maximum Slit TI Figure 32 1 Diffraction pattern A simplistic view of the diffraction pattern two orders produced by a diffrac tion grating Pattern and angles exaggerated illustration www ATIBOOK ir 464 EXPERIMENT 32 The Transmission Diffraction Grating Measuring the Wavelengths of Light a Collimator Light source TI Figure 32 2 Grating spectrometer a A student views a diffraction pattern through the telescope of a grating spectrom eter The light source and collimator are on the right b A diagram of a top view of a grating spectrometer When the sym metric images of a particular order n are viewed from both sides of the central maximum the angle between the two viewing positions is 20
230. d stirrer are not of the same material they must be treated separately and the denominator term in Eq 17 4 becomes mcy mc mjc T T Eq 17 4 Look up the accepted values in Appendix A Table A4 and compute the percent errors www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Lab Partner s Section Date EX PERIMENT 1 7 Specific Heats of Metals Ay Laboratory Report DATA TABLE Purpose To determine the specific heats of metal samples Room temperature T Mass of Specific heat Mass of Type Mass of calorimeter of calorimeter water of metal and stirrer and stirrer My ym Ty T metal ma ma Ces C6 C6 J Calculations Percent show work Type of metal Cm experimental Cm accepted error Don t forget units TE 265 www ATIBOOK ir EXPERIMENT 17 Specific Heats of Metals Laboratory Report RV QUESTIONS 1 a The percent errors of your experimental values of the specific heats may be quite large Identify several sources of experimental error b Why does it improve the accuracy of the experiment if 7 T T T 2 The specific heat of aluminum is 0 22 cal g C What is the value of the specific heat in a kcal kg C b J kg C Show your calculations 3 a If wet shot had been poured into the calorimeter cup how would the experimental value of the specific heat have bee
231. d the densities of several materials will be determined experimentally After performing this experiment and analyzing the data you should be able to do the following 1 Use the vernier caliper and read the vernier scale 2 Use the micrometer caliper and read its scale 3 Distinguish between mass and density and know how to determine experimentally the density of an object or substance EQUIPMENT NEEDED Laboratory balance Vernier caliper Micrometer caliper metric Meter stick Graduated cylinder Cylindrical metal rod for example aluminum brass or copper Sphere metal or glass for example a ball bearing or marble Short piece of solid copper wire Rectangular piece of metal sheet for example aluminum Irregularly shaped metal object THEORY A Laboratory Balances Some common types of laboratory balances are shown in e Fig 2 1 Mechanical balances or scales are used to balance the weight of an unknown mass m against that of a known mass m that is mg m g or m m The mass of the unknown is then read directly in mass units usually grams The weight w of an object is its mass m times a constant g the acceleration due to gravity g 9 80 m s 980 cm s that is w mg or m w g Some scales such as bath room scales are commonly calibrated in weight force units such as pounds rather than in mass units A set of known masses is used to balance an unknown m
232. de of the velocity v d At of the car where At t t The actual timing of the motion of a car moving between the two sets of refer ence marks is done by either method In A involv ing four observers each has a timer and is assigned to an individual reference mark In B involving two observers each has a timer and is assigned to one set of reference marks as described below Time trials will be done to determine the better method set of reference marks after collision Carry out this In addition to giving timing P Taeng and deter procedure three times and record the data in TI Data mining the better method of timing the time trials Table 1 check out the experimental setup for possible system atic errors The time intervals for the individual cars to travel the equal distances between the reference marks should be very similar for any one trial If not the air track may need leveling and or there may be some frictional problem with part of the track Should this be the case notify your instructor Do not attempt to level the air track on your own vi v2 0 Experimentally carry out each of the following timing methods to determine which is better Method A Four Timers Set one of the cars in Case 1 motion with a slight push so that it moves with mod TT TTS ST TO erate speed up and down the track A few practice L m v 0 starts help As the car hits the bumper at one e
233. difference for the total mo ments in the timing procedure to measure the veloc mentum before and after collision for each trial ity of m before and after collision Record the data and the required calculations in TI Data Table 2 Be OPTIONAL PROCEDURE careful with the directional signs of the velocities and Another procedure which may be done at the instructor s momenta option is as follows 8 Attach pieces of Velcro to the collision bumpers of both CASE 3 COLLISION BETWEEN Two CARS OF NEARLY cars and repeat one or more of the preceding cases as EQUAL Mass INITIALLY TRAVELING IN OPPOSITE directed by your instructor Make up a data table and DiRECTIONS analyze your results as done previously Hint Read in 7 With m and m initially moving toward each other your textbook about elastic and inelastic collisions in TI Fig 7 1 determine the total momentum before particular completely inelastic collisions www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Lab Partner s Section Date Conservation of Linear Momentum RW Laboratory Report Distance between marks RV TRIAL DATA TABLE Purpose To determine the better method of timing JN EX PERIMENT 7 METHOD A METHOD B Car mass ti b Atiz tz ty Atz4 Percent Atiz At34 Percent J yp CDC J diff C diff m m nm RV DATA TABLE 1 Purpose
234. does this illustrate Use the accompanying table Consider values significant to two decimal places Circuit Current Tower dissipated element I P R 40 R 6 Q R Ex 3 Q total Power supplied Battery V 12V Show calculations 5 Given three resistors of different values how many possible resistance values could be obtained by using one or more of the resistors List the specific combinations for example R and R in series 348 www ATIBOOK ir C E X P E R MENT 2 3 Resistances in Series and Parallel AD Equipment NEEDED This activity is designed for the Science Workshop 750 Interface which has a built in function generator Voltage sensor PASCO CI 6503 Science Workshop 750 Interface Cables and alligator clips e Three 1000 0 resistors THEORY According to Ohm s law the current through a resistor is proportional to the voltage but inversely proportional to the resistance ee CI 23 1 E CI 23 1 Thus if the resistance of a circuit increases the current decreases and if the resistance of a circuit decreases the current increases On the other hand the larger the voltage the larger the current The overall current in a circuit thus depends on the interplay between the amount of voltage and the amount of resistance In this experiment the total amount of resistance in a circuit will be varied by connecting resistors in series
235. dow will open and you will see a picture of the Science Workshop interface There are seven channels to choose from Digital channels 1 2 3 and 4 are the small buttons on the left analog channels A B and C are the larger buttons on the right as shown in CI Figure 10 3 Click on the channel A button in the picture A win dow with a list of sensors will open Choose the Force Sensor from the list and press OK Connect the sensor to channel A of the interface as shown on the computer screen The properties of the force sensor are shown directly under the picture of the interface Set the sample rate to 200 Hz 7 Create a digits display by double clicking on Digits in the displays list lower left of the screen A display window called Digits 1 will open It will show the force readings from the sensor when data are collected 8 Double click anywhere on the Digits 1 window The Digits Setting window will open 9 Select the Statistics button from the Toolbar box and click OK There will now be a drop menu with the sigma symbol on the Digits 1 window toolbar 10 Press the sigma symbol and choose Mean This will show the average of a series of measurements on the display 11 The size of the display window can be adjusted for easier viewing if needed The bigger the screen the more digits you will be able to see once data are col lected For the purpose of this experiment keep the size such th
236. e The Speed of Sound in Air TI Latent Heats Heats of Fusion and Vaporization of Water CI Latent Heat of Fusion Water Newton s Law of Cooling The Time Constant of a Thermometer The Potentiometer emf and Terminal Voltage The Voltmeter and Ammeter Resistivity Multiloop Circuits Kirchhoff s Rules The Earth s Magnetic Field Introduction to the Oscilloscope TI CI Phase Measurements and Resonance in AC Circuits TI CI Electromagnetic Induction The Mass of an Electron e m Measurement www ATIBOOK ir Preface Physics Laboratory Experiments was written for students of introductory physics in fact it was originally writ ten at the request of students The main purpose of lab oratory experiments is to augment and supplement the learning and understanding of basic physical principles while introducing laboratory procedures techniques and equipment The seventh edition of Physics Laboratory Experi ments has 35 experiments with 15 additional customized experiments All 50 experiments are available for customi zation at TextChoice com See Experiments Available for Customized Publishing This provides an ample num ber of experiments to choose from for a two semester or three quarter physics course Those features that proved effective in previous editions have been retained along with the introduction of a new feature Guided Learning GL Basically this is an effort to supplement the cookbook style expe
237. e it is helpful to report how widely the individual measurements are scattered from the mean A quantitative description of this scatter or dispersion of measurements will give an idea of the precision of the experiment The absolute deviation d is the absolute difference between a measured value x and the mean x of a set of measurements C 1 a x a x Mean Absolute Deviation To obtain what is called the mean or average absolute deviation of a set of N measurements the absolute devia tions d are determined Eq C 1 The mean absolute deviation d is then J Id d T d aie Sr epe lay N C 2 1 N naa The mean absolute deviation is sometimes referred to as simply the mean deviation Example C 1 What is the mean deviation of the set of numbers given in Example 1 6 in Experiment 1 Solution First find the absolute deviation of each of the numbers using the determined mean of 5 93 520 d 5 42 5 93 0 51 d 6 18 5 93 0 25 d 5 70 5 93 0 23 d 6 01 5 93 0 08 ds 6 32 5 93 0 39 Then 1 d d nla 0 51 0 25 0 23 0 08 0 39 5 0 29 The mean absolute deviation is a measure of the dis persion of experimental measurements about the mean that is a measure of precision It is common practice to report the experimental value E of a quantity in the form E xXx d In
238. e possible sources of uncertainty 2 Which collision took a longer time the elastic or the inelastic collision Discuss the pos sible reasons 3 Was the kinetic energy of the system conserved Discuss by comparing the results for the elastic collision and the inelastic collision 4 During the inelastic collision the kinetic energy was obviously not conserved What do you think happened to the lost energy continued 125 www A TIBOOK ir EXPERIMENT 7 Conservation of Linear Momentum Laboratory Report 5 During the collision both cars changed their momentum How does the change in momen tum of each car compare to that of the other Does one car change more than the other What do you think would happen if the cars had different mass If time is available try it 6 For an object to undergo a change in its momentum a net force needs to be applied The amount of change in momentum produced by the force depends on the length of the time during which the force acts and is called the impulse That is Impulse Ap FAr where the force F is assumed to be constant or to be an average force For each of the collisions calculate the average force acting on the cars during the collision and compare them 7 Suppose a ball falls on your head What is better for you less damage for the ball to bounce straight back off your head or for it to stop and stick to you Justify your answer 126 www A TIBOOK ir
239. e the laboratory timer is started t 0 and allowed to run continuously Simultaneously with the starting of the timer the activity is measured on the Geiger counter for 15s and the count rate cpm together with the time elapsed on the timer is recorded in the data table Note If using a rate meter take the average of the high and low meter readings over the 15 s inter val as the count rate If a scaler is used with or with out an internal timer the count rate in cpm must be computed For example suppose that 500 counts are Observed for the 15 s G min interval The count rate is then 500 counts 1 min 500 x 4 2000 cpm Repeat the 15 s count of activity at the beginning of each minute of elapsed time for 10 min to 12 min A dry run of the counting procedure is helpful 4 The instructor will milk the cow or supervise you in doing so Only a few 2 to 3 drops of the eluate milk are needed There doesn t seem to be a son nucleus in nuclear physics www ATIBOOK ir Caution Care should be taken in handling the sample The milking should be done over a sheet of paper that can be discarded in case of a spill and if you should come in contact with the sample imme diately wash your hands The instructor may wish to give you a sample for a trial run of the counting procedure When given the actual data sample carry out the counting procedure as described above Correct for background radiation if necessa
240. e analyzer is rotated with respect to the polarizer The voltage versus time graph background is used to calibrate the sensor Reprinted courtesy of PASCO Scientific Aperture bracket holder Light sensor Aperture perture disk Transluscent Open circular eed mask aperture CI Figure 29 3 The aperture bracket The aperture disk is CI Figure 29 4 Details of the aperture bracket Rotate the mounted in front of the light sensor The sensor and the disk until the translucent mask covers the opening into the apertures sit on the holder and install on the optics bench light sensor www ATIBOOK ir 436 EXPERIMENT 29 Malus s Law Polarizer holder Polarizer with groove Polarizer with Accessory holder with mounting bracket stic belt Polarizer Thumbscrews a b CI Figure 29 5 Polarizers and holders The polarizer and analyzer are mounted directly on the holders One of the holders must have a mount for the rotary motion sensor Thumbscrew storage holes switch on top of the light sensor If the maxi d Case 1 mum was less than 0 5 V increase the gain of the 1 On the graph locate the first minimum of in light sensor tensity and record the angle at which it hap 3 Data Collection pened in CI Data Table 1 a Bring Graph 2 to the front on the screen Increase 2 Now locate and record the angle at which the size if needed to see it well the light intensity reached a maximum b With
241. e angle of incline Show that for an inclined plane the TMA 1 sin0 In the not so ideal case where friction is present the actual mechanical advantage AMA is determined the same way AMA F F GL 13 4 However in this case the conservation of energy principle includes the work associated with friction Wp Total work input total work output Wi W We or Fid Fyd Ws GL 13 5 where W is the magnitude of the energy used to overcome friction From GL Eq 13 5 it can be seen that W lt W and Fd lt Fid How will the AMA compare to the TMA for any simple machine that is not frictionless 204 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 13 Experimental Planning 7 Machines are often rated in terms of their efficiency which is defined as the ratio of the work output to the work input work output W work input W GL 13 6 As a ratio of work efficiency is unitless and is often expressed as a percentage The efficiency is always less than 1 or 100 Explain why this is the case and show that AMA GL 13 7 TMA l Hint Use the distance form of the TMA 8 Note that efficiency tells how much of the work input ends up as useful work output Useful work output W e work input W If the efficiency of a machine is 0 75 how many joules of energy are required to do 1000 J of work 205 www A TIBOOK ir This page intentionally left blank
242. e apparatus www ATIBOOK ir EXPERIMENT 30 The Prism Spectrometer Dispersion and the Index of Refraction 443 particular spectral color The divided circle makes it possible to measure the angle s of deviation After being given instructions by the instructor study the various clamps and adjustment screws of your spectrometer In particular study the divided circle scale Some spectrometers are equipped with vernier scales that permit readings to 1 min of arc Be careful because the adjustments and alignments of the spec trometer are critical and it can be time consuming to restore proper adjustment For spectrometer with telescope With the prism not on the spectrometer table sight the telescope on some distant object and adjust the eyepiece until the cross hairs are in good focus Then mount the lamp near the collimator slit adjusted to a small slit width Move the telescope into the line of sight and adjust so that a sharp image of the illuminated slit is seen focused on the cross hairs Measurement of the prism angle A Mount the prism in the center of the spectrometer table and orient it as shown in e Fig 30 4 With the unaided eye locate the white image of the slit reflected from a face of the prism on either side of the prism angle A The prism may have to be adjusted slightly You may also note the color spectrum in the prism face opposite A Move the telescope in front of the eye and adjust the cross hai
243. e block and the angle of decline Neglect any friction and mass effects of the pulley 5 On the basis of your experimental results draw and justify conclusions about the validity of the empirical rules for friction What does this tell you about applying general rules to all materials and about the nature of friction 166 www ATIBOOK ir C EX PERIMENT 1 0 Friction a EQUIPMENT NEEDED 1 straight smooth track PASCO dynamics track force sensor PASCO CI 6537 wooden block The block used in the TI procedure 1 constant speed motorized car PASCO ME 9781 can be used here also Another option is the Friction Block included in the PASCO Classic Dynamics System Additional blocks as needed to make the string horizontal when connected to the force sensor Two Extra weights to load the sliding object 200 g or 500 g pieces will work fine The PASCO Classic Dynamics System includes mass bars that can be used in this part Graph paper PASCO cars ME 9430 or 9454 stacked upside down on top of each other and on top of the friction block will make a tower of the correct height a THEORY CI Fig 10 2 shows a free body diagram of a block as it slides with constant speed along a level track The horizontal forces are F the tension of the string and f the frictional force provided by the track With the speed constant there is no acceleration From Newton s second law we have In this experime
244. e circuit it is necessary to know the equiva lent resistances of the series and parallel arrangements In this experiment the circuit characteristics of resis tors in series and parallel will be investigated A particular circuit will first be analyzed theoretically and then those predictions will be checked experimentally After performing this experiment and analyzing the data you should be able to TI CI 1 Describe the current voltage relationships for resistances in series TI CI2 Describe the current voltage relationships for resistances in parallel TI3 Reduce a simple series parallel resistance circuit to a single equivalent resistance and compute the voltage drops across and the currents through each resistance in the circuit CI3 Describe the changes in the slopes of V versus graphs as more resistors are connected in a series and b parallel 337 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir f r9 EX PER MENT 2 3 Resistances in Series and Parallel RV EQUIPMENT NEEDED Battery or power supply 3 V Ammeter 0 to 500 mA Voltmeter 0 to 3 V Single pole single throw SPST switch Four resistors 10 Q 20 Q 100 Q and 10 KQ composition type 1 W Connecting wires The ranges of the equipment are given as examples These may be varied to apply to available equipment AY THEORY A Resistances in Series Resistors a
245. e closing the switch Close the switch to position a and note the voltage rise of the capacitor on the voltmeter When the capacitor is fully charged move the switch to position b and note the voltage decrease as the capacitor discharges In the following procedures the voltage is read as a function of time You should try trial time runs to become familiar with the procedures Simultaneously close the switch to position a and start the timer Read and record the capacitor voltage at small time intervals for example 3 s 5 s until the capacitor is fully charged V This should be done with two persons working together If necessary however the switch may be opened and the timer stopped to stop the charging process after a given interval without appreciable error if a high quality low leakage capacitor is used After the capacitor is fully charged open the switch to the neutral position and reset the timer Then simultaneously close the switch to position b and start the timer Read and record the decreasing voltage at small time intervals Open the switch when the capacitor is discharged Replace R and C with R and C smaller resistance and larger capacitance and repeat Procedures 3 and 4 using Data Table 2 to record your findings Compute the quantity V V for the charging and discharging processes respectively Then find the value of In V V and In V Ona Cartesian graph plo
246. e frictional force of the pulley or the mass m needed to provide the weight to balance the frictional force Hence the expression for the theoretical acceleration of the system Eq TI 6 4 may be written m m m g m m m TI 6 6 a eq acceleration theoretical where a is used to distinguish the theoretical acceleration from the experimentally measured acceleration am Thus part of the weight of m goes into balancing or canceling the frictional force of the pulley In the experi mental acceleration trials the m determined in each case is left on the descending hanger as part of m to compen sate for the opposing frictional force www ATIBOOK ir 90 EXPERIMENT 6 Newton s Second Law The Atwood Machine To determine the acceleration of the system experi mentally so that it may be compared to that predicted by theory the time f for the descending mass to fall a given distance y is measured Then using the kinematic equation y vet lar with the mass starting from rest v 0 and y 0 t 0 y 73at or _ 2 Om ou TI 6 7 acceleration measured where a is the experimentally measured acceleration When ap is determined experimentally using dis tance and time measurements friction and pulley inertia are involved These are taken into account in the theoreti cal expression Eq TI 6 6 so that the experimental and theoretical values of a will be m
247. e least accurate quantity used That is you cannot gain accuracy in performing mathematical operations These rules come into play frequently when doing mathematical operations with a hand calculator that may give a string of digits Fig 1 5 shows the result of the division of 374 by 29 The result must be rounded off to two significant figures that is to 13 Why Tt should be noted that these rounding rules give an approximation of accuracy as opposed to the results provided by more advanced statistical methods www ATIBOOK ir EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis 7 I fe Gy 3 DW EJ NES Figure 1 5 Insignificant figures The calculator shows the result of the division operation 374 29 Because there are only two significant figures in the 29 a reported result should have no more than two significant figures and the calculator display value should be rounded off to 13 Example 1 3 Applying the rules Multiplication 2 5m X 1 308 m 33 m Q sf 4 sf Q sf Division 4 sf 882 0 s 3 60 X 10 0245 s 3600 s 3 60 O s 3 sf represented to three significant figures why Addition 46 4 1 37 0 505 48 275 48 3 rounding off 46 4 has the least number of decimal places Subtraction 163 4 5 158 5 gt 159 rounding off 163 has the least number of decimal places none E Expressing Experimental Error and Uncertainty PERCENT ERROR The objec
248. e magnetic field is mapped using the north pole by convention of a mag netic dipole for example the magnetic needle of a com pass The torque on the compass needle resulting from the magnetic force causes the needle to line up with the field and the north pole of the compass points in the direction of the field Fig 19 2 If the compass is moved in the direction indicated by the north pole the path of the com pass traces out a field line Another observation is that an electric charge q mov ing nonparallel to a magnetic field experiences a force www ATIBOOK ir Figure 19 2 Magnetic field The magnetic force causes a compass needle to line up with the field and the north pole of the compass points in the direction of the field If the compass is moved in the direction indicated by the north pole the path of the compass needle traces out a magnetic field line For the special case in which the velocity vector v of the charge is perpendicular to the magnetic field B the magni tude of the force is given by F qvB This gives an expression for the strength magnitude of the magnetic field in terms of familiar quantities B 19 4 ri qv magnetic field where the direction of B is perpendicular to the plane of v and F Note that the SI unit of magnetic field is N A m or tesla T The magnetic field may then be thought of as the mag netic force per unit charge per velocity The B field has
249. e open area at the lower right corner of the laboratory report sheet construct a ray diagram with several rays parallel to the optic axis to show they converge at f c Using the spherical mirror equation determine the image distance for an object at infinity oo 2 This focal property makes possible the experimental determination of the focal length of the mirror An object a great distance from the mirror is essentially at infinity relative to the dimensions of the mirror Take the mirror and screen to a window Holding the mirror in one hand and the screen in the other adjust the distance of the screen from the mirror until the image of some outside distant object is observed on the screen hence a real image Measure the distance f from the mirror vertex to the screen and record it in the laboratory report Repeat this procedure twice and take the average of the three measurements as the focal length of the mirror 3 Case I d gt R a Sketch a ray diagram for an object at a distance slightly beyond R that is d gt R and note the image characteristics b Set this situation up on the optical bench as illus trated in e Fig 28 5 with the object placed several centimeters beyond the radius of curvature known from the determination of fin Procedure 2 with R 2f Measure the object distance d and re cord it in Data Table 1 It is usually convenient to hold the mirror manually and adjust the object distance b
250. e other end to a weight hanger Place the block flat on the board and run the string over the pulley so that the weight hanger is suspended over the end of the table Be sure that the string is parallel to the board otherwise there will be a vertical compo nent of the force F With the rectangular block lying on one of its sides of larger area add weights to the hanger until the block just begins to move Note If the 50 g hanger causes the block to move add some weights to the block and add this mass to the mass of the block mj Determine the required suspended mass within 1 g Record the weight force Mg required to move the block in TI Data Table 1 This is equal in magnitude to the fric tional force f Friction of the pulley neglected www ATIBOOK ir 3 string parallel to table o TI Figure 10 2 Coefficient of static friction Experimental setup to determine jx See text for description Suggested experimental technique a Keep the block in the middle of the plane b Lift the block gently lower it onto the plane restrain it from moving for a count of 5 do not press it against the plane and then release the block If the block moves the suspended mass M is too large if it doesn t move M is too small if the block moves about half the time M is about right 4 Repeat Procedure 3 with m 100 200 300 400 and 500 g masses respectively added to t
251. e positive electrode is approached Draw a smooth curve through these points on the graph paper map Then starting again at a new position near the neg ative electrode repeat these procedures for another field line Trace out four to six field lines in this manner Do not forget to indicate the field direction on the lines Place the negative probe near the center of the field region and rotate the positive contact until a position is found that gives a zero meter reading Record several of these points on the graph paper with a sym bol different from that used for the field lines Check the zero on the voltmeter frequently particularly when changing scales Use the second point as a new pivot point as before and determine a series of null zero points Draw a dashed line curve through these equipotential points Determine three to five equipotential lines in this manner Repeat this procedure for the parallel linear plate electrode configuration Be sure to investigate the regions around the ends of the plate electrodes Optional Your instructor may wish to have you map the electric field for a nonsymmetric electrode con figuration or a configuration of your own choosing EXPERIMENT 19 Fields and Equipotentials 287 These can be prepared by painting the desired elec trode configuration on a conducting sheet with silver paint B Magnetic Field 13 14 15 16 Covering the magnets with sheets of paper o
252. e right or above the origin or zero point as 1 2 or 5 or multiples or submultiples thereof for example 10 or 0 1 so that the minor intermediate scale divisions can be easily interpolated and read 40 30 Ww 8 20 e 10 1 5 3 0 4 5 6 0 Displacement x Figure 1 6A Poor graphing An example of an improperly labeled and plotted graph See text for description www ATIBOOK ir 10 EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis Force F versus displacement x of a spring 3 5 3 0 2 5 2 0 Force N 15 1 0 e 0 50 Name Jane MM Sept 21 2009 0 0 10 0 20 0 30 0 40 0 50 0 60 Displacement m Figure 1
253. e screen Increase its size 1f needed to see it well b c d e f Remove the holder that contains the RMS from the track and set it aside Slide all the other components close to each other and dim the room lights Turn on the laser Use the horizontal and verti cal adjust on the back of the laser if needed so that the light shines centered on the light sensor opening Press the START button and rotate the polarizer until the voltage on the graph reaches a maxi mum You may have to press the Scale to Fit button the leftmost button on the graph toolbar to expand the graph scale while data are collected Press STOP once the maximum is reached Now put the analyzer with RMS back on the track Press the START button and rotate the analyzer until the voltage on the graph reaches a maximum If this maximum exceeds 4 5 V decrease the gain on the light sensor This is a www ATIBOOK ir EXPERIMENT 29 Malus s Law 435 DataStudio Daa Nr V Voltage ChA V i Light Intensity Ch A 96 rr sil Angular Position Ch 182 12 Light Intensity Ch A vs Ar Light Intensity Ch A vs Angular Position Ch 1 amp 2 No Data a Digits hu FFT Eb Graph Graph 1 i Graph li Histogram gt Meter i Scope E Table E Workbook Angular Position Ch 1 amp 2 deg 4 5 6 7 CI Figure 29 2 Data Studio setup A graph of light intensity versus angular position will show the variations in light intensity as th
254. e slats of the fence represent the oriented chains and the light E vector passes through vertically parallel to the pickets In actuality however the E vector passes perpendicular to the molecular chain pickets www ATIBOOK ir 424 EXPERIMENT 29 Polarized Light E E E Unpolarized Partially polarized Linearly or plane polarized ia th tel TI Figure 29 2 Polarization axis of propagation The direction perpendicular to the oriented molec ular chains is commonly called the transmission axis plane of polarization or polarization direction Hence when unpolarized light falls on a polarizing sheet polar izer polarized light is transmitted This is illustrated in TI Fig 29 3 The polarization of light may be analyzed detected by means of another polarizer which acts as an analyzer TI Fig 29 3 The magnitude of the component of the E vector parallel to the transmission axis of the analyzer is E cos 0 Since the intensity varies as the square of the amplitude the transmitted intensity of light through the analyzer is I I cos 0 TI 29 1 where is the maximum intensity of light through the ana lyzer and 0 is the angle between the transmission axes of the polarizer and analyzer If 0 90 we have a condition Transmission axis light Polarized gt Dic Polarizer a TI Figure 29 3 Polarizer and analyzer Analyzer Si An illustration of the polarizati
255. each reading for the lead sheets to obtain the corrected intensities To find the half thickness plot the corrected intensity IL versus the number n of lead sheets on Cartesian graph paper and note the shape of the curve From the graph make a determination of the num ber of sheets n n needed to reduce the intensity from its initial value to 5 of the initial value Try to express this number to the nearest 0 05 of a sheet The half thickness is xi Xn n where x is the thickness of an individual sheet From the half thickness compute the linear absorption coefficient u from Eq 35 4 and record this value in Data Table 3 The absorption coefficient may be found graphically by putting the exponential Eq 35 1 into linear form by taking the natural base e logarithm of both sides But first note that in terms of the number of sheets n Eq 35 1 has the form T Le ye 605 35 5 where x is the individual sheet thickness and the ab sorber thickness is x nx Then taking the natural log of both sides of Eq 35 5 yields In InZ e 9 Ine n or www A TIBOOK ir 504 EXPERIMENT 35 The Absorption of Nuclear Radiation InJ ux n In J 35 6 Note that Eq 35 6 has the form of a straight line y mx b See Experiment 1 for general discussion Find In J for each value of J in Data Table 3 Make a column for these to the right of the table Plot In 7 versus n on Cartes
256. eceived an acceleration Is the car accelerating as it passes between the reference marks Explain 4 In each of the three cases was kinetic energy conserved Justify your answers with a sample calculation for a trial from each case If the kinetic energy is not conserved where did it go 113 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir C EX PER IM ENT 7 Conservation of Linear Momentum SJ courment NEEDED e 2 rotary motion sensors PASCO CI 6538 Brackets and pulley mounts 2 cart string brackets CI 6569 2 dynamics track mount accessories 2 RMS IDS adapters e 2 collision carts PASCO Classic Cars ME 9454 e 1 track Clay or Velcro strips String Optional track end stop CI 6692 to mount the RMS to the track ME 6569 track pulley bracket A cor The purpose of this experiment is to investigate the mo mentum and kinetic energy for elastic and inelastic col lisions The momentum and kinetic energy before the collision of two cars are compared with the momentum and kinetic energy after the collision by looking at a plot of these quantities versus time In a collision between two objects the total momen tum at any time is found by adding the momentum of one of the objects to that of the other er This is vector addition which means the directions of motion of both objects must be taken into account The sensor used to measure the speeds of the objects will al
257. ect that the result of a mathematical operation can be no more reliable than the quantity with the least reliability or smallest num ber of significant figures used in the calculation That is reliability cannot be gained through a mathematical operation It is important to report the results of mathematical operations with the proper number of significant figures This is accomplished by using rules for 1 multiplication and division and 2 addition and subtraction To obtain the proper number of significant figures one rounds the results off The general rules used for mathematical opera tions and rounding follow SIGNIFICANT FIGURES IN CALCULATIONS 1 When multiplying and dividing quantities leave as many significant figures in the answer as there are in the quantity with the least number of significant figures 2 When adding or subtracting quantities leave the same number of decimal places rounded in the answer as there are in the quantity with the least number of decimal places RULES FOR ROUNDING 1 If the first digit to be dropped is less than 5 leave the preceding digit as is 2 If the first digit to be dropped is 5 or greater increase the preceding digit by one Notice that in this method five digits 0 1 2 3 and 4 are rounded down and five digits 5 6 7 8 and 9 are rounded up What the rules for determining significant figures mean is that the result of a calculation can be no more accurate than th
258. ed light After performing this experiment and analyzing the data you should be able to 1 Explain the polarization of light using a polarizer and an analyzer 2 Describe the intensity of light transmission through a polarizer and an analyzer from complete transmission to crossed polaroids 421 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir T d Polarized Light RV EQUIPMENT NEEDED 3 polarizing sheets Polarizing sunglasses Optional Light meter Lamp and converging lens for parallel beam if needed Protractor 6 8 glass microscope slides EXPER MENT 2 9 Glass plate Tripod stand open ring top Calcite crystal Mica sheet Cellophane tape not polymer tape Lucite or other plastic pieces for example U shaped hook or hollow triangle LCD as on a wristwatch or hand calculator RV THEORY Light like all electromagnetic radiation is a transverse wave That is the directions of the vibrating electric and mag netic field vectors are at right angles to the direction of propa gation as illustrated schematically in TI Fig 29 1 If the vector vibrations were parallel to the direction of propagation light would be a longitudinal wave The phenomenon of polarization is firm evidence that light is a transverse wave The term polarization refers to the orientation of the vibrating vectors of electromagnetic radiation Light from an ordinary lig
259. edes principle the magnitude of the buoyant force F should equal the weight of the displaced water F t wy Myg or F m m g mg Compute the buoyant force and compare it with the weight of the displaced water by finding the percent difference B Density of a Heavy Solid Object ps gt Pw 4 Determine the specific gravity and density of the metal sample This can be computed using the data from Part A C Density of a Light Solid Object p lt py 5 Determine the specific gravity and density of the wooden block by the procedure described in the Theory section First measure the mass of the wooden block alone in air Then set up as in Fig 18 3 Tie the sinker to the wood block and tie the block to the lower hook of the balance With the beaker empty check that the sinker does not touch the bottom of the beaker and that the top of the wooden block is below the top of the beaker Pour enough water into the bea ker to cover the sinker weigh add more water until the wooden block is submerged and then weigh again Make certain that no air bubbles adhere to the objects during the submerged weighing procedures The block is waxed so that it does not become waterlogged D Density of a Liquid p A convenient way to measure the density of a liquid is with a hydrometer which is a weighted glass bulb and a calibrated stem that floats in liquid The higher the bulb floats the greater the density of
260. eed to be measured to determine the work done by friction 5 The previous strategy to calculate W was based on the definition of work force distance method The work done by friction for this experimental setup can also be obtained by an energy method Note in e GL Fig 11 1 that there is a decrease in potential energy of the descending mass AU and an increase of the potential energy of the cart AU Are these changes in potential energy equal in magnitude 6 Since a nonconservative force is present f some energy is used in the work done to overcome friction W and this energy is no longer available as potential energy Write the conservation of energy equation for this case in terms of the potential energies and solve for Wy Why have the kinetic energy terms been omitted in this analysis 7 Check with a classmate or the instructor to verify your result Then find a corresponding expressionfor W for the case of the car moving down the plane You now have two ways of determining Wp a force distance method and an energy method Both of these methods will be used in the Experimental Procedure that follows 177 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 1 1 Work and Energy RV Advance Study Assignment Read the experiment and answer the following questions 1 Distinguish between the conservation of mechanical energy and the con
261. eight to the heat generated in the liquid The result was 1 cal 4 186 J or kcal 4186 J A similar electrical experiment may be done to determine the electrical equivalent of heat By the conservation of energy the heat equivalents of mechan ical and electrical energy are the same that is 1 cal 4 186 J Experimentally the amount of electrical joule heat generated in a circuit element of resistance R is measured by calorimetry methods If a current is passed through a resistance immersion heater in a calorimeter with water in an arrangement as illustrated in Fig 24 1 then by the conservation of energy the electrical energy expended in the resistance is equal to the heat energy joule heat Q gained by the system electrical energy expended heat gained W g IVt mc AT Or IVt myCw F MaC MeoitCcoit Te T 24 6 where the m s and c s are the masses and specific heats of the water calorimeter cup and immersion coil respectively as indicated by the subscripts 7 and T are the final and initial temperatures of the system respectively See Experiment 17 for a detailed theory of calorimetry procedure EXPERIMENTAL PROCEDURE 1 Determine and record in the laboratory report the masses of the inner calorimeter cup without ring and the coil of the immersion heater The latter may be supplied by the instructor if the coil is permanently mounted Also record the types of material
262. ement Instruments Mass Volume and Density The physical property of density can be used to identify substances in some cases If a substance is not pure or is not homogeneous that is its mass is not evenly distributed an average density is obtained which is generally different from that of a pure or homogeneous substance EXPERIMENTAL PROCEDURE A Least Count of an Instrument Scale 1 List the least count and the estimated fraction of the least count for each of the measuring instruments in Data Table 1 of the laboratory report For example for a meter stick these would be 1 mm and 0 1 mm respectively Review Experiment 1C if necessary B Thickness Measurements 2 Using the micrometer caliper take a zero reading and record it in Data Table 2 Then take several measurements of a single page of this manual incor porating the zero correction if necessary to determine the average thickness per page Record the data and result in Data Table 2 3 With the micrometer take thickness measurements of a group of several pages together for example 10 pages sheets of paper and record the data in Data Table 2 Calculate the average thickness per page 4 With the vernier caliper take several measurements of the total thickness of the manual excluding covers Record the data in Data Table 2 and compute the aver age overall thickness of the manual Did you remem ber to take a zero reading and record in Data Table 2
263. en until you are ready to take measurements Place the stationary probe on the electric dipole sheet at some general point near the edge of the grid area in the region between the electrodes The poten tial at this point will serve as a reference potential Mark the probe position on your graph paper map The movable probe is then used to determine the location of a series of other points that have the same potential When the movable probe is at a point with the same potential as that of the stationary reference probe no deflection will be observed on the galvanometer Close the switch and place the movable probe on the conducting paper at some location an appreciable dis tance away from the stationary probe Move the probe until the galvanometer shows zero deflection indicat ing a point of equipotential and record this point on the graph paper map Locate a series of eight or ten points of the same potential across the general field region and draw a dashed line curve through these points on the graph paper map Choose a new location for the reference probe 2 to 3 cm from the previous reference position and locate another series of equipotential points Continue this 8 procedure until you have mapped the field region Open the switch Draw curves perpendicular to the equipotential lines on the graph paper map to represent the electric field lines Do not forget to indicate the field direction on the field lines Repea
264. en using F ma 141 continued www ATIBOOK ir EXPERIMENT Advance Study Assignment 5 If the centripetal force acting on an object in uniform motion suddenly ceased to act went to zero what would happen to the object That is what would be its subsequent motion 6 Suppose that the centripetal force acting on an object in circular motion were increased to a new value and the object remained in a circular path with the same radius How would the motion be affected 7 Explain how the centripetal force is directly determined for the apparatus you will be using in the experiment 142 www A TIBOOK ir EX PER Centripetal Force INTRODUCTION AND OBJECTIVES The Earth revolves about the Sun atomic electrons move around the nucleus What keeps these objects in orbit The answer is centripetal force centripetal means center seeking The centripetal force is supplied by gravitational and electrical interactions respectively for each of these cases The study of centripetal force in the laboratory is simplified by considering objects in uniform circular motion An object in uniform circular motion moves with a constant speed a scalar but has a changing velocity a vector because of the continual change in direction This change in velocity results from centripetal accelera tion due to a centripetal force In the experimental situation s of this experiment the centripetal force will be supplied by a spring
265. ence That is they have different indices of refraction in different directions and light passing through the crystal is separated into two components or rays The rays are also linearly polarized Birefringence is discussed in more detail in Section C Some birefringent crystals such as tourmaline exhibit the interesting property of absorbing one of the polarized components more than the other selective absorption so to speak This property is called dichroism Another dichroic crystal is quinine sulfide periodide commonly called herapathite after W Herapath an English physician who discovered its polarizing properties in 1852 This crystal was central in the development of modern polarizers Around 1930 Edwin H Land an American sci entist found a way to align tiny dichroic crystals in sheets of transparent celluloid The result was a thin sheet of polar izing material that was given the name polaroid Better polarizing films have been developed using polymer materials During the manufacturing process this kind of film is stretched in order to align the long molecu lar chains of the polymer With proper treatment the outer valence molecular electrons can move along the oriented chains As a result the molecules readily absorb light with E vectors parallel to the oriented chains and transmit light with the E vectors perpendicular to the chains In a common analogy plane polarization is likened to a picket fence Th
266. ength and the radius of curvature for a spherical lens is not as simple as for a spherical mirror Eq 28 1 For a lens the focal length is given by what is known as the lensmaker s equation n s L 28 4 f Ri R l where n is the index of refraction for the lens material and the R s are taken as positive for convex surfaces See your textbook The index of refraction of glass varies n 1 5 1 7 For example for glass with n 1 5 and symmetric con verging lenses R R and R R Eq 28 4 yields f R Keep in mind however that the focal length of a lens depends in general on the R values which can be dif ferent as well as on n In computations the experimentally determined value of f will be used For f to be equal to R 2 for a symmetric lens as may be for a spherical mirror requires n 2 which is greater than the index of refraction of glass EXPERIMENTAL PROCEDURE A Spherical Mirrors CONCAVE MIRROR 1 a Construct a ray diagram for a concave mirror with an object located at its focal point Drawing pro vided in the laboratory report It should be ob served from the diagram that the reflected rays are parallel In this case we say that the rays converge at infinity or that the image is formed at infinity Inversely rays coming from an object at in finity converge to form an image at the focal point or in the focal plane the plane perpendicular to the optic axis b In th
267. ent we will investigate the relative ori an analyze the transmitted intensity is given by entations of polarizer and analyzer that produce maximum Malus s law and minimum transmission Light from a laser will be I I cos 8 CI 29 1 incident on a fixed polarizer An analyzer placed in front of the polarizer will be rotated Both the transmitted light intensity and the angular rotation of the analyzer will be measured simultaneously using sensors SETTING UP DATA STUDIO Set the Sample Rate to 20 Hz i a The Data list on the left of the screen should now boob Dee aoon phones oe Experiment have three icons one for voltage one for light inten 2 The Experiment Setup window will open and you will Si and one f r theansul r nositon data see a picture of the Science Workshop interface There 11 Rae a graph by face Vol ChA icon are seven channels to choose from Digital Channels i fromthe Data list and dionpisis mas the Graph icon d iu uid a pira nes e Tet ae on the displays list A graph of voltage versus time HER n ib E da g Lon Mc S will open in a window called Graph 1 This graph will PR I EP b aee oe be used later to adjust the light sensor gain 3 Click on the Channel A button in the picture A win 12 Create a second graph by dragging the Light 4 Edd ipie n s named n ra in t nd OK Intensity ChA icon and dropping it on the Graph QU don P REEL QM MESES toe j icon on the displays list A graph of li
268. ent of linear expansion of the rod with increasing temperature With the steam generator about one half full turn on the hot plate or light the Bunsen burner and boil the expansion for each metal Compare these o s with the accepted values given in Appendix A Table A3 by computing the percent errors www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 6 The Thermal Coefficient of Linear Expansion RW Laboratory Report DATA TABLE Purpose To determine the thermal coefficients of expansion of metal samples Initial Initial Final Initial Final a a length micrometer micrometer AL temp temp AT meas accepted Lj setting setting T T 1 Type of rod 2 Type of rod 3 Type of rod Calculations show work Metal Percent error Don t forget units continued 255 www ATIBOOK ir EXPERIMENT 16 The Thermal Coefficient of Linear Expansion Laboratory Report RV QUESTIONS 1 What are the probable sources of error in this experiment Which will cause the largest error 2 Would the numerical values of the thermal coefficients of linear expansion have been the same if the temperatures had been measured in degrees Fahrenheit Explain and give an example 3 For a contraction with a negative fractional change would the coefficient of thermal expansion be negative E
269. ent on 0 90 B Levers DATA TABLE 2 Load mass Load weight F L length 50 cm 60 cm 70 cm 80 cm F F F F Trial 1 2 3 4 5 Average F Efficiency 50 cm Calculations 60 cm show work 70 cm 80 cm Dont forget units 215 continued www ATIBOOK ir ES PE IR WM IE IN C Pulleys DATA TABLE 3 13 Simple Machines Mechanical Advantage Laboratory Report Pulleys Output force or load w mg Input force F W Mg C Output distance d or h C Single fixed Single movable Double movable Calculations show work D Wheel and Axle DATA TABLE 4 Input distance di or h C AMA TMA Axle radius C 2 Wheel radius 6 Output force or load wi mig E Input force F W2 mog AMA TMA Eff Calculations show work 216 Eff www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 13 Simple Machines Mechanical Advantage Laboratory Report RV QUESTIONS 1 Simple machines are sometimes divided into two basic classes inclined planes and levers where the wedge and screw are included in one class and the pulley and the wheel and axle are included in another Explain why these four simple machines can be included in the basic classes of inclined planes and levers 2 A machine mult
270. ependence of these properties on the various types of errors continued www A TIBOOK ir EX PET I IMIE WN 1 1 Advance Study Assignment 5 What determines how many figures are significant in reported measurement values What would be the effect of reporting more or fewer figures or digits than are significant 6 In expressing experimental error or uncertainty when should a experimental error and b percent difference be used 7 How could the function y 3 4 be plotted on a Cartesian graph to produce a straight line What would be the numerical values of the slope and intercept of the line www A TIBOOK ir EXPER MENT 1 Experimental Uncertainty Error and Data Analysis INTRODUCTION AND OBJECTIVES Laboratory investigations involve taking measurements of physical quantities and the process of taking any measure ment always involves some experimental uncertainty or error Suppose you and another person independently took several measurements of the length of an object It is highly unlikely that you both would come up with exactly the same results Or you may be experimentally verifying the value of a known quantity and want to express uncertainty perhaps on a graph Therefore questions such as the following arise Whose data are better or how does one express the degree of uncertainty or error in experimental measurements How do you compare your experimental result with an accepted value How d
271. equal amplitude and frequency traveling in opposite directions gives rise to what is known as a standing or stationary wave The periodic constructive and destructive interference causes the formation of a standing wave pattern as illus trated in Fig 15 2 Notice that some of the particles on the axis are stationary These positions are called nodal points or nodes and the points of maximum displace ment are called antinodes The energy of the particles in a standing wave envelope alternate between the kinetic and potential energies In a stretched string being oscillated or shaken at one end waves traveling outward from the oscillator interfere with waves that have been reflected at the other fixed end However standing waves in a given length of string occur only for certain wave frequencies That is for a given stretching tension or force the string must be driven or oscillated with certain vibrational frequencies to produce standing waves www ATIBOOK ir 242 EXPERIMENT15 Standing Waves in a String Antinode Figure 15 2 Standing wave Periodic constructive and destructive interferences give rise to a standing wave form as illustrated here The length of one loop of the standing wave is equal to one half the standing wave s wavelength Note the positions of the nodes and antinodes The frequencies at which large amplitude standing waves are produced are called na
272. er band The mechanism then acts as a pointer to indicate the highest notch which is observed by a lab partner Holding some reference object such as a pencil by the notched track helps to determine the proper notch number 5 Loosen the screw of the pendulum support and care fully remove the pendulum Weigh and record the masses of the ball m and the pendulum M Note The mass of the pendulum is that of the bob and the support rod Do not attempt to remove the support rod from the bob Consult your instructor for the proce dure if a different model is used 6 From the data compute the magnitude of the initial ve locity using Eq 8 4 g 9 80 m s 980 cm s B Determination of the Initial Velocity of a Projectile from Range Fall Measurements With the pendulum removed or in the upper catch mechanism notch so as not to interfere with the pro jectile position the apparatus near one edge of the laboratory table as shown in Fig 8 3 Shoot the ball from the gun and note where the ball strikes the floor The range of the ball is appre ciable so you may have to shoot the ball down an aisle Be careful not to hit anyone with the ball par ticularly the instructor ge Place a sheet of paper where the ball hits the floor Tape the paper to the floor or weight it down so that www ATIBOOK ir 10 C 11 EXPERIMENT 8 Projectile Motion The Ballistic Pendulum 135 it will not move When the ball
273. ered trademark Union Carbide nucleus and the resulting nucleus Ba is called the daughter nucleus The Ba 137m is washed or eluted from the generator by passing a hydrochloric acid saline solution through the generator Because of this process the generator is com monly referred to as a cow and the Ba 137m is said to be milked from the cow The generator cow may be milked many times but as with an actual cow a time inter val must elapse between milkings Eluting removes the Ba 137m from the generator and time is required for the regeneration of Ba 137m from the decay of Cs 137 Normally the parent and daughter isotopes exist in equilibrium with equal activities After eluting or milking the cow it takes about 12 min for the Ba 137m to build up and again reach equilibrium with the Cs 137 EXPERIMENTAL PROCEDURE Caution Review the radiation safety procedures at the beginning of Experiment 33 1 Before the Minigenerator is eluted turn on the Geiger counter Apply the appropriate tube voltage for nor mal operation see Experiment 33 Over a period of 4 min or 5 min measure and record the count of the background radiation as was done in Experiment 33 2 Mount the Geiger probe so that a planchet with the radioactive Ba 137m sample can be quickly and care fully placed below and near the probe opening at a fixed distance 3 The counting procedure is as follows When the sam ple is in plac
274. erial and the wavelength or energy of the gamma radiation Notice that the unit of u is inverse length such as l cm or cm The absorption of gamma radiation of a given wavelength or energy is related to the atomic number of a substance and macroscopically to the density p of the material Thus it is convenient to define a mass absorption coefficient up Um 35 2 p The mass absorption coefficient provides a stan dardized coefficient Samples of a particular absorbing material may have different densities Each sample would have a different linear absorption coefficient u but the mass absorption coefficient um would have the same value for all the samples Notice from Eq 35 2 that the units of um are cm g u 1 em p gicm m p 2 em g p g If um is used in Eq 35 1 in place of u then I Le Le POD g be 35 3 and the absorber thickness x xp is in g cm Absorber thicknesses are frequently expressed in these units A beta gamma source will be used to study the absorption of nuclear radiations The decay scheme of the suggested Cs 137 source is illustrated in e Fig 35 2 The chief decay mode 94 is beta decay to the excited isomeric state of Ba 137 This decays by gamma emission to the stable ground state of Ba 137 Only 696 of the Cs 137 beta decays directly to ground state Ba 137 Hence for the most part Cs 137 is a beta gamma source of 0 511 MeV beta
275. eriments After 5 years what is a the strength of the source in uCi b the activity of the source in disintegrations per second 1 Ci 3 70 x 10 disintegrations s c What is the strength of the source in becquerels Bq The becquerel is the official SI unit 1 Ci 3 7 X 10 Bq 4 Cesium 136 is also radioactive and decays into barium 136 Write the nuclear equation for this reaction 498 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 5 The Absorption of Nuclear Radiation RV Advance Study Assignment Read the experiment and answer the following questions 1 On what parameters does the absorption of nuclear radiation depend 2 Do the three basic types of nuclear radiation have definite ranges of penetration in materials Explain What is meant by half thickness 3 What is the mass absorption coefficient and what are its units Are there any advantages to using the mass absorption coefficient rather than the linear absorption coefficient Explain 499 continued www ATIBOOK ir EXPERIMENT amp amp Advance Study Assignment 4 Explain how a source that has only one radioactive isotope can emit both beta and gamma radiation 5 Why is a beta gamma source that is shielded with a relatively thin sheet of aluminum effectively a gamma source 500 www A TIBOOK ir E X P E RI The Absorption ENT 3 5 of Nuclear Radiation INTRODUCTION AND OBJECTIVES The obse
276. ermission From Wilson Buffa College Physics Sixth Edition Copyright 2007 Reprinted by permission of Pearson Education coefficient of expansion may vary slightly for different temperature ranges but this variation is usually negli gible for common applications and is considered to be constant By Eq 16 1 is defined in terms of experimentally measurable quantities AL A S 16 2 LAT pen Hence by measuring the initial length L of an object for example a metal rod at an initial temperature T and the change in its length AL for a corresponding temperature change AT a can be computed This development may be extended to two dimen sions The linear expansion expression Eq 16 1 may be written L L 1 AT 16 3 and for an isotropic material its areais A L X L or Figure 16 2 Linear thermal expansion At the initial tem perature 7 the length of the rod is L At some higher temperature 7 the rod has expanded to a length L and the change in length is AL L L for the temperature change AT I2 1 aAT A 1 2aAT a AT where A LZ Since typical a s are of the order of 10 C the a term may be dropped with negligible error and to a good approximation A A 1 2aAT 16 4 Comparing this expression with Eq 16 3 the thermal coefficient of area expansion is seen to be approximately twice the coefficient of linear
277. es sheets in manual Computed number of pages from single page measurement from multiple page measurement Calculations show work 30 Percent error www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 2 Measurement Instruments Mass Volume and Density Laboratory Report C Density Determination DATA TABLE 3 Purpose To record dimensional measurements Zero reading Vernier caliper Micrometer caliper Rod Wire Sphere Rectangular sheet Instrument used Diameter Length Diameter Length Diameter Length Width Thickness Reading J 9 5 5 J FC D Average Calculations show work continued 31 www ATIBOOK ir EXPERIMENT 2 Measurement Instruments Mass Volume and Density DATA TABLE 4 Purpose To compare experimental and accepted density values Laboratory Report Object Rod Type of material Wire Type of material Mass Volume E Experiment density Accepted density from Table A1 Percent error Sphere Type of material Rectangular sheet Type of material Irregularly shaped object Type of material Calculations attach additional sheet if necessary 32 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 2 Measurement Inst
278. es emit line spectra 3 Tell what is meant by the Balmer series and the Rydberg constant EQUIPMENT NEEDED Prism spectrometer Incandescent light source Mercury or helium discharge tube Hydrogen discharge tube Discharge tube power supply 2 sheets of Cartesian graph paper THEORY The electrons in an incandescent light source undergo thermal agitation and emit electromagnetic radiation light of many different wavelengths producing a continuous spectrum However when light emitted from excited gases or vaporized liquids or solids is analyzed line spectra such as those illus trated in e Fig 31 1 are observed Modern theory explains spectra in terms of photons of light of discrete wavelengths being emitted as the result of electron transitions between atomic energy levels Different substances have characteristic spectra that is they have a characteristic set of lines at specific wavelengths In a manner of speaking the spectrum of a substance acts as a fingerprint by which the substance can be identified The characteristic color of light from a gas discharge tube is often indicative of the most intense spectral line s in the visible region For example light from a hydrogen discharge tube has a characteristic red glow resulting from an intense emission line with a wavelength of 656 1 nm Similarly when table salt is vaporized in a flame yellow light is observed because of the intense yellow discharge line in
279. ese reports provide a place for recording data calculations experimental results and analyses Only the Laboratory Report and post lab Questions that follow it need to be submitted for grading The Laboratory Report tables are organized for easy data recording and analysis Students are reminded to include the units of measurement Maximum Application of Available Equipment Labo ratory equipment at many institutions is limited and often only standard equipment purchased from scientific suppli ers is available The TI experimental procedures in this man ual are described for different types of common laboratory apparatus thus maximizing the application of the manual Instructor s Resource Manual The Instructor s Resource Manual is a special feature and resource for the instructor Itis available online on the instructor Web site prepared to accompany the seventh edition of Physics Laboratory Experiments To view a sampling of instructor materials go to www cengage com Physics and click on the link for Algebra and Trigonometry Based Lab Manuals For the seventh edition of Physics Laboratory Experiments click ing the About This Product link will allow you to view online resources including the Instructor s Resource Manual You may contact your Cengage representative if you need new access to this password protected material Professor Fred B Otto previously of the Maine Maritime Academy who has over 20 years of teaching an
280. esolution of Vectors The Force Table AY Advance Study Assignment Read the experiment and answer the following questions 1 Distinguish between scalar and vector quantities and give an example of each 2 How are vectors represented graphically and how are scalars and vector quantities distinguished when written as symbols 3 What is meant by drawing a vector to scale Give a numerical example 4 Why is the triangle method called the head to tail or tip to tail method 73 continued www A TIBOOK ir 74 SPE I MEN NES Advance Study Assignment How may the resultant of two vectors be computed analytically from a vector triangle How many vectors may be added by the polygon method Are other methods of vector addition limited to the number of vectors that can be added Explain What is meant by resolving a vector into components Give an example Briefly describe the steps in the component method of vector addition On a force table what is the difference between the equilibrant and the resultant Why is only one of these actually determined experimentally www A TIBOOK ir E X P ER MENT 5 The Addition and Resolution of Vectors The Force Table INTRODUCTION AND OBJECTIVES Physical quantities are generally classified as either scalar or vector quantities The distinction is simple A scalar quantity or scalar is one with magnitude only includ ing units for example speed 15 m s a
281. everal meters across the room from the Geiger tube and apply the midplateau volt age to the tube as determined from the graph If using an end window tube with a tube mount remove the tube from the mount and lay the tube on the table www ATIBOOK ir 486 EXPERIMENT 33 Detection of Nuclear Radiation The Geiger Counter You will observe an occasional count on the counter This is due to background radiation arising from cosmic rays and radioactive elements in the environment for example in building materials Let the counter run for a measured time for ex ample 4 min to 5 min and determine the background count rate in counts per minute and record this value in Part B of the laboratory report If the background count rate is small compared to the source count it may be considered negligible C Inverse Square Relationship 9 10 11 Bring the source toward the Geiger tube and locate the source at a distance from the tube where the counting rate begins to increase significantly over background Record the distance r and the count rate N in Data Table 2 Record this r as the farthest distance Then bring the source relatively close to the tube and determine the distance from the source that gives a full scale count rate Record the count rate and dis tance closest Divide the length between the two measured distances into eight intervals or steps Measure and record the count rate and source distance
282. expansion that is 2a A similar development can be carried out for the coef ficient of volume expansion which is approximately equal to 3a EXPERIMENTAL PROCEDURE 1 A typical arrangement for determining thermal coef ficients of linear expansion is shown in e Fig 16 3 The apparatus consists of a steam jacket with a mi crometer attachment for measuring AL of a metal rod A thermometer in the steam jacket measures the temperature of the rod Steam is supplied to the jacket by a steam generator and a beaker is used to catch the condensate 2 Before assembling the apparatus measure the lengths L of the metal rods with a meter stick to the nearest 0 1 mm and record these lengths in the data table Avoid handling the rods with your bare hands in order not to raise their temperature Use a paper towel or cloth www ATIBOOK ir EXPERIMENT 16 The Thermal Coefficient of Linear Expansion 253 a b a The heat of steam admitted to the steam jacket causes a metal rod to expand Rods of different metals may be used b The expansion is measured with a dial indicator Photos Courtesy of Sargent Welch Figure 16 3 Linear thermal expansion apparatus 3 Assemble the apparatus placing one of the rods in the water so that steam passes through the jacket The steam jacket Initially have one end of the rod placed firmly against the fixed end screw and the other end not touching the micrometer screw Carefully turn the mi
283. f a wave by means other than reflection or refraction It occurs when a wave encounters an obstacle and bends around it reaching places that would otherwise be shadowed The amount of bending depends on the wavelength of the wave relative to the size of the obsta cle For waves of visible light that have wavelengths in the nanometer range 10 m some obstacles that will produce diffraction are sharp edges point objects and thin slits Let s consider monochromatic light that passes through a single thin slit The light flares out as it goes through producing on a screen a distance L away what is called a i Central i single slit diffraction pattern A sketch of such a pattern is 2nd maximum l 2nd shown in CI Fig 32 1 The diffraction pattern has a bright uU miram central region Other less intense regions are symmetri a cally distributed around the central region These bright re gions or bright bands are called maxima and are regions of NN j NN constructive interference The dark regions in between are called minima and are regions of destructive interference m 2 i l 1 2 From an analysis of the geometry it can be shown that CI Figure 32 1 Single slit diffraction As the diagram the condition for dark bands or minima is given by shows the minima are distributed symmetrically on both sides of the central maximum The first minimum is desig nated m 1 and occurs between the central maximum an
284. f action that is 7 r F distance r from the axis of rotation to the force s line of action a straight line through the force vector arrow That is T r F 12 2 The perpendicular distance r is called the lever arm or moment arm The unit of torque can be seen to be the meter newton m N Notice that these units are the same as those of work W Fd newton meter N m joule J The unit of torque is commonly written meter newton m N to emphasize the distinction Keep in mind that although work and torque have the same units they are not physically the same Torque is a vector quantity that points along the axis of rotation in one direction or the other However to distinguish torques and rotations it is convenient to use a simple conven tion If a torque tends to rotate the body in a counterclockwise direction as viewed from above then the torque is taken to be positive If a torque tends to rotate the body in a clock wise direction then the torque is taken to be negative The plus and minus notation is helpful in torque calculations For example in Fig 12 2 taking the axis of rotation at the 50 cm position F and F produce counterclockwise lt I4 h e e 50 cm e e 0 cm 100 cm m m ms m 4 yf Fy mg F mjg Fz m g F mg Figure 12 2 Torques in different directions The forces F and F give rise to countercl
285. f meter stick L on the opposite side of the support from m is at its center position see Fig 12 5 Compute the mass m of this length of stick see Example 12 2 and record Also record the center position of L where this mass is considered concentrated x and find the length of the lever arm r It should be evident that r L 2 Compute the torque due to m and record it as T From the linear mass density compute the m of the portion of the meter stick remaining to the left of the pivot Calculate the torque due to this portion of the meter stick add it to the torque due to mass m to find the total counterclockwise torque and record it as 7 Compare the torque differences with those found in Case 5 a 8 Case 6 Center of gravity a With a mass m 100 g positioned at or near one end of the meter stick as in Case 5 suspend a mass m 100 g on the opposite side of the sup port stand at the 60 cm position Adjust the meter stick in the support stand clamp until the stick is in balance This locates the center of gravity x of the system Record in Data Table 2 and find r and rp b Repeat the procedure with m positioned at 70 cm c Repeat the procedure with m positioned at 80 cm Notice how the position of the center of gravity moves as the mass distribution is varied www ATIBOOK ir 198 EXPERIMENT 12 Torques Equilibrium and Center of Gravity d Based on the experimental data what would
286. f the Procedure section Apply a sufficient push so the masses move at a reasonable speed they should not move too slowly You may find it easier to recognize uniform motion by observing the rotating pulley rather than the masses Record m and m in TI Data Table 1 in the first column marked with an asterisk These values are used to calculate the frictional mass m m m needed in the theoretical calculation of the accelera tion of the system Eq TI 6 6 5a i Add 10 g to m leaving m in place This cre ates an unbalanced force that should cause the system to accelerate from rest Measure the dis tance y Record y m and the new value of m in TI Data Table 1 Trial 1 See Comments on The data tables are arranged to facilitate data taking and analysis The upper seven rows include all the experimental measurements and the lower six rows are for calculations based on these measurements www ATIBOOK ir 6a Ta B 1 1b EXPERIMENT 6 Newton s Second Law The Atwood Machine 91 Experimental Technique at the end of the Proce dure section ii Make three independent measurements of the time it takes for m to travel the distance y from rest Record the data as Trial 1 iii Remove m and the 10 g mass before proceeding to the next trial i Add 100 g to each hanger for a total of 150 g each ii Repeat Procedure 4a measurement of frictional mass and record data in the nex
287. face are needed for ray diagrams A convex lens is called a converging lens because rays parallel to the principal axis converge at the focal point A concave lens is called a diverging lens because rays parallel to the principal axis appear to diverge from the focal point As with spherical mirrors the characteristics of the images formed by spherical lenses can be determined graphically or analytically The chief 1 and parallel 2 rays for the graphical method are illustrated in the ray diagrams in Fig 28 4 In the case of a convex lens Fig 28 42 the chief ray 1 through the center of the lens passes straight through A ray parallel 2 to the principal axis is refracted in such a way that it goes through the focal point on the far side of the lens Also a focal ray 3 through the near focal point is refracted by the lens so it leaves parallel to the axis In the case of a concave lens Fig 28 4b the chief ray 1 still goes straight through the center of the lens The ray parallel 2 to the principal axis is refracted upward so that it appears to have passed through the focal point on the object side of the lens The focal ray 3 which is headed for the focal point on the far side of the lens is refracted so that it leaves parallel to the principal axis Image real K 4 d 4H ta Biconvex Lens Object Image et 2 virtual b Biconcave Lens Figure 28 4 Lens ray diagrams
288. ferent densities p m V Because the volume of the ball is greater than that of the marble its density is less Cengage Learning where r is the radius of the sphere To illustrate how density provides a measure of compactness of matter consider the marble and Styrofoam ball in Fig 2 6 Both have the same mass 5 0 g but the marble has greater density Why With measured radii of ra 0 75 cm and r 6 0 cm for the marble and ball respectively the calculated densities are My My 5 0 g EE m 2 8 g cm Pu V imn im 0 15cmy n 5 0 p apt 0 0055 g cm VY fnr n 6 0 cm Notice that the calculated results have only two significant figures Why In standard SI units these results are 2 8 X 10 kg m and 5 5 kg m respectively But how does one find the volume of an irregularly shaped object This may be done by immersing it in water or some other liquid in a graduated container Since the object will displace a volume of water equal to its own volume the difference in the container readings before and after immersion is the volume of the object Cylinders commonly have scale divisions of milliliters mL and 1 mL 1 cm cm cubic centimeter is sometimes written on glassware as cc Milliliter is abbreviated both ml and mL The mL abbreviation is gener ally preferred in order to avoid confusion of a lowercase ell with the number 1 www ATIBOOK ir 28 EXPERIMENT 2 Measur
289. friction neglected W in W out and Fis Fos or F F s s where s represents arc length distance The two arcs subtend the same angle 0 so s L 0 and s L and s s L L Then by Eq 13 3 Fulcrum a Static case b Work in work out Fidi Fod Figure 13 2 The lever a A static case of maintaining a load b In lifting a load the work in equals the work out neglecting friction See text for description and Li TMA 13 6 L lever Note that the TMA is given by the geometry of the sys tem For example if L 75 cm and L 25 cm then TMA L L 75 cm 25 cm 3 and the lever ideally multiplies the force by a factor of 3 Frictional losses are normally quite small in the lever action So for most practical purposes the actual mechan ical advantage AMA can be taken to be approximately equal to the TMA However the AMA can be determined experimentally by F AMA 13 7 F C Pulleys A pulley is actually a continuous lever with equal lever arms Fig 13 3a When a pulley or system of pulleys is used to lift a load of weight w by an applied force F the AMA is Fy w AMA 13 8 FA F pulley s www ATIBOOK ir EXPERIMENT 13 Simple Machines Mechanical Advantage 211 Output Input a Single fixed pulley F Wo mg b Single movable pulley Figure 13 3 Pulley arrangements a A single fixed pulley b A single
290. from rest Record the time in TI Data Table 1 4 Add 100 g to each hanger Repeat Procedure 3 mea surement of time with a 10 g mass imbalance Record the data in the Trial 2 column Note The distance y should be remeasured for each trial The length of the string and y distance may vary noticeably because of stretching 5 Repeat Procedure 3 for two more trials with another 100 g being added for each trial Procedure using inertia and friction corrections 2a As noted in the Theory section the pulley contributes to the inertia of the system as though an equivalent mass m were part of the total mass being acceler ated For better results a m will be added in the cal culations The instructor will provide the value of meq or tell you how to measure it nstructor s Resource Manual Record the value of m in the data tables 3a Begin with the descending mass m and the ascend ing mass m each equal to 50 g that is the masses of the hangers alone With m my the system is in equilibrium equal forces m g mg In the absence of friction a slight tap or momentary force applied to m should set the system in uniform motion constant speed Why However because of the opposing frictional force the motion will not persist 4a Add small masses to m until a downward push causes m to descend with a uniform constant velocity See Comment 4 in the Comments on Experimental Tech nique at the end o
291. from the tube for each step as the source is moved away from the tube 12 The inverse square relationship N A r where A is a constant can be put into linear form by taking the logarithm of both sides log N log Ar log r log A or log N 2logr log A 33 4 where log is the common logarithm base 10 Note that Eq 33 4 has the form of a straight line y mx b See Experiment 1 for general discussion Take the logs of the r and N values in Data Table 2 On Cartesian graph paper plot log N versus log r and draw a straight line that best fits the data Determine the slope of the line and compare it to the theoretical value by finding the percent error Optional Your instructor may wish to introduce you to log log graph paper This special graph paper automatically takes the log values See Appendix D for a discussion of graphing on log log and semi log graph papers There is optional use of the latter in Experiments 34 and 35 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 3 Detection of Nuclear Radiation The Geiger Counter RW Laboratory Report A Tube Voltage and Count Rate DATA TABLE 1 Purpose To determine dependence of the count rate on tube voltage Tube voltage Count rate cpm Threshold voltage B Background Radiation Number of counts Counting time min Counts min Don t
292. g Archimedes principle it is necessary to use another object of sufficient weight and density to submerge the light object completely Letting w indicate a submerged weight w is the measured weight of the object w and the sinker c with only the sinker submerged and w wi o is the measured weight when both object and sinker are sub merged Then w w Wy Ws w e e Wy or in terms of mass m m m m and the specific gravity and density can be found from Eq 18 6 That is Mo sp gr p 18 7 m m of a heavy object that sinks EXPERIMENTAL PROCEDURE A Direct Proof of Archimedes Principle 1 Weigh the metal sample and record its mass m and the type of metal in the laboratory report Also deter mine the mass of an empty beaker m and record Fill the overflow can with water and place it on the balance platform Attach a string to the sample and suspend it from the balance arm as illustrated in Fig 18 3 2 The overflow from the can when the sample is im mersed is caught in the beaker Take a mass reading m of the submerged object Make certain that no bubbles adhere to the object It is instructive to place the overflow can on a second balance if available and note that the weight of the overflow does not change as the sample is submerged Next weigh the beaker and water so as to determine the m
293. g is left in symbol form e g 0 250 g N even when graphing Calculations Ms show work from graph Don t forget units continued 163 www A TIBOOK ir EXPERIMENT 10 Friction Laboratory Report B DETERMINATION OF ux RV DATA TABLE 2 Purpose To investigate f AN where N depends on m my by measuring uy on a level plane N m m g jk F Mg Calculations Hk show work from graph Percent decrease of Hx relative to u RV DATA TABLE 3 Purpose To investigate ju tan 0 where 0 is independent of m m by measuring uy by the inclined plane method see TI Fig 10 3 0 Average h L tan 0 Calculations Percent difference between show work tan 0 ux and u from TI Data Table 2 164 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 10 Friction Laboratory Report C Dependences of y optional RV DATA TABLE 4 Purpose To investigate dependences of u by various measurements using the inclined plane method and other materials if available No Conditions 0 p tan 0 1 Wooden block on larger area static 44 2 Wooden block on smaller area static 2 3 Wooden block on smaller area kinetic my Other materials 4 Plastic block 5 Aluminum block moving slowly 6 Aluminum block moving faster 7 Wheeled cart 8 Aluminum block with dry l
294. ge across the capacitor increase with time The voltage V as a function of time is given by v W 1 e v 1 e 7 25 1 charging voltage Figure 25 1 Capacitor charging and discharging The circuit diagram for charging switch S in position a and discharging switch S in position b a capacitor through a resistor 369 where the exponential e 2 718 is the base of natural logarithms and V is the voltage of the source The quantity 7 RC is called the time constant of the circuit The curve of the exponential rise of the voltage with time during the charging process is illustrated in Fig 25 2 Time t Figure 25 2 Voltage versus time A graph illustrating voltage versus time for capacitor charging and discharging The steepness of the curve depends on the time constant RC www A TIBOOK ir 370 EXPERIMENT 25 The RC Time Constant Manual Timing At time f 7 RC one time constant the voltage across the capacitor has grown to a value of 1 2 of V thatis V V 1 eS v 1 e V 3 0 63 V When the fully charged capacitor is discharged through a resistor switch S in position b in Fig 25 1 the voltage across and the charge on the capacitor decays or decreases with time according to the equation V Ve tke 25 2 discharging voltage The exponential decay of the voltage with time is also illustrated in Fig 25 2 After a time t 7 RC
295. ge and Count Rate Lower the high voltage control to the minimum setting Then slowly raise the voltage until the first indication of counting is observed rate meter selection on volts Record this threshold voltage in Data Table 1 Increase the voltage to 25 V above the threshold volt age and record the tube voltage Measure and record the number of counts per minute at this voltage set ting A rate meter is switched to a counting position Because the meter needle fluctuates it is best to watch the meter for 30 s and note the highest and lowest me ter readings The count rate is then taken as the mean or average of these readings Continue to repeat Procedure 5 increasing the voltage by 25 V each time Record the voltage and the corre sponding count rate for each voltage setting You will notice that the count rate first increases rapidly with voltage It then levels off increasing only slightly with increases in voltage This is the plateau region of the Geiger tube Eventually with a particular voltage step a sharp increase in the count rate will be observed Do not in crease the voltage above this value Quickly lower the tube voltage to the minimum setting after this reading to avoid damaging the tube Plot the count rate N counts min versus voltage V on Cartesian graph paper Include the threshold voltage Draw a smooth curve that best fits the data Background Radiation Remove the source s
296. ge drops across each resistor and across all three resistors as a group Remove the voltmeter and connect the ammeter so as to measure the current J supplied by the source Then move the ammeter to measure the current through each resistor by connecting the meter between a given resistor and one of the common junctions The ammeter positions are shown in TI Fig 23 2 Leave the switch closed only while readings are being taken Compare the theoretical and experimental values by computing the percent errors Optional Repeat Procedures 8 through 11 with R replaced by R C Resistors in Series Parallel 13 14 Compute the following and record in the laboratory report If R were connected in series with R and R3 in parallel TI Fig 23 3 a What would be the equivalent resistance Ry of the resistors b How much current would be supplied by the source c What would be the voltage drop across R d What would be the voltage drop across R and R5 e What would be the voltage drop across all three resistors f What would be the currents through R and R3 Set up the actual circuit and trace the current flow to check the circuit With the voltmeter and ammeter measure and record the calculated quantities You need not compute the percent errors in this case However make a mental comparison to satisfy yourself that the measured quantities agree with the computed values within experimental error www
297. ge intentionally left blank www A TIBOOK ir T d Friction RV EQUIPMENT NEEDED Board with attached low friction pulley Rectangular wooden block with hook for example a piece of 2 X 4 lumber or commercially available block Weight hanger and set of weights String Protractor Laboratory balance Table clamp and support Meter stick EX PER MENT 1 0 Masking tape 2 sheets of Cartesian graph paper Optional Plastic block Aluminum block Wheel cart Dry lubricating powder for example graphite or molybdenum sulfide MoS AY THEORY general TI and Cl It is sometimes assumed that the oad or the contact force that presses the surfaces together is simply the weight of the object resting on a surface Consider the case of a block resting on a horizontal surface as illustrated in e TI Fig 10 1a The force that presses the surfaces together is the downward weight force of the block magnitude mg which is the load However on an inclined plane only a component of the weight contributes to the load the component perpendicular to the surface See TI Fig 10 3 where the magnitude of the load is mg cos 0 In order to take such differences into account the frictional force f is commonly taken to be directly propor tional to the normal force N which is the force of the sur face on the block that is f N see TI Fig 10 1 In the absence of other perpendicular forces the normal force
298. ght intensity 5 Connect the sensor to Channel A of the interface as verstis Ume wili open ina window called Giaph E COMPUT ware 13 Drag the Angular Position icon from the Data list m iiae Papa pnis Nd UE par i 2n He and drop it on top of the time axis of Graph 2 The dd d s channel buttonan Mie picture vo time axis will change into an angular position axis ee ee Graph 2 should now be a plot of light intensity versus 8 Choose the Rotary Motion Sensor RMS from the list angular position CI Fig 29 2 shows how the screen and press OK MN 9 Connect the RMS to Channels 1 and 2 of the inter shoulab pear ater Ie Setup qs GORUDISUS face as shown on the computer screen 10 On the same window adjust the properties of the RMS a EXPERIMENTAL PROCEDURE as follows First Measurements tab select Angular Position 1 CI Figures 29 3 through 29 6 show the equipment Ch 1 and 2 and select the unit of measure to be de setup grees Deselect all others a CI Fig 29 3 The aperture disk is mounted Rotary Motion Sensor tab set the Resolution to on the aperture bracket holder The light sensor is low 360 divisions rotations and set the Linear Scale then mounted on the aperture bracket behind the to Large Pulley Groove aperture disk and connected to the interface 433 www ATIBOOK ir 434 Add Sersor ox Instrument Selup Tiers EXPERIMENT 29 Malus s Law Rolaty Mchon Sensor Measurements Measurements Rota
299. grating with 300 lines mm Express the constant in nanometers continued 457 www ATIBOOK ir EXPERIMENT 82 3 Explain why there is a spectrum for each diffraction order when multicolored light is analyzed 4 Will the red or the violet end of the first order spectrum be nearer the central maximum Justify your answer 5 It will be observed that the second order spectrum is spread out more than the first order spectrum Why A Advance Study Assignment Read the experiment and answer the following questions 1 What is diffraction 458 Advance Study Assignment www ATIBOOK ir Name Section Date Lab Partner s EXPERIMEN T amp 2 Advance Study Assignment 2 What type of pattern is produced by a double slit By a single slit 3 What causes dark and bright fringes 459 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir EXPERI J M ENT 3 2 F The Transmission Diffraction Grating Measuring the Wavelengths of Light EH Single Slit and Double Slit Diffraction OVERVIEW Experiment 32 examines diffraction but the TI and CI procedures differ in focus The TI procedure uses a trans mission diffraction grating to measure the wavelengths of light from an incandescent source and the mercury Hg line spectrum The CI procedure complements this by investigating single slit and double slit diffraction By using the diffraction patterns formed by laser l
300. gths or colors of light However when a beam of white light falls obliquely on the surface of a glass prism and passes through it the light is spread out or dispersed into a spectrum of colors This phenomenon led Newton to believe that white light is a mixture of compo nent colors The dispersion arises in the prism because the wave velocity is slightly different for different wavelengths A spectrometer is an optical device used to observe and measure the angular deviations of the components of incident light due to refraction and dispersion Using Snell s law the index of refraction of the prism glass for a specific wavelength or color can easily be determined After performing this experiment and analyzing the data you should be able to 1 Explain the dispersion of light in a dispersive medium 2 Describe the operation of a prism spectrometer 3 Tell how the index of refraction of a prism can be measured EQUIPMENT NEEDED Prism spectrometer ncandescent light source and support stand THEORY A monochromatic single color or wavelength light beam in air obliquely incident on the surface of a transparent medium and transmitted through the medium is refracted and deviated from its original direction in accordance with Snell s law see Experiment 27 c sin 0 n Cm sin 30 1 where n is the index of refraction c is the speed of light in vacuum air Cm is the speed of lig
301. h A of the laser light It is printed on the back of the diode laser A The Single Slit Pattern 1 Select the 0 04 mm wide single slit from the disk Make a note of the value in the laboratory report 2 Place the laser on the side opposite the light sensor on the track The slit disk should be a few centimeters in front of the laser Record in the laboratory report the distance L between the slit and the sensor 3 Set the light sensor aperture bracket to slit 6 4 Turn the laser on and set the gain switch to X10 If the light intensity goes offscale when you are measuring turn it down to X1 5 The pattern should be visible on the aperture bracket of the light sensor Move the light sensor to one side of the laser pattern 6 Turn the classroom lights off 7 Press the START button and slowly move the sensor across the pattern by rotating the large pulley of the RMS Click the STOP button when you are finished 8 Use the magnifier button on the graph toolbar a but ton that shows a magnifier lens to enlarge the central maximum and the first maximum on each side 9 Use the Smart Tool on the graph toolbar a button la beled with xy axes to measure the distance between the centers of the first minima on the two sides of the central maximum That is measure the distance between m 1 and m 1 Record the value in CI Data Table 1 10 Determine the distance y from the center of the pattern to one of the m 1
302. h I have no data I cannot tell he said Arthur Conan Doyle The Adventures of the Copper Beeches 1892 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Contents Key GL Guided Learning TI Traditional Instruction and CI Computer Instruction GL is associated only with TI experiments See Preface Preface Vil Introduction 1X Why We Make Experimental Measurements ix General Laboratory Procedures ix Experiments in the bound volume 1 Measurement Instruments Mass Volume and Density 21 GL The Scientific Method The Simple Pendulum 35 TI GL CI Uniformly Accelerated Motion Includes TI free fall AUN OOo 1 ON tA 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Experimental Uncertainty Error and Data Analysis 1 spark timer apparatus method at end of experiment 47 The Addition and Resolution of Vectors The Force Table 73 TI GL CI Newton s Second Law The Atwood Machine 83 TI CI Conservation of Linear Momentum 103 GL Projectile Motion The Ballistic Pendulum 127 Centripetal Force 141 10 GL Work and Energy 175 12 13 14 15 16 17 18 19 20 21 TI CD Friction 155 GL Torques Equilibrium and Center of Gravity 189 GL Simple Machines Mechanical Advantage 203 TI CI Simple Harmonic Motion 219 Standing Waves in a String 239 The Thermal Coefficient of Linear Expansion 249 Specific Heats of Me
303. h circuit component in series Remember an ammeter is always connected in series and for proper polarity is connected to Connect the voltmeter across in parallel with the voltage source After having the circuit checked by the instructor close the switch If using a variable power supply adjust the voltage if necessary to the sug gested value 3 0 V Read and record the voltmeter value V This is the voltage rise of the source Note If the needle of the ammeter goes in the wrong direction reverse the polarity that is reverse the hook up of the leads of the ammeter Open the circuit after completing the reading Using the resistor values and the measured voltage compute a the equivalent resistance R of the circuit b the current in the circuit and c the voltage drop across each resistor Show your calculations in the laboratory report Returning to the experimental circuit close the switch and read the current Compare this with the com puted value by finding the percent difference Open the switch and move the ammeter in the circuit to the position after the first resistor that is on the oppo site side of the resistor from the voltage source so as to measure the current through coming from the resistor Record this as J Carry out this procedure for each resistor and record the currents in the laboratory report Leave the switch closed only while readings are being taken Remove the ammeter
304. h is directly proportional to the time The results apply to any type of uniformly accelerated motion AY B Linear Air Track Types of linear air tracks are shown in TI Fig 4 2 Air is supplied to the interior of the hollow track and emerges through a series of small holes in the track This provides a cushion of air on which a car or glider travels along the track with very little friction an example of the use of a gaseous lubricant To have the car move under the influence of gravity one end of the air track is elevated on a block The acceleration of the car along the air track is then due to a component of the force due to gravity F ma mgsin0 e TI Fig 4 3 The acceleration a of the glider along the air track is a gsin TI 4 1 and from the geometry sin h L side opposite the angle over the hypotenuse Hence a TI 4 2 The magnitude of the instantaneous velocity v of the uniformly accelerating glider at a time t is given theoreti cally by v v at TI 4 3 Hence a graph of v versus t is a straight line y mx b with a slope m a Av At and an intercept b v If the car starts from rest the initial velocity v is zero and v at TI 4 4 www A TIBOOK ir T I EX PER IM ENT 4 Uniformly Accelerated Motion AY EQUIPMENT NEEDED A Object in Free Fall see TI Experimental Planning at the beginning of the experiment B Li
305. hanger Trial 1 Unbalance the system by transferring the l g piece from the ascending to the descending hanger At this time make a note of the ascending and the descending masses and enter the values in CI Data Table 2 Do not forget to include the mass of the hangers Collect the data as before and determine the experi mental acceleration Trial 2 Move one of the 2 g pieces from the ascend ing to the descending hanger and repeat the data collection process Note that this changes the amount of unbalanced force without changing the total mass of the system Trial 3 Move the other 2 g piece from the ascending to the descending hanger and repeat the data collection process 10 11 Trial 4 Move the 5 g piece from the ascending to the descending hanger and repeat the data collection process Calculate the net unbalanced force in newtons of each trial and enter the results in CI Data Table 2 Clear the graph window of any fit information and print the graph Label each of the plots with the unbalanced force corresponding to each trial Paste the graph to the laboratory report Calculate the theoretical acceleration for each trial using Eq CI 6 1 Compare the theoretical value with the experimental value by taking a percent error www ATIBOOK ir Name Section Date Lab Partner s C 1 EXPERIMENT 6 Newton s Second Law The Atwood Machine Rd Laboratory Report ED
306. hannel A of the interface as shown on the computer screen 7 Click on the picture of the signal generator The Sig nal Generator window will open 8 The default form of the signal generator function is a sine wave Change it to a positive square wave of amplitude 3 0 V Note Be sure to choose the Posi tive Square Wave not the one that says just Square Wave Scrolling down the list may be needed The frequency of the signal will depend on the values of R and C and will be entered later on g EXPERIMENTAL PROCEDURE 1 Measure the resistance of the resistor using a multi meter and record the value in CI Data Table 1 2 Measure the capacitance of the capacitor using a multi meter and record the value in CI Data Table 1 If the available multimeter does not measure capacitance then use the manufacturer s value as the capacitance 3 Calculate the theoretical time constant and enter the value in CI Data Table 1 www ATIBOOK ir EXPERIMENT 26 The RC Time Constant Electronic Timing 389 l The frequency is adjusted after a calculation See the Procedure Voltage Sensor Measurements Visibility Name Tm 700 fe Lon fx Sensor Sampling Options 1 Reduce comple te by ave mang zl Etfectrve Sample Rate E Hz Zeo senior automatic sly on start Zeto Sensor Reves sign of e sandes CI Figure 26 4 The Experiment Setup Window The voltage sensor is connected
307. harges that is in the direction of the force experienced by the positive test charge The electric field vectors for several series of radial points from a positive source charge are illustrated in e Fig 19 1a Notice that the lengths magnitudes of the vectors are smaller the greater the distance from the charge Why By drawing lines through the points in the direction of the field vectors the lines of force are formed Fig 19 1b www ATIBOOK ir 284 EXPERIMENT 19 Fields and Equipotentials Equipotentials E E a a SY X b Electric Field Lines a Electric Field Vectors lines of force N et LOE 4 Va PX Z 4 x c Dipole Electric Field Figure 19 1 Electric field a Electric field vectors near a positive charge b Lines of force with equipotentials for a positive charge c An electric dipole and its electric field The direction of the electric field at a particular location is tangent to the line of force through that point as illustrated on the bottom line of force which give a graphical representation of the electric field The direction of the electric field at a particular location is tangent to the line of force through that point Fig 19 1c The magnitudes of the electric field are not customarily listed only the direction of the field lines However the closer together the lines of force the stronger the field If a positive charge were rele
308. hat would be the period of a pendulum with a length of 1 0 m 5 Suppose the 1 0 m pendulum were operated on the Moon What would its period be there gum 8 6 45 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s A3 4 EX PERIMENT 4 Uniformly Accelerated Motion aj Experimental Planning 2 GL Figure 4 1 A daring experimenter See Experi mental Planning text for description A Object in Free Fall An object in free fall falls under the influence of gravity only resistance is neglected A good approximation to free fall in the laboratory is when dense objects fall for relatively short distances Use the following equipment to determine the acceleration due to gravity g continued www A TIBOOK ir EXPERIMENT 4 Experimental Planning EQUIPMENT NEEDED 3 objects of different masses for example steel balls and or lead weights Meter stick Laboratory timer or stopwatch One sheet of graph paper Review the definition of acceleration Which of the quantities involved can be directly measured with the given equipment The defining equation is not practical to use in many cases However the units for acceleration are distance and time m s and these quantities can be measured with the equipment given Can you give a kinematic equation for an object that is dropped no initial velocity that only involves length time
309. he Measurement of Resistance Laboratory Report B Wheatstone Bridge Method DATA TABLE 5 DATA TABLE 6 Purpose To measure resistance values Purpose To measure resistance values Accepted value of R Accepted value of R R L L R R L L R C C 3 6 C 2 C o o 1 1 2 2 3 3 Average R Average R Percent error Percent error Calculations show work AY QUESTIONS A Ammeter Voltmeter Methods 1 An ideal ammeter would have zero resistance and an ideal voltmeter would have an infinite resistance Explain why we would desire these ideal cases when using the meters continued 319 www A TIBOOK ir EXPERIMENT 21 The Measurement of Resistance Laboratory Report 2 If in general R were calculated as R V I which circuit arrangement in Part A of the experiment would have the smallest error Explain 3 a Prove that the true resistance R is given by R a R 1 3 R where R V I is the measured resistance as given by the voltmeter and ammeter readings for measurements done by the arrangement in Fig 21 2 or Fig 21 5b Is the true resistance larger or smaller than the apparent resistance b Prove that the true resistance R is given approximately by R R e 7 R where R V I is the measured resistance as given by the voltmeter and ammeter readings for measurements done by the arrangement in Fig 21 1 or Fig 21 5a Hint Use the bi
310. he SHM of a simple pendulum and the resulting conversion of energy kinetic and potential that occurs during the motion An electronic sensor measures the angular speed A0 At of the pendulum from which the tangential speed is computed and the energies calculated INTRODUCTION AND OBJECTIVES Elasticity implies a restoring force that can give rise to vibrations or oscillations For many elastic materials the restoring force is proportional to the amount of deformation if the deformation is not too great This is best demonstrated for a coil spring The restoring force F exerted by a stretched or compressed spring is proportional to the stretching compressing distance x or F x In equation form this is known as Hooke s law F kx where x is the distance of one end of the spring from its unstretched x 0 position k is a positive constant of proportionality and the minus sign indicates that the dis placement and force are in opposite directions The con stant k is called the spring or force constant and is a relative indication of the stiffness of the spring A particle or object in motion under the influence of a linear restoring force such as that described by Hooke s law undergoes what is known as simple harmonic motion SHM This periodic oscillatory motion is one of the common types found in nature In this experiment Hooke s law will be investigated along with the parameters and descrip
311. he block Record the results in TI Data Table 1 5 Plot the weight force just required to move the block or the maximum force of static friction F f versus the normal force N of the surface on the block N my m g Draw a straight line that best fits the data Include the point 0 0 Why Since f uN the slope of the straight line is us Determine the slope and record it in TI Data Table 1 B Determination of y HORIZONTAL BOARD 6 In the experimental setup in Fig 10 2 when the block moves with a uniform constant speed its accelera tion is zero The weight force F and the frictional force f are then equal and opposite F fi ma 0 and F f 7 Using the larger side surface area of the block and the series of added masses as in Part A add mass to the weight hanger until a slight push on the block will cause it to move with a uniform speed It may be EXPERIMENT 10 Friction 161 helpful to tape the weights to the block The required weight force for the motion in each case should be less than that for the corresponding case in Part A Why Record the data in TI Data Table 2 Suggested experimental technique Begin with the block at one end of the plane and give it a push so that it slides across the entire plane b Observe the behavior of the block in the same region as before namely in the middle of the plane This is where the block should be observed for constant speed wa
312. he floor determined 6 Besides the range what else is needed to determine the magnitude of the initial velocity of the ball C Projectile Range Dependence on the Angle of Projection 7 For a given initial velocity how does the range of a projectile vary with the angle of projection 0 8 Theoretically the angle of projection for maximum range is 45 Does this set a limit on the range Explain 130 www ATIBOOK ir EX PER Projectile Motion MENT 8 The Ballistic Pendulum INTRODUCTION AND OBJECTIVES Projectile motion is the motion of an object in a plane two dimensions under the influence only of gravity free fall air resistance neglected The kinematic equations of motion describe the components of such motion and may be used to analyze projectile motion In most textbook cases the initial velocity of a projectile speed and angle of projection is given and other quantities calculated However in this experiment the unknown initial velocity will be determined from experimental mea surements This will be done 1 through the use of the ballistic pendulum and 2 from range fall distance mea surements The dependence of the projectile range on the angle of projection will also be investigated so as to obtain an experimental indication of the angle of projection that gives the maximum range EQUIPMENT NEEDED Ballistic pendulum Sheets of plain paper and carbon paper Meter stick Protractor
313. he time constant or the decay constant is known Example 34 1 A radioactive sample has an activity of 4000 cpm What is the observed activity after three half lives Solution After one half life the activity decreases by 5 and after another half life by another 4 and so on Hence after three half lives the initial activity decreases by a fac tor of 1 X X i With N 4000 cpm 1 1 N aN z 4000 500cpm Notice that in general N N p where n is the number of half lives www ATIBOOK ir 494 EXPERIMENT 34 Radioactive Half Life Figure 34 1 The Cesium 137 Barium 137m Minigenerator system See text for description Fisher Scientific Com pany LLC Theory of Minigenerator The Cesium 137 Barium 137m Minigenerator Fig 34 1 is an eluting system in which a short lived daughter radioactive isotope is eluted separated by washing from a long lived parent isotope A small generator contains ra dioactive Cs 137 which has a half life of 30 years Cs 137 beta decays into Ba 137m which is an isomeric excited state of the stable nucleus Ba 137 The excited isomer Ba 137m has a relatively short half life and gamma decays into Ba 137 The nuclear equation for the decay is ICs gt ZBa e cesium barium electron excited Wa 7 barium gamma ray where the asterisk indicates an excited state The origi nal nucleus Cs is commonly referred to as the parent Regist
314. heat and also the mechanical equivalent of heat ENT 2 4 In many electrical applications such as electrical motors joule heat is an undesirable loss of energy How ever in other applications such as toasters and electrical heaters electrical energy is purposefully converted into heat energy In this experiment the heating effect of an electrical current and the electrical equivalent of heat will be investigated After performing this experiment and analyzing the data you should be able to 1 Describe what is meant by joule heat 2 Explain the factors on which joule heat depends 3 Tell how joule heat may be measured experimentally EQUIPMENT NEEDED Electrocalorimeter immersion heater and calorimeter Power supply or battery 12 V Ammeter 0 A to 3 A Voltmeter 30 V Rheostat 40 Q Connecting wires Thermometer Stopwatch or laboratory timer Laboratory balance Ice THEORY The work W done or energy expended per unit charge in moving a charge q from one point to another is the poten tial difference or voltage V that is or W qV 24 1 The time rate of flow of charge is described in terms of current J and 24 2 2 Hence Eq 24 1 may be written W qV IVt 24 3 which represents the work done or the energy expended in a circuit in a time f Dividing this by gives the work or energy per time or power P 361 2
315. hen www ATIBOOK ir 4 EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis the measurement is repeated several times Determinate means that the magnitude and sign of the uncertainty can be determined if the error is identified Conditions from which systematic errors can result include 1 An improperly zeroed instrument for example an ammeter as shown in Fig 1 1 2 A faulty instrument such as a thermometer that reads 101 C when immersed in boiling water at standard atmospheric pressure This thermometer is faulty because the reading should be 100 C 3 Personal error such as using a wrong constant in cal culation or always taking a high or low reading of a scale division Reading a value from a measurement scale generally involves aligning a mark on the scale The alignment and hence the value of the reading can depend on the position of the eye parallax Examples of such personal systematic error are shown in e Fig 1 2 OC AMPERES FISHER STANS Figure 1 1 Systematic error An improperly zeroed instrument gives rise to systematic error In this case the ammeter which has no current through it would systematically give an incorrect reading larger that the true value After correcting the error by zeroing the meter which scale would you read when using the ammeter Avoiding systematic errors depends on the skill of the Observer to recognize the sources of such errors and to prevent
316. here C is the capacitance of the capacitor in farads F The rate of voltage rise depends on the capacitance of the capacitor and the resistance in the circuit Similarly when a charged capacitor is discharged the rate of voltage decay depends on the same parameters Both the charging time and discharge time of a capacitor are characterized by a quantity called the time EQUIPMENT NEEDED e Two capacitors for example 1000 uF and 2200 uF electrolytic Two resistors for example 4 5 kO and 10 KQO Power supply or battery 12 V constant 7 which is the product of the capacitance C and the series resistance R that is 7 RC In this experiment the time constants and the charging and discharging char acteristics of capacitors will be investigated After performing this experiment and analyzing the data you should be able to 1 Explain the RC time constant and what its value means in terms of circuit characteristics 2 Describe how a capacitor charges and discharges through a resistor as a function of time 3 Tell how an RC time constant may be measured experimentally High resistance digital readout voltmeter Single pole double throw SPDT switch Connecting wires Laboratory timer 2 sheets of Cartesian graph paper THEORY When a capacitor is charged through a resistor by a dc voltage source the single pole double throw switch S in position a in Fig 25 1 the charge in the capacitor and the volta
317. hip between the angle of rotation of a mirror and the angle of deflection of a ray Figure 27 6 Mirror rotation An illustration of the exper imental arrangement and procedure for the rotation of a mirror See text for description B Refraction INDEX OF REFRACTION OF A GLASS PLATE 10 Lay the glass plate in the center of a sheet of paper 11 and outline its shape with a pencil Fig 27 7 Draw a line normal to one of the sides of the plate and place a pin R at the intersection of this line and the face of the plate Measure an angle 0 of 15 relative to this line and place a pin A about 6 to 8 cm from the plate at this angle Then sighting through the edge of the plate from the eye position shown in Fig 27 7 place a pin A adjacent to the face of the plate so that it is aligned with R and A Mark and label the locations of the pins Repeat with pins B and C at angles of 30 and 45 respectively For the 45 angle case align an additional pin C Fig 27 7 Trace the various rays and measure and record 0 and 0 for each case Also measure and record the displacement d of ray C C from the normal and the thickness of the plate Using Eq 27 3 compute the index of refraction of the glass Compare the average experimental value of the index of refraction with the general range of the index of refraction of glass n 1 5 1 7 depending on type Figure 27 7 Index of refraction An illustration
318. his with your eyes on a level with the index screw Caution Why is it a good precaution to wear safety glasses while doing this The pointer will be slightly erratic and as a particular speed is reached it will jump and may point slightly above the index screw 7 If so adjust the speed so that the pointer is horizontally toward the index screw Z Do not exceed this speed The pointer should be aimed at the head of the index screw when the rotor is spinning at higher speeds too Why Do not lock the friction disk Rather observe and adjust the speed of the rotor continuously during each timed interval in order to keep the pointer as steady as possible Continuous adjustment is necessary because the rotor speed varies when the counter is engaged Because the pointer will point horizontally at excessive speeds and induce experimental error an alternative technique is to adjust the rotor speed con tinually so that the pointer is not quite horizontal that is so that it is aimed midway or just below the head of the index screw Experiment with your apparatus and see which technique is better trying to maintain the pointer horizontally at the critical jump speed or aiming the pointer at a lower position on the screw at a slightly slower speed Practice engaging the counter and adjusting the rotor speed Do not engage the counter too forcefully or you will overly slow down the rotor yet don t engage the counter so ligh
319. hold voltage the number of counts per minute increases rap idly In this region about 50 V wide beginning at about 600 V to 700 V depending on the tube the count rate is almost linearly proportional to the voltage This is because as the voltage increases more of the less ener getic particles are counted Hence in this region the tube discriminates between particles of different energy At a given voltage only particles above a certain energy are detected The tube then acts as a proportional counter the voltage being proportional to the energies of the inci dent particles Eventually as the voltage is increased the number of counts per minute becomes almost independent of the applied voltage the level region in Fig 33 3 This region about 200 V wide is called the plateau of the tube A change in voltage has little effect on the number of counts detected Normally the Geiger tube is operated at a volt age in about the middle of the plateau Fluctuations in the applied voltage from the power supply will then have little effect on the counting rate The tube voltage should never be raised to a value far above that of the end of the plateau At such high voltages a continuous discharge sets in and if allowed to persist this may destroy the tube H PI E ateau z i Voltage V Threshold voltage Figure 33 3 Count rate versus tube voltage A typical graph showing how the count rate varies with Geiger tube voltage No
320. how 3 Compute the values of R and the voltage drops across this resistance for the two situations in TI Data Table 1 reading 1 How do the values compare 302 www ATIBOOK ir C Ohm s Law S courment NEEDED This activity is designed for the Science Workshop 750 Interface which has a built in function generator It is eas ily adapted to use with an external wave function genera tor Just substitute the available triangle function generator for the signal generator in the procedure E X P ER M ENT 2 0 100 0 resistor 2 cables with alligator clips 6 V lightbulb Voltage sensor PASCO CI 6503 Science Workshop 750 Interface ED mory As discussed in the TI Theory section for many materials the resistance remains constant over a range of voltages Such materials are called ohmic and they obey Ohm s law IR CI 20 1 For such a material a graph of voltage versus current is a straight line the slope of which is the value of the resis tance as shown in TI Fig 20 1 In this CI part of the experiment the relationship between current and voltage for both an ohmic and a nonohmic component of a circuit will be investigated The current will be measured as the voltage across a component is steadily increased and decreased If the component is ohmic the current should be directly proportional to the voltage To achieve a steadily increasing and decreasing volt age a signal generator is used
321. hree terms in the series for an angle of 5 Is it bigger than 1 0 by very much At what angle 0 would the first three terms add up to 1 05 a 5 difference Do you think it is reasonable to say that as long as the angle 6 is less than a certain value then to a very good approximation T That is sin J F sinf 2 lt lt 1 Why or why not 5 gt WT PP g A 2 64 2 y y 36 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 The Scientific Method The Simple Pendulum RW Advance Study Assignment Read the experiment and answer the following questions 1 Describe what is meant by the scientific method and how it is applied 2 What are the physical parameters in the investigation of a simple pendulum 3 A period is an interval of time How is this applied to a pendulum 4 What is the difference between an independent variable and a dependent variable Give an example of each 37 continued www A TIBOOK ir EXPERIMEN T 5 How does the period of a pendulum vary theoretically with a length b mass of bob c angular displacement 6 How will you experimentally check the theoretical predictions in the preceding question 7 What is meant by a small angle approximation 8 How can the parabolic form y ax be plotted as a straight line on Cartesian graph paper 38 Advance Study Assignment www A TIBOOK ir EX PER MENT 3 The Scientifi
322. hs as required Note In this experiment and throughout attach an additional sheet for calculations if necessary www ATIBOOK ir Figure 1 8 Straight line slope Displacement cm 90 80 70 60 50 40 30 20 10 EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis 13 7A Displacement d vs time t for uniform motion O i 1 i i Ay 85 40 45cm 1 T i Ay 45 i Slope amp 507S cm s i i i 1 ME e AX IBERBEREEREREA Ax 11 0 5 0 6 0s LLL T T T T Ay 25 10 15cm i Ay _ 15 Slpe 7 zg 9 ems S Ra Hoo Ax 3 0 1 0 2 0s 0 2 0 4 0 6 0 8 0 10 0 Time s Examples of intervals for determining the slope of a straight line The slope is the ratio of Ay Ax or Ad At Any set of intervals may be used but the endpoints of an interval should be relatively far apart as for Ay AX www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Na
323. ht in the medium and 0 and 0 are the angles of incidence and refraction respectively If the incident light beam is not monochromatic each component wavelength color is refracted differently This is why white light incident on a glass prism forms a spectrum Fig 30 1 The material is said to exhibit dispersion The explanation of this effect has to do with the speed of light In vacuum the speed of light is the same for all wavelengths of light but in a dispersive medium the speed of light is slightly different for different wavelengths The frequencies of the light components are unchanged Since the index of refraction n of a medium is a function of the speed of light n c v c A f where the wave speed 441 in the medium is v m f the index of refraction will then be different for different wavelengths It follows from Snell s law Eq 30 1 that different wavelengths of light will be refracted at different angles The dispersion of a beam of white light spreads the transmitted emergent beam into a spectrum of colors red through violet see Fig 30 1 The red component has the longest wavelength so it is deviated least The angle violet Red Orange Yellow Green Blue Violet The dispersion of light by a glass Figure 30 1 Dispersion prism causes white light to be spread out into a spectrum of colors The angle between the original direction of the beam and the emergent component is called the a
324. ht source consists of a large number of waves emitted by the atoms or molecules of the source Each atom produces a wave with its own orientation of the E and B vibration corresponding to the direction of the atomic vibration However with many atoms all directions are possi ble The result is that the emitted light is unpolarized The vibration vectors are randomly oriented with all directions equally probable This is represented schematically in TI Fig 29 2a which views the E vectors along the axis of propagation B vectors are not represented If for some reason the light vectors become preferen tially oriented the light is partially polarized TI Fig 29 2b Should there be only one direction of vibration for the E TI Figure 29 1 Electromagnetic wave An illustration of an electromagnetic wave The electric and magnetic field vectors E and B vibrate at right angles to each other and perpendicularly to the direction of propagation vectors TI Fig 29 2c the light is then linearly polarized This is sometimes called plane polarized or simply polarized light The direction of vibration of the E vector defines the plane or direction of polarization The polarization of light may be effected by several means a selective absorption b reflection c refrac tion and d scattering Let s take a look at these A Polarization by Selective Absorption Certain crystals are doubly refracting or exhibit birefring
325. ian graph paper and draw a straight line that best fits the data Determine the slope of the line and compute the linear absorp tion coefficient u Note from Eq 35 6 that the slope has a magnitude of ux 13 Optional Your instructor may wish you to use semi log graph paper This special graph paper auto matically takes in values of the variable plotted on the y axis See Appendix D for a discussion of graphing on semi log and log log graph paper Compute the mass absorption coefficient um for lead Pp 11 3 g cm Compare the experimental values to the accepted value of ju 0 10 cm g for gamma rays by computing the percent error for each www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 5 The Absorption of Nuclear Radiation RW Laboratory Report DATA TABLE 1 Purpose To determine sheet thicknesses Cardboard Aluminum Lead 6 2 6 Average sheet thickness Calculations show work Don t forget units 505 continued www ATIBOOK ir EXPERIMENT 8 amp 8 A Absorption of Beta Radiation DATA TABLE 2 Purpose To determine the relation between intensity and thickness Cardboard Number of sheets n 0 1 Intensity The Absorption of Nuclear Radiation Number of sheets Laboratory Report Aluminum Intensity cpm Qj Range of beta radiation cm Range of beta radiati
326. iation of the i data point from this line is then y y The principle of least squares may be stated as fol lows The best fitting straight line is the one that mini mizes the sum of the squares of the deviations of the measured y values from those of the predicted equation y 2 m x b The numerical values of the slope m and intercept that minimize the sum of the squares of the deviations Y y may be found using differential calculus i l The results are as follows and Exercises b y mx where x and y are the mean values x N y 25 and Me ll x and N ay x eo N My XG x ll zm Sa i 1 where the sums of the deviations for example X x x are Zero 1 Plot the data given in Data Table 1 on a sheet of graph paper and draw the straight line you judge to fit the data best 2 Using the method of least squares find the slope and intercept of the best fitting straight line and compare them with the slope and intercept of the line you drew in Exercise 1 Plot this best fitting line on the graph Recall that the slope of a line is the change in y for a unit increase in x DATA TABLE 1 Ji Xi 25 12 44 28 78 47 80 70 43 16 58 53 95 72 67 38 Sums 2 i 1 www A TIBOOK ir APPENDIX E Graphing Exponential Functions In some cases exp
327. ical values with the measured ones by taking a percent difference Using the printout of the graph or the Smart Tool on the graph toolbar determine the maximum value of the voltage and the maximum value of the current for each run Report them in CI Data Table 2 Resistances in Parallel Delete all the data to clear the graph Also clear all the fits Run 1 Connect resistor R alone to the voltage source and take data as before Do a linear fit and report the measured resistance in CI Data Table 3 Introduce resistor R to the circuit by connecting it in parallel with resistor R Connect the voltage sensor across both R and R See CI Fig 23 6 Run 2 Press START and collect the data Do a linear fit and report the measured resistance in CI Data Table 3 Now introduce resistor R to the circuit by connecting it in parallel with R and R Connect the voltage sensor across the three resistors See CI Fig 23 6 Run 3 Press START and collect the data Do a linear fit and report the measured resistance in CI Data Table 3 RUN 3 Output current p Voltage Voltage sensor sensor Three different series circuits will be analyzed each time adding an extra resistor www A TIBOOK ir EXPERIMENT 23 Resistances in Series and Parallel 353 RUN 1 Output current Signal v Voltage generator sensor RUN 2 RUN 3 ae at eg a ll qe ee Cer ae eee mI UPS Output Output current current i e Ro
328. icon to view a D 324 measurement EXPERIMENT 32 Single Slit and Double Slit Diffraction 473 Light Intensity Ch Avs Postion Ch 1 amp 2 No Data Postion Cn 162 m CI Figure 32 4 Data Studio setup A light sensor together with a rotary motion sensor will be used to produce a plot of light intensity versus position for diffraction and interference patterns Reprinted courtesy of PASCO Scientific 11 12 Create a graph by dragging the Light Intensity icon from the Data list and dropping it on top of the Graph icon of the Displays list A graph of intensity versus time will open in a window called Graph 1 Now drag the Position icon from the data list and drop it on top of the horizontal axis of the graph The horizontal axis will change to measure position in stead of time CI Fig 32 4 shows what the screen should look like after the setup is complete a EQUIPMENT SETUP 1 Mount the single slit accessory to the optics bench The slit disks are mounted on a ring that snaps into an empty lens holder Rotate the ring in the lens holder so that the slits at the center of the ring are vertical in the holder Then tighten the screw on the holder See e CI Fig 32 5 Align the laser beam with the slit a Mount the diode laser at one end of the bench Put the slit holder a few centimeters away from the laser with the disk side closer to the laser Plug in the laser and turn it on b Adjust
329. idth 0 04 mm This time title the graph Graph 4 Double Slit Pattern d 0 50 mm w 0 04 mm www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s C EXPERIMENT 3 2 Single Slit and Double Slit Diffraction amp Laboratory Report Wavelength of light A A The Single Slit Pattern Slit width w Distance between slit and pattern L ED omame Purpose To compare the experimental single slit pattern with the pattern predicted by theory Order of Distance Distance y Calculated Predicted Percent distance from from center Ym R mA difference sin 0 sin 0 mtom to m L w m 1 m 2 m 3 m 4 ED omame Purpose To determine the wavelength of light using a single slit diffraction pattern Calculated Order of Calculated LENS Ym minimum sin 0 L m 1 m 2 m 3 m 4 Average Percent error Be sure to attach a copy of the graph to the report Don t forget units continued 477 www A TIBOOK ir EXPERIMENT 3 2 _ Single Slit and Double Slit Diffraction Laboratory Report B The Double Slit Pattern Slit width w Separation of slits d Distance between slit and pattern L Hy DATA TABLE 3 Purpose To compare the experimental double slit pattern with the pattern predicted by theory Distance Distance y Calculated
330. iently possible After completing Procedure 6 ask the instructor to elevate one end of the air track on a block or obtain permission to do so Measure h and L see TI Fig 4 3 and enter your results in TI Data Table 2 Tf electronic photogate timers are available your instructor will give you instruction in their use Electronic timing greatly improves the accuracy and precision of the results Why 8 10 11 12 Start the car from rest near the elevated end of the air track To minimize error it is better to put a block or pencil in front of the car and pull this away smoothly rather than releasing the car by hand Measure and record the times required for the car to travel the distances listed and record your results in TI Data Table 2 Use the experimental method described in Procedure 6 Have the end of the air track elevated to a different height and repeat the time measurements for this height Using Eq TI 4 5 compute the instantaneous veloc ity of the car for each of the times in the three experi mental sets of data in TI Data Table 2 Plot v versus t for each case on the same graph and determine the slope of each line Using Eq TI 4 2 compute an experimental value of the acceleration due to gravity a g for each of the elevated air track cases Compute the percent error for each experimental result www ATIBOOK ir Name Section Date Lab Partner s T EX PERIMENT
331. ight it examines the conditions for single slit dark fringes and double slit bright fringes INTRODUCTION AND OBJECTIVES In Experiment 30 the prism spectrometer had to be cali brated in terms of known wavelengths before being able to determine unknown wavelengths of light experimentally How then are the wavelengths of spectral lines or colors initially determined This is most commonly done with a diffraction grating a simple device that allows for the study of spectra and the measurement of wavelengths By replacing the prism with a diffraction grating a prism spectrometer Experiments 30 and 31 becomes a grating spectrometer When a diffraction grating is used the angle s at which the incident beam is diffracted relate simply to the wavelength s of the light In this experiment the properties of a transmission grating will be investi gated and the wavelengths of several spectral lines will be determined RV OBJECTIVES After performing this experiment and analyzing the data you should be able to 1 Describe the principle of a diffraction grating 2 Explain the operation of a grating spectrometer 3 Tell how the wavelength of light can be measured with a grating spectrometer ET ossectives A diffraction grating has many slits But what about us ing a single slit or a double slit When illuminated with monochromatic light these slits produce interference and diffraction patterns with bright and dark fringes
332. ight in the medium Hence the index of refraction of vacuum is n c c 1 and for air n c c 1 For water n 1 33 Snell s law can then be written sin v c n m sin 0 vo c n5 ny ni sin 0 n sin 0 27 3 where n and n are in indices of refraction of the first and second media respectively From Eq 27 2 it can be seen that the index of refraction is a measure of the speed of light in a transparent material or a measure of what is called the optical density of a material For example the speed of light in water is less than that in air so water is said to have a greater optical density than air Thus the greater the index of refraction of a material the greater its optical density and the lesser the speed of light in the material In terms of the indices of refraction and Snell s law Eq 27 3 there are the following relationships for refraction or If the second medium is more optically dense than the first medium n gt n the refracted ray is bent toward the normal 0 lt as in Fig 27 3 If the second medium is less optically dense than the first medium n lt n the refracted ray is bent away from the normal 05 gt 0 as for the reverse ray trac ing in Fig 27 3 EXPERIMENTAL PROCEDURE A Reflection GLASS PLATE AS A MIRROR 1 Place a sheet of white paper on the table As illustrated in Fig 27 4 draw a line where the candle or object will be placed The line
333. ill make sure the calcu lation of the cosine is done in degrees not in radians www ATIBOOK ir 13 14 15 16 d Press the Accept button after entering the equa tion The variables M L and x will appear in a list with x waiting to be defined e Define x as a Data Measurement and when prompted choose Angular Position deg f Press the Accept button Close the calculator window The data list on the upper left of the screen should now include icons for the three quantities that are cal culated V KE and PE A small calculator icon will show on the left of the calculated data quantities Create a graph by dragging the Angular Position deg data icon and dropping it on top of the Graph icon on the displays list A graph of angular position deg versus time will open The window will be called Graph 1 Drag the KE equation icon and drop it somewhere on top of the graph created in step 15 The graph will then split in two with the graph of angular po sition versus time on top and the graph of KE versus time on the bottom The graphs will have matching time axes DataStudio F e Edt Exe Window Dey Hob EXPERIMENT 14 Simple Harmonic Motion 235 17 Repeat step 15 to create a second graph window Graph 2 will also be a graph of angular position deg versus time 18 Drag the PE equation icon and drop it on Graph 2 Graph 2 will then split in two showing both the posi tion and the P
334. illustrate each case using the Case 1 diagram as an example Attach a sheet to the Laboratory Report showing calculations for each use Don t forget units continued 199 www ATIBOOK ir EXPERIMENT 12 Torques Equilibrium and Center of Gravity Laboratory Report Moment Diagram Values add m to masses lever Results if clamps are used arms Case 3 X1 ni my known measured T m X m ___ known from expt calculated Percent error Case 4 instructor s option Draw a diagram to illustrate each case using the Case 1 diagram as an example Attach a sheet to the Laboratory Report showing calculations for each use B Apparatus Supported at Different Pivot Points DATA TABLE 2 Linear mass density of meter stick y m L Values Moment i T Diagram add m if applicable lever Results arms Case 5 a x T 7 Tien My X2 P Tow Lm N im i x Torque difference show below table Case 5 b m X ri Tee n X5 ra Tow M3 X3 Ta Torque differences show below table Xo Draw a diagram to illustrate each case using the Case 5 a diagram as an example Put the mass of a length of stick in parentheses as in that diagram Attach a sheet to the Laboratory Report showing calculations for each use 200 www ATIBOOK ir Name Section Lab Partner s EXPERIMENT 12 Torques Equilibrium and Center of G
335. imble is in the first or the second half of the www A TIBOOK ir EXPERIMENT 2 Measurement Instruments Mass Volume and Density 27 main scale division Notice that the zero mark on the thim ble is used to indicate both 0 00 mm beginning of the first rotation and 0 50 mm beginning of the second rotation Measurements are taken by noting the position of the edge of the thimble on the main scale and the position of the reading line on the thimble scale For example for the drawing in Fig 2 5 the mike has a reading of 5 785 mm On the main scale is a reading of 5 000 mm plus one 0 500 mm division scale below reading line giving 5 500 mm That is in the figure the thimble is in the second rota tion of a main scale division The reading on the thimble scale is 0 285 mm where the 5 is the estimated or doubtful figure That is the reading line is estimated to be midway between the 28 and the 29 marks Some mikes have vernier scales on the sleeves to help the user read this last signifi cant figure and further extend the precision As with all instruments a zero check should be made and a zero correction applied to each reading if neces sary as described in Section B A zero reading is made by rotating the screw until the jaw is closed or the spindle comes into contact with the anvil The contacting surfaces of the spindle and anvil should be clean and free of dust Micrometers can be adjusted to zero readings by means of a
336. in CAR MOVING UP THE PLANE The situation for a car moving up an inclined plane with a car moving up constant velocity is illustrated in GL Fig 11 1 Since the car is not accelerating the force up the plane F must be CAR MovivG DOWN THE PLANE 2L equal in magnitude to the sum of the forces down parallel The situation for a car moving down an inclined plane with to the plane that is the same constant speed is illustrated in Fig 11 2 Again since the car is not accelerating the sum of the forces up F F f the plane must be equal in magnitude to the force down the plane taken as positive and where f is the force of friction and F m g sin is the component of the car s weight parallel to the plane See ae ea GL Fig 11 1 here in thi he directi ffi ien Si Since the magnitude of F is equal to the weight w of M aah a ae a ea aa F wy the suspended mass m then w2 H w tf H f w and expressing f as before Solving for f and expressing the other forces in terms of the experimental parameters GL Fig 11 1 f mg sind mg 11 2 f w Fi car moving down 181 www ATIBOOK ir 182 EXPERIMENT 11 Work and Energy T F Al aft Fatt Ww Figure 11 2 Car moving down the incline with the same con stant speed as in Fig 11 1 With no acceleration the force on the car is zero and Fj F f w f see free body diagrams Then in either case the frictional work is given by W fd 11 3
337. in a horizontal circle around one s head 6 Fig 9 1 the centripetal force F ma is supplied by the person and transmitted to the ball through the rope In the absence of the centripetal force for example if the rope breaks or if the person re leases the rope the ball would no longer be held in orbit and would initially fly off in the direction of its tangential velocity v An object in uniform circular motion moves with a constant speed Even though the object s speed is constant its velocity is changing because the direction of the motion is continually changing This change in velocity results from a centripetal acceleration a that is due to the applied centripetal force F The direction of the acceleration and 143 force is always toward the center of the object s circular path and it can be shown see your textbook that the mag nitude of the acceleration is given by 9 1 centripetal acceleration where v is the tangential or orbital speed of the object and r is the radius of the circular orbit By Newton s second law F ma the magnitude of the centripetal force is 9 2 F ma centripetal force www A TIBOOK ir 144 EXPERIMENT 9 Centripetal Force Figure 9 1 Centripetal acceleration An object in uni form circular motion must have a centripetal acceleration with a magnitude of a v r directed toward the center of the circular path In the case of swinging
338. ing back and forth is called the period T of the pendulum If your physics lab has the appropriate equipment available you could verify that statement d above is the most accurate negligible friction Now consider what might affect the pendulum s period Look at Fig 3 1 again and list the physical parameters that could be changed 3 Did you find three things Let s consider the length L first How do you think the pendulum s length might affect the period If the length of the pendulum were doubled would the period 7 also double directly proportional Or would it be half of what it was before inversely proportional Or could it be larger or smaller by some other proportion Write down the relationship that you think is most appropriate 4 The mass rn of the pendulum bob may be varied The effect this would have on the period might possibly depend on air resistance so let s suppose there isn t any If the pendulum were swinging in a vacuum would the mass make any difference continued 35 www ATIBOOK ir EXPERIMENT Experimental Planning To verify your response look at the forces acting on the bob Draw a free body diagram one showing the forces for the bob when it would be in the position shown in Fig 3 1 What is the component of the weight force mg that acts in the direction of motion 5 Check with one of your fellow students or your instructor to see if the results agree Notice that there are no other f
339. ing the pendulum parameters of length and period as was done previously Squaring both sides of Eq 3 2 3 3 or Hence the equation has the form y ax that of a parabola This can be plotted as a straight line with the general form y ax by letting L y and x T that is plotting 7 on the X axis The line will have a slope of a g 4zr Plot L versus T for the best experimental data lowest percent error in Data Table 3 and determine the slope of the graph Compute the experimental value of g Record this in the Laboratory Report and compute the percent error of the result www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Lab Partner s Section Date EX P ER MENT 3 The Scientific Method The Simple Pendulum RV Laboratory Report DATA TABLE 1 Purpose To investigate the small angle approximation Mass m Pendulum length L Period T Angle 6 PIENE Conclusion Experimental Theoretical EOD 5 o 10 20 30 45 DATA TABLE 2 Purpose To investigate period dependence on mass 0 L m T Percent Conclusion C Experimental Theoretical SHOE Don t forget units 43 www ATIBOOK ir EXPERIMENT 3 The Scientific Method The Simple Pendulum Laboratory Report DATA TABLE 3 Purpose To investigate period dependence on length 0 m L T Percent
340. ing the switch A Variation of Current with Voltage 3 After the instructor has checked the circuit close the switch and read the voltage and current on the meters Open the switch after the readings are taken and record them in TI Data Table 1 Repeat this procedure for a series of four successively lower rheostat settings along the length of the rheostat It is convenient for data analysis to adjust the rheostat after closing the switch so that evenly spaced and convenient ammeter readings are obtained The switch should be closed only long enough to obtain the necessary readings This prevents unnecessary heating in the circuit and running the battery down Repeat Procedure 3 for another value of R about 30 2 Repeat Procedure 3 for the unknown resistance and record the data in TI Data Table 2 Relatively low values of voltage may be required Your instructor will discuss this and the proper connection Do not perform this procedure without instructions 6 B 8 10 EXPERIMENT 20 Ohm s Law 297 Plot the results for both decade box resistances on a single V versus graph and draw straight lines that best fit the sets of data Determine the slopes of the lines and compare them with the constant values of R of the decade box by computing the percent errors According to Ohm s law the corresponding values should be equal Plot V versus J for the unknown resistance What conclusions about the unkn
341. ion Stop rotating the prism at the position of the reversal of motion of the yellow component of the A77 Figure 30 5 Determination of the angle of minimum Figure 30 4 Determination of the prism angle An illustra deviation An illustration of the prism orientation for the tion of the prism orientation for the experimental procedure experimental procedure to determine the angle of minimum to determine the prism angle A deviation www ATIBOOK ir i4 EXPERIMENT 30 The Prism Spectrometer Dispersion and the Index of Refraction spectrum This is the position for minimum deviation of this component Being careful not to disturb the prism center the tele scope cross hairs on the middle of the yellow color band and record the divided circle reading Also mea sure the angle readings for each end of the visible spectrum that is the red and blue violet ends Do this by setting the cross hairs of the telescope at the locations where the spectrum ends are just visible not at the center of the extreme bands Compute the index of refraction for yellow light using Eq 30 2 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 0 The Prism Spectrometer Dispersion and the Index of Refraction RWV Laboratory Report Measurement of Prism Angle A Calculations Circle readings show work for reflected images Computation of 2A Prism angle A Measurement of Angle of Minimum Deviation
342. iplies force but what is reduced or sacrificed for this force multiplica tion Give a specific example 3 a State how the AMA and TMA of an inclined plane vary with the inclination of the plane b State how the efficiency of an inclined plane varies with the inclination of the plane and explain the reason for this variation 4 In going up stairs the climb seems easier when going up in a zig zag fashion rather than straight up Why is this 5 Show that the TMA of a lever can be derived from torque considerations See Fig 13 2a 6 A single fixed pull is often called a direction changer rather than a force multiplier Explain why this is an appropriate name continued 217 www ATIBOOK ir EXPERIMENT 13 Simple Machines Mechanical Advantage Laboratory Report 7 The TMA of a pulley system with movable pulley s or a block and tackle is equal to the number of supporting strands of the movable pulley or block a Do your experimental results support this statement b Explain the physical basis of this statement 8 Give three common applications of the wheel and axle Hint Is a screwdriver a wheel and axle 9 Estimating the radii of a common doorknob and its shaft how much force is applied to the shaft mechanism when the knob is turned with an applied force of 2 0 N 218 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 414 Simple Harmonic Motion f Advance Study A
343. is continually stressed and highlighted in the manual This critical issue is expanded upon in the Introduction to the manual Advance Study Assignments Students often come to the laboratory unprepared even though they should have read the experiment before the lab period to familiarize themselves with it To address this problem an Advance Study Assignment precedes each experiment The assignment consists of a set of questions drawn from the Theory and Experimental Procedures sections of the experiment To answer the questions students must read the experiment before the lab period consequently they will be better pre pared It is recommended that the Advance Study Assignment be collected at the beginning of the laboratory period www ATIBOOK ir viii PREFACE Example Calculations In the Theory section of some experiments sample calculations that involve the equations and mathematics used in the experiment have been included where appropriate These demonstrate to the student how experimental data are applied Illustrations Over 200 photographs and diagrams illustrate experimental procedures equipment and computer pro grams To allow for variation in laboratory equipment differ ent types of equipment that can be used are often illustrated Laboratory Reports Because a standardized format for laboratory reports greatly facilitates grading by the instructor a Laboratory Report is provided for both TI and CI experiments Th
344. istor As the charge in the capacitor decreases the voltage across the capacitor also decreases The decrease is exponential and as a function of time it is described by the equation V Vie CI 26 6 In this case notice that one time constant after the dis charge begins the voltage across the capacitor will be 37 of the original fully charged voltage of V V Ve V e o Ve 0 37V CI 26 7 Thus the discharging of the capacitor can also be used to find the time constant experimentally by determining how long it takes for the voltage to decrease to 37 of the initial maximum value In this experiment the charging and discharging of the capacitor will be observed in a plot of voltage versus time The time constant of the circuit will be directly measured from the plot SETTING UP DATA STUDIO 1 Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There are seven channels to choose from and a signal gen erator Digital channels 1 2 3 and 4 are the small buttons on the left analog channels A B and C are the larger buttons on the right the signal generator is all the way to the right as shown in CI Fig 26 4 4 Click on the channel A button in the picture A win dow with a list of sensors will open 5 Choose the Voltage Sensor from the list and press OK 6 Connect the sensor to c
345. ith a slow uniform speed on being given a slight tap Use as close to the same speed as for the upward case as is possible This cor responds to the situation in Fig 11 2 Record the total suspended mass in Data Table 1 For convenience use the same d or h as in Procedure 4 Compute the frictional force f Eqs 11 1 and 11 2 and work done against friction W Eq 11 3 for each case Show your calculations and record the results in Data Table 1 Te EXPERIMENT 11 Work and Energy 183 b a Inclined plane with board and stand b Calibrated incline plane Photos Courtesy of Compare the frictional work for the two cases by com puting the percent difference 8 Adjust the angle of the inclined plane to 0 45 and repeat Procedures 3 through 7 recording your mea surements in Data Table 2 Energy Method 9 10 Knowing that d h compute W for the previous cases using the energy method Eqs 11 4 and 11 5 on the appropriate laboratory report pages Compare these values of W with those found using the force distance method by computing the percent differences www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Lab Partner s Section Date EX PER Work and Energy RWV Laboratory Report DATA TABLE 1 Purpose To determine work done against friction Car moving up incline m Suspended mass MENT 1 1 d Angle
346. ith the tension force in the string and or the linear mass density of the string 5 Standing waves in a string can be produced by oscillating the string at the various natural frequencies However in this experiment the string vibrator has only one frequency How then are standing waves with different wavelengths produced 240 www A TIBOOK ir EX P E RI MENT 1 5 Standing Waves in a String INTRODUCTION AND OBJECTIVES A wave is the propagation of a disturbance or energy When a stretched cord or string is disturbed the wave travels along the string with a speed that depends on the tension in the string and its linear mass density Upon reaching a fixed end of the string the wave is reflected back along the string For a continuous disturbance the propagating waves interfere with the oppositely moving reflected waves and a standing or stationary wave pattern is formed under certain conditions These standing wave patterns can be visually observed The visual observation and measurement of standing waves serve to provide a better understanding of wave properties and characteristics In this experiment the relationship between the tension force and the wavelength in a vibrating string will be studied as applied to the natural frequencies or normal modes of oscillation of the string After performing this experiment and analyzing the data you should be able to 1 Explain how standing waves are formed 2 Disting
347. itted light intensity Note the orientation of the plane of polarization of the middle polarizer relative to the planes of the outer two for maximum transmission Make a sketch of the polarizers in the laboratory report and indicate the planes of polarization for the polarizers for this condition Hint Draw three polarizers of different sizes and label the outer two as 1 and 2 and the middle po larizer as 3 Is there more than one orientation of the middle polarizer for maximum transmission Rotate through 360 If so are the angles between the po larization planes different Explain in the laboratory report why this transmission through the outer crossed polarizers is observed www ATIBOOK ir EXPERIMENT 29 Polarized Light B Polarization by Reflection and Refraction 4 Using a general value of the index of refraction of glass as n 1 6 compute in the laboratory report the reflection polarization angle 6 5 a With a single glass microscope slide on the tri pod stand positioned near the edge of the table shine light on the slide at an angle of incidence equal to the computed 0 Observe the reflected light through an analyzer at the angle of reflec tion and examine for polarization Note the axis of polarization of the reflected light Observe the reflected light through polarizing sunglasses and comment Observe the light transmitted through the glass slide with an analyzer for any evidence of polariza
348. ity Newton s first law of motion A stationary object is said to be in translational static equilibrium 193 In this experiment the rigid body a meter stick is restricted from linear motion so this is not a consideration To be in static equilibrium a rigid body must also be in rotational static equilibrium Although the sum of the forces on the object may be zero and it is not moving linearly it is possible that it may be rotating about some fixed axis of rotation However if the sum of the torques is zero r 0 the object is in rotational equilibrium and either it does not rotate static case or it rotates with a uniform angular velocity Forces produce linear motion and torques produce rotational motion Torque is a quantitative measure of the tendency of a force to cause or change the rotational motion of a rigid body A torque or moment of force results from the applica tion of a force acting at a distance from an axis of rotation e Fig 12 1 The magnitude of the torque is equal to the product of the force s magnitude F and the perpendicular www ATIBOOK ir 194 EXPERIMENT 12 Torques Equilibrium and Center of Gravity Axis of rotation perpendicular to Force plane on paper line of action F Figure 12 1 Torque The magnitude of a torque is equal to the product of the magnitude of the force F and the perpendicular distance lever arm r from the axis of rotation to the force s line o
349. ks as a multimeter The signal generator of the Science Workshop interface is used as the voltage source that produces a positive ramp up function Reprinted courtesy of PASCO Scientific Signal Generator PSI ES E Positive Up Ramp wave un Off Frequency Amplitude 2 000 V 0 200 Hz Tano 1 000 lt gt 100 Measurements And Sample Rate MiMeasure Output Voltage Sample Rate Measure Output Current 100 Hz CI Figure 23 2 The Signal Generator window Choose a positive up ramp wave function adjust the amplitude and the frequency as specified in the setup procedure and choose to measure the output current Reprinted courtesy of PASCO Scientific d Press the Accept button e Click on the New button again to define another calculation f Clear the definition box and enter the following formula in it Current smooth 20 x g Press the Accept button after entering the formula Notice that the variable x will again appear wait ing to be defined h This time define x as a Data Measurement and when prompted choose Output Current i Press Accept again 13 The data list on the top left of the screen should now have the following items Voltage ChA Output Current Voltage and Current where a small calculator icon iden tifies the quantities that are calculated not measured 14 Drag the Voltage calculator icon from the data list and drop it on the Graph ico
350. l 1 sheet of log log log graph paper 3 cycle THEORY The three types of nuclear radiation alpha beta and gamma are all capable of ionizing a gas The degree of ionization depends on the energy of the particles and the amount of radiation absorbed by the gas The ionization of gas molecules by nuclear radiation is the principle of the Geiger tube A Geiger tube consists of a fine wire running axially through a metal cylinder filled with a gas usually argon at a pressure of about 0 1 atm 6 Fig 33 1 A potential dif ference or voltage is maintained between the central wire and the cylinder the central wire being at a positive poten tial with respect to the cylinder Energetic nuclear particles ionizing radiation passing through the cylinder and entering the tube ion ize the gas molecules The freed electrons are attracted toward the wire and the positive ions toward the cyl inder If the voltage between the wire and cylinder is great enough the accelerated electrons acquire enough energy to ionize other gas molecules on their way to the positive wire The electrons from the secondary ioniza tions produce additional ionizations This process is called cumulative ionization As a result an avalanche discharge sets in and a current is produced in the resistor This reduces the poten tial difference between wire and cylinder to the point where cumulative ionization does not occur After the momentar
351. l tape label on the cars so that you will not confuse them later This information will be needed during the setup of Data Studio 115 Cart string bracket IDS cart IDS track CI Figure 7 1 Installing cart string brackets The cart string brackets are installed on top of the collision carts secured with a side screw The top screw is used to tie a string When mea suring the mass of the car include the cart string bracket www ATIBOOK ir 116 EXPERIMENT 7 Conservation of Linear Momentum SETTING UP DATA STUDIO Second Measurements tab select Velocity and deselect all others 1 Open Data Studio and choose Create Experiment Rotary Motion Sensor tab set the Resolution to 2e Tis Experiment Setup window sillopen atd you wall high 1440 divisions rotations and set the Linear see a picture of the Science Workshop interface There Scale to Large Pulley Groove are seven channels to choose from Digital channels Set the Sample Rate to 100 Hz 1 2 3 and 4 are the small buttons on the left ana log channels A B and C are the larger buttons on the right as shown in CI Fig 7 2 10 3 Click on the Channel 1 button in the picture A win dow with a list of sensors will open 4 Choose the Rotary Motion Sensor from the list and 9 Click on the icon of the second sensor and repeat the process of adjusting the properties as done in step 8 Open the program s calculator by clicking on the Calculate button on the t
352. lanced for a reading and not rotating about some point or axis of rotation The criterion for rotational static equilibrium is that the sum of the torques or moments of force acting on a rigid body be equal to zero To study torques and rota tional equilibrium we will use a beam balance in the form of a meter stick and suspended weights The torques of a setup will be determined experimentally by the moment of force method and the values compared Also the concepts of center of gravity and center of mass will be investigated After performing this experiment and analyzing the data you should be able to 1 Explain mechanical equilibrium and how it is applied to rigid bodies 2 Distinguish between center of mass and center of gravity 3 Describe how a laboratory beam balance measures mass EQUIPMENT NEEDED Meter stick Support stand Laboratory balance String and one knife edge clamp or four knife edge clamps three with wire hangers Four hooked weights 50 g two 100 g and 200 g Unknown mass with hook THEORY A Equilibrium The conditions for the mechanical equilibrium of a rigid body are YXF 0 x7 0 12 1a 12 1b That is the vector sums of the forces F and torques 7 acting on the body are zero The first condition XF 0 is concerned with translational equilibrium and ensures that the object is sta tionary not moving linearly orthatitis moving withauniform linear veloc
353. larization rotate your analyzer to see whether there is any preferential direction of polarization Should it not be a sunny day try this with your own polarizing sunglasses some fine day E Optical Activity 9 10 11 12 View a mica sheet between crossed polarizers Rotate the analyzer and note the change What changes the general pattern shape or its colors Form a pattern or symbol by sticking various layers of cellophane tape on a glass plate or slide For example try a V or wedge shape with one two three etc layers of tape in different parts of the V Observe the tape symbol between crossed polarizers Rotate the analyzer You may wish to make letters or symbols for example your school letters with pieces of tape cut with a sharp knife or razor blade Could you give the letters your school colors Observe the various shaped pieces of plastic between crossed polarizers Stress the pieces by pulling or pushing on them but not so hard as to break them Can you explain what is observed View an LCD through an analyzer Rotate the ana lyzer Is the light coming from the lighted portion of the display polarized Note You can do this at home using polarizing sunglasses www ATIBOOK ir Name Section Date Lab Partner s T EXPERIMENT 29 Polarized Light RWV Laboratory Report A Plane of Polarization Transmission 1 Transmission Angle 0 between polarizer planes
354. laws But the thermal expansion of liquids and solids is no less impor tant For example such expansions are used to measure temperature in liquid in glass thermometers and bimetallic oven thermometers In general for solids a temperature increase leads to the thermal expansion of an object as a whole This expansion results from a change in the average distance separating the atoms or molecules of a substance The atoms are held together by bonding forces which can be represented simplistically as springs in a simple model of a solid e Fig 16 1 The atoms vibrate back and forth and with increased temperature more internal energy they become increasingly active and vibrate over greater distances With wider vibrations in all dimensions the solid expands as a whole This may be different in different directions however if the expansion is the same in all directions it is referred to as isotopic expansion The change in one dimension length width or thickness of a solid is called linear expansion For 251 small temperature changes linear expansion is approxi mately proportional to AT or the change in temperature T T Fig 16 2 The fractional change in length is L L L or AL L where L is the original length of the solid at the initial temperature This ratio is related to the change in temperature by aAT or AL aL AT 16 1 where AL L L and AT T T and a is the
355. led y and the elapsed time f of fall are measured variables for determining acceleration Now consider the other two variables in Newton s second law F and m For the Atwood machine can you think of how the net force can be expressed in terms of both masses weights on the hangers Remember the m in F 4 ma represents the total mass of the system that moves with acceleration a A free body diagram may be helpful here Substitute your expression for the net force in Newton s second law F ma and solve for a m m Did you get a Uni cum m m Note for the Atwood machine how both hanging masses can be varied How could you 1 vary the total mass while keeping the net force F constant and 2 vary the net force while keeping the total mass constant Think about it 84 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 6 Newton s Second Law The Atwood Machine RV Advance Study Assignment Read the experiment and answer the following questions 1 Write Newton s second law in mathematical form and describe how the acceleration of an object or system varies with a net force and mass of the system 2 What are F and m in Newton s second law in terms of the Atwood machine 3 Explain how F and m are individually varied while the other is held constant Why is this done 85 continued www ATIBOOK ir EXPERIMEN TT 6 Advance Study Assignment 4 How can the friction
356. ler Set the high voltage control to the mini mum setting Rate meter Set the high voltage control to the minimum setting The off on switch is commonly on the high voltage control A selector switch is labeled with volts and counts per minute multiplier positions X1 X10 etc When the Geiger tube voltage is ad justed by means of the high voltage control the selec tor switch should always be set on volts The selector switch is then turned to the appro priate count multiplier range for counting The meter display scale usually has dual calibrations in volts and counts per minute 2 Plug in and turn on the counter Place the radioactive source near the Geiger tube with the source facing the probe opening as in Fig 33 2 A tube mount may be available for an end window tube The source is placed at the bottom of the tube mount in this case Note The end window is very fragile and can be punctured easily Slowly increase the tube voltage by means of the high voltage control until the first indication of count ing is observed Then increase the voltage to about 75 to 100 V above this value Set the counter to the counting mode and adjust the distance of the source from the tube or add alumi num sheets to the end window tube mount so that the count rate is several thousand 3000 to 5000 counts per minute The Geiger tube is then operating nor mally and the dead time will not cause serious error Tube Volta
357. ltage V can be maintained constant by adjusting R AY EXPERIMENTAL PROCEDURE 1 With the voltmeter measure the terminal voltage of the power supply or battery and record it in the lab oratory report Start with the voltmeter connection to the largest scale and increase the sensitivity by changing to a smaller scale if necessary Most com mon laboratory voltmeters and ammeters have three scale connections and one binding post common to all three scales It is good practice to take measurements initially with the meters connected to the largest scales This prevents the instruments from being pegged the www A TIBOOK ir needle forced off scale in galvanometer type meters and possibly damaged should the magnitude of the voltage or current exceed the smaller scale limits A scale setting may be changed for greater sensitivity by moving the connection or turning the switch on a multimeter to a lower scale after the general magni tude and measurement are known Also take care to ensure the proper polarity and connect plus to plus and minus to minus Otherwise the meter will be pegged in the opposite direction Set up the circuit shown in the circuit diagram TI Fig 18 3 with the switch open A standard decade resistance box is used for R Set the rheostat resistance R for maximum resistance and the value of the R to about 50 O Have the instructor check the circuit before clos
358. ltage source constant Do not forget to recalculate and adjust the required frequency of the positive square wave func tion Report the results as Trial 2 in CI Data Table 1 www A TIBOOK ir Name Section Date Lab Partner s C EXPERIMENT 2 6 The RC Time Constant Electronic Timing Rd Laboratory Report ED ons nie Purpose To experimentally determine the time constant of the RC circuit Trial 1 Trial 2 Theoretical R Values C T theo Time to fully charge 2d TT theo Output Period T Signal Frequency f Experimental Vmax Values Charging 0 63 of Vinax Texp Percent error Discharging 0 37 of Vinax Texp Percent error Don t forget units 391 www A TIBOOK ir EXPERIMENT 26 TheRC Time Constant Electronic Timing Laboratory Report ED questions 1 Show by dimensional analysis that the time constant 7 RC has units of time 2 Compare the charging and discharging of the capacitors from Trial and Trial 2 What things were similar and what things were different Be specific 3 Suppose that a particular RC series circuit has a time constant of 5 0 seconds What does that mean in terms of the charging and discharging How would this circuit compare to the ones you tried Explain qualitatively and quantitatively 4 What could be a practical application of an RC circuit 392 www A TIBOOK ir Name Section Date
359. luminum before being completely absorbed Beta radiation then does penetrate a Geiger tube Both 501 alpha and beta particles of a given energy therefore have a definite range of penetration in a particular material e Figure 35 1 illustrates the radiation intensity in counts per minute cpm versus absorber thickness for a relatively low density absorber for radiation from a beta gamma source The bend in the curve indicates the range of the beta radiation The penetration for thickness beyond this is due to gamma radiation Gamma rays which consist of electromagnetic radiation of very short wavelength are not readily absorbed A sig nificant number of high energy gamma rays can penetrate cm or more of a dense material such as lead In a given material a beam of gamma rays is absorbed exponentially The intensity in cpm of the beam after passing through a certain thickness x of a material is given by where is the original intensity at x 0 and the decay constant u is called the linear absorption coefficient 35 1 www ATIBOOK ir 502 EXPERIMENT 35 The Absorption of Nuclear Radiation Intensity cprn Absorber thickness Figure 35 1 Radiation intensity versus absorber thickness A typical graph of radiation intensity versus absorber thickness for beta gamma radiation by a low density absorber The range is that of the beta radiation The absorption coefficient is characteristic of the absorb ing mat
360. ly but carefully lift the cup with the hot metal from the boiler and pour the metal shot into the calorimeter cup with as little splashing as possible so as not to splash out and lose any water If a solid piece of metal is used carefully lower the metal piece into the calorim eter cup by means of the attached string Replace the lid with the thermometer and stir the mixture gently The thermometer should not touch the metal While stirring watch the thermometer and re cord the temperature when a maximum equilibrium temperature is reached 7 For best results the final temperature T should be above room temperature T by about as many degrees as T was below it If this is not approximately the case repeat Procedures 4 through 6 adjusting T until the relationship 7 T T T is satisfied Place the calorimeter cup with the water and stir 7 Repeat Procedures 1 through 6 for another kind of rer in the calorimeter jacket and put on the lid with a metal sample Make certain that you use fresh water thermometer extending into the water in the calorimeter cup Dump the previous metal shot and water into a strainer in a sink so that it may After the water in the boiler boils and the thermome be dried and used by others doing the experiment ter in the metal has stabilized allow several minutes later read and record the temperature of the metal Tn 8 Compute the specific heat of each metal using Tf the cup an
361. lyzed as follows The average velocity v of an object traveling a distance y in a time t is defined as y 2 TI 4 2A f 3 Keep in mind that y and are really length and time intervals or the differences between corresponding instan taneous lengths and times Referenced to an initial posi tion and time y and Ay y y and At f f arbitrarily taking y 0 and Af 1 It is these intervals that will be measured from the data tape For a uniformly accelerated object moving with a constant acceleration as in the case of free fall the aver age velocity is given by Vi F Vs TI 4 3A 5 y where v and v are the instantaneous velocities at times f and t respectively Why is this Consult your textbook Then equating the expressions for v given by TI Eq 4 2A and TI Eq 4 3A and solving for v we have YitVo Ji EM ti and 2y v Ys TI 4 4A If v 0 that is the object falls from rest then 2yi y TI 4 5A AY EXPERIMENTAL PROCEDURE 1 Your laboratory instructor will make a data tape for you or assist and direct you in obtaining one Care must be taken in aligning the apparatus D Caution When working with high voltages one must be careful not to receive an electrical shock Do not touch metal parts when the spark timer is on 2 Record the time interval of the spark timer used on the data tape and draw s
362. m as the ascending and descending masses respectively the magnitude of their acceleration is given by F a net m m g CI 6 1 Moora m m where the friction and inertia of the pulley have been ignored In this part of the experiment the motion of the ascending and descending masses is analyzed by using a motion sensor to look at the motion of the pulley The main idea is that all the objects in the system the ascend ing mass the descending mass and the pulley must be moving with the same linear speed at any moment The linear speed of the pulley is measured as the speed of a point on the rim The sensor detects how many revolutions per second the pulley is making the angular speed For a known radius of pulley the linear speed on the rim is eas ily determined v ro where o is the angular speed The sensor performs this calculation automatically Notice that by measuring the linear speed of the pulley the ascending speed of mass m and the descending speed of mass m are also measured The measured speeds will then be plotted as a function of time Because the acceleration of the system is constant the plot of speed versus time will be a straight line with slope equal to the acceleration of the system The experi mental acceleration of the system will be determined by finding the slope of the graph It will then be compared to the theoretical value predicted by Eq CI 6 1 See Eq
363. m maximum range Angle of projection for Angle of Average range maximum range from graph projection 20 30 40 45 50 60 70 138 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 8 Projectile Motion The Ballistic Pendulum Laboratory Report fr questions A The Ballistic Pendulum 1 Is the collision between the ball and the pendulum elastic or inelastic Justify your answer by calculating the kinetic energy of the system before collision using the value of found v found in the experiment and the kinetic energy just after collision using the experimental value of h in Eq 8 2 2 Using the results of Question 1 that would apply if the collision were inelastic find the fractional kinetic energy loss during the collision Express the loss as a percent What became of the lost energy 3 Expressing the kinetic energy in terms of momentum K mv p 2m prove using symbols not numbers that the fractional loss during the collision is equal to M m M 4 Compute the fractional energy loss from the experimental mass values using the equation developed in Question 3 and compare this to the result in Question 2 Explain the difference if any continued 139 www ATIBOOK ir EXPERIMENT 8 _ Projectile Motion The Ballistic Pendulum Laboratory Report 5 Is the friction of the pendulum catch mechanism support axis e
364. machine is defined as F AMA 13 1 F where F and F are the output and input forces respec tively The AMA is the force multiplication factor of the machine For example if AMA 2 F F then F 2F or the output force is twice the input force In no case is work multiplied by a machine If this were the case for more work output than work input en ergy would have to be created However the total work energy is conserved Total work in total work out useful work work done against friction 209 or W Wo We Fd Fd We 13 2 where d and d are parallel distances through which the respective forces or component of forces act work force X parallel distance W Fd and W is the work done against friction In actual situations there is always some work energy input lost to friction If a machine were frictionless W 0 then Fid F d For this theoretical situation a theoretical mechanical advantage TMA can be expressed as F di TMA F d This is an ideal situation and the theoretical mechani cal advantage is sometimes called the ideal mechanical advantage IMA 13 3 www ATIBOOK ir 210 EXPERIMENT 13 Simple Machines Mechanical Advantage Note that the TMA is the ratio of the distances through which the forces act and thus depends on the geometrical configuration of the machine That is the distances can be determined by measurement from the machine
365. mage can be formed on a screen Common plane mirrors form vir tual images In general an image is described in terms of whether it is 1 Real or virtual 2 Upright erect or inverted relative to the object orientation and 3 Magnified or reduced or smaller In Fig 28 2a the image is real inverted and reduced in Fig 28 2b the image is virtual upright and reduced The distance from the object to the vertex along the optic axis is called the object distance d and the dis tance from the vertex to the image is the image distance d Knowing the focal length f of the mirror the position of the image d can be found using the spherical mirror equation 28 2a Another convenient form of this equation is do f d f In the case of a concave mirror the focal length is taken to be positive for a convex mirror the focal length is taken to be negative The object distance d is taken to be positive in either case The resulting sign con vention is as follows If d is positive the image is real and if d is negative the image is virtual The magnification factor M is given by d 28 2b M 28 3 If M is positive with d negative the image is upright if M is negative with d positive the image is inverted The sign convention is summarized in Table 28 1 TABLE 28 1 Sign Convention for Spherical Mirrors and Lenses Quantity Conditions Sig
366. mall circles around the burn spots so that their locations can be easily seen Occasionally a spot of the sequence may be missing for example due to local misalignment of the wires However it is usually easy to tell that a spot is missing by observa tion of the tape Do not try to guess where the spot should be Simply make a mark on the tape to indicate that a spot is missing Through each spot draw a straight line perpendicular to the length of the tape Using the line through the beginning spot as a reference y 0 measure the distance of each spot line from the reference line y4 Yo Y3 etc Write the measured value of the distance on the tape by each respective spot line Making use of the known spark timer inter val write the time taken for the object to fall a given distance on the tape by each spot line taking f 0 at y 0 For example if the timer interval is djs the time interval between the reference line y 0 and the first spot line yj is t djs and the time taken to fall to the second spot line y is b d qas Do not forget to account for the time intervals associated with missing spots if any Record the data measured from the tape in TI Data Table 1 Using TI Eq 4 5A compute the instanta neous velocity of the falling object at each spot line from the experimental data and record At this point you should realize that the instantaneous velocities given by TI Eq
367. mass and hanger set a 50 g hanger will work fine with no added mass For all data collection and calculations keep track of the total ascending and descending masses including the mass of the hanger www A TIBOOK ir EXPERIMENT 6 Newton s Second Law The Atwood Machine 99 n Photogate Smart Pulley Rod Descending and mass clamps Ascending mass CI Figure 6 3 Experimental setup A Photogate Pulley System Smart Pulley is used instead of a conventional pulley to set up the Atwood machine The ascending mass starts near the bottom close to but not touching the floor The descending mass starts from rest at the top The Smart Pulley measures the speed of the system as it moves 3 When the ascending and descending masses are equal the system should not move If it does check that the pulley is level 4 Trial 1 Add a 5 g piece to the descending mass to unbalance the system Make a note of the ascending and descending masses in CI Data Table 1 Do not forget to account for the mass of the hangers 5 Place the ascending mass at the bottom and the ascending mass at the top as shown in CI Fig 6 3 Gently hold the pulley to prevent the system from moving 6 Let the system start from rest by letting go of the pul ley Once it starts moving press the START button Keep your eyes on the system and press the STOP button before the masses reach the end of their line and bounce If the hangers
368. me Section Date Lab Partner s EX PERIMENT 31 Experimental Uncertainty Error and Data Analysis RV Laboratory Report 1 Least Counts a Given meter length sticks calibrated in meters decimeters centimeters and millimeters respectively Use the sticks to measure the length of the object provided and record with the appropriate number of significant figures in Data Table 1 DATA TABLE 1 Purpose To express least counts and measurements Object Length m dm cm mm Actual length Provided by instructor after measurements Comments on the measurements in terms of least counts b Find the percent errors for the four measurements in Data Table 1 DATA TABLE 2 Purpose To express the percent errors Object Length Least Count Error Comments on the percent error results 2 Significant Figures a Express the numbers listed in Data Table 3 to three significant figures writing the numbers in the first column in normal notation and the numbers in the second column in powers of 10 scientific notation 15 continued www ATIBOOK ir EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis Laboratory Report DATA TABLE 3 Purpose To practice expressing significant figures 0 524 5280 15 08 0 060 1444 82 453 0 0254 0 00010 83 909 2 700 000 000 b A rectangular block of wood is measured to have the dimensions 11 2
369. mentally A ossectives Experimentally verify Newton s second law of motion in two ways 1 By keeping the net force on a system constant and varying the mass and 2 By keeping the mass of the system constant and vary ing the net force 87 www A TIBOOK ir 88 EXPERIMENT 6 Newton s Second Law The Atwood Machine TI Figure 6 1 The Atwood machine a A single or double pulley system is simply a direction changer and it is sometimes convenient to draw a horizontal diagram for analysis b A double pulley system eliminates the possibility of the passing weights hitting each other which may occur with a single pulley of small diameter c A wall mounted precision Atwood machine A trip platform sup ports the upper weight before the start of each run and is released and reset by control cords Photos courtesy of Sargent Welch www A TIBOOK ir T I EX P E R IM ENT 6 Newton s Second Law The Atwood Machine RV EQUIPMENT NEEDED Pulley preferably low inertia precision ball bearing type Clamps and support rods Two weight hangers Set of slotted weights including small 5 2 and 1 g weights Paper clips String Laboratory timer or stopwatch Meter stick 2 sheets of Cartesian graph paper RV THEORY The light string is considered to be of negligible mass Masses m and m are taken as the ascending and descend ing sides of the system respectively Fig TI
370. ments RV QUESTIONS 1 Look up the density of the metal of the object used in Parts A and B of the procedure and compare it with the experimental value If there is any difference comment on the reason s continued 277 www A TIBOOK ir EXPERIMENT 18 Archimedes Principle Buoyancy and Density Laboratory Report 2 In Part B the string will cause error When does it lead to an experimental density that is too high Too low 3 Discuss the situation that occurs when an object is immersed in a fluid that has the same density as the object 4 a Explain how a submarine is caused to submerge and surface without the use of its propulsion propeller and fins b Which has the greater density 1 ice or water 2 milk or cream 5 A block of wood floats in a beaker of water According to Archimedes principle the block experiences an upward buoyant force If the beaker with the water and floating block were weighed would the measured weight be less than the sum of the weights of the individual components Explain 278 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 18 Archimedes Principle Buoyancy and Density Laboratory Report 6 A person can lift 45 kg 100 Ib Using the experimental value of the specific gravity for the metal object in Part B how many cubic meters of the metal could the person lift a in air b in water How many actual kilograms of metal is this in air and in wate
371. meter does not have a ratchet mechanism so as not to damage the measured object and or the micrometer The axial main scale on the sleeve is calibrated in millimeters and the thimble scale is calibrated in 0 01 mm hundredths of a millimeter The movement mechanism of the micrometer is a carefully machined screw with a pitch of 0 5 mm The pitch of a screw or the distance between screw threads is the lateral linear distance the screw moves when turned through one rotation Fig 2 5b The axial line on the sleeve main scale serves as a reading line Since the pitch of the screw is 0 5 mm and there are 50 divisions on the thimble when the thimble is turned through one of its divisions the thimble moves and the jaws open or close s of 0 5 mm or 0 01 mm a5 X 0 5 mm 0 01 mm One complete rotation of the thimble 50 divisions moves it through 0 5 mm and a second rotation moves it through another 0 5 mm for a total of 1 0 mm or one scale division along the main scale That is the first rotation moves the thimble from 0 00 through 0 50 mm and the second rotation moves the thimble from 0 50 through 1 00 mm It is sometimes instructive to think of the 1 mm main scale divisions as analogous to dollar divisions and of the thimble scale divisions as cents 0 01 The first rotation of the thimble corresponds to going from 0 00 to 0 50 50 cents and the second rotation corresponds to Anvil Spindle Sleeve Digi osa f f E
372. metrical optics these phenomena are ex plained by the behavior of light rays Through ray tracing the physical laws of reflection and refraction can be con veniently investigated in the laboratory In this experiment a plane mirror and a glass plate will be employed to study these laws and the parameters used in describing the reflec tion and refraction of light After performing this experiment and analyzing the data you should be able to 1 Describe the law of reflection and explain how it can be verified experimentally 2 Explain Snell s law and its application to transparent materials 3 Explain what the index of refraction tells you about a transparent material and how it can be measured experimentally EQUIPMENT NEEDED Pins Pin board cardboard or poster board suffices Sheets of white paper 83 X 11 in Ruler and protractor Short candle less than 5 cm or some similar light source Rectangular mirror and holder if available Thick glass plate approximately 8 X 10 cm Note Ray boxes may be used if available THEORY A Reflection When light strikes the surface of a material some light is usually reflected The reflection of light rays from a plane surface such as a glass plate or a plane mirror is described by the law of reflection The angle of incidence 0j is equal to the angle of reflection 0 that is 0 0 These angles are measured from a line perpendicular or normal
373. minary investigation it is found that the period of a pendulum depends on its length the longer the length the greater its period How do you think the other parameters m and 0 affect the period 39 Figure 3 1 The simple pendulum The physical parameters of a simple pendulum are its length L the mass m of the bob and the angle of swing 0 The period T of a pendulum is the time it takes for one completed oscillation for example the time it takes to swing from A to B and back to A www ATIBOOK ir 40 EXPERIMENT 3 The Scientific Method The Simple Pendulum From physical principles and advanced mathematics the theoretical expression for the period of a simple pendu lum oscillating in a plane is L 1 0 9 0 T 1 sin 4 sint 3 1 g 4 2 64 2 where g is the acceleration due to gravity and the terms in parentheses are part of an infinite series In calculating T for a given angular distance 0 the more terms of the series that are evaluated the greater the accuracy of the theoretical result For small angles 0 x 20 the 0 terms in the series are small compared to unity that is 1 sin Z sin lt lt 1 and in this case to a good approximation 3 2 This is called a first order approximation If the second term in the series is retained the approximation is to sec ond order and so on Notice that even without an approximation Eq 3 1 the period i
374. movable pulley Notice that the weight of the movable pulley is part of the load The TMA is the ratio of the distances through which the forces act and since ideally W W as in the previous case TMA 2 13 9 d h pulley s where h and h are the vertical heights through which the input and output forces act respectively For example for a single movable pulley Fig 13 3b suppose the load is moved a distance h upward To move the load an up distance h each suspending string must be shortened a distance h and therefore the applied force must move downward a distance 2h Note that the sus pended movable pulley adds to the weight of the load since the weight of the pulley is also lifted by the applied force The AMA is measured when the load is lifted with a uniform speed so that acceleration is not a consideration The mechanical advantage is based on the minimum input force which may be obtained when the system is in static equilibrium in which case the net vertical force is zero To lift the load a slight tap or force would have to be given to put the system in motion A set of fixed and movable pulleys is called a block and tackle The pulleys called sheaves pronounced shevs may be arranged in tandem which is the config uration commonly used in the laboratory to make it easier to thread the pulleys Fig 13 4a Or the pulleys may have a common axis of rotation for compactness in many practic
375. n Focal length f Concave mirror Concave mirror Concave lens Concave lens Object distance d Usually always in this experiment os Image distance d Image real Image virtual Magnification M Image upright Image inverted In some cases of lens combinations d may be negative when the image of one lens is used as the object for the next lens www A TIBOOK ir Example 28 1 An object is placed 45 cm in front of a concave mirror with a focal length of 15 cm cor responding to the case in Fig 28 2a Determine the image characteristics analytically Neglect significant figures Solution With d 45 cm and f 15 cm Eq 28 2a 1 1 1 3 45 d 15 45 Then 1 1 4 or dge son d 45 45 45 2 Then di 22 5 cm 1 M d 45 cm 2 Thus the image is real positive d inverted nega tive M and reduced by a factor of that is one half as tall as the object B Spherical Lenses The shapes of biconvex and biconcave spherical lenses are illustrated in Fig 28 3 A radius of curvature is ra eo Principal axis F Te F ES ito Biconcave Diverging Lens Figure 28 3 Sphericallenses a A biconvex or converg ing lens and b a biconcave or diverging lens showing the refraction of parallel incident rays EXPERIMENT 28 Spherical Mirrors and Lenses 407 defined for each spherical surface but only the focal points one for each spherical sur
376. n B oix Case 3 Omin B osx Case 4 Omin osx Average Attach the graph to the laboratory report Don t forget units 437 continued www ATIBOOK ir EXPERIMENT 29 Malus s Law Laboratory Report ED questions 1 Discuss how well the experimental results match the theory 2 What are sources of experimental error in this activity 438 www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 0 The Prism Spectrometer Dispersion and the Index of Refraction AY Advance Study Assignment Read the experiment and answer the following questions 1 What is meant by dispersion 2 Is the index of refraction of a dispersive medium the same for all wavelengths Explain this in terms of the speed of light in the medium 3 What is meant by the angle of deviation for a prism 439 continued www A TIBOOK ir EXPERIMENT amp Advance Study Assignment 4 What is the condition for the angle of minimum deviation At this angle what is the relation of the transmitted ray to the base of the prism 5 What are the four major components of the prism spectrometer and their functions 6 Which color of visible light has the greatest prism dispersion 440 www A TIBOOK ir EX PE RI M ENT 3 0 The Prism Spectrometer Dispersion and the Index of Refraction INTRODUCTION AND OBJECTIVES In vacuum the speed of light c 3 0 X 105 m s is the same for all wavelen
377. n Date Lab Partner s TI EXPERIMENT 4A Uniformly Accelerated Motion RWV Laboratory Report Free Fall Timer Apparatus RV DATA TABLE 1 Purpose To determine g experimentally Spark timer interval Distancey Timef Computed velocity v 2y f y ti Vi y2 ty Y ys ts V3 Y4 t4 Va M ts Vs Y6 t6 V6 Y7 t V7 Js tg Vg Yo ty Vo X10 fio Vio Yu ty Vu Ju fi Vi X13 13 V13 Y14 fj Via Js fis Vis Calculations Value of g from graph show work attach graph to lab report units Percent error Initial velocity at y continued 71 www ATIBOOK ir EXPERIMENT 4A Uniformly Accelerated Motion Laboratory Report Ary questions 1 Suppose that a different spark timer interval were used How would this affect the slope of the graph of v versus 2 What would be the shape of the curve of a y versus t graph of the experimental data 3 If t O were taken to be associated with some line spot other than y for example y instead how would this affect the v versus t graph 4 Calculate v directly from the first two measurement entries in TI Data Table 1 using the equation v 2y t yj t Your instructor can derive this for you How does this compare with the value determined from your graph 72 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 5 The Addition and R
378. n affected 266 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 17 Specific Heats of Metals Laboratory Report b If some water had splashed out as you were pouring dry shot into the cup how would the experimental value of the specific heat have been affected 4 In solar heating applications heat energy is stored in some medium until it is needed for example to heat a home at night Should this medium have a high or a low specific heat Suggest a substance that would be appropriate for use as a heat storage medium and explain its advantages 5 Explain why specific heat is specific and how it gives a relative indication of molecular configuration and bonding 267 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 8 Archimedes Principle Buoyancy and Density AY Advance Study Assignment Read the experiment and answer the following questions 1 Describe the physical reason for the buoyant force in terms of pressure 2 Show that the buoyant force is given by F p gV using the development in the Theory section 3 Give the conditions on densities that determine whether an object will sink or float in a fluid 4 Distinguish between density and specific gravity and explain why it is convenient to express these quantities in cgs units 269 continued www ATIBOOK ir Ee ee Ve Ne Advance S
379. n of the displays list A graph of voltage versus time will open in a window called Graph 1 15 Drag the Current calculator icon from the data list and drop it on top of the time axis of Graph 1 The time axis will change into a current axis The graph should now be of voltage versus current CI Fig 23 3 shows what the screen should look like at this point 16 Double click anywhere on the graph The graph settings window will open Make the following selections Under the tab Appearance Data Connect data points in bold Deselect the buttons marked Show Data Points and Show Legend Symbols Click OK to accept the changes and exit the graph settings window www ATIBOOK ir DataStudio Ee Edt Expetment Window Display Help EXPERIMENT 23 Resistances in Series and Parallel 351 BE E Setup gt w E Rd ChA V i Voltage smooth 20 x Output Current A li Current smooth 20 x 12 Voltage vs Current an Digits ka FFT Graph Graph 1 i Histogram Q Meter Scope E Table E Workbook BENEXEE 008 Voltage vs Current No Data Current CI Figure 23 3 Data Studio setup A graph of voltage versus current will be used to examine different simple circuits The slope of the graph will represent the resistance of the circuit Reprinted courtesy of PASCO Scientific g EXPERIMENTAL PROCEDURE A Measuring Resistance 1 Get three resistors and label them R R3 an
380. n spectroscopic analysis two types of spectra are observed continuous spectra and line or discrete spectra The spectrum of visible light from an incandescent source is found to con sist of a continuous spectrum or band of merging colors and contains all the wavelengths of the visible spectrum However when the light from a gas discharge tube for example mercury or helium is observed through a spectroscope only a few colors or wavelengths are observed The colored images of the spectroscope slit appear as bright lines separated by dark regions hence the name line or discrete spectra Each gas emits a particular set of spectral lines and hence has a characteristic spectrum Thus spectroscopy the study of spectra provides a method of identifying elements The discrete lines of a given spectrum depend on the atomic structure of the atoms and are due to electron transitions The line spectrum of hydrogen was explained by Bohr s theory of the hydrogen atom However before this the line spectrum of hydrogen was described by an empirical rela tionship involving the Rydberg constant In this experiment line spectra will be observed and the relationship of the Rydberg constant to the theoretical quantities of the Bohr theory will be investigated After performing this experiment and analyzing the data you should be able to 1 Clearly distinguish between continuous and line discrete spectra 2 Explain why gas discharge tub
381. nation that uses water as a comparison standard Since it is a weight ratio specific gravity has no units The specific gravity can also be expressed as a ratio of densities sp gr Ex 18 3 WwW For practical purposes the density of water is 1 g cm over the temperature range in which water is liquid ps _ ps g em _ P d g em sp gr Archimedes 287 212 BCE was a Greek scientist with many accomplish ments He is probably best known from the legend of determining whether a gold crown made for the king was pure gold or whether the craftsman had substituted a quantity of silver for an equivalent amount of gold According to a Roman account while pondering the question Archimedes went to the baths and on immersing himself in a full bath noticed that water flowed out presumably equal to his body volume Archimedes recognized a solution to the problem and excitedly jumped out of the bath running home unclothed through the streets shouting Eureka Eureka Greek for I have found it Supposedly he then put quantities of pure gold and silver equal in weight to the king s crown in basins full of water More water overflowed for the silver than the gold Testing the crown more overflowed than for pure gold imply ing some silver content Although Archimedes solution to the problem in volved density and volume it may have gotten him thinking about buoyancy www ATIBOOK ir EXPERIMENT
382. nd Sample Rate Workbook Sample Rate Measure Output Current 100 Hz CI Figure 20 4 Data Studio setup A graph of voltage versus current will show the variations for an ohmic and a nonohmic resistor The Signal Generator window remains active to manually control the output during experimental Procedure B Reprinted courtesy of PASCO Scientific 15 e CI Fig 20 4 shows what the screen should look like once the setup is complete The size of the graph win dow can be changed if needed The Signal Genera tor window will need to stay visible for Procedure B of the experiment where the output voltage will be manually controlled a EXPERIMENTAL PROCEDURE A Ohmic Component 1 Connect the signal generator to the 100 0 resis tor The voltage sensor will measure the voltage drop across the resistor as shown in the circuit of e CI Fig 20 5 2 Press the START button and click on the Scale to Fit button of the graph toolbar That is the leftmost but ton of the graph toolbar After a few seconds press the STOP button A cycle is complete after 2 seconds but it will not affect the experiment if it runs longer than that In fact let it run longer and follow the plot on the screen as it appears What is happening to the current as the voltage changes Signal Voltage generator sensor output voltage CI Figure 20 5 The experimental setup The resistor ohmic or nonohmic is connected to the signal generator The voltage sens
383. nd count rate meters A scaler displays the cumulative number of counts on a lighted panel By using a separate timer the number of counts per minute cpm can be obtained Some scalers have internal timers that stop the counting after a preset time interval A rate meter displays the average counting rate directly via a dial needle Fig 33 2 The needle reading fluctuates back and forth This is due to the electronic averaging of the number of counts received during a short period of time A scaler timer is usually preferred over a rate meter because of this effect Figure 33 2 Apparatus for radioactive experiments The standard side window Geiger tube probe on the mount ing board is connected to a count rate meter A radioactive source is on the board in the foreground Notice the radio activity warning sign on the source Cengage Learning A Tube Voltage and Count Rate When a Geiger tube is in the vicinity of a radiation source with particles of varying energy and there is no voltage on the tube no counts are observed on the counter Counters usually have a loudspeaker circuit so that the counts may also be heard as audible clicks If the tube voltage is slowly increased from zero then at some applied voltage counts will be observed The lowest applied voltage that will produce a count in the instrument is called the starting voltage or threshold voltage Fig 33 3 As the tube voltage is increased above the thres
384. nd of the track all four observers should start their timers m m As the leading edge of the car passes the assigned ref erence marks each respective observer stops his or her aaa ee ie a ee a eae as Daa a timer Making a dry run or two to become familiar with the timing sequence is helpful Carry out this I vi V2 1 Compute the velocities and the total momentum before and after collision and the percent difference in these values for each trial m mz Case 3 f electronic photogate timers are available your instructor will give you N m instruction in their use Electronic timing greatly improves the accuracy T1 Figure 7 1 Experimental collision cases See text for and precision of the results Why descriptions www ATIBOOK ir EXPERIMENT 7 Conservation of Linear Momentum 109 CASE 2 COLLISION BETWEEN Two CARS OF UNEQUAL Mass WITH THE MORE MASSIVE CAR INITIALLY AT REST 6 Repeat Procedure 5 with m replaced by m4 more and after collision Note Speeds do not have to be and probably won t be equal Make appropriate adjustments in the timing pro cedure to measure the velocities of m and m before massive than m and m See TI Fig 7 1 In this case m will travel in the opposite direction after collision as a trial run will show Make appropriate adjust and after collision Carry out the procedure three times and record the data in TI Data Table 3 Compute the percent
385. nd temperature 20 C A vector quantity or vector on the other hand has both magnitude and direction Such quantities include displacement velocity acceleration and force for exam ple a velocity of 15 m s north or a force of 10 N along the x axis Because vectors have the property of direction the common method of addition that is scalar addition is not applicable to vector quantities To find the resultant or vector sum of two or more vectors special methods of vector addition are used which may be graphical and or EQUIPMENT NEEDED Force table with four pulleys Four weight hangers Set of slotted weights masses including three of 50 g and three of 100 g THEORY A Methods of Vector Addition Graphical TRIANGLE METHOD Vectors are represented graphically by arrows 6 Fig 5 1 The length of a vector arrow is proportional to the magni tude of the vector drawn to scale on graph paper and the arrow points in the direction of the vector The length scale is arbitrary and is usually selected for convenience and so that the vector graph fits nicely on the graph paper A typical scale for a force vector might be 1 cm 10 N That is each centimeter of vector length repre sents 10 newtons The scaling factor in this case in terms of force per unit length is 10 N cm Note the similarity with the common food cost factor of price Ib for example 10 Ib When two vectors are added by the triangle method A
386. nd you lost 100 of your investment the next would you still have any money left 258 www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 7 Specific Heats of Metals fr Advance Study Assignment Read the experiment and answer the following questions Distinguish between heat capacity and specific heat 2 Why is the specific heat of water equal to unity that is 1 0 cal g C or 1 0 kcal kg C 3 Given that the specific heat of one material is twice that of another compare the relative amounts of heat required to raise the temperature of equal masses of each material by 1 C 4 Say the same amount of heat was added to samples of the materials in Question 3 and each sample had the same increase in temperature Compare the relative masses of the samples 259 continued www ATIBOOK ir EXPERIMEN TF 77 Advance Study Assignment 5 What is the method of mixtures and how is it used to determine specific heat 6 On what does the accuracy of the method of mixtures depend That is what are possible sources of error Would these be random or systematic errors See Experiment 1 260 www A TIBOOK ir EXPERI ENT 1 7 Specific Heats of Metals INTRODUCTION AND OBJECTIVES Different substances require different amounts of heat to produce a given temperature change For example about three and one half times as much heat is needed to raise the temperature of 1 kg of iron thro
387. near Air Track Linear air track Several laboratory timers or stopwatches Wooden blocks of two different heights sheet of Cartesian graph paper Optional A TI 4A experiment for the free fall spark timer is given near the end of the experiment TI Figure 4 2 Air tracks a A blower supplies air to the track through the hose on the right The cars or gliders travel on a thin cushion of air which greatly reduces friction b An air track may be equipped with photogates for automatic timing Photos Courtesy of Sargent Welch It can be shown that the instantaneous velocities of the car can be found from the experimental data of the measured displacements x of the glider along the air track at times t with v 0 by TI 4 5 53 TI Figure 4 3 Accelerating car on air track When one end of an air track is elevated the acceleration of the car is due to the component of the weight force mg and a g sin0 AY EXPERIMENTAL PROCEDURE A Object in Free Fall 1 One person should drop the object and do the timing Lab partners should alternate 2 Distinguish the objects as m mz and m3 Drop one of them from a fixed height y above the floor and measure its time of fall Drop it with the arm held horizontally or held upward Depending on your height it may be advantageous to stand on a small step stool Why Do a couple of practice runs to become familiar with the procedure Record the data for four
388. ner s EXPERIMENT 29 ky Polarized Light pg Malus s Law f Advance Study Assignment Read the experiment and answer the following questions 1 Is the plane of polarization of a polarizing polymer sheet in the same direction as the molecular chain orientation Explain 2 What is the condition for optimum polarization by reflection Is the polarization angle the same for every material Explain 3 Describe how light can be polarized by refraction Would two images be formed Explain 4 Why is sky light partially polarized and why does it appear blue 419 continued www ATIBOOK ir EXPERIMENT 29 Advance Study Assignment 5 What is meant by optical activity 6 Describe the principle of optical stress analysis 7 On a wristwatch or calculator why are some portions of an LCD light and other portions dark MY Advance Study Assignment Read the experiment and answer the following questions 1 What is an analyzer How is it different from and how is it similar to a polarizer 2 What is the range of intensities for light passing through a polarizer and analyzer On what does this depend 420 www A TIBOOK ir EX PE RI J ky Polarized Light pg Malus s Law OVERVIEW Experiment 29 examines the polarization of light but the TI and CI procedures differ in focus The TI procedure examines the plane of polarization and illustrates some M ENT 2 9 methods of polarization reflection refraction
389. ners Ry R 2 or ge TI 23 7 PR R two resistances in parellel This particular form of R for two resistors may be more convenient for calculations than the reciprocal form Also in a circuit with three resistors in parallel the equivalent resistance of two of the resistors can be found by TI Eq 23 7 and then the equation may be applied again to the equivalent resistance and the other resistance in parallel to find the total equivalent resistance of the three parallel resistors However if your calculator has a 1 x function the reciprocal form may be easier to use Note that the voltage drops across R and R in parallel are the same and by Ohm s law IR DR or I R xl TI 23 8 h RN TI Example 23 1 Given two resistors R and Ro with R 2R4 in parallel in a circuit What fraction of the current from the voltage source goes through each resistor Solution With R 2R or R R 2 by TI Eq 23 8 n Ez il R 2 2 Since h T 1 h 2h h 3h or Hence the current divides with one third going through R and two thirds going through R Thus the ratio of the resistances gives the relative magni tudes of the currents in the resistors www A TIBOOK ir Raf R TI Figure 23 3 Circuit reduction Series and parallel resis tances are combined to find the equivalent resistance of a series parallel circuit See text for description Consider the circuit in T
390. ng the Unbalanced Force Total Mass 1 2 Constant Erase all previous data by going to the main menu and under Experiment choosing Delete all data runs Place the following mass pieces on the ascending hanger 5 g 2 g 2 g 1 g If you are using the PASCO mass and hanger set the hangers should also have a 50 g piece as discussed previously If you are using a conventional 50 g hanger no extra weight is needed CI Fig 6 4 shows the ascending and descending masses for the PASCO mass and hanger set Place a 10 g piece on the descending hanger Again with the PASCO mass and hanger set the hanger should also have a 50 g piece but with a conventional 50 g hanger no extra weight is needed www ATIBOOK ir 100 EXPERIMENT 6 Newton s Second Law The Atwood Machine Ascending mass m as 5 g hanger m 2 g 1 2g E 5g 50g E 5 g hanger Added to slow the System down Descending mass A 10g CI Figure 6 4 Ascending and descending masses using PASCO mass and hanger set ME 8967 A 50 g piece is added to each of the small 5 g hangers to prevent them from moving too fast The ascending mass has a combination of small pieces 5 g 2 g 2 g 1 g that add to 10 g A 10 g piece is placed in the descending mass hanger To unbalance the system small pieces from the ascending hanger are moved to the descending
391. nge Determine this angle from the graph and record it in Data Table 3 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 8 Projectile Motion The Ballistic Pendulum AY Laboratory Report A The Ballistic Pendulum DATA TABLE 1 Modify the Data Table if it does not apply to your ballistic pendulum Purpose To determine the magnitude of initial projectile velocity Height h of pointer with pendulum catch in closest to Notch number of Trials pendulum catch average notch number 1 Height A of pointer with pendulum freely suspended 2 3 h hy h 4 Mass of ball m 5 Mass of pendulum M bob and support Average Calculations Computed v show work units Don t forget units continued 137 www ATIBOOK ir EXPERIMENT 8 Projectile Motion The Ballistic Pendulum Laboratory Report B Determination of the Initial Velocity of a Projectile from Range Fall Measurements DATA TABLE 2 Purpose To determine the magnitude of initial projectile velocity Trial Range Vertical distance of fall y 1 Computed v 2 units 3 Percent difference between results of Parts A and B 4 5 Average Calculations show work C Dependence of Projectile Range on the Angle of Projection DATA TABLE 3 Purpose To investigate projection angle fro
392. ngle of deviation D for that particular component www ATIBOOK ir 442 EXPERIMENT 30 The Prism Spectrometer Dispersion and the Index of Refraction Figure 30 2 Minimum angle of deviation The geometry for determining the minimum angle of deviation Dm for a light ray See text for description between the original direction of the beam and an emergent component of the beam is called the angle of deviation D it is different for each color or wavelength As the angle of incidence is decreased from a large value the angle of deviation of the component colors decreases then increases and hence goes through an angle of minimum deviation D The angle of minimum deviation occurs for a particular component when the component ray passes through the prism symmetrically that is parallel to the base of the prism if the prism is isosceles Fig 30 2 The angle of minimum deviation and the prism angle A are related to the index of refraction of the prism glass for a particular color component through Snell s law by the relationship sin A D 2 303 DU sn A 2 0 2 The derivation of this equation can be seen from the geom etry of Fig 30 2 Note from the top triangle that 2 90 05 A 180 and therefore 05 D 30 3 Also for the symmetric case it can be seen that D 26 or 2 i Note the interior triangle 26 a 180 a Dn Then A D A t D 2
393. nier caliper A good instrument for mea suring rectangular dimensions and circular diameters This caliper has scales for both metric and British measurements See text for description Courtesy of Sargent Welch d The main scale is calibrated in centimeters with a millimeter least count and the movable vernier scale has 10 divisions that cover 9 divisions on the main scale When making a measurement with a meter stick it is necessary to estimate or eyeball the fractional part of the smallest scale division tenth of a millimeter The function of the vernier scale is to assist in the accurate reading of the fractional part of the scale division thus increasing the precision The leftmost mark on the vernier scale is the zero mark lower scale for metric reading and upper scale for inches The zero mark is often unlabeled A measurement is made by closing the jaws on the object to be measured and reading where the zero mark on the vernier scale falls on the main scale See Fig 2 3 Some calipers as the one in Fig 2 2 have vernier scales for both metric and British units In Fig 2 3 the first two significant figures are read directly from the main scale The vernier zero mark is past the 2 mm line after the 1 cm major division mark so there is a reading of 1 2 cm for both a and b The next significant figure is the fractional part of the smallest subdivision on the main scale This is obtained by referring to
394. nomial theorem Is the true resistance larger or smaller than the apparent resistance Explain 320 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 21 The Measurement of Resistance Laboratory Report 4 For each of the circuits used in the preceding question for what values of R large or small does the error in taking R as equal to V I become large enough to be important B Wheatstone Bridge Method 5 Why should the wires connecting the resistances and the bridge be as short as possible 6 Suppose that the slide wire on the bridge did not have a uniform cross section How would this affect your measurements Was there any experimental evidence of this 321 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 2 The Temperature Dependence of Resistance AY Advance Study Assignment Read the experiment and answer the following questions 1 Does the resistance of all substances increase with temperature Explain 2 What is the temperature coefficient of resistance and what are its units 3 Distinguish between a positive and a negative temperature coefficient of resistance 4 Are the a of a metal conductor and the f of a thermistor the same Explain 323 continued www ATIBOOK ir EXPERIMENT 22 Advance Study Assignment 5 What are the circuit conditions when a Wheatstone bridge is bal
395. nt we will study two of the general em pirical rules used to describe the friction between solid surfaces In the first part we will examine the relation ship between friction and the normal force to verify that they are proportional to each other In the second part we will examine the effect of the speed of the object on the XF F f ma 0 amount of frictional force In both cases a force sensor will be used to measure the frictional force between a slid Or F f ing wooden block and a track CI Fig 10 1 illustrates the experimental situation In this experiment the force sensor will directly measure F The sliding object is a wooden block Other blocks are the tension in the string Notice that as long as the car moves shown added as needed so that the string is horizontal when at a constant speed the magnitude of F is equal to the mag connected to a force sensor riding on a motorized car As an nitude of the frictional force acting on the sliding block alternative the figure also shows the setup using the sug On the other hand the vertical forces balance each other gested PASCO equipment where a stack of cars is used to out so the magnitude of the normal force N can be determined make the object the correct height Other alternatives include as the magnitude of the weight of the object N mg using a single 2 X 4 board with a nail that makes it possible to attach the string at the proper height not pictured SETTING UP DATA
396. nt of the body about which the sum of the gravitational torques about an axis through this point is zero For example consider the meter stick shown in e Fig 12 3 If the uniform meter stick is visualized as being made up of individual mass particles and the point of support is selected such that X 0 then Ate XT or Sgr M mgr cc cw Center of gravity mg mg mg mig Mg Figure 12 3 Center of gravity A rod may be considered to be made up of individual masses in rotational equilibrium when the vertical support is directly through the center of gravity and miri Myr Marg Joo m r myr mr Yow where g cancels When the meter stick is in equilibrium it is supported by a force equal to its weight and the support force is directed through the center of gravity Hence it is as though all of the object s weight Mg is concentrated at the center of gravity That is if you were blindfolded and supported an object at its center of gravity on your finger weight wise you would not be able to tell from its weight alone whether it was a rod a block or an irregu larly shaped object of equal mass For a uniform meter stick the center of gravity would be at the 50 cm position Why If an object s weight is concentrated at its center of gravity so should its mass be concentrated there An object s center of mass is often referred to as its center of gravity These points are the same as long as the accel e
397. nt with Voltage AY DATA TABLE 1 Terminal voltage V Constant R Constant R Reading Voltage V Current J Voltage V Current 1 2 3 4 5 Calculations Slope of lines Percent error from R show work Don t forget units continued 299 www A TIBOOK ir EXPERIMEN T 20 Ohm s Law AY DATA TABLE 2 Unknown Resistance Reading Voltage V Current Conclusions from graph 300 Laboratory Report www ATIBOOK ir Name Date Lab Partner s EXPERIMENT 20 B Variation of Current with Resistance V constant RV DATA TABLE 2 Ohm s Law Laboratory Report Constant voltage V Reading Current J Resistance R 1 R Calculations show work RV QUESTIONS Slope of lines Percent error from V 1 If the switch were kept closed during the procedures and the circuit components heated up how would this affect the measurements Hint See Experiment 22 continued 301 www ATIBOOK ir EXPERIMENT 20 _ Ohm s Law Laboratory Report 2 Devise and draw a circuit using a long straight wire resistor instead of a decade box that would allow the study of the variation of voltage with resistance constant According to Ohm s law what would a graph of the data from this circuit s
398. nted on a variable speed rotor is shown in Fig 9 3 Before turning on the rotor a By means of the threaded collar on the centripetal force apparatus adjust the spring to a minimum tension 0 5 on the scale above the threaded collar b By means of the milled screw head near the base of the rotor move the rubber friction disk to near the center of the driving disk The driving disk can be pushed back so that the friction disk can be moved freely This will give a low angular starting speed when the rotor is turned on but don t turn it on yet The speed of the rotor is increased or de creased by moving the friction disk in up or out down respectively along the radius of the driv ing disk Caution Excessive speeds can be dangerous Do not go beyond the speeds needed c Make certain that the force apparatus is locked securely in the rotor mount by means of the lock ing screw Have the instructor check your setup at this point 10 Referring to Fig 9 4 When the motor is turned on and adjusted to the proper speed the cylindrical mass m in 1S a direct measure of the centripetal force supplied The following procedures apply particularly to the belt driven rotor by the spring during rotation Compare this with the model www ATIBOOK ir 146 EXPERIMENT 9 Centripetal Force Figure 9 3 Centripetal force apparatus a A model for which the speed of the rotor is adjusted by moving a rubber friction di
399. nter of the first order minimum and so on see CI Fig 32 2 B Double Slit Interference When light passes through two slits the diffraction pattern is again bright and dark regions but regions smaller than those seen with the single slit These small dots are usu ally called fringes CI Fig 32 3 shows a diagram of the fringes of this interference pattern Source Central i maximum 190000 n 3 2 1 0 i 2 3 Interference fringes CI Figure 32 3 Double slit interference pattern The in terference pattern from two slits produces a smaller and sharper set of bright and dark fringes than the diffraction pattern from a single slit From the geometry it can be shown that the positions of the bright fringe maxima are given by dsin nd n 1 2 3 CI32 3 condition for bright fringes where d is the distance between the double slits 0 1s the angular distance between the central maximum and an other bright fringe of order n and A is the wavelength of the light Using a small angle approximation as before we find that CI Eq 32 3 becomes nla w 7 0 1 2 3 CI324 lateral distances to bright fringes small angles only SETTING UP DATA STUDIO 1 Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There are seven channels to choose from Digital channels 1
400. ntial function R Rett 22 3 where R resistance at a temperature T in kelvins K R resistance at temperature T K T initial temperature K near ambient room temperature in the experiment e 2 718 the base of natural logarithms B exponential temperature coefficient of resis tance which has Kelvin temperature units K In this case as T increases the exponential function and hence the resistance R becomes smaller This expression can be written in terms of the natural logarithm to the base e as n 2 s 22 4 R T T Hence when y In R R versus x 1 T 1 T is plot ted on a Cartesian graph p is the slope of the line This too is an approximation but B is reasonably constant for moderate temperature ranges The temperature coefficient of resistance of a material can be determined by using an experimental arrangement with a slide wire Wheatstone bridge circuit as illustrated in Fig 22 1 The resistance R of a material coil of wire when the bridge circuit is balanced is given by Ry R R R or 22 5 where R is a standard resistance and R R and LL are the ratios of the resistances and lengths of the slide wire segments respectively See Experiment 21 for the theory of the Wheatstone bridge By measuring the resistance of a material at various temperatures the temperature coef ficient can be determined EXPERIMENTAL PROCED
401. nts alone Because of the wide variety of electronic balances available if you are using one in this experiment you should first familiarize yourself with its operation Your in structor may brief you or an operation manual should be available When first using an electronic instrument it is always advisable to read the operation manual supplied by the manufacturer www ATIBOOK ir 24 EXPERIMENT 2 Measurement Instruments Mass Volume and Density a b c Figure 2 1 Laboratory balances a A double beam double platform Harvard trip balance which is also called an equal arm balance b A single platform triple beam balance c High form beam balances The balance on the left has a dial mechanism that replaces the lower mass beams d A digital electronic balance Courtesy of Sargent Welch B The Vernier Caliper In 1631 a French instrument maker Pierre Vernier devised a way to improve the precision of length measurements The vernier caliper Fig 2 2 commonly called a vernier consists of a rule with a main engraved scale and a movable jaw with an engraved vernier scale The span of the lower jaw is used to measure length and is particularly convenient for measuring the diameter of a cylindrical object The span of the upper jaw is used to measure distances between two surfaces such as the inside diameter of a hollow cylindrical object e yam mi rss M feet ECC I Te e F e Figure 2 2 A ver
402. o tail method forms a polygon Fig 5 1b For three vectors the resultant R A B C isthe vector arrow from the tail of the A arrow to the head of the C vector The length magnitude and the angle of orientation of R can be measured from the vector diagram Note that this is equivalent to applying the head to tail method twice the head of A to the tail of B and the head of B to the tail of C The magnitude length R and the orientation angle 0 of the resultant vector R in a graphical method can be measured directly from the vector diagram using a ruler and a protractor Example 5 1 To illustrate scaling and the graphi cal triangle method let A and B represent forces at angles of 0 and 60 respectively with magnitudes of A 2 45 Nand B 1 47 N www ATIBOOK ir 76 EXPERIMENT 5 The Addition and Resolution of Vectors The Force Table R A 4B a Triangle Headd to Tail Method R ATEAE fti Folygen Method Figure 5 1 Vector addition Methods of vector addition Vectors are represented graphically by arrows See text for description Then choosing a scaling factor say 0 50 N cm a vector length is found by dividing its magnitude by the scaling factor magnitude scaling factor Note the unit cancellation A 2 45 N 0 50 N cm 4 9 cm B 1 47 N 0 50 N cm 2 9 cm Here the 0 50 N cm scaling factor was chosen so as to keep e Fig 5 2 an appropriate size In drawing your vector diagrams you should ch
403. ockwise torques and F and F4 clockwise torques on the pivoted meter stick torques and F and F produce clockwise torques but no rotation takes place if the torques are balanced and the sys tem is in rotational static equilibrium It is convenient to sum the torques using magnitudes and directional signs as determined by the counterclock wise cc and clockwise cw convention In this case the condition for rotational equilibrium Eq 12 1b becomes XT Wee 0 Ira Xn 12 3 sum of counterclockwise torques sum of clockwise torques Hence we may simply equate the magnitudes of the cc and cw torques For example for the meter stick in Fig 12 2 writing the force first that is Fr Counterclockwise Clockwise T T5 T4 t T4 or Fir Fr P3r3 Far The forces are due to weights suspended from the rod and with F mg mgr Mgr mgr magr 12 4 and canceling g Mr m r mr M4r Example 12 1 Let m m 50 g m m 100g in Fig 12 2 where m Ms and m are at the 10 40 and 60 cm marks or positions respectively on the meter stick Where would m have to be suspended for the stick to be in static equilibrium Solution In static equilibrium the sum of the torques is zero or the sum of the counterclockwise torques is equal to the sum of the clockwise torques Eq 12 3 Vee Xn In terms of forces and lever arms Fur Fr Fr Far
404. oes one graphically analyze and report experimental data In this introductory study experiment types of experi mental uncertainties will be examined along with some methods of error and data analysis that may be used in subsequent experiments After performing the experiment and analyzing the data you should be able to do the following 1 Categorize the types of experimental uncertainty error and explain how they may be reduced 2 Distinguish between measurement accuracy and pre cision and understand how they may be improved experimentally 3 Define the term least count and explain the meaning and importance of significant figures or digits in reporting measurement values 4 Express experimental results and uncertainty in appro priate numerical values so that someone reading your report will have an estimate of the reliability of the data 5 Represent measurement data in graphical form so as to illustrate experimental data and uncertainty visually Although experimental uncertainty is more descriptive the term error is commonly used synonymously EQUIPMENT NEEDED Rod or other linear object less than 1 m in length Four meter long measuring sticks with calibrations of meter decimeter centimeter and millimeter respectively Pencil and ruler Hand calculator 3 sheets of Cartesian graph paper French curve optional A 4 sided meter stick with calibrations on each side is commercially
405. of incline Mass of car m AJ Wi Car moving down incline My Calculation show work Energy method calculations for W Don t forget units 185 Percent difference in W continued www A TIBOOK ir EXPERIMENT 11 Work and Energy DATA TABLE 2 Purpose To determine work done against friction Laboratory Report Angle of incline Mass of car m Suspended mass d f We Car moving e m up incline Car moving down incline ue Calculation show work Energy method calculations for W 186 Percent difference in W www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 11 Work and Energy RV QUESTIONS 1 What was the work done by the suspended weight when the car a moved up the incline and b moved down the incline Show your calculations Le 2 What was the work done by gravity acting on the car when it a moved up the incline and b moved down the incline Show your calculations Lm 3 a For the car going up the incline what percentage of the work done by the suspended weight was lost to friction b For the car moving down the incline what percentage of the work done by gravity was lost to friction Show your calculations CL Laboratory Report continued 187 www ATIBOOK ir EXPERIMENT 11 Workand Energy Laboratory Report 4 Su
406. of maximum amplitude If sufficiently small weights are not available a fine adjustment can be made by loosening the clamp holding the vibrator rod and sliding it slightly back and forth so as to find the optimum string length be tween the ends that gives the maximum loop width or amplitude for a given tension When this is accomplished measure with a me ter stick the distance from the point where the string contacts the pulley to the center nodal point The me ter stick can be held alongside the vibrating string or you may find it more convenient to grasp the string at the nodal point with your fingers shut off the vibrator and measure the distance from the pulley contact to the nodal point along the nonvibrating string Make certain not to pull the string toward the vibrator for that would increase the length by raising the weight hanger Apply a slight tension in the string away from the vibrator if necessary EXPERIMENT 15 Standing Waves in a String 243 Record this length L and the total suspended mass in the data table Since the length of one loop is one half of a wavelength L A 2 Remove enough weights from the weight hanger and adjust so that a standing wave pattern of maximum amplitude with three loops two nodal points in the string is formed Measure the distance from the pul ley contact to the nodal point nearest the vibrator The fixed end nodal point at the vibrator is not used because in vibrating up
407. of the calculator window and enter the name of the constant as L the value as the length of the pendulum measured before and the units as meters m b Click the lower Accept button c Click on the New button again and enter the name of the constant as M the value as the mass of the pendulum measured before and the units as kilograms kg d Click the lower Accept button e Close the experiment constants portion of the calculator window by pressing the button marked Experiment Constants again EXPERIMENT 14 Simple Harmonic Motion 233 10 Calculation of the linear speed a In the same calculator window clear the defini tion box and enter the following equation V L smooth 6 w This is the calculation of the linear speed v wL which will be called V Note that the length L of the pendulum is multiplied by the angular speed which is called w here The smooth function is to produce a sharper graph b Press the Accept button after entering the for mula The variables L and w will appear in a list L will have the value defined before but w will be waiting to be defined c To define the variable w click on the drop menu button on the left side of the variable A list of op tions will show asking what type of variable this is Define w as a Data Measurement and when prompted choose Angular Velocity rad s 11 Calculation of the kinetic energy a Still in the same calculator window press
408. om the 90 cm mark and the support stand is placed at the 40 cm mark What is the mass of the meter stick 202 www ATIBOOK ir Name Section Date Lab Partner s A gt EXPERIMENT 1 3 Simple Machines Mechanical Advantage faj Experimental Planning GL Figure 13 1 A simple machine the inclined plane Less input force F is required to move a load a vertical distance A but the load must be moved through a greater distance L See Experimental Planning text for description Machines are used every day Although most common machines such as can openers lawn mowers or automobile engines are thought of as complex mechanical devices they all utilize the basic principles and components of simple machines Machines make it easier to do work But how is this done You should know from conservation principles that you don t get work done without using energy So how do machines make work easier The idea of mechanical advantage will be ex plored in this section A simple machine is a device that can change the magnitude or direction of an applied force The work done by the force always depends on the force component F parallel to the displacement d that is W Fd The conservation of energy prin ciple does not allow the energy or work output of a machine to exceed the energy or work input In the ideal case Work input work output Wi Wo Fd Fd GL 13 1 1 If a simple machine produces an output force
409. ommonly given as so many ohms per volt which is the total resistance of the meter divided by the full scale reading ib For example if the meter has a resistance of 1000 0 V and the full scale reading of a particular range is 3 V then R 3 V 1000 O V 3000 Q The resistance in ohm volt applies to any range setting of the meter Note If voltmeter scales are changed during read ings R will be different for different sets of V and J measurements Be sure to record this if it occurs Using Eq 21 3 compute the value of R for each cur rent setting and find the average value Compare this with the accepted value by finding the percent error Set up a circuit as shown in Fig 21 5b This is accom plished by changing only one wire in the previous cir cuit Repeat the measurements as in Procedure 2 for this circuit recording your findings in Data Table 2 a Compute the resistance R V I directly from each set of current and voltage measurements and find the average value b When one is not taking into account the ammeter resistance R is taken to be the value of the resis tance R Compare the average experimental value of R with the accepted value of R by finding the per cent error c Using the values of R and R compute R Eq 21 5 Mentally compare the magnitudes of the ammeter and voltmeter resistances Repeat the previous procedures with a large known resistance Record its accepted
410. on cm Calculations show work 506 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 35 The Absorption of Nuclear Radiation Laboratory Report B Absorption of Gamma Radiation DATA TABLE 3 Purpose To determine the relationship of intensity and thickness Number of lead sheets Intensity 7 Corrected intensity n cpm IL I I 0 I Calculations Background Radiation show work Number of counts Time interval Intensity cpm continued 507 www ATIBOOK ir EXPERIMENT 35 The Absorption of Nuclear Radiation Laboratory Report Absorption Coefficient Measurements for Gamma Rays Number of sheets to reduce initial intensity to one half n Half thickness x1 Linear absorption coefficient u Mass absorption coefficient 4m Percent error Slope of graph x Linear absorption coefficient u Mass absorption coefficient 4m Percent error RV QUESTIONS 1 Was there a large difference in the percent errors of the experimental mass absorption coefficients If so why do you think this was the case 2 Compute what percent of an incident beam of 0 662 MeV gamma rays is absorbed while passing through 2 5 mm of lead 508 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 35 The Absorption of Nuclear Radiation 3 Would the Cartesian graph of In 7 versus n or x
411. on net force total mass Q Percent different between apn and a Measurement of frictional mass my Masses move with constant velocities when given an initial push Calculations show work Don t forget units continued 93 www A TIBOOK ir EXPERIMENT 6 Newton s Second Law The Atwood Machine Laboratory Report RV DATA TABLE 2 Purpose To investigate a F m by holding m constant If not considering pulley inertia and friction ignore columns and Meg and m symbols Meg Descending mass m Trial 5 6 7 8 Ascending mass m Distance of travel 2 Run 1 Time of Eun travel t Run 3 Average Measured acceleration as 2ylP Total mass m m tma Measured frictional mass m m m spe e Net force m m m g Theoretical acceleration net force total mass a Percent different between am and a KAN Measurement of frictional mass rm Masses move with constant velocities when given an initial push 94 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 6 Newton s Second Law The Atwood Machine Laboratory Report Calculations show work RV QUESTIONS 1 In the experiment should the mass of the string be added to the total mass moved by the unbalanced force for
412. on has the masses and the velocities before and after the collision If not review your result with a classmate or your instructor Solve the equation for the initial velocity of the projectile v Note that to calculate the initial projectile velocity v the velocity V of the block and projectile combination needs to be known The values of the masses can be determined with a balance So far only one conservation principle has been used the conservation of linear momentum Now consider the mechanical energy of the system after the collision Write an expres sion for the kinetic energy of the system the mass and bob combo immediately after collision and label it Eq 2 As the bob swings upward from h to a maximum height h GL Fig 8 1 what is happening to the kinetic energy of the system neglecting friction If the kinetic energy is decreasing is there another form of mechanical energy in the system that may be increasing If so what is it Write an equation for the mechanical energy of the system at h and call it Eq 3 5 How are Eq 2 and 3 related by the conservation of mechanical energy 6 If you apply the conservation of mechanical energy for the system after the collision the expressions in Eq 2 and Eq 3 are equal Set them equal to each other and call the resulting equation Eq 4 7 What is the only variable in this equation that cannot be measured directly You should recognize that it is the velocity V h and
413. on of light as denoted by the E vector viewed along the of cross polarizers and no light is transmitted through the analyzer B Polarization by Reflection When light is incident on a material such as glass some of the light is reflected and some is transmitted The reflected light is usually partially polarized and the degree of polar ization depends on the angle of incidence For angles of incidence of 0 and 90 grazing and normal angles the reflected light is unpolarized However for intermediate angles the light is polarized to some extent Complete polarization occurs at an optimum angle called the polarization angle 0 TI Fig 29 4 This occurs when the reflected and refracted beams are 90 apart and 6 is specific for a given material Referring to TI Fig 29 4 since 0 0 then 0 90 0 180 and 0 6 90 or 6 90 0 By Snell s law Experiment 27 The expression is known as Malus s law after E I Malus 1775 1812 the French physicist who discovered it a The transmission axis or plane of polarization or polarization direction is per pendicular to the oriented molecular chains When the transmission axes of the polarizer and analyzer are not parallel less light is transmitted b For cross polaroids 0 90 little light ideally no light is transmitted as shown in the crossed polarizing sunglasses lenses Cengage Learning www A TIBOOK ir sin 0
414. one time constant the voltage across the capacitor has decreased to a value of 1 of V that is V V e 7 Ve FCRC y e V e 0 37 V In order to analyze the voltage versus time it is helpful to put Eqs 25 1 and 25 2 in the form of a straight line From Eq 25 1 V V V e and taking the natural logarithm of both sides of the equation gives 1 In V V ac T In Vo 25 3 charging voltage Taking the natural logarithm base e of Eq 25 2 InV 41 nV RC n V 25 4 discharging voltage Both of these equations have the form of the equation of a straight line y mx b Can you identify the variables and constants Both have negative slopes of magnitude 1 RC Hence the time constant of a circuit can be found from the slopes of the graphs of In V V versus t and or In V Versus f EXPERIMENTAL PROCEDURE 1 Setup the circuit as shown in Fig 25 1 with the capac itor of smaller capacitance and resistor of larger resis tance It is often necessary to use a series combination of resistors to obtain the large resistances required in the experiment The resistance of a resistor may be determined from the colored bands on the resistor See Appendix A Table A5 for the resistor color code Record the value of the capacitance C and the resistance R in Data Table 1 Also prepare the labora tory timer for time measurements Have the instructor check the circuit befor
415. onential functions of the form N Ner or y Ae E 1 are plotted on Cartesian coordinates in linear form by first taking the natural or Naperian logarithm base e of both sides of the equation For example N N e In N In N e InN In e InN At or InN Ar InN E 2 Similarly for y Ae In y InA Ine In A ax or In y ax lnA E 3 These equations have the general form of a straight line when plotted on a Cartesian graph y mx b For example when we plot In N versus f as Cartesian coordinates the slope of the line is A and the intercept is In N The value of N is obtained by taking the antilog of the intercept value In N For a decaying exponential N N e the slope would be negative Note that before plotting In N versus f on Cartesian graph paper we must find In N for each value of N Because logarithmic functions occur quite often in physics special graph paper called semi log graph paper is printed with graduations along the y or ordinate axis that are spaced logarithmically rather than linearly The x or abscissa axis is graduated linearly Look at a sheet of semi log graph paper If a quantity is plotted on the ordinate axis of semi log paper the logarithmic graduated scale automatically takes the logarithm so it is not necessary to look up the loga rithm for each y value However commercial logarithmic graph paper i
416. onents of the motion are described by x vt 8 5 and reign 8 6 Figure 8 3 Range fall The configuration for range fall measurements See text for description Eliminating from these equations and solving for v we have neglecting air resistance je EY Vy 2y x 8 7 Hence by measuring the range x and the distance of fall y the initial speed of the projectile can be computed C Projectile Range Dependence on the Angle of Projection The projectile path for a general angle of projection 0 is shown in Fig 8 4 The components of the initial velocity have magnitudes of cd 6 8 At the top of the arc path v 0 and since Vy vy gt vsin gt downward taken as negative then v sind gt 0 or tr a 8 9 8 where f is the time for the projectile to reach the maxi mum height of ym If the projectile returns to the same elevation as that from which it was fired then the total time of flight f is 2v sin 0 t 2t 8 10 8 During the time f the projectile travels a distance R range in the x direction 2v sin 0 cos 0 R vut v cos Ot 0o57 where f is from Eq 8 10 y Figure 8 4 Projectile motion For an arbitrary projection angle above the horizontal the range R of a projectile depends on the initial velocity that is on the speed and angle of projection www ATIBOOK ir
417. onfiguration or for the magnetic case the magnetic force per unit pole or moving charge Knowing these the electric force or magnetic force an interacting object would experience at different locations can easily be calculated The electric force per unit charge is a vector quan tity called the electric field intensity or simply the electric field E By determining the electric force on a test charge at various points in the vicinity of a charge configuration the electric field may be mapped or represented graphi cally by lines of force The English scientist Michael Faraday 1791 1867 introduced the concept of lines of force as an aid in visualizing the magnitude and direction of an electric field Similarly the magnetic force per unit pole is a vector quantity called the magnetic field intensity or magnetic field B In this case the field is mapped out by using the pole of a magnetic compass In this experiment the concept of fields will be inves tigated and some electric and magnetic field configurations will be determined experimentally After performing this experiment and analyzing the data you should be able to 1 Describe clearly the concept of a force field 2 Explain lines of force and the associated physical interpretations 3 Distinguish between lines of force and equipotentials and describe their relationships to work EQUIPMENT NEEDED A Electric Field Field mapping board and pro
418. oose a scaling fac tor that will use most of the allotted space on the graph paper much as in plotting a graph in Experiment 1 Also a factor with two significant figures was chosen because graph paper grids are usually not fine enough to plot more digits accurately The triangle has been drawn in Fig 5 2 where R A B The R vector is measured with ruler and protractor to have a length of 6 8 cm and a direction angle of 0 22 relative to the A vector The magni tude of R in newtons is found using the scaling factor R scaling factor measured length 0 50 N cm 6 8 cm 3 4 N 1 0 20 A 3 0 4 0 5 0 6 0 cm Scale 0 50 N cm Figure 5 2 Drawing to scale Figures are often scaled down so as to maintain a convenient size Here the vector triangle is shown to scale with a scaling factor of 0 50 N cm See text for description B Methods of Vector Addition Analytical TRIANGLE METHOD A resultant vector R is determined by using the head to tail method as shown in Fig 5 2 When not a simple right triangle the magnitude of R can be computed from the law of cosines if the angle y the angle opposite R is known R A B 2AB cos y 5 1 The angle 0 between R and A can then be computed using the law of sines with the magnitudes of sides B and R known B R cese 5 2 sin siny From Example 5 1 the magnitudes of A and B are 2 45 N and 1 47 N respectively and as can be
419. op main menu Usually a small version of the calculator opens as shown in e CI Fig 7 3 Expand the calculator window by click press OK ing on the button marked Experiment Constants 5 Click on the Channel 3 button in the picture and again 8 peni s 11 The expanded window shown in CI Fig 7 4 is choose a Rotary Motion Sensor from the list and press i OK used to establish values of parameters that will remain constant throughout the experiment In this case these are the masses m and m of the carts which have al ready been measured This is how to do it a Click on the lower New button within the Experi ment Constants section of the calculator window and enter the name of the constant as m1 the value as the mass of Car 1 measured before and the units as kg 6 Connect the sensors to the interface as shown on the computer screen one goes to Channels 1 and 2 the other goes to Channels 3 and 4 7 The properties of each RMS sensor are shown directly under the picture of the interface See CI Fig 7 2 8 Click on the icon of the first sensor and adjust the properties as follows First Measurements tab deselect all options 4 b Rotary Motion Sensor C1 6538 ta Measurements M Rotary Motion Sensor Sample Rate Visbity Name re Unit of Measure wH hz z T Rotation Counts 2 tab Coms Semple J Rotation Counts Ch 152 counts z Measurements Measurements R
420. opists in the late 1800s For example the wavelengths of spectral lines in the visible region called the Balmer 9c series were found to fit the formula i B ri 3 4 5 31 3 1 1 1 hc 5 5 a 3 n 3 4 5 31 1 A 2 n Comparing this theoretical equation with the empirical equation Eq 31 1 reveals that the forms are identical with where R is the Rydberg constant with a value of the prediction that R 13 6 eV he 1 097 x 10 nm The hydrogen spectrum is of particular theoretical interest because hydrogen having only one proton and EXPERIMENTAL PROCEDURE one electron is the simplest of all atoms Niels Bohr 1 A prism spectrometer will be used to analyze and study 1885 1962 a Danish physicist developed a theory spectra in this experiment The prism spectrometer is for the hydrogen atom that explains the spectral lines illustrated and its use described in Experiment 30 as resulting from electron transitions between energy Review the operation of this instrument Place the in levels or discrete electron orbits Fig 31 2 with candescent source in front of the collimator slit and the wavelengths of the spectral lines being given by the observe the continuous spectrum that results from the theoretical equation prism dispersion see Experiment 30 List the colors of the spectrum in the laboratory report beginning 31 2 with red where 2 A convenient type of discharge tube and powe
421. or measures the voltage drop across the resistor 3 Print a copy of the graph and paste it to the laboratory report 4 As expected the graph for the ohmic resistor is a straight line Use the Fit drop menu on the graph tool bar to select a Linear Fit for the data Record the slope of the line and compare it to the known value of the resistance by calculating a percent error www ATIBOOK ir 306 EXPERIMENT 20 Ohm s Law Nonohmic Component 1 Change the 100 resistor for a small 6 V lightbulb Click on the button labeled Auto in the Signal Gen erator window This will cancel the automatic ON OFF feature of the generator and give manual control of the signal Press the On button of the signal generator Press the START button and collect data for a few seconds enough to observe the pattern on the screen Press the Scale to Fit button if needed to see the data better What is happening to the current now as the voltage changes Press the STOP button to end the data collection Press the Off button of the signal generator to turn off the output voltage Print a copy of the graph and paste it to the laboratory report www ATIBOOK ir Name Section Date Lab Partner s C EXPERIMENT 2 0 Ohm s Law amp Laboratory Report A Ohmic Component Don t forget to attach the graph to the laboratory report Calculations Slope of line show work Per
422. or reading N mg The object with no load 1 2 3 The object with increasing load 4 5 Slope of graph continued www A TIBOOK ir EXPERIMEN 1 i B The Effect of Speed on Friction ED orate Purpose To investigate the effect of speed on the frictional force Different speed trials from low speed to high Average frictional force 1 10 172 Laboratory Report www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 10 Friction Laboratory Report EF cuestions 1 Is it true that the frictional force is directly proportional to the normal force Discuss the experimental evidence 2 What is the physical significance of the slope of the graph of friction versus normal force 3 Is there a clear pattern for the frictional force as the speed of the object increases Com pare to the pattern observed when increasing the load What can be concluded about the effect of the speed Discuss 4 Why was it so important that the string connecting the sensor and the object remain hori zontal during the experiment Discuss what would happen if it did not 5 Refer to step 3 of the Experimental Procedure for Part A which says Set the motorized car for a medium speed and do not change it during the experiment Given the results of Part B of the experiment discuss whether changing the speed would have made a dif ference in the results of
423. orate Purpose To investigate how the acceleration of a system varies as the mass of the system increases without changing the net applied force Trial Ascending Descending Total mass Measured accel Unbalanced force Theoretical error m m m m eration from m m g acceleration graph 1 2 3 4 ED vatatasie2 Purpose To investigate how the acceleration of a system varies as the net applied force on the system increases while the mass remains constant Trial Ascending Descending Total mass Measured accel Unbalanced force Theoretical error m m m m eration from m m g acceleration graph 1 2 3 4 Don t forget units continued 101 www ATIBOOK ir EXPERIMENT 6 Newton s Second Law The Atwood Machine Laboratory Report EF cuestions 1 What happens to the acceleration of a system when the mass of the system increases but the net force stays constant 2 What happens to the acceleration of a system when the net applied force increases but the mass of the system does not change 3 Refer to the data in CI Data Table 2 Make a one page graph of unbalanced force versus measured acceleration and draw the best fitting straight line Determine the slope of this line Show the details of the calculation on the graph and attach the graph to the lab report 4 What are the units of the slope
424. orb and reradiate scatter part of the light In effect the elec trons absorb the light by responding to the electric field of the light wave An electron can be thought of as a small antenna it radiates light in all directions except along its axis of vibration Hence the scattered light is partially polarized Polarized rays Unpolarized light o ray HH TI Figure 29 5 Polarization by double refraction or bire fringence An unpolarized beam entering a crystal is split into two polarized beams Dots indicate electric field vec tors oscillating normal to the page Calcite e ray www ATIBOOK ir 426 EXPERIMENT 29 Polarized Light Such scattering of sunlight occurs in the atmosphere and is known as Rayleigh scattering The condition for interaction and scattering is that the size d diameter of the molecules be much less than the wavelength A of the light d lt A The intensity of the scattering then varies as 1 A This condition is satisfied for O oxygen and N nitrogen molecules in the atmosphere Sunlight incident on the atmosphere is white light with a spectrum of wavelength components or colors As a result of the 1 A scattering relationship the blue end shorter wavelength of the spectrum is scattered more than the red end longer wavelength The blue light is scattered and rescattered When looking at the sky we see this scattered light and as a result the sky appears to be blue
425. orce Table Laboratory Report Ary questions 1 Considering the graphical and analytical methods for obtaining the resultant which method is more accurate Give the probable sources of error for each method 2 Vector subtraction A B is a special case of vector addition since A B A B Suppose that the cases of vector addition I II and III in this experiment were vector sub traction F F a What effect would this have on the directions of the resultants Do not calculate explicitly Simply state in which quadrant the resultant would be in each case b Would the magnitude of the resultant be different for vector subtraction than for vector addition in each case If so state whether the subtractive resultant would be greater or less than the additive resultant 3 A picture hangs on a nail as shown in Fig 5 7 The tension T in each string segment is 3 5 N a What is the equilibrant or the upward reaction force of the nail b What is the weight of the picture PHYSICS GOOD FOR YOU Figure 5 7 See Question 3 82 www A TIBOOK ir Name Section Date Lab Partner s A3 4 EXPERIMENT 6 Newton s Second Law The Atwood Machine fy Experimental Planning Newton s second law expresses a relationship between the net force acting on a specific mass and the resulting acceleration of that mass This relation is often written in magnitude form F et ma force mass X
426. orces acting in the direction of motion remember no air resistance Then use this force component in Newton s second law and solve for a Does your result for the acceleration of the bob and ultimately its pattern of motion include the mass 6 Finally you probably listed the initial release angle 0 as a factor that would affect the period Your result for the acceleration above should include this factor in the form of sin Since the acceleration depends on sin 0 instead of 0 the situation is more complicated than those usually encountered in this course Advanced mathematics is needed to derive the theoretical equation for the period of a simple pendulum oscillating in a plane This equation includes the factors discussed previously as well as one constant factor you probably wouldn t expect L 1 0 9 0 T jJ 1 sin sin g 4 2 64 2 This equation predicts that the period will be longer if the length is longer and if the angle is larger but the relation is not directly proportional Does this agree with your predictions A major problem in using this theoretical equation to make predictions that can be tested by experiment is the 1 0 9 0 infinite series 1 4 sin 5 F 6A sinf 2 dope If we could find an approximation of this equation it would be more useful Since sin 0 0 if 0 0 if the angle is small enough the terms with 0 might be negligible Test this by calculating the resultant sum of the first t
427. ore comparable Even so keep in mind that these are approximations and the percent differences may be large The main purpose of the experi ment is to demonstrate how the acceleration of a system depends on the net force and total mass AY EXPERIMENTAL PROCEDURE 1 Set up the Atwood machine as shown in Fig TI 6 1 Use enough string so that the distance of travel y is slightly less than 1 m for convenient measuring To measure y hold one hanger against the floor and mea sure from the floor to the bottom of the other hanger Measure and record y in TI Data Table 1 A Varying the Total Mass Net Force Constant 2 If using inertia and friction corrections go to Proce dure 2a below Begin by placing a 10 g mass on the descending hanger so as to create an unbalanced or net force that should cause the system to accelerate from rest Make a trial run to see if the system moves at an acceleration suitable for timing If not adjust the mass accordingly See Suggestions 1 3 in the Comments on Experimental Technique at the end of the Proce dure section Taking the descending mass as m record m and m in TI Data Table 1 as Trial 1 Ignore the columns headed with asterisks and the m and mn symbols Refinements in the Experimental Procedure section were developed by Professor I L Fischer Bergen Community College New Jersey 3 Make three independent measurements of the time it takes for m to travel the distance y
428. ory report B The Double Slit Pattern 1 Change the slit accessory to a multiple slit disk and realign the laser if needed Choose the double slit with slit separation 0 25 mm and slit width 0 04 mm 2 Set the light sensor aperture bracket to slit 4 3 The pattern should be visible on the aperture bracket of the light sensor Move the light sensor to one side of the laser pattern 4 Turn the classroom lights off www ATIBOOK ir 10 11 12 Press the START button and slowly move the sensor across the pattern by rotating the large pulley of the RMS Click the STOP button when you are finished Use the magnifier button to enlarge the central maxi mum and the first maximum on each side Use the Smart Tool to measure the distance between the first maxima on the two sides of the central maxi mum That is measure the distance between n 1 and n 1 Record the value in CI Data Table 3 Determine the distance y to one of the n 1 fringes by dividing the previous distance by 2 Record the result in CI Data Table 3 Repeat the measurements for the second third and if possible all the way to the sixth order maxima Use the magnifier button to enlarge the parts of the graph as needed Calculate sin 0 for each case using the derived for mula from the small angle approximation Enter the values in both CI Data Tables 3 and 4 To check how well the observed pattern matches the theory use
429. ostat 10 Q e Resistors for example 10 Q and 25 Q Battery or power supply 3 V Connecting wires THEORY A Ammeter Voltmeter Methods There are two basic arrangements by which resistance is measured with an ammeter and a voltmeter One circuit is shown in Fig 21 1 The current J through the resistance R is measured with an ammeter and the potential differ ence or voltage drop V across the resistance is measured with a voltmeter Then by Ohm s law R V I Strictly speaking however this value of the resis tance is not altogether correct since the current registered on the ammeter divides between the resistance R and the voltmeter in parallel A voltmeter is a high resistance in strument and draws relatively little current provided that 311 After performing this experiment and analyzing the data you should be able to 1 Describe the two ways to measure resistance with an ammeter and voltmeter and explain how they differ 2 Describe the basic principle and operation of the Wheatstone bridge 3 Discuss the relative accuracy of the ammeter volt meter methods and the Wheatstone bridge method of measuring resistance The Wheatstone bridge was popularized and promoted by Sir Charles Wheatstone however the British mathematician Samuel Christie invented it B WHEATSTONE BRIDGE METHOD Slide wire Wheatstone bridge Galvanometer Standard decade resistance box 0 1 0 to 99 9 Q Single pole single thr
430. otal of five times and then compute the average of the readings 5 Repeat Procedure 4 for L 60 cm 70 cm and 80 cm 6 Compute the AMA and the TMA for each case 7 Compute the efficiency for each case C Pulleys 8 Determine the mass of one of the single pulleys and one of the multiple sheave pulleys on a laboratory balance and record in Data Table 3 These pulleys will be used as the movable pulleys in the following situations and their weights must be included in the loads 9 Assemble a single fixed pulley as illustrated in Fig 13 3a with enough weights on the force input hanger so that it moves downward with a slow uniform speed when given a slight tap A single pulley or one pulley of multiple sheaves may be used Record the forces due to these masses in Data Table 3 10 The next step is to measure the distances d or h and d or h with a meter stick Pull down the weight hanger supplying the input force F a distance d of 20 cm or more and note the distance the load moves upward d Record these distances in Data Table 3 11 Calculate the AMA TMA and efficiency s for this case www ATIBOOK ir EXPERIMENT 13 Simple Machines Mechanical Advantage 213 Figure 13 5 Wheel and axle a The wheel and axle consists of a larger wheel fixed to a smaller shaft or axle with the same axis of rotation It is equivalent to a lever with unequal lever arms b A practical example of a wheel and axle
431. otary Motion Sensor I Angula Position Ch 142 dec z Visby Name Unit of Measure V Velocity Ch 182 Angular Velocity Ch 182 deg s Angular Acceleration Ch 182 deg s s Y Position Ch 182 fr z Insets High X Large Puley Groove The 2 Measurements tab and Divisions Retation Distance for one ful rotation the Rotary Motion Sensor tab 1440 MP m CI Figure 7 2 The Experiment Setup window The seven available channels are numbered through 4 and A B or C One rotary motion sensor is connected to Channels 1 amp 2 and the other is connected to Channels 3 amp 4 The sensor properties are adjusted by selecting appropriate tabs Make sure the properties of both sensors are adjusted equally Reprinted courtesy of PASCO Scientific www ATIBOOK ir Calculator EXPERIMENT 7 Conservation of Linear Momentum 117 CI Figure 7 3 The calculator window This small version of the calculator window opens when the Calculate button is pressed The calculator will be used to enter formulas that handle the values measured by the sensor The computer will perform the calculations automatically as the sensor takes data Reprinted courtesy of PASCO Scientific im Calculator v Mme poenas pio 5 e Scenic Sietstcat v Special ipea rx oss o E fe El e HETIBYE pu SS SSS VLSGGBII EE Experiment Constants 1 Press New 2 Enter
432. ou measure the mass of the meter stick take one third and add m you can determine the total mass of the short end of the broomstick Do this now Now the mass on the other side of the balance point is just that of the longer piece of the meter stick and is 67 of the total mass of the meter stick Compute this value and compare it to the total mass of the short end of the broomstick Does your result match up with your answer to the first question above Explain your result in reference to the definition for torque 190 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 2 Torques Equilibrium and Center of Gravity RWV Advance Study Assignment Read the experiment and answer the following questions What conditions must be present for a translational equilibrium and b rotational equilibrium of a rigid body 2 If these conditions for equilibrium are satisfied is the rigid body necessarily in static equilibrium Explain 3 Write a definition and a mathematical expression for torque Don t forget units 191 continued www A TIBOOK ir EXPERIMEN TF 12 Advance Study Assignment 4 If torque is a vector with specific direction in space what is meant by clockwise and coun terclockwise torques If the sums of these torques on a rigid body are equal what does this imply physically 5 What defines the center of gravity of a rigid body and how is it related to the center of mass 6
433. ow switch The ranges of the equipment are given as examples These may be varied to apply to available equipment voltmeter resistance R is much greater than R Hence it is more appropriate to write if R gt gt R 21 1 V R I For more accurate resistance measurement one must take the resistance of the voltmeter into account The current drawn by the voltmeter is V R Since the total current divides be tween the resistance and the voltmeter in the parallel branch ISRIEL www ATIBOOK ir 312 EXPERIMENT 21 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method Figure 21 1 Resistance measurement One of the basic ar rangements for measuring resistance with an ammeter and a voltmeter The ammeter measures the sum of the cur rents through the resistance and the voltmeter Therefore the true value of R is greater than the measured value if the measured value is taken to be V I or Jj eger 21 2 where is the true current through the resistance Then by Ohm s law Another possible arrangement for measuring R is shown in the circuit diagram in Fig 21 2 In this case the ammeter measures the current through R alone but now the voltmeter reads the voltage drop across both the ammeter and the resistance Since the ammeter is a low resistance instrument to a good approximation V R T if R amp R 21 4 Figure 21
434. own resistance can you draw from the graphs Variation of Current and Resistance V constant This portion of the experiment uses the same circuit arrangement as before In this case the voltage V is maintained constant by adjusting the rheostat resis tance R when the R is varied Initially set the rheostat near maximum resistance and the resistance R of the decade box to about 100 Q Record the value of R in TI Data Table 3 Close the circuit and adjust the rheostat for a convenient voltmeter reading about 4 V Record the voltmeter reading as the constant voltage V in TI Data Table 3 Record the current and resistance in the table Open the circuit after making the readings Repeat this procedure for four more successive steps of current by reducing the value of R of the decade box Keep the voltage across R constant for each set ting by adjusting the rheostat resistance Ry Do not reduce R below 30 Q Plot the results on an versus 1 R graph and draw a straight line that best fits the data Reciprocal ohms 1 R is commonly given the unit name mhos Determine the slope of the line and compare it with the constant value of V by computing the percent error According to Ohm s law these values should be equal www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s JEN EXPERIMENT 2 0 Ohm s Law RW Laboratory Report A Variation of Curre
435. paper as with the glass plate used previously The mirror may be propped up by some means or a holder may be used if available Draw a line along the silvered side of the mirror Then lay an object pin about 10 cm in front of the mirror and parallel to its length Fig 27 5 Mark the locations of the ends of the object pin on the paper with a pencil b Stick a reference pin R in the board to one side of the object pin and near the edge of the paper as illustrated in Fig 27 5 and mark its location c Place another pin nearer the mirror so that it is vi sually aligned with the reference pin and the head of the object pin s image in the mirror Mark the position of this pin and label it with an H Then move this pin over so that it aligns with the ref erence pin and the tail of the image pin Mark this location and label it with a T d Repeat this procedure on the opposite side of the object pin with another reference pin 6 Remove the equipment from the paper and draw straight lines from the reference points through each of the H and T locations and the mirror line The H lines and T lines will intersect and define the locations of the head and tail of the pin image respectively Draw a line between the line intersections the length of the pin image Measure the length of this Pin image R Reference pin Figure 27 5 Plane mirror The arrangement for the ex perimental procedure for a plane mirror See te
436. particles and 0 662 MeV gamma rays The emitted beta particles actually have a spectrum of energies from 0 to 0 511 MeV E 0 511 MeV 94 137 gay p 0 172 MeV m y 0 662 MeV 137 Sipa Figure 35 2 Decay scheme of Cs 137 Most of the cesium 137 Cs 137 nuclei 94 decay to an excited state of barium 137 7Ba which then gamma decays to a stable state Since the gamma intensity decays exponentially there is no definite penetrating or stopping range as there is in the case of beta radiation Hence it is convenient to speak in terms of a half thickness x1 the material thick ness required to reduce the intensity by one half that is Ij IJ2 or h h gt Then by Eq 35 1 Tua e ua Taking the logarithm base e of both sides of the equation 1 In e In 2 or HAXy In2 and In2 0 693 Xo P u 35 4 Hence knowing the absorption coefficient of a material the half thickness can be calculated EXPERIMENTAL PROCEDURE Caution Review the radiation safety procedures at the beginning of Experiment 31 1 A radioactivity setup is shown in Fig 35 3 First measure the individual thickness of three different sheets of a cardboard b aluminum and c lead with the micrometer and determine the average sheet thickness of each Record in Data Table 1 2 Set up the Geiger counter with the probe on the mount ing board see Fig 35 3 If an end window tube i
437. pe to the other red end of the the telescope crosshairs on each of the four brightest spectrum and record the divided circle reading of spectral lines and record the divided circle readings its visible limit read to the nearest minute of arc Repeat the read c Repeat this procedure for the first order spectrum ings for the first order spectrum on the opposite side on the opposite side of the central maximum The of the central image angular difference between the respective readings corresponds to an angle of 20 TI Fig 32 2b 7 Repeat the measurement procedure for the four lines Compute the grating constant d in millimeters and with the experimentally measured 0 s compute the range of the wavelengths of the visible spectrum in nanometers in the second order spectra and using TI Eq 32 2 compute the wavelength of each of the lines for both orders of spectra Compare with the accepted values by computing the percent error of your measurements in each case Note In the second order spectra two yellow DETERMINATION OF THE WAVELENGTHS OF SPECTRAL LINES 5 Mount the mercury discharge tube in its power supply holder and place in front of the collimator slit lines a doublet may be observed Make certain that you choose the appropriate line Hint See the wave lengths of the yellow lines in Appendix A Table A8 Which is closer to the red end of the spectrum www ATIBOOK ir This page intentionally left blank ww
438. perates at high voltage and you could receive an electrical shock Make certain the power sup collimator slit Move the spectrometer telescope into the line of the slit of the collimator and focus the crosshairs on the central slit image Notice that this central maximum or zeroth order image does not depend on the wavelength of light so a white image is observed Then move the telescope to either side of the incident beam and observe the first and second order spectra Note ply is turned off before inserting the tube If a large mercury source is used it should be properly shielded because ofthe ultraviolet radiation that may be emitted Consult with your instructor Turn on the power supply and observe the first and second order mercury line spectra on both sides of the central image which is spread out more 6 Because some of the lines are brighter than others and the weaker lines are difficult to observe in the second a Focus the crosshairs on the blue violet end of order spectra the wavelengths of only the bright the first order spectrum at the position where you est lines will be determined Find the listing of the judge the spectrum just becomes visible Record mercury spectral lines in Appendix A Table A8 and the divided circle reading to the nearest minute record the color and wavelength in TI Data Table 2 of arc in TI Data Table 1 Then beginning with either first order spectra set b Move the telesco
439. physics is y ax E 7 For example the electric field E kq kqr is of this form with a kq and n 2 By plotting y ver sus x on Cartesian graph paper we obtain a straight line with a slope of a However in an experiment the measured values are usually y and x so computation of the x s is required But in some instances the exponent n may not be known This constant along with the constant a may be found by plotting y versus x on log graph paper This is commonly called log log graph paper because of the logarithmic graduations on both axes Look at a sheet of log log graph paper www ATIBOOK ir 524 APPENDIX E Graphing Exponential Functions At logarithmic graduations on axes we again auto matically take the logarithms of x and y Working with common logarithms base 10 in this instance we find that the log log plot of y versus x yields a straight line as can be seen by taking the common log of both sides of Eq E 7 log y log ax log a log x loga nlogx or log y nlogx loga E 8 which has the general form of a straight line with a slope of n and an intercept of log a For the electric field example this would be BE E PA kqr log E 21og r log kq Again care must be taken in determining the slope of a straight line on a log log graph In this case log y log y log y2 y log x logx log x x
440. pment is broken or does not function properly it should be reported to the laboratory instructor www ATIBOOK ir x INTRODUCTION Also after you complete an experiment the experimental setup should be disassembled and left neatly as found unless you are otherwise instructed If you accidentally break some equipment or the equipment stops working properly during an experiment report it to your instructor Otherwise the next time the equipment is used a great deal of time may be wasted trying to get good results Laboratory Reports A laboratory report form is provided for each experiment in which experimental data are recorded This should be done neatly Calculations of experimental results should be included Remember the neatness organization and explanations of your measurements and calculations in the laboratory report represent the quality of your work www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 31 Experimental Uncertainty Error and Data Analysis RV Advance Study Assignment Read the experiment and answer the following questions 1 Do experimental measurements give the true value of a physical quantity Explain 2 Distinguish between random statistical error and systematic error Give an example of each 3 What is the difference between determinate and indeterminate errors 4 What is the difference between measurement accuracy and precision Explain the general d
441. position of the object at a time t is given by xx vnt tat 4 1 where v is the initial velocity and a is the constant ac celeration For an initial position arbitrarily chosen to be X 0 and for an object starting from rest v 0 the position at any time reduces to x tar 4 2 where y is taken as the vertical direction downward taken as positive to Or for an object in free fall y 5 gt avoid minus signs Hence by measuring the time f it takes for an object to fall a distance y the acceleration due to gravity g can be easily calculated Note that for any case where the acceleration is constant the relationship between position and time is not linear The position is proportional to the square of the time 2 not just to the time 7 A graph of x versus f will be a parabola not a straight line On the other hand if the object has constant accel eration then the velocity is changing at a steady rate The velocity of the object at any time after it starts from rest v 0 is given by 4 3 y at www ATIBOOK ir 52 EXPERIMENT 4 Uniformly Accelerated Motion which is a linear function of time A graph of v versus t will be a straight line The motion of an object undergoing constant accel eration is analyzed to better understand what it means to say that the position varies with the square of the time This is compared to the velocity function whic
442. ppose the car accelerated up and down the incline How would this affect the experimental determinations 5 Is the assumption justified that f would be the same for both up and down cases for the same constant speed If not speculate as to why there is a difference 6 Assuming that f uN see Experiment 10 show that the coefficient of rolling friction for the car moving down the inclined plane with a constant speed is given m by u tan m cos0 Use symbols not numbers 188 www ATIBOOK ir Name Section Date Lab Partner s A EXPERIMENT 1 2 Torques Equilibrium and Center of Gravity 33 cm 0 cm 100 cm GL Figure 12 1 From broomstick to meter stick See Experimental Planning text for description aj Experimental Planning A torque gives rise to rotational motion of a rigid body through the application of a force at some distance from an axis of rotation The magnitude of a torque 7 may be found from the product of the force F and the perpendicular distance from the axis of rotation to the force s line of action r called a lever arm 7 r F see Fig 12 1 in the Theory section When there is no net torque r 0 acting on a stationary rigid body the body will be in static rotational equilibrium and there is no rotational motion As an example of the role of torque in static rotational equilibrium consider a conventional straw broom It is not very difficult to balan
443. r 7 Explain the principle and construction of a hydrometer What is the purpose of the common measurements of the specific gravities of an automobile s radiator coolant and battery electrolyte 279 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 19 Fields and Equipotentials AY Advance Study Assignment Read the experiment and answer the following questions A Electric Field 1 What is an electric field and what does it tell you 2 What are lines of force and what force is it 3 What are equipotentials and how are they experimentally determined What is their relationship to the electric field lines 281 continued www A TIBOOK ir EXPERIMEN TF 19 Advance Study Assignment B Magnetic Field 4 What is a magnetic field how is it defined and what does it tell you 5 Does the magnetic B field have the same relationship to electric charge as the electric E field Explain 6 How may a magnetic pole be moved in a magnetic field without doing work 282 www A TIBOOK ir EX PER ENT il g Fields and Equipotentials INTRODUCTION AND OBJECTIVES When buying groceries we are often interested in the price per pound Knowing this the price for a given amount of an item can be determined Analogously it is convenient to know the electric force per unit charge at points in space due to an electric charge c
444. r readings Difference in readings Final Initial rotations min 1 2 3 4 5 Average Number of rotation N Computation of centripetal force ERICH Average rotational frequency f N 60 Suspended mass M Cylinder mass m Total suspended mass M M m Direct measure of F F Mg Radius of circular path r Computed F Percent difference Don t forget units TE 151 www ATIBOOK ir EXPERIMEN T 8 DATA TABLE 6 Centripetal Force Purpose To determine rotational frequency for Minimum spring tension computation of centripetal force scale reading Laboratory Report Trial Counter readings Difference Final in readings Initial rotations min Computation of centripetal force show work 152 Average Number of rotation V Average rotational frequency f N 60 Suspended mass M Cylinder mass m Total suspended mass M M m Direct measure of F F Mg Radius of circular path r Computed F Percent difference www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 9 Centripetal Force Laboratory Report RV QUESTIONS 1 How does the centripetal force vary with the radius of the circular path Consider a constant frequency and b constant speed Was this substantiated by experimental results 2 If the centripetal force on an object in uniform circular motion is increased what is the
445. r supply is shown in Fig 31 3 AE Caution Great care should be taken because the dis 4 charge tube operates at high voltage and you could is the energy difference between the initial and final receive an electrical shock states n and nj h 6 63 X 107 J s 4 14 X 107 eV s Mount a mercury or helium discharge tube in Planck s constant and c 3 00 X 10 m s speed of the power supply holder and place it in front of the light in vacuum The values n 1 2 3 4 are called collimator slit the principal quantum numbers Different final states Caution If a larger mercury source is used it should M account for the different series be properly shielded because of the ultraviolet radia For spectral lines in the visible region the final state tion that may be emitted Consult your instructor is n 2 and The three such spectral series shown in Fig 31 2 are named after After J R Rydberg 1854 1919 the Swedish physicist who developed 19th century scientists the Swiss mathematician Johann Balmer and the the series relationship German physicists Theodore Lyman and Friedrich Paschen www A TIBOOK ir Figure 31 3 Experimental apparatus A gas discharge tube and power supply Photo Courtesy of Sargent Welch Turn on the power supply observe the mercury or helium spectrum through the telescope and note its line nature With the slit as narrow as possible rotate the prism slightly back
446. r the value 4 Accept of this constant and the units b CI Figure 14 5 The expanded calculator window a After the button marked Experiment Constants is pressed the calculator window expands to full size b The Experiment Constants section is the lower part of the expanded calculator window This section is used to define parameters that are to remain constant during the experiment The diagram shows the steps needed to enter experimental constants into the calculator Reprinted courtesy of PASCO Scientific d M is the value entered before for the mass and v is waiting to be defined To define the variable v click on the drop menu button on the left side of the variable The list of options will show asking what type of variable this is Define v as a Data Measurement and when prompted choose V the equation defined previously 12 Calculation of the potential energy a Press the New button once again to enter a new equation b Clear the definition box and enter the follow c ing equation PE M 9 81 L L cos smooth 6 x This is the calculation of the potential energy U mgh mg L L cos 0 which will be called PE Note that M is the mass 9 81 is the value of g and the variable x in this formula will stand for the angular posi tion 0 of the pendulum in degrees Press the button marked DEG that is under the definition box This w
447. r trans parency material sprinkle iron filings to obtain an iron filing pattern for each of the arrangements shown in e Fig 19 5 Laboratory Report For the bar magnet arrangements the magnets should be separated by several centimeters depending on the pole strengths of the magnets Experiment with this distance so that there is enough space between the ends of the magnets to get a good pattern Sketch the observed magnetic field patterns on Fig 19 5 After the patterns have been sketched collect the iron filings on a piece of paper and return them to the filing container recycling them for someone else s later use Economy in the laboratory is important Place the magnets for each arrangement on a piece of graph paper or regular paper Draw an outline of the magnets for each arrangement on the paper and label the poles N and S Using a small compass trace out marking on the paper the magnetic field lines as smooth curves Draw enough field lines so that the pattern of the magnetic field can be clearly seen Do not forget to indicate the field direction on the lines Draw dashed line curves perpendicular to the field lines www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 9 Fields and Equipotentials RW Laboratory Report Attach graphs to Laboratory Report N a On c Figure 19 5 See Procedure Section B AY ques
448. ration due to gravity g is constant uniform gravitational field Notice how g can be factored and divided out of the previous weight equations leaving mass equations Also it should be evident that for a symmetric object with a uniform mass distribution the center of gravity and center of mass are located at the center of symmetry For example if a rod has a uniform mass distribution its cen ters of mass and gravity are located at the center of the rod s length For a uniform sphere the centers are at the center of the sphere LINEAR Mass DENSITY In part of the experiment the masses of certain lengths of the meter stick will need to be known These may be obtained from the linear mass density u of the stick that is the mass m per unit length L m 12 5 wae 12 5 with units of grams centimeter g cm or kilograms meter kg m For example suppose a meter stick is measured to have a mass of 50 g on a balance Then since the stick is 100 cm long L 100 cm the linear mass density of the stick is u m L 50 g 100 cm 0 50 g cm If the mass distribution of the stick were uniform then every centime ter would have a mass of 0 50 g However meter sticks are not uniform so this is an average value Example 12 2 If a meter stick has a linear mass density of 0 50 g cm what is the mass of a 16 cm length of the stick Solution With u m L then m uL and for u 0 50 g cm and L 16 cm m
449. ravity Laboratory Report Values Moment 1 ok Diagram add m if applicable ph Results Case 6 a m x Ocm n m xX 60cm r2 a Case 6 b same except n x 70cm D Xo Case 6 c same except ri X2 80 cm r Xo Case 6 d same except Tog x measured X2 90 cm Tow ko Percent Percent predicted diff diff Draw a diagram to illustrate each case using the Case 5 a diagram as an example Put the mass of a length of stick in parentheses as in that diagram Attach a sheet to the Laboratory Report showing calculations for each use RV QUESTIONS 1 Explain how the condition F 0 is satisfied for the meter stick in part A of the experiment continued 201 www ATIBOOK ir EXPERIMENT 12 Torques Equilibrium and Center of Gravity Laboratory Report 2 Why are clockwise and counterclockwise referred to as senses rather than directions 3 Suppose in a situation like Case 2 a in the experiment m 200 g were at the 20 cm position and m 100 g at the 65 cm position Would there be a problem in experimentally balancing the system with m 50 g Explain If so how might the problem be resolved 4 Describe the effects of taking the mass of the meter stick into account when the balancing position is not near the 50 cm position 5 Optional A uniform meter stick is in static rotational equilibrium when a mass of 220 g is suspended from the 5 0 cm mark a mass of 120 g is suspended fr
450. rce supplies a voltage rise that is equal to the voltage drop across the resis tance and is given by V IR Ohm s law In an electrical circuit with two or more resistances and a single voltage source Ohm s law may be applied to the entire circuit or to any portion of the circuit When it is applied to the entire circuit the voltage is the terminal input voltage supplied by the voltage source and the resis tance is the total resistance of the circuit When Ohm s law is applied to a particular portion of the circuit the indi vidual voltage drops currents and resistances are used for that part of the circuit Consider the circuit diagram shown in e TI Fig 20 3 This is a series circuit The applied voltage is supplied by a power supply or battery R is a rheostat a variable resis tor that allows the voltage across the resistance R to be varied This combination is sometimes called a voltage divider because the rheostat divides the applied voltage across itself and R An ammeter measures the current through the resistor R and a voltmeter V registers the voltage drop across both R and the ammeter S is a switch for clos ing and opening activating and deactivating the circuit TI Figure 20 3 Circuit diagram The voltmeter is con nected in parallel across the ammeter and the resistance R The other resistance R is that of the rheostat continu ously variable resistor Any component in a circuit th
451. rded data This is particularly important in graphical analysis where Four more TI CI experiments are available in the customized listing in the Table of Contents graphs are immediately plotted on monitor screens without a firm understanding of the parameters involved Experiments Available for Customized Publishing These provide a handy customizable option a way for instructors to build their own lab manual that fits the need of their specific courses All 35 experiments available in the printed manual and an additional 15 experiments which includes four TI CI experiments are available through TextChoice Cengage Learning s digital library TextChoice enables you to build your custom version of Physics Laboratory Experiments from scratch You may pick and choose the content you want included in your lab manual and even add your own original materials creating a unique all in one learning solution Visit www textchoice com to start building your book today A list of the additional experiments can be seen in the Table of Contents Organization of the Seventh Edition Both the TI and CI experiments are generally organized into the following sections In some instances TI Experimental Planning for Guided Learning Advance Study Assignment Introduction and Objectives Equipment Needed Theory Experimental Procedure Laboratory Report Post lab Questions Features include Laboratory Safety Safety
452. re 9 0 X 10 N m C 8 85 x 10 C N n 4r X 1077 1 26 x 1075 Wb A m T M A 3963 mi 6 378 X 106 m 3950 mi 6 357 X 106m 6 4 X 10 km for general calculations 6 0 x 10 kg 7 4 X 10 kg d mass of the Earth 2 0 X 10 kg 93 X 10 mi 1 5 X 10 km 2 4 X 10 mi 3 8 X 105 km 2160 mi 3500 km 864 000 mi 1 4 105 km 517 www ATIBOOK ir 518 APPENDIX B Mathematical and Physical Constants TABLE B3 Conversion Factors Mass Length Area Volume Time Angle Speed Force Pressure Energy Power Rest mass energy equivalents 1g 107k 1 gt 103 z metric ton 1000 kg lu 1 66 X 107 g 1 66 x 107 kg 1 cem 10 m 0 394 in 1m 10 km 328 ft 394 in 1 km 10 m 0 621 mi lin 2 54 cm 2 54 X 10 m 1 ft 12in 30 5 cm 0 305 m 1 mi 5280 ft 609 m 1 609 km 1 cm 10 n 0 1550 in 1 08 10 f 1 n 10 cm 10 76 ft 1550 in 1 in 6 94 x 10 ft 6 45 cm 645 x 1074 m 1 f 144 in 9 29 x 10 m 929 cm lcm 1075 m 3 53 x 10 ft 6 10 x 107 in 1 m 106 cm 10 liters 35 3 ft 6 10 x 10 in 264 gal 1 liter 10 cm 10 m 1 056 qt 0 264 gal 1l in 5 79 x 107 ff 16 4 cm 1 64 X 10 n 1f 1728 in 7 48 gal 0 0283 n 28 3 liters 1 qt 2 pt 946 5 cm 0 946 liter 1 gal 4 qt 231 in 3 785 liters 1h 60 min 3600s 1 day 24h 1440 min 8 64 X 10
453. re quite different physically a b TI Figure 23 1 Resistances in series a A circuit diagram for resistors connected in series The resistors are con nected head to tail The a symbol represents an ammeter that will be used in experimental setups b A liq uid analogy on the left for the circuit diagram of resistors in series on the right The analogies are pump voltage source valve switch liquid flow current and paddle wheels resistors See text for more description where R is the equivalent resistance of the resistors in series That is the three resistors in series could be replaced by a single resistor with a value of R with the same current Iin the circuit B Resistances in Parallel Resistors are said to be connected in parallel when con nected as in TI Fig 23 2a In this arrangement all the heads are connected together as are all of the tails The voltage drops across all the resistors are the same and equal to the voltage V of the source However the www ATIBOOK ir 340 EXPERIMENT 23 Resistances in Series and Parallel a b TI Figure 23 2 Resistances in parallel a A circuit diagram for resistors in parallel All the heads are connected together as are all of the tails b A liquid analogy on the left for the circuit diagram of resistors in parallel on the right See text for description current J from the source divides among
454. re said to be connected in series when connected as in e T1 Fig 23 1a The resistors are connected in line or head to tail so to speak although there is no distinction between the connecting ends of a resistor When connected to a voltage source V and the switch is closed the source supplies a current to the circuit By the conservation of charge this current J flows through each resistor The voltage drop across each resistor is not equal to V but the sum of the voltage drops is V V V V TI 23 1 In an analogous liquid gravity circuit T1 Fig 23 1b a pump corresponding to the voltage source raises the liquid a distance h The liquid then falls or drops through three series paddle wheel resistors and the distances h h and h The liquid rise supplied by the pump is equal to the sum of the liquid drops h h h h Analogously the voltage rise supplied by the source is equal to the sum of the voltage drops across the resistors TI Eq 23 1 The voltage drop across each resistor is given by Ohm s law for example V IR TI Eq 23 1 may be written V V V V IR IR IR TI 23 2 KR R R3 For a voltage across a single resistance R in a circuit V IR and by comparison R Ri R R TI 23 3 resistances in series Keep in mind that an analogy represents only a resemblance Liquid and electrical circuits a
455. reading the value from a calibrated scale only a certain number of figures or digits can properly be obtained or read That is only a certain number of figures are significant This depends on the least count of the instrument scale which is the small est subdivision on the measurement scale This is the unit of the smallest reading that can be made without estimat ing For example the least count of a meter stick is usually the millimeter mm We commonly say the meter stick is calibrated in centimeters numbered major divisions with a millimeter least count See Fig 1 4 The significant figures sometimes called signifi cant digits of a measured value include all the numbers that can be read directly from the instrument scale plus one doubtful or estimated number the fractional part of the least count smallest division For example the length of the rod in Fig 1 4 as measured from the zero end is 2 64 cm The rod s length is known to be between 2 6 cm and 2 7 cm The estimated fraction is taken to be 4 10 of imm E f Figure 1 4 Leastcount Meter sticks are commonly calibrated in centimeters cm the numbered major divisions with a least count or smallest subdivision of millimeters mm www ATIBOOK ir 6 EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis the least count mm so the doubtful figure is 4 giving 2 64 cm with three significant figures Thus measured values contain
456. revolution or period Then using Eq 9 2 calculate the centripetal force Attach a string to the bob opposite the spring and sus pend a weight hanger over the pulley Add weights to the hanger until the bob is directly over the pointer Record the weight Mg in the data table Do not for get to add the mass of the weight hanger This weight EXPERIMENT 9 Centripetal Force 145 calculated value and compute the percent difference of the two values 6 Variation of mass Unscrew the nut on the top of the bob insert a slotted mass of 100 g or more under it and retighten the nut Repeat Procedures 11 through 13 for determining the period of rotation and compar ing the computed value of the centripetal force with the direct measurement of the spring tension Ques tion Does the latter measurement need to be re peated Record your findings in Data Table 2 7 Variation of radius Remove the slotted masses from the bob and if pointer P is adjustable move it far ther away from the axis of rotation to provide a larger path radius Measure and record this distance in Data Table 3 Repeat Procedures 11 through 13 for this experimental condition 8 Variation of spring tension optional Replace the spring with another spring of different stiffness Repeat Procedures 11 through 13 recording your findings in Data Table 4 B Centripetal Force Apparatus with Variable Speed Rotor 9 The centripetal force apparatus mou
457. ribe all things that look different between Graphs 2 and 3 What is the effect of changing the slit width continued 479 www ATIBOOK ir EXPERIMENT 32 Single Slit and Double Slit Diffraction Laboratory Report 3 Comparison between Graphs 2 and 4 a What parameters of the experiment were kept constant in producing Graphs 2 and 4 What parameters were changed b Describe all things that look different between Graphs 2 and 4 What is the effect of changing the separation between the slits 480 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 3 Detection of Nuclear Radiation The Geiger Counter RWV Advance Study Assignment Read the experiment and answer the following questions 1 What is the principle of operation of the Geiger tube 2 Define each of the following a threshold voltage b cumulative ionization c plateau and d dead time 3 Are any radiations counted when the tube voltage is below the threshold voltage Explain 481 continued www ATIBOOK ir EXPERIMENT 838 Advance Study Assignment 4 Approximately how many volts above the threshold voltage is the normal operating voltage of the Geiger tube and why is the operating voltage selected this way 5 What is background radiation 6 How does the count rate vary with distance from a point source If the counter is moved twice the distance from the source how is the count rate affected NUCL
458. ric field when connected to a voltage source for example a battery The common electrode configurations ordinarily provided are two dots representing point charges of an electric dipole configuration and two parallel linear electrodes representing a two dimensional cross sec tion of a parallel plate capacitor Fig 19 4b 2 Draw the electric dipole configuration on a sheet of graph paper to the same scale and coordinates as those of the painted dipole on the imprinted grid on the conducting sheet Then place the dipole conducting sheet on the board and set the contact terminals firmly on the painted electrode connections If you are using a galvanometer do Procedures 3 through 7 If you are using a voltmeter do Procedures 8 through 12 www ATIBOOK ir 286 Figure 19 4 Electric field mapping equipment EXPERIMENT 19 Fields and Equipotentials b a Equipment for painting electrodes on conductive paper in preparation for mea suring voltages to map equipotentials b A parallel plate capacitor configuration on the board and an electric dipole configuration to the right Photos Courtesy of Sargent Welch GALVANOMETER MEASUREMENTS 3 Connect the probes to the galvanometer as shown in Fig 19 4b The probes are used to locate points in the field that are at equipotential Connect the voltage source 1 5 V battery to the board terminals Place a switch in the circuit not shown in the figure and leave it op
459. riment For better learning and understanding an Experimental Planning section gives a brief introduction and guides the students though the basics of an experiment by a series of related questions which they answer The GL Experimental Planning is limited to selected Traditional Instruction TI experiments about which students should have some knowledge These are labeled GL in the table of contents Traditional Instruction TI and Computerized Instruction CI The use of computerized instruction and equipment has become increasingly popular in introductory physics labo ratories To accommodate this 10 experiments have both TI and CI sections the latter of which describes an experiment using computerized equipment The TI and CI components generally treat the same principles but from different per spectives These experiments give the instructor the option of doing the TI experiment the CI experiment or both It is suggested that in some instances students do the hands on TI experiment first so as to gain a basic knowledge of what is being measured It is here that the physical parameters of the experiment are clearly associated with prin ciples and results Once students have this type acquaintance with experimental concepts they can better perform the CI experiment or view it as a demonstration if limited CI equip ment is available Then the student can better understand the computer procedure and analysis of electronic reco
460. ritus Professor of Physics Lander University Greenwood South Carolina jwilson 9 greenwood net Cecilia A Hern ndez Hall Professor of Physics American River College Sacramento California hernanc Q arc losrios edu www ATIBOOK ir Introduction WuHy WE MAKE EXPERIMENTAL MEASUREMENTS When you can measure what you are speaking about and express it in numbers you know something about it but when you cannot measure it when you cannot express it in numbers your knowledge is of a meager and unsatisfac tory kind LORD KELVIN 1824 1907 As Lord Kelvin so aptly expressed we measure things to know something about them so that we can describe objects and understand phenomena Experi mental measurement is the cornerstone of the scientific method which holds that no theory or model of nature is tenable unless the results it predicts are in accord with experiment The main purpose of an introductory physics laboratory is to provide hands on experiences of various physical principles In so doing one becomes familiar with laboratory equipment procedures and the scientific method In general the theory of a physical principle will be presented in an experiment and the predicted results will be tested by experimental measurements Of course these well known principles have been tested many times before and there are accepted values for certain physical quanti ties Basically you will be comparing your experimen t
461. rm with standard units a F m or more commonly Fe ma This relationship will be investigated using an Atwood machine which consists of two masses connected by a string looped over a pulley TI Fig 6 1a The Atwood machine is named after the British scientist George Atwood 1746 1807 who used the arrangement to study motion and measure the value of g the acceleration due to gravity In this experiment the relatively slow uniform accel eration of the masses will be used to investigate Newton s second law Since the acceleration a of the system depends on two variables F et and m where a F m one of the variables will be held constant while the other is varied This is common experimental procedure By varying the net weight force and the total mass of the system the resulting accelerations can be experimentally determined from distance and time measurements and compared with the predictions of Newton s second law net RV OBJECTIVES After performing this experiment and analyzing the data you should be able to do the following 1 Tell how the acceleration of a system varies with changes in the net force or mass in particular for a mass variations with a constant net force and b force variations with constant mass 2 Articulate the precise meanings of the variables F m and a in Newton s second law 3 Explain how the acceleration of the masses of an Atwood machine may be determined experi
462. rmal operation is the plateau region See text for description www ATIBOOK ir EXPERIMENT 33 Detection of Nuclear Radiation The Geiger Counter 485 B Inverse Square Relationship In normal operation the count rate depends on the number of particles per unit time entering the Geiger tube Hence the count rate depends on the distance of the tube from the source For a point source emitting a total of N particles min the particles are emitted in all directions The num ber of particles min N passing through a unit area of a sphere of radius r is N N N t 5 A Amr counts min area 33 1 where A 47 is the area of the sphere A Geiger tube with a window area A at a distance r from a point source then intercepts or receives N counts min given by N A N N A 33 2 Amr Although the effective area A of the Geiger tube is usu ally not known the equation shows that the count rate is inversely proportional to r inverse square form N 33 3 Hence for a point source the count rate falls off as yr with the distance from the source EXPERIMENTAL PROCEDURE Caution Review the radiation safety procedures before performing this experiment 1 Connect the Geiger tube probe to the counter by means of the coaxial cable Before plugging the coun ter into an ac outlet familiarize yourself with the con trols particularly the high voltage control Sca
463. rmine the slope of the best fitting line for the plot and enter the result in the table Attach the graph to the laboratory report B The Effect of the Speed 1 Set up the equipment as shown in CI Fig 10 1 It is important that the string connecting the force sensor to the pile of objects be horizontal If using additional blocks instead of the PASCO cars tape the blocks to gether so that they will not fall off Set the motorized car for a slow speed Turn on the motorized car Wait until the string tenses before pressing the START button to begin collecting data Let the car move pulling along the block for about 20 cm and then press the STOP button Stop the car Report the average frictional force reading in CI Data Table 2 Increase the speed of the motorized car and measure the average frictional force again Repeat by increas ing the speed for each trial until the table is complete www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s C Friction E X P ETR ff Laboratory Report A The Effect of the Load ED orate MENT 1 0 Purpose To investigate the effect of changing the load on an object and thus changing the normal force on the magnitude of the frictional force Don t forget units 171 Total mass of Frictional force Normal force Trial sliding object sens
464. rowded go to Experi ment in the main menu top of the screen and choose Delete all Data Runs This will completely erase the data already collected The fits can also be removed by deselecting them in the Fit menu B Resistances in Series 1 CI Figure 23 5 Resistors connected in series Delete all the data to clear the graph Also clear all the fits Run 1 Connect resistor R alone to the voltage source and take data as before Do a linear fit and report the measured resistance in CI Data Table 2 Introduce resistor R to the circuit by connecting it in series with resistor Aj Connect the voltage sensor across both resistors R and R See CI Fig 23 5 Run 2 Press START and collect the data Do a lin ear fit and report the measured resistance in CI Data Table 2 Now introduce resistor R to the circuit by connecting it in series with R and R Connect the voltage sensor across all three resistors See CI Fig 23 5 Run 3 Press START and collect the data Do a linear fit and report the measured resistance in CI Data Table 2 Remove the fit information boxes and print the graph Label it Series Circuits and attach it to the labora tory report RUN 1 Output Output current current t E t Signal Voltage generator sensor to the series RUN 2 10 11 C 1 Calculate the theoretical expected value of the equivalent resistance of each circuit Compare the theoret
465. rs an elastic collision 2 What mechanism will be used to make the collision between the cars an inelastic collision 104 Advance Study Assignment www ATIBOOK ir EX PER d MENT 7 Conservation of Linear Momentum OVERVIEW Experiment 7 examines the conservation of linear momentum by TI procedures and or CI procedures The TI procedure uses distance time measurements to deter mine the velocities of air track cars before and after col lisions in the investigation of the conservation of linear momentum The CI procedure measures the velocities electroni cally and graphs the data The velocities total momentum and total kinetic energy are obtained from the graphs INTRODUCTION AND OBJECTIVES The conservation of linear momentum p mv is an important physical concept However the experimental investigation of this concept in an introductory physics laboratory is hampered by ever present frictional forces An air track provides one of the best methods to investigate linear momentum see TI Fig 4 2 Aluminum cars or gliders riding on a cushion of air on the track ap proximate frictionless motion a necessary condition for the conservation of linear momentum In the absence of friction and other external forces the total linear momentum of a system of two cars will be conserved during a collision That is the total linear mo mentum of the system should be the same after collision as before collision
466. rs on the center of the slit image with the fine adjustment screw if available Make the slit Source as narrow as possible so that the best setting can be made On a force table apparatus adjustment is not required Read the angle from the divided circle and record it in the laboratory report Repeat this procedure for the other face of the prism As shown in Fig 30 4 the angle between the positions is equal to 2A Compute the angle A from the circle readings 5 Measurement of the angle of minimum deviation Remove the prism and move the telescope into the line of sight of the slit It is convenient but not necessary to adjust the setup so the telescope has a zero reading on the divided circle This makes finding the deviation angles easy by reading directly Adjust the telescope so that a sharp image of the illuminated slit is seen on the cross hairs Note and record the reading of the divided circle Replace and rotate the prism to a position as shown in Fig 30 5 and with the unaided eye locate the emergent spectrum of colors Move the telescope in front of the eye and examine the spectrum Change the slit width if applicable and note any difference List the sequence of colors beginning with red in the laboratory report With the slit set as narrow as possible rotate the prism back and forth slightly and note the reversal of the direction of motion of the spectrum when the prism is rotated in one direct
467. ruments Mass Volume and Density Laboratory Report RV QUESTIONS 1 Explain the probable source of error s in the experimental determination of the number of manual pages 2 In the first four density determinations in Data Table 4 what major factors might account for the experimental errors that were obtained 3 In determining the volume of the irregularly shaped object any air bubbles sticking to the surface of the object when it is submerged cause systematic errors Will this error give an experimental density that is too high or too low Explain 4 Suppose that you were given an irregularly shaped object that floats Describe how you would experimentally determine its volume continued 33 www ATIBOOK ir EXPERIMENT 2 Measurement Instruments Mass Volume and Density Laboratory Report 5 6 34 A thin circular sheet of aluminum has a radius of 20 cm and a thickness of 0 50 mm Find the mass of the sheet Archimedes a famous Greek scientist was given a problem by King Hieron II of Syracuse Sicily The king suspected that his crown which was supposed to be made of pure gold contained some silver alloy and he asked Archimedes to prove or disprove his suspicion It turned out that the crown did contain silver How would you experimentally determined whether or not the crown was pure gold Hint the method came to Archimedes when getting into a full bathtub See the footnote in Experiment 18 for Archimedes
468. rved activity of a radioactive source of a given strength depends on several factors for example the dis tance of the counter from the source For a point source the Observed activity varies inversely with the distance from the source inverse square relationship This decrease is due to the geometrical spreading of the emitted nuclear radiation outward from the source If a Geiger probe is a fixed distance from a long lived source the observed activity is relatively constant However if a sheet of material is placed between the source and the counter a decrease in the activity may be observed That is the nuclear radiation is absorbed by the material The amount of absorption depends on the type and energy of the radiation and on the kind and density of the absorbing material The absorption or degree of penetration of nuclear radiation is an important consideration in applications such as medical radioisotope treatment and nuclear shielding for example around a nuclear reactor Also in industrial manufacturing processes the absorption of nuclear radiation is used to monitor and control automatically the thickness of metal and plastic sheets and films In this experiment the absorption properties of various materials for different kinds of nuclear radiation will be investigated After performing this experiment and analyzing the data you should be able to 1 Describe the parameters on which the penetration of nuclear radia
469. ry Plot the sample activity N in cpm versus the elapsed time f in minutes on Cartesian graph paper and note the shape of the curve From the graph make two determinations of the half life by finding the time required for the sample activ ity to decay from its initial value to i of the initial value and from 5 to of the initial value Average and compare with the half life for Ba 137m in Appendix Table A9 by computing the percent error Also compute the decay constant A from the average value of the half life EXPERIMENT 34 Radioactive Half Life 495 7 The decay constant may be found graphically by putting the exponential function N N e into linear form by taking the natural logarithm base e of both sides In N In N e Ince In N or InN At InN 34 3 Note that Eq 34 3 has the form of a straight line y mx b See Experiment 1 for general discussion Find In N for each value of N in the Data Table Make a column for these to the right of the table Plot In N versus f on Cartesian graph paper and draw a straight line that best fits the data Determine the slope of the line and compare it to the value of the decay constant computed in the preceding procedure by finding the percent difference Optional Your instructor may wish to introduce you to semi log graph paper This special graph paper automatically takes the log values of the variable plot ted on the Y a
470. ry Motion Sensor Resolubor Linear Scale Low Divisions ARotation L ge Pulley Groove Measuremerits Visib ity Name fv Voltage ChA Light Imensity ChA Ceabbrate Sensors Samping D phon Choose Inleslace 016533 Sample Rate fu 20 77 Hz Sersor Samping Options CI Figure 29 1 The Experiment Setup window A light sensor will measure the intensity of the light that crosses the analyzer The rotary motion sensor will measure the angular rotation of the analyzer with respect to the polarizer Reprinted courtesy of PASCO Scientific b c d e CI Fig 29 4 Rotate the aperture disk so that the translucent mask covers the opening of the light sensor CI Fig 29 5a Mount the polarizers into the holders Mount the RMS bracket on the holder that has the polarizer with groove CI Fig 29 5b The rotary motion sensor is mounted on the polarizer bracket and the plastic belt is used to connect the large pulley of the RMS with the polarizer groove The polarizer with the RMS will be the analyzer in this experiment CI Fig 29 6 The components are placed on the optics track in the order shown in this figure The light from the laser will pass a polarizer first then pass the analyzer with the RMS and finally make it into the light sensor 2 Setting the correct light sensor gain a Bring Graph 1 voltage versus time to the front on th
471. s T Rotation Courts Ch 142 coum Angus Position Ch 152 Iv Ange Velocity Ch 152 tad T Angus Acceleration Ch 152 deg s s Position Ch 182 Unit ol Measure Courte Sample Zeo enter eu 7 fe z Revese apn of al sanpies CI Figure 14 3 Experimental setup The seven available channels are numbered 1 through 4 and A B or C The rotary motion sensor connected to Channels 1 and 2 will measure the angular position and the angular velocity of the pendulum Make sure that the angular position is being measured in degrees but the angular velocity in rad s Reprinted courtesy of PASCO Scientific www ATIBOOK ir Set the Sample Rate to 20 Hz The Data list on the left of the screen should now have two icons one for the angular position data the other for the angular velocity data 8 Open the program s calculator by clicking on the Calculate button on the top main menu Usually a small version of the calculator opens as shown in e CI Fig 14 4 Expand the calculator win dow by clicking on the button marked Experiment Constants 9 The expanded window shown in e CI Fig 14 5 is used to establish values of parameters that will remain constant throughout the experiment In this case these are the length of the pendulum ZL and the mass of the pendulum M which have already been measured This is how to do it a Click on the lower New button within the Experiment Constants section
472. s used lay the tube in the mounting board groove and tape it down to immobilize it or tape it to a meter stick 4 www ATIBOOK ir Figure 35 3 Geiger counter setup Fisher Scientific Com pany LLC M Turn on the counter Place the radioactive source near the probe and adjust the tube voltage to the plateau operating voltage A Absorption of Beta Radiation 3 Adjust the distance of the source from the probe so that the observed count rate is about 8000 cpm For a rate meter the count rate is taken as the average of the high and low meter readings for 30 s time intervals Record the count rate J in the cardboard column in Data Table 2 Place a sheet of cardboard between the source and the probe and measure and record the count rate Allow a rate meter to come to equilibrium before tak ing a 30 s reading 4 Add cardboard sheets between the source and the probe one at a time measuring and recording the count rate after the addition of each sheet Continue until the count rate is relatively constant with the addi tion of four successive sheets 5 Remove the cardboard sheets and repeat the proce dure with aluminum sheets 6 Without recording data repeat the procedure with lead sheets and mentally note the degree of beta ab sorption or penetration in lead 7 Plot the intensity in cpm versus the number n of absorber sheets for both cardboard and aluminum on the same Cartesian graph Dual label
473. s across a capacitor in dc and ac RC circuits 2 How is the time base of the horizontal oscilloscope trace determined 3 What is the significance of the RC time constant for the circuit 4 Explain how the time constant of an RC circuit is determined from a stationary oscilloscope pattern 375 continued www ATIBOOK ir EXPERIMENT 26 Advance Study Assignment Ef Advance Study Assignment Read the experiment and answer the following questions 1 What is the time constant of an RC circuit and what are the units of measurement 2 How many time constants will you have to wait before you can consider the capacitor fully charged 376 www A TIBOOK ir EX P E Rl d ENT 2 6 The RC Time Constant Electronic Timing OVERVIEW Experiment 26 examines the RC time constant using complementary electronic TI and CI approaches In the TI procedure the time constant of an RC circuit is deter mined from an oscilloscope trace of voltage versus time This is done for combinations of RC values In the CI procedure a voltage sensor monitors voltage changes for charging and discharging and supplies data to the computer From computer drawn graphs of voltage versus time the time constant is determined the point of 63 of maximum voltage for charging and 37 of the maximum voltage for discharging The procedure is done for two resistances INTRODUCTION AND OBJECTIVES The oscilloscope can be used to stud
474. s and Parallel Run 1 R alone Run 2 R and R in series Run 3 R Ry and R in series Measured equivalent resistance Theoretical equivalent resistance R R Rte Percent difference Maximum voltage Maximum current 356 Laboratory Report www ATIBOOK ir Name Section Date Lab Partner s EXPERTMEN TT 23 C Resistances in Parallel ED vata taste s Purpose To experimentally measure the equivalent resistance of parallel circuits Resistances in Series and Parallel Run 1 R alone Run 2 Run 3 R and R in parallel in parallel R R and R3 Measured equivalent resistance Theoretical equivalent resistance Percent difference Maximum voltage Maximum current Don t forget units Laboratory Report continued 357 www ATIBOOK ir EXPERIMENT 23 Resistances in Series and Parallel Laboratory Report ED questions 1 As more resistors were added to the series circuit what happened to the total resistance of the circuit 2 For approximately the same maximum voltage what happened to the maximum current as more resistors were added to the series circuit 3 As more resistors were added to the parallel circuit what happened to the total resistance of the circuit 4 For approximately the same maximum voltage what happened to the maximum current as more resistors were added to the p
475. s and their specific heats in cal g C The type of material and specific heat of the calorimeter cup are usually stamped on the cup For the coil usually copper a table of spe cific heats is given in Appendix A Table A4 2 Fill the calorimeter cup about two thirds full of cool tap water several degrees below room temperature The cup should be filled high enough that the immer sion heater will be completely covered when immersed later Determine and record the mass of the calorim eter cup with the water 3 Place the immersion heater in the calorimeter cup and set up the circuit as illustrated in Fig 24 1 with the rheo stat set at its maximum resistance Make certain that the heating coil is completely immersed If not add more water and reweigh the cup and water as in Procedure 2 Reweigh the cup and water as in Procedure 2 Do not www A TIBOOK ir plug in the power supply or connect the battery until the circuit has been checked by the instructor After the circuit has been checked plug in the power supply set to 10 V to 12 V Adjust the rheostat until there is a constant current between 2 A and 3 A in the circuit as indicated on the ammeter If a variable power supply is used it may also be used to make fine current adjustments Then unplug the power supply This procedure should be done as quickly as possible to avoid heating the water Add some ice to the water in the calorimeter cup with the immersion
476. s equal to the object s weight The upward force resulting from an ob ject being wholly or partially immersed in a fluid is called the buoyant force How the buoyant force arises can be un derstood by considering a buoyant object being held under the surface of a liquid Fig 18 2 The pressures on the upper and lower surfaces of the block are given by the pressure depth equations Di pgh and p pgh respectively where p is the density of the fluid Thus there is a pressure difference Ap p p pyg h hi which gives an upward force the buoyant force In this case the buoyant force is balanced by the downward applied force and the weight of the block It is not difficult to derive an expression for the mag nitude of the buoyant force If both the top and bottom ar eas of the block are A the buoyant force F is given by F ApA pi gV where V is the volume of the fluid dis placed But p V is simply the mass of the fluid displaced by the block recall that p m V Hence the magnitude of the buoyant force is equal to the weight of the fluid displaced by the block This general result is known as Archimedes principle An object immersed wholly or partially in a fluid experi ences a buoyant force equal in magnitude to the weight of the volume of fluid that it displaces Thus the magnitude of the buoyant force depends only on the weight of the fluid displaced by the object not on the weight of the obje
477. s f and f are placed in contact the lens combination has focal length f given by il 1 1 28 5 Ep PE Place the concave lens in contact with the convex lens convex surface to concave surface in a lens holder and determine the focal length of the lens combination by finding the image of a distant object as in f Procedure 8 Record in the laboratory report Using Eq 28 5 with the focal length of the convex lens determined in Procedure 8 compute the focal length of the concave lens www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 8 Spherical Mirrors and Lenses fry Laboratory Report A Spherical Mirrors Concave Mirror Ray diagrams d f f d HR Don t forget units continued 411 www ATIBOOK ir EXPERIMENT 28 Spherical Mirrors and Lenses Laboratory Report Calculation of d for object at oc Experimental focal length f Average DATA TABLE 1 Purpose To determine the image distance and magnification Experimental Computed r i t d d M factor d percen pog C estimated TE M difference d gt R d R f d R d f Calculations show work 412 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 28 Spherical Mirrors and Lenses Laboratory Report Convex mirror Ray diagrams f lt d lt R do lt
478. s law of gravitation It is a special case there being no law that materials must have constant resistance To understand the relationships of the quantities in Ohm s law it is often helpful to consider the analogy of a liquid circuit TI Fig 20 2 In a liquid circuit the force to move the liquid is supplied by a pump The rate AAMA x Los Fi Y cattery Electr ca circu Lic aid z spi TI Figure 20 2 Analogy to a liquid circuit In the analogy between a simple electric circuit and a liquid circuit the pump corresponds to a voltage source the liquid flow corresponds to electric current and the paddle wheel hindrance to the flow is analogous to a resistor Keep in mind that an analogy only illustrates a resemblance Liquid and electrical circuits are physically quite different www ATIBOOK ir 296 EXPERIMENT 20 Ohm s Law of liquid flow depends on the resistance to the flow for example due to some partial obstruction in the circuit pipe here a paddle wheel the greater the resistance the less the liquid flow Analogously in an electrical circuit a voltage source a battery or power supply supplies the voltage potential difference for charge flow and the magnitude of the cur rent is determined by the resistance R in the circuit For a given voltage the greater the resistance the less current through the resistance as may be seen from Ohm s law I VIR Notice that the voltage sou
479. s of the potential differences or voltage drops across circuit components 291 continued www ATIBOOK ir EXPERIMENT 20 A Advance Study Assignment Read the experiment and answer the following questions 1 What is a triangle wave voltage function 2 What is a nonohmic resistance How can we distinguish between an ohmic and a nonohmic resistance 292 Advance Study Assignment www A TIBOOK ir EX PE RI d Ohm s Law OVERVIEW Experiment 20 examines Ohm s law by TI and CI proce dures In the TI procedure an experimental circuit makes it possible to investigate 1 the variation of current with voltage and 2 the variation of current and resistance ENT 2 0 constant voltage The CI procedure looks at the voltage current relationship not only for an ohmic resistance but also for a nonohmic resistance Steadily increasing and decreasing voltages are obtained by using a signal generator to produce a triangle wave voltage INTRODUCTION AND OBJECTIVES One of the most frequently applied relationships in cur rent electricity is that known as Ohm s law This rela tionship discovered by the German physicist Georg Ohm 1787 1854 is fundamental to the analysis of electrical circuits Basically it relates the voltage V and current associated with a resistance R Ohm s law applies to many but not all materials Many materials show a constant resistance over a wide range of applied vol
480. s set up for common base 10 logarithms rather than natural base e logarithms Exponential func tions may be treated as follows Taking the common log of each side of y Ae yields log y log A log e log A axloge log A 0 4343 ax E 4 where log e 0 4343 523 Hence the slope of the resulting straight line is 0 4343 a rather than simply a The logarithmic ordinate scale is called one cycle two cycle and so on depending on the number of pow ers of 10 covered on the axis The beginnings of the cycles are consecutively labeled in multiples of 10 for example 0 1 1 0 10 or 1 0 10 100 etc depending on the range cycles of the function Common logarithms can also be plotted on semi log paper Care must be taken in determining the slope of the line on a semi log plot On an ordinary Cartesian graph the slope of a line is given by Ay Ax y yix xj However on a semi log graph the slope of a line is given by Alog y or ae E 5 a da At On a semi log plot the listed ordinate values are y not In y Hence one must explicitly take the logs of the ordinate values of the endpoints of the slope interval y and y or the log of their ratio i Alogy _ logy log y slope 4 Ax X27 log y g Y Y1 E 6 Xj X The value of N can be read directly from the y intercept of the graph Another common equation form in
481. s theoretically independent of the mass of the pendulum bob Also within the limits of the small angle approximation Eq 3 2 the period is independent of the displacement angle It is sometimes helpful to visualize a physical system as a black box with inputs and outputs The black box is the relationship between the input and output parame ters The term parameter refers to anything in the physical system that can be measured The input parameters are the physical variables that may control or influence the behavior of the output parameters the physical quantities that are measured and describe the resulting behavior of the system The Input M m 0 L 4 4 4 Simple Pendulum L 1 0 T s sin g 4 2 li T T Output Figure 3 2 Input and output parameters For a simple pendulum the input parameters m 0 and L influence the output parameter T Suggested by Professor I L Fischer Bergen Community College New Jersey input parameters are often called independent variables because they can be varied independently of each other The output parameters on the other hand may be called dependent variables because their values depend on the inputs In any given system some of the inputs may have little or no effect on the outputs 8 Fig 3 2 You may find that drawing black box diagrams will help you understand the physical systems investigated in later experiments EXPERIMENTA
482. s to the accepted value provided by the instructor by computing the percent error www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 2 The Temperature Dependence of Resistance RV Laboratory Report A Metal Conductor s DATA TABLE 1 Purpose To determine the temperature coefficient of resistance Material Decade box Coil resistance Temperature resistance L L R L L R C R C 2 Calculations Slope Ra show work Intercept R Experimental a Accepted a Percent error Don t forget units 329 continued www ATIBOOK ir EXPERIMENT 22 DATA TABLE 1A Optional The Temperature Dependence of Resistance Purpose To determine the temperature coefficient of resistance Decade box Temperature resistance Li L Coil resistance C RC R Calculations show work 330 Material Slope R amp Intercept R Experimental a Accepted a Percent error Laboratory Report www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 22 The Temperature Dependence of Resistance Laboratory Report B Thermistor DATA TABLE 2 Calculations show work Purpose To determine the exponential temperature coefficient of resistance
483. scale mark Hence the marks change phase between the 2 and 3 marks which means the reading is between 1 22 cm and 1 23 cm Most vernier scales are not fine enough for us to make an estimate of the doubtful figure so a suggested method is to take the middle of the range Thus a 5 would be put in the thousandth of a centimeter digit for a reading of 1 225 cm ZEROING Before making a measurement one should check the zero of the vernier caliper with the jaws completely closed It is possible that through misuse the caliper is no longer zeroed and thus gives erroneous readings systematic E S Oberhofer The Vernier Caliper and Significant Figures The Physics Teacher Vol 23 November 1985 493 error If this is the case a zero correction should be made for each reading In zeroing if the vernier zero lies to the right of the main scale zero measurements will be too large and the error is taken to be positive In this case the zero correction is made by subtracting the zero reading from the measure ment reading For example the zero reading in Fig 2 4 is 0 05 cm and this amount must be subtracted from each measurement reading for more accurate results 0 00 a Properly zeroed 0 05 b Positive arror 0 05 cm subtracted from measurement reading Figure 2 4 Zeroing and error The zero of the vernier caliper is checked with the jaws closed a Zero error b Positive error 0 05 cm
484. servation of total energy 2 Is mechanical energy conserved in real situations Is the total energy conserved Explain 3 Discuss the relationship between work and energy for a car moving with a constant speed a up an incline and b down an incline 4 Under what conditions would the frictional forces be expected to be equal in magnitude for a car moving up an incline and a car moving down an incline continued 179 www ATIBOOK ir EXPERIMENT 11 Advance Study Assignment 5 Is the force of friction the same for different angles of incline if all other parameters are equal Explain by specifically considering the angles used in the experiment 6 What are possible sources of error in this experiment Identify them as personal or systematic errors See Experiment 1 180 www ATIBOOK ir EXPERIMENT 1 1 INTRODUCTION AND OBJECTIVES the cases of a car rolling up and down an inclined plane ses The ever present frictional forces and the work done Work and energy are intimately related as emphasized in a En common dehinition ot enemy as the ability to do work That against friction will be investigated and taken into account is an object or system possessing energy has the capability sore toque a boner enn GTS anes oe pa x of daine work When wot is done by a systeui energy is work energy To simplify matters experimental conditions Gxeande dins system loses netos Conversel isa there
485. sk by means of a milled screw head as illustrated in the photo b For this apparatus when the centripetal force is equal to the spring force the pointer P will rise and point horizontally toward the tip of the index screw J See also Fig 9 4 c Motor with belt guard and rotating arm in horizontal storage position Note The belt guard has been removed in a and b for more complete illustration Caution When in operation the motor should always be equipped with a belt guard for safety lt 4 d A self contained centripetal force apparatus that eliminates any belt guard problem The apparatus has a digital readout Photos Courtesy of Sargent Welch Figure 9 4 Pointer and screw index When the apparatus is rotating the mass acting against the pointer P will cause it to rise and point toward the index screw J www ATIBOOK ir 11 12 the centripetal force apparatus in contact with pointer P will cause the pointer to rise and horizontally point toward the index screw J In this condition the mass will be in uniform circular motion around the axis of rotation through J Caution When taking measurements be careful not to come in contact with the rotating apparatus The rotor should not be operated without a belt guard cov ering the belt and pulleys See Fig 9 3 c Put on your safety glasses and turn on the rotor Ad just the speed until the pointer rises and is opposite the head of the index screw Fig 9 4 Observe t
486. so assign a positive or negative sign depending on direction In general an object moving toward the sensor is assigned a positive velocity and an object moving away from the sensor is assigned a negative velocity An object in motion also has kinetic energy The total kinetic energy in a system can be determined by adding the kinetic energies of all objects in the system CI 7 2 2 l 2 Kyo Ki Ky m vi oymyv The total momentum and the total kinetic energy just before and just after a collision are determined and compared First an elastic collision between two cars is considered The cars have magnets that make them repel each other when they get close enough The effect is that the cars bounce off each other collide without touching Next an inelastic collision is considered The magnets are replaced by a piece of clay or Velcro that will make the cars stick to each other after the collision BEFORE YOU BEGIN 1 Install a cart string bracket on each of the collision carts The cart string bracket is mounted on the side of the cart as shown in e CI Fig 7 1 2 Choose one cart to be Car 1 and measure its mass in kilograms including the cart string bracket Report the mass of Car 1 in the laboratory report 3 The other cart will be Car 2 Measure its mass and also record that mass in the laboratory report 4 Do not lose track of which is Car 1 and which is Car 2 If needed put a smal
487. sor IF Reverse sp of S targes CI Figure 20 2 The Experiment Setup window The voltage sensor is connected to Channel A and works as a multimeter The signal generator of the Science Workshop interface is used as the voltage source that produces a triangle wave function Reprinted courtesy of PASCO Scientific iid Gn Amplitude Off Frequency 5 000 y 0500 Hz Tag 1 000 010 E3 Measurements And Sample Rate ll Measure Output Voltage Sample Rate Measure Output Current 100 Hz CI Figure 20 3 The Signal Generator window Choose a triangle wave function adjust the amplitude and the frequency as specified in the setup procedure and choose to measure the output current Reprinted courtesy of PASCO Scientific www ATIBOOK ir EXPERIMENT 20 Ohm s Law 305 DataStudio a EEEREEEEEEEEEEEEEEEEENEeLLECOGIGGGLLLE EOLLL ZCAL LZ L Z ZLLLL LL LLLLIIQLLLLLAU EJ Ele Edt Experiment Window Display Help pz Summary Setup gt Start ME i Calculate Voltage ChA V 42 Voltage ChA vs Output Cur v Output Current A 3 Digits Ja FFT 5 4 Graph Graph 1 idi Histogram 7 Meter t gt Scope K Sound Creator Daal ie AA Al oom dx el e Voltage ChA V on 3 4 5 Output Current A Oy ce Wave x Frequency SP 000 v 0 500 amp Sound Analyzer M Hs 1 000 o10 E Table Measurements A
488. spend it from a support as shown in Fig 9 5 Sus pend enough mass on the hanger to produce the same extension of the spring as when on the rotor pointer aimed at the index screw position Record this mass M includes mass of hanger in the laboratory report below Data Table 1 Also re cord the mass of the cylinder m in the force apparatus stamped on the end of the cylinder i i S tervals but do not use the previous final counter read ing for the next initial interval reading Advance the counter to a new arbitrary initial reading for each trial Figure 9 5 Spring tension Arrangement for the applica tion of gravitational force to measure the spring tensions Photo Courtesy of Sargent Welch www A TIBOOK ir 148 EXPERIMENT 9 Centripetal Force Add the masses to find the total suspended mass M M m and compute the direct measure of F weight of total suspended mass Mg With the spring at the same tension setting and the apparatus still hanging from the support with the same mass M suspended use a vernier caliper to measure the distance r or the radius of the circular rotational path and record This is the distance between the axis of rotation line through the index screw and the cen ter of mass of the cylinder see Fig 9 4 The distance is conveniently measured between a line scribed on the upper part of the force apparatus frame above the index screw and a line scribed on the center of the c
489. ssible for the first order spectrum to overlap the second order spectrum Explain assuming a continuous spectrum 4 Is there a theoretical limit to the order of the spectrum you would be able to observe with your diffraction grating Justify your answer mathematically continued 469 www ATIBOOK ir EXPERIMENT 32 The Transmission Diffraction Grating Laboratory Report 5 Reminder about rounding errors In Example 32 1 values were rounded to the proper number of significant figures in each step Recall that in Experiment it was suggested that one or two insignificant extra figures usually be carried along and stated that if a calculator is used rounding off may be done only on the final result of multiple calculations If you applied these rules to the calculations in Example 32 1 would you get 589 nm Justify your answer 470 www A TIBOOK ir C I EXPERIMENT 3 2 Single Slit and Double Slit Diffraction g EQUIPMENT NEEDED Light sensor CI 6504A Single slit disk from Slit Accessory OS 8523 SM S EQDIONUDSIDARTODHES Seem ened Multiple slit disk from Slit Accessory OS 8523 OS 8515 Diode laser OS 8525 Note The light sensor needs to be calibrated before use Linear translator OS 8535 Refer to the owner s manual for instructions on how to Aperture bracket OS 8534 calibrate the sensor Rotary motion sensor CI 6538 ED mory A Single Slit Diffraction Diffraction is the bending o
490. ssignment Read the experiment and answer the following questions 1 What are Hooke s law and simple harmonic motion and how are they related 2 What is the physical significance of the spring constant of a spring What does it tell you 3 How is the spring constant determined in this experiment 4 In the equation of motion for simple harmonic motion Eq TI 14 2 what physically determines A and T continued 219 www ATIBOOK ir EXPERIMENT 14 Advance Study Assignment 5 How is the period of a mass oscillating on a spring related to the spring constant Express your answer mathematically and verbally Advance Study Assignment Read the experiment and answer the following questions 1 What are the requirements for an object to move with simple harmonic motion 2 Why is simple harmonic motion an idealization 3 What is a simple pendulum 4 Under what conditions can a pendulum be considered a simple harmonic oscillator 5 Why is it important to start taking data when the pendulum is still at rest in its equilibrium position 220 www A TIBOOK ir EX PE Rl d ENT 14 Simple Harmonic Motion OVERVIEW Experiment 14 considers simple harmonic motion SHM with TI and or CI procedures The TI procedure examines Hooke s law using rubber band and spring elongations Simple harmonic motion is investigated through the period of oscillation of a mass on a spring The CI procedure investigates t
491. stance from the origin triple also Can you see the pattern 2 Discuss what it means to say that the position function is not directly proportional to the time t but to the time squared t7 3 Judging on the basis of the observed pattern and without using theoretical equations predict the position of the car when the time is 10 What will the position be at 201 4 In CI Data Table 2 you repeated the procedure for the velocities What is the pattern now 5 On the basis of the observed pattern predict the velocity of the car for times 10 and 20f 6 A graph of x versus t is a parabola because x f But if you plot x versus 7 the resulting graph will be a straight line with slope Ja as shown below Make a graph with your values of x on the vertical axis and your times squared on the horizontal Determine the slope and use it to find the acceleration of the car Attach a graph to Lab Report d x d 2 x 5a t Y V d m x 7 By determining a percent difference compare the acceleration of the car determined from your graph to that measured as the slope of the velocity graph 64 www ATIBOOK ir Section Date Name Lab Partner s T EXPERIMENT 4 A OPTIONAL Uniformly Accelerated Motion Free Fall Spark Timer Apparatus RV Advance Study Assignment Read the experiment and answer the following questions 1 How are data recorded on the tape strip and what information does the
492. t In V V versus t for both sets of data On the other graph plot In V versus for both sets of data Draw the straight lines that best fit the data and determine the slope of each line Record the slopes in the data tables Compute the time con stants from the average slope values Compute 7 RC and 7 R C from the given resistance and capacitance values and compare with the experimental values by finding the percent errors Note The resistors and capacitors may have appreciable tolerances 96 or vary from the given values www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 2 5 The RC Time Constant Manual Timing RW Laboratory Report DATA TABLE 1 C Purpose To determine the RC time constant R Charging Discharging V t V t Vos Vv In V ln V C C BREED ue S C r Vo Vo Calculations Slope charging show work Slope discharging Average slope RC from slope R C from given values Percent error Dont forget units continued 371 www ATIBOOK ir EXPERIMENT 25 TheRC Time Constant Manual Timing Laboratory Report DATA TABLE 2 C Purpose To determine the RC time constant R Charging Discharging V t t l E In V C a ee C r Vo Calculations show work 372 Slope charging
493. t asterisked column in TI Data Table 1 iii Repeat timing measurements Procedure 5a measurement of acceleration with a net 10 g mass imbalance Record the data in the Trial 2 column The calculations for Trial 2 should utilize the value of m obtained for the immediately pre ceding asterisked column Note The values of m and y should be remeasured for each of the trials in TI Data Table 1 As the total mass is changed the friction will change likewise The length of the string y distance may vary noticeably be cause of stretching Repeat Procedures 4a and 5a for two more trials with another 100 g being added for each trial Varying the Unbalanced Force Total Mass Constant If using inertia and friction corrections go to Proce dure 1b below Begin with an ascending mass of 260 g 50 g hanger 200 5 2 2 1 g masses and a similar descending mass m 260 g 50 g hanger 200 10 g masses Transfer 1 g from m to m in order to create an unbalanced force without affecting the total mass Make three measurements of the travel time as done previously in Procedure A3 Record the data as Trial 5 in TI Data Table 2 Leaving the previously transferred 1 g mass in place a transfer an additional 2 g for Trial 6 b transfer an additional 2 g for Trial 7 c transfer an additional 5 g for Trial 8 Procedure using inertia and friction corrections Begin with an ascending mass m 260 g 50 g hanger
494. t button after entering the for mula Notice that the variables m1 m2 v1 and v2 will appear in a list The masses were already assigned values but v1 and v2 are waiting to be defined c To define variables v1 and v2 do them one at a time by clicking on the drop menu button on the left side of each variable A list of options appears asking what type of variable this is Define vl as a Data Measurement and when prompted choose Velocity Ch1 amp 2 Define v2 as a Data Measurement and when prompted choose Velocity Ch3 amp 4 d Press the Accept button again Please notice that Channels 1 amp 2 will keep track of Car 1 and that Channels 3 amp 4 will track Car 2 Make sure the equipment is set up accordingly Calculation of the total kinetic energy of the system a Still in the same calculator window press the top New button again to enter a new equation b Clear the definition box and enter the following equation TotalKE 0 5 m1 smooth 10 v1 2 0 5 m2 smooth 10 v2 2 This is the calculation of the total kinetic energy Kroa mv tmv that we will call TotalKE Press the Accept button after entering the formula Notice that the variables will again appear in a list Define them exactly as before d Press the Accept button again Close the calculator window The data list at the top left of the screen should now have four items Velocity from Chl amp 2 Velocity from Ch3 amp 4 TotalP and To
495. t measurement of centripetal force Percent difference continued 149 www ATIBOOK ir EXPERIMENT 9 Centripetal Force DATA TABLE 3 Purpose To observe the effect of varying radius Trial 1 Trial 2 Trial 3 Number of revolutions Total time Time revolution Computation of centripetal force attach additional sheet DATA TABLE 4 Optional Purpose To observe the effect of varying spring tension Trial 1 Trial 2 Trial 3 Number of revolutions Total time Time revolution Computation of centripetal force attach additional sheet 150 Mass of bob Radius of circular path Average time per revolution Average speed of bob v Computed value of centripetal force Direct measurement of centripetal force Percent difference Mass of bob Radius of circular path Average time per revolution Average speed of bob v Computed value of centripetal force Direct measurement of centripetal force Percent difference Laboratory Report www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 9 Centripetal Force Laboratory Report B Centripetal Force Apparatus with Variable Speed Rotor DATA TABLE 5 Purpose To determine rotational frequency for Minimum spring tension computation of centripetal force scale reading Trial Counte
496. t of some experiments is to determine the value of a well known physical quantity for example the value of 7 The accepted or true value of such a quantity found in textbooks and physics handbooks is the most accurate value usually rounded off to a certain number of significant figures obtained through sophisticated experi ments or mathematical methods The absolute difference between the experimen tal value E and the accepted value A written E Al is the positive difference in the values for example 2 4 2 22 and 4 2 2 Simply subtract the smaller value from the larger and take the result as positive For a set of measurements E is taken as the aver age value of the experimental measurements The fractional error is the ratio of the absolute differ ence and the accepted value absolute difference Fractional error accepted value or E Al Fractional error EE UEE 1 1 The fractional error is commonly expressed as a percentage to give the percent error of an experimental value absolute difference Percent error x 100 accepted value or E A Percent error E x 10096 1 2 Example 1 4 A cylindrical object is measured to have a diameter d of 5 25 cm and a circumference c of 16 38 cm What are the experimental value of a and the percent error of the experimental value if the accepted value of 7 to two decimal places is 3 14 Solution with
497. t the procedure for the parallel linear plate electrode configuration Be sure to investigate the regions around the ends of the plate electrodes Optional Your instructor may wish to have you map the electric field for a nonsymmetric electrode configu ration or a configuration of your own choosing These can be prepared by painting the desired electrode con figuration on a conducting sheet with silver paint VOLTMETER MEASUREMENTS For the high resistance voltmeter or VTVM the field probe should have two contacts mounted about 2 cm apart Connect the voltage source 10 V dc to the board terminals Place a switch in the circuit not shown in Fig 19 4b and leave it open until you are ready to take measurements Close the switch and with the zeroed voltmeter set on the 10 V scale position the negative contact of the field probe near the negative electrode Using the negative probe point as a pivot rotate the positive contact around the fixed negative contact until the posi tion with the maximum meter reading is found Record the positions of the probe contacts on the graph paper map The sensitivity of the voltmeter www A TIBOOK ir 10 11 12 may be increased by switching to a lower scale A midscale reading is desirable Using the second probe point as a new negative probe point repeat the procedure to determine another point of maximum meter reading and record Continue this procedure until th
498. t what temperature would the resistance of the coils be equal 332 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 22 The Temperature Dependence of Resistance Laboratory Report B Thermistor 4 Explain why the ambient temperature T for the thermistor cannot be taken as T 0 C and why the expression for the resistance is written R Re where T is in degrees Celsius 5 Assuming that 6 remained constant what would be the resistance of the thermistor in the experiment as the temperature approached absolute zero 6 Assume the temperature coefficient of resistance to be defined over the temperature range AT T T where T gt 273 K 0 C by R R R a T T Show that for a thermistor o is a function of temperature given by ePam vr T T a 333 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 23 Resistances in Series and Parallel AY amp Advance Study Assignment RV ED cuestions Read the experiment and answer the following questions TI CI 1 Explain the difference between series and parallel connections TI CI 2 Consider resistors connected in series a How are the voltage drops across the individual resistors related to the voltage supplied by the battery b How are the currents through the individual resistors related to the current supplied by the b
499. tages and are said to be ohmic Those that do not are said to be nonohmic Common circuit resistors are ohmic which allows Ohm s law to be used in simple circuit analysis As will be seen in the theory section Ohm s law is really a special case of the definition of resistance In this experiment Ohm s law will be investigated as applied to components in a simple circuit RV OBJECTIVES After performing this experiment and analyzing the data you should be able to 1 Distinguish between ohmic and nonohmic resistances 2 Explain current voltage relationships by Ohm s law 3 Apply Ohm s law to obtain values of current or volt age in investigating a circuit resistance d ossectives 1 Verify Ohm s law experimentally 2 Study the behavior of the current in both an ohmic and a nonohmic resistance 293 www ATIBOOK ir This page intentionally left blank www A TIBOOK ir T J Ohm s Law RV EQUIPMENT NEEDED Ammeter 0 to 0 5 A Voltmeter 0 to 10 V dc or multimeters Decade resistance box 0 1 Q to 99 9 Q e Rheostat 200 Q e Unknown resistance EX PER M ENT 2 0 Battery or power supply 6 V Switch Connecting wires 2 sheets of Cartesian graph paper The ranges of the equipment are given as examples These may be varied to apply to available equipment RV THEORY When a voltage or potential difference V is applied across a material the current
500. talKE A small calculator icon identifies the quantities that are calculated Create a graph by dragging the Velocity Ch1 amp 2 icon from the data list and dropping it on the Graph icon on the displays list A graph of velocity versus time will open in a window titled Graph 1 17 18 19 20 21 22 Double click anywhere on the graph The Graph Settings window will open Make the following changes and selections Under the tab Appearance Data Connect data points in bold deselect the buttons marked Show Data Points and Show Legend Symbols Under the tab Layout Multiple graphs Vertical Layering Do not layer Measurement adding Replace matching measurement Group measurement Do not group Click OK to accept the changes and to exit the graph settings window Drag the Velocity Ch3 amp 4 data icon and drop it in the middle of Graph 1 The graph will split in two At the top you will see the Velocity Ch1 amp 2 and at the bottom the Velocity Ch3 amp 4 on separate y axis Drag the TotalP icon and drop it on the split graph The graph will split again this time into three sections Drag the TotalKE icon and also drop it on the graph The result should be a graph split into four sections one section for each of the quantities Press the Align Matching X Scales button on the graph s toolbar It is a button with a picture of a pad lock This will make all graphs aligned to a common t
501. tals 259 Archimedes Principle Buoyancy and Density 269 Fields and Equipotentials 281 TI CI Ohm s Law 291 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method 309 The Temperature Dependence of Resistance 323 TI CTI Resistances in Series and Parallel 335 Joule Heat 359 The RC Time Constant Manual Timing 367 TI CI The RC Time Constant Electronic Timing 373 Reflection and Refraction 393 Spherical Mirrors and Lenses 403 TD Polarized Light CI Malus s Law 419 The Prism Spectrometer Dispersion and the Index of Refraction 439 Line Spectra and the Rydberg Constant 447 TI The Transmission Diffraction Grating Measuring the Wavelengths of Light CI Single Slit and Double Slit Diffraction 457 Detection of Nuclear Radiation The Geiger Counter 481 Radioactive Half Life 491 The Absorption of Nuclear Radiation 499 www ATIBOOK ir vi CONTENTS Appendix A Material Properties 511 Appendix B Mathematical and Physical Constants 517 Appendix C Absolute Deviation and Mean Absolute Deviation 520 Appendix D Standard Deviation and Method of Least Squares 521 Appendix E Graphing Exponential Functions 523 Experiments available in customized orders 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 TI CI Rotational Motion and Moment of Inertia Conservation of Angular Momentum and Energy The Ballistic Pendulum Elasticity Young s Modulus Air Column Resonanc
502. tc a random or system atic error Will this source of error cause your calculated velocity to be less than or greater than the actual velocity B Determination of the Initial Velocity of a Projectile from Range Fall Measurements 6 What effect does the force of gravity have on the horizontal velocity of the projectile Explain 7 What effect would air resistance have on the range of the projectile C Dependence of Projectile Range on the Angle of Projection 8 Using experimental data compute the magnitude of the initial velocity v of the projectile from Eq 8 12 and compare this to the results of Parts A and B of the procedure 9 If for a given initial velocity the maximum range is at a projection angle of 45 then there must be equal ranges for angles above and below this Show this explicitly 140 www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 9 Centripetal Force AY Advance Study Assignment Read the experiment and answer the following questions 1 Define centripetal force 2 What supplies the centripetal force for a a satellite in orbit around the Earth b the mass in uniform circular motion in this experiment 3 An object moving in uniform circular motion is accelerating How can this be since uniform motion implies constant motion 4 For an object in uniform circular motion on what parameters does the experimental determination of the centripetal force depend wh
503. th of the graph on the screen Repeat for the other 5 Set Car 2 somewhere on the middle of the track three graphs at rest 10 If any of the graphs of velocity is reading negative 6 Set Car 1 all the way to the end of the track values switch the yellow and black cables of the www ATIBOOK ir 11 12 13 14 15 16 17 18 corresponding rotary motion sensor in the interface so that the yellow cord connects to where the black cord was and vice versa Repeat the data collection pro cess and use the new data in the rest of the analysis Print the graph If no printer is available make a care ful drawing of the graph paying special attention to dips and peaks in the graphs Attach the graph to the laboratory report Click anywhere on the Velocity Ch1 amp 2 graph and then press the Smart Tool button on the graph tool bar The Smart Tool is a button on the graph toolbar labeled XY A set of crosshairs will appear on the graph Repeat for each of the other graphs to get a set of crosshairs on each graph The crosshairs can be dragged around to determine the exact x y value of any point in the graphs Use the Smart Tools to find the time f that corre sponds to the moment just before the collision Report the value of t in the laboratory report Hint Use the velocity graphs and think of what the cars were doing just before the collision In the graph printout mark the time f in all graphs by dr
504. that best fits the data points Determine the slope of the line and compute the spring constant k Note from TI Eq 14 3 that k is not simply equal to the slope rather k Qarylslope Compare this value of k with that determined from the slope of the spring elongation graph in Part B by computing the percent difference and finish answering the TI Questions www A TIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s T EX PERIMENT 14 Simple Harmonic Motion RW Laboratory Report A Rubber Band Elongation B Spring Elongation AY DATA TABLE 1 AY DATA TABLE 2 Total suspended Scale reading Total suspended Scale reading weight C weight 3 mig y msg MI Ng y2 Mg y mag ys mag J3 mag Y4 mag Y4 msg y5 msg y5 meg Y6 Meg Yo mg y7 m Y7 mag Js mag Js Ttisconvenienttoleave g theaccelerationduetogravity insymbolicform It is convenient to leave g in symbol form even when graphing that is if m 100 g or 0 100 kg then weight m g 0 100 kg g N but your instructor may prefer otherwise Be careful not to confuse the symbol for acceleration due to gravity g italic with the abbreviation for gram g roman Calculations k slope of graph show work Don t forget units 227 units continued www A TIBOOK ir EXPERIMENT 14 Simple Harmonic
505. that is larger than the input force F gt F what does GL Eq 13 1 tell you about the input and output distances 2 A ramp or inclined plane is an example of a simple machine that makes it easier to raise objects to a higher elevation GL Fig 13 1 What is the applied force needed to push a block up a frictionless inclined plane at a constant speed Express your result in terms of the weight of the block and the angle of incline continued 203 www A TIBOOK ir EXPERIMEN TF 18 Experimental Planning 3 How does this force F compare to the weight of the block F The output force in this case is the force needed to lift the object directly a vertical distance h without the ramp 4 Now consider d and d If the output distance d is the vertical distance h what is d the distance through which the applied force F acts Express your result in terms of the height and the angle of incline 5 The theoretical mechanical advantage TMA of a simple machine for the ideal frictionless case is defined as TMA F F GL 13 2 but F and F cannot be measured directly since there is always friction 6 Note that GL Eqs 13 1 and 13 2 can be combined to show that TMA dj d GL 13 3 Use your results from Question 4 above to compute the TMA with this equation Thus the TMA can be determined in terms of either the forces or the distances In the case of the inclined plane the TMA may be obtained directly from th
506. the New button again to enter a new equation b Clear the definition box and enter the following equation KE 0 5 M v This is the calcula tion of the kinetic energy K mv that will be called KE c Press the Accept button after entering the for mula The variables M and v will appear in a list Click Accept to enter changes Definition y B a Scientific Statistical v Special pea JAAD Properties Variables Please define variable w al Experiment Constants T CI Figure 14 4 The calculator window This small version of the calculator window opens when the Calculate button is pressed The calculator will be used to enter equations that handle the values measured by the sensor The computer will perform the calculations automatically as the sensor takes data Reprinted courtesy of PASCO Scientific www ATIBOOK ir 234 EXPERIMENT 14 Simple Harmonic Motion New x Remove v Accept ick Accept to enter changes Definition 1 El Scientific Statistical Special DEG RAD Properties 5 Variables Please define variable x E Experiment Constants F p New anA v Accent Value Precision Comment Units mena EN Q 1 Press New t Experiment Constants 2 Enter constant gt L New Remove Accept symbol Value 0 35 Units m E 3 Ente
507. the IDS track pulley to the track a This figure shows how to mount the rotary motion sensor to one end of the track using the mount accessory b This figure shows how the IDS RMS adapter the track pulley bracket should be mounted to the track Optional end stop CI Figure 7 8 Example of one side of the experimental setup This diagram illustrates one of the carts completely set up Notice the string connecting the pulleys to the cart bracket is to have tension but not be so tight that the cart cannot move freely 4 A string will make a loop starting from the cart string 7 Press the START button and then give Car 1 a good bracket on top of the car to the large pulley of the push toward Car 2 RMS to the small pulley of the RMS IDS adapter and back to the cart as shown in e CI Fig 7 8 Do 8 Press the STOP button after the collision before Car 2 this for both cars as shown in the complete set up of bounces at the end of the track Several practice runs CI Fig 7 6 Adjust the height of the pulleys so that the and the help of a partner may be needed strings are tense not sagging but the cars are able to move freely 9 Click anywhere on the Velocity Ch1 amp 2 graph and then press the Scale to Fit button on the graph tool CASE 1 ELASTIC COLLISION BETWEEN Two CARS bar The Scale to Fit button is the leftmost button on OF NEARLY EQUAL Mass WITH ONE INITIALLY the graph toolbar This will make the data scale to the AT REST leng
508. the data tables TI Figure 14 3 Hooke s law apparatus The variables of Hooke s law F mg and x are measured using spring elongation Photo Courtesy of Sargent Welch C Period of Oscillation 6 a On the weight hanger suspended from the spring place a mass just great enough to prevent the spring from oscillating too fast and to prevent the hanger from moving relative to the end of the spring during oscillations when it is pulled down for example 5 to 10 cm and released Record the total mass in TI Data Table 3 b Using a laboratory timer or stopwatch release the spring weight hanger from the predetermined ini tial displacement and determine the time it takes for the mass to make a number 5 to 10 of com plete oscillations or cycles The number of cycles timed will depend on how quickly the system loses energy or is damped Make an effort to time enough cycles to get a good average period of oscillation Record in the data table the total time and the number of oscillations Divide the total time by the number of oscillations to determine the average period 7 Repeat Procedure 6 for four more mass values each of which is several times larger than the smallest mass and record the results in TI Data Table 3 The initial displacement may be varied if necessary This should have no effect on the period Why Plot a graph of the average period squared 7 ver sus the mass m and draw a straight line
509. the position of the beam from left to right and up to down until the beam is centered on the slit The knobs to do this are on the back of the diode laser See CI Fig 32 6 Ring accessory s Lens holder CI Figure 32 5 Slit accessory on lens holder The slit acces sory is mounted on a ring that snaps into the lens holder 3 Prepare the rotary motion sensor and the light sensor a Mount the RMS in the rack of the linear translator Then mount the linear translator to the end of the optics bench b The light sensor with the aperture bracket set to slit 6 is mounted on the RMS rod clamp See CI Fig 32 7 4 Plug the RMS and the light sensor into the interface as shown in the Setup window on the computer screen www A TIBOOK ir 474 EXPERIMENT 32 Single Slit and Double Slit Diffraction Tag To s sensors On Off and Horizontal Vertical controls Optics bench CI Figure 32 6 Diode laser and slits on track The diode laser is placed in the track a few centimeters behind the lens holder with the slits Light sensor Aperture y bracket Linear translator CI Figure 32 7 The RMS mounted in the rack with the light sensor The RMS is mounted on the linear translator The light sensor with the apertures is mounted on the RMS Hy EXPERIMENTAL PROCEDURE Start by making a note in the laboratory report of the wave lengt
510. the properties of the RMS as follows pulley can be moved as far down as needed for the First Measurements tab select Position Ch 1 amp 2 blades to clear the string Deselect all others Fan accessory RMS IDS Adapter RMS Small i Strin H gt i g TTA te comaine pulley N Le ol Track lt Cart string Mount accessor bracket y CI Figure 4 1 Rotary motion sensor and cart setup A string makes a full loop from the cart string bracket to the RMS pul ley to the small pulley on the opposite end of the track and back to the cart The height of the RMS and the pulley must be adjusted so that the fan blades do not touch the string as they spin 59 www ATIBOOK ir 60 EXPERIMENT 4 Uniformly Accelerated Motion In The 2 Measurements tab T Acceimition Ch A2 CI Figure 4 2 The Experiment Setup Window Top of the screen the Science Workshop interface and the seven avail able channels Once a sensor is chosen an icon for the sensor appears under the appropriate channel Here for example is the RMS icon directly under Channels 1 and 2 Bottom of the window the properties of the selected sensor can be adjusted as needed Reprinted courtesy of PASCO Scientific Second Measurements tab select Velocity Ch 1 amp 2 Deselect all others The Data list on the left of the screen should now have two icons one for the position data the other for the velocity data 8 Cre
511. the resistors such that I h ht h TI 23 4 In the liquid circuit analogy TI Fig 23 2b the height h the pump raises the liquid is equal to the distance the liquid drops through each parallel paddle wheel resistor The liquid flow coming into the junction of the parallel arrange ment divides among the three pipe paths analogously to the current dividing in the electrical circuit The current in a parallel circuit divides according to the magnitudes of the resistances in the parallel branches the smaller the resistance of a given branch the greater the current through that branch The current through each resistor is given by Ohm s law for example V R and TI Eq 23 4 may be written V V pd crc RU TI 23 5 For the current through a single resistance R in a circuit I VIR and by comparison 1 1 1 R gt R R R TI 23 6 two resistances in parellel where R is the equivalent resistance of the resistors in parallel That is the three resistors in parallel could be replaced by a single resistor with a value of R and the same current J would be drawn from the battery The previous developments for equivalent resis tances may be extended to any number of resistors that is R Ri R R Ry and 1 R VR 1 R 1 R t VR gt In many instances two resistors are connected in parallel in a circuit and 1 1 mu ne
512. the same form as that mapped out using compass needle poles It is instructive for comparative purposes to draw equipotential lines perpendicular to the field lines as in the electric field case No work would be done on a mag netic pole or electric charge when it is moved along these equipotential lines Why A common method of demonstrating a magnetic field is to sprinkle iron filings over a paper or transparency material covering a magnet 8 Fig 19 3 The iron filings become induced magnets and line up with the field as would a com pass needle This method allows one to visualize the mag netic field configuration quickly Other units of magnetic field are the weber m Wb m and the gauss G These units are named after early investigators of magnetic phenomena EXPERIMENT 19 Fields and Equipotentials 285 sa ANNAE T P ANN N LT MM ESSE Figure 19 3 Iron filing pattern for a bar magnet The iron filings become induced magnets and line up with the field as would a compass needle Courtesy of PSSC Physics D C Heath and Company with Educational Development Center Inc Newton Massachusetts EXPERIMENTAL PROCEDURE A Electric Field 1 Anelectric field mapping setup is shown in Fig 19 4a The apparatus consists of a flat board on which is placed a sheet of carbonized conducting paper imprinted with a grid The sheet has an electrode configuration of con ducting silver paint which provides an elect
513. the spectrum of sodium It is the presence of sodium 449 that gives candles and wood fires their yellow glow You may have noticed that many highway and parking lot lights are bright yellow They are sodium lights used because sodium discharge is a very efficient way to produce light Wavelengths are commonly measured in nanometers nm 1 nm 10 m 107 cm a Mercury I LI b Helium E TET II c Hydrogen ulii bra l ereite in bona lena 400 500 600 700 nm Wavelength Figure31 1 Linespectra Illustrations of visible line spec tra for a mercury b helium and c hydrogen From Wilson Buffa College Physics 5th ed Copyright O 2010 Reprinted by permission of Pearson Education www ATIBOOK ir 450 EXPERIMENT 31 Line Spectra and the Rydberg Constant Visible spectrum Balmer series Paschen series E linfrared ey d e 0 n o 0 544 eV nes 0 85 eV FET 1 51 eV n 3 f 3 40 eV n 2 ee py s e ait Fi a a NOM Lyman series om ultraviolet ae e 13 6 aV a Figure 31 2 Energy level transitions The energy level transmissions for the hydrogen atom The Balmer series n 2 produces a line spectrum in the visible region The systematic spacing of the spectral lines in the he he a A n 3 4 5 hydrogen spectrum was empirically described by spec AE 13 6 0 2 1 n trosc
514. the system that is how far the mass was initially dis placed from its equilibrium position If the mass were initially t 0 pulled below its equilibrium position to y A and released the equation of motion would be y A cos 2art T which satisfies the initial condition at t 0 with cos 0 1 and y A The argument of the cosine 27t T is in radians rather than degrees TI 14 2 T One period TI Figure 14 2 Simple harmonic motion A marker on a mass oscillating on a spring traces out a curve as illustrated on the moving paper The curve may be represented as a function of displacement magnitude y versus time such as y A cos 27r T where y Aat t 0 In actual practice the amplitude decreases slowly as energy is lost to friction and the oscillatory motion is slowly damped In some applications the simple har monic motion of an object is intentionally damped for example the spring loaded needle indicator of an electrical measurement instrument or the dial on a common bathroom scale Otherwise the needle or dial would oscillate about the equilibrium position for some time making it difficult to obtain a quick and accurate reading The period of oscillation depends on the parameters of the system and for a mass on a spring is given by TI 14 3 period of mass oscillating on a spring AY EXPERIMENTAL PROCEDURE A Rubber Band Elongation 1 Hang a rubber band on a support
515. the vernier scale markings below the main scale www ATIBOOK ir EXPERIMENT 2 Measurement Instruments Mass Volume and Density 25 Vernier PPT TTT 0 03 cm 0 000 cm 1 230 cm zero mark 1 cm t 0 2 cm major division minor division aligned mark estimate of doubt Vernier zero mark 1cm 0 2 cm b 0 025 cm 1 225 cm major division minor division phase change for 2 and 3 marks Figure 2 3 The vernier scale An example of reading the vernier scale on a caliper See text for description If a vernier mark coincides with a mark on the main scale then the vernier mark number is the fractional part of the main scale division see Fig 2 3a In the figure this is the third mark to the right of the vernier zero so the third significant figure is 3 0 03 cm Finally since the 0 03 cm reading is known exactly a zero is added as the doubtful figure for a reading of 1 230 cm or 12 30 mm Note how the vernier scale gives more significant figures or extends the precision However a mark on the vernier scale may not always line up exactly with one on the main scale Fig 2 3b In this case there is more uncertainty in the 0 001 cm or 0 01 mm figure and we say there is a change of phase between two successive vernier markings Notice how in Fig 2 3b the second vernier mark after the zero is to the right of the closest main scale mark and the third vernier mark is to the left of the next main
516. the vertex of the mirror along the optic axis is called the radius of curvature R This also may be measured to any point on the surface of the mirror Why The focal point F is midway between C and the vertex and the focal length f is one half the radius of curvature f R 28 1 Center of Focal curvature point Vertex NE Optic axis C F R Concave surface Convex surface Figure 28 1 Spherical mirrors The parameters used to describe spherical mirror surfaces See text for description 405 If the reflecting surface is on the inside of the spherical section the mirror is said to be concave For a convex mirror the reflecting surface is on the outside of the spher ical section The characteristics of the images formed by spherical mirrors can be determined either graphically or analyti cally Examples of the graphical ray method are shown in the ray diagrams in e Fig 28 2 As illustrated for a concave mirror Fig 28 2a 1 A chief ray from the object goes through the center of curvature C and is reflected back through C 2 A parallel ray from the object is parallel to the optic axis and is reflected through the focal point F 3 A focal ray from the object passes through the focal point F and is reflected parallel to the optic axis The intersection of these rays defines the location of the tip of the image arrow which extends to the optic axis The focal ray is a mirror image of the par
517. ting the force sensor to the pile of objects be horizontal If using additional blocks instead of the PASCO cars tape the blocks to gether so that they will not fall off Set the motorized car for a medium speed and do not change it during the experiment Trial 1 The object with no extra load a With the string slack press the TARE button on the side of the force sensor to zero the sensor b Turn the motorized car on Wait until the string tenses before pressing the START button to begin collecting data Let the car move pulling along the pile of blocks the object for about 20 cm and then press the STOP button d Stop the car e Report the average fictional force reading in CI Data Table 1 Do not worry if the sensor reading is negative That is a convention for direction pull or push In this experiment we need only the magnitude e Trials 2 3 4 and 5 The object with a load a Place a load on top of the sliding object and re cord the new mass of the sliding object in CI Data Table 1 b Repeat the data collection process as described in steps a to e for Trial 1 6 c Repeat by continuing to add mass on top of the ob ject until the table is complete Calculate the normal force for each trial by determin ing the weight of the object plus load in each case Record the results in CI Data Table 1 Use a full page of graph paper to make a plot of fric tion versus normal force Dete
518. tion b Observe the transmitted light for an increasing number of glass slides and report and explain any observable differences C Polarization by Crystal Double Refraction 6 Place the calcite crystal on some written or printed material and observe the double image The images may appear slightly fuzzy because of small defects in the crystal Lay the crystal on the side that gives the clearest images Notice that when the crystal is rotated the images move one more than the other Examine the images with an analyzer With a pencil or pen make a linear series of small heavy dots on a piece of paper The line of dots should be long enough to extend beyond the edges of the crystal Placing the crystal on the line of dots rotate the crystal Notice that as the crystal is rotated one of the dots of a double image remains relatively stationary and the second dot rotates about the first The image of the nearly stationary dot is formed by the ordinary 0 ray and that of the rotating dot by the extraordinary e ray Examine a set of dots with an analyzer and record the polarization direction of each ray D Polarization by Scattering Optional 8 If it s a sunny day go outside with the instructor s permission and observe the sky light from different portions of the sky with an analyzer Look in direc tions away from the sun and at angles of 90 Once you find a region from which the light shows appreciable po
519. tion Transmission 1 Inspect your polarizers to see whether the planes of polarization or transmission are indicated on them If not these planes need to be determined Polarizer and analyzer directions will be needed later One method is to use a pair of polarizing sunglasses that has a ver tical plane of polarization Determine the planes of polarization for your polar izers by observing the orientations of maximum and minimum transmissions through a polarizer and a polarizing sunglass lens Remember sunglasses are vertically polarized Mark the planes of polarization of the polarizers by some means for example a wax pencil or pieces of tape 2 Investigate the transmission through two polarizers as a function of the angle 0 between the planes of polarization TI Fig 29 3 At what angles is the trans mission estimated by brightness or intensity optional lightmeter a a maximum b reduced by one half and c a minimum Record these angles in the laboratory report and show the theoretical prediction using TI Eq 29 1 of the angle for one half transmission that is I I 0 5 3 Orient two polarizers in a crossed position for mini mum intensity Place the third polarizer between these two Viewing through the polarizer rotate the middle one keeping the outer two in a crossed orientation and observe any intensity changes As the middle po larizer is rotated you should observe variations in the transm
520. tion and Resolution of Vectors The Force Table 79 AR resultant F F R E F Figure 5 6 Resultant and equilibrant On a force table the magnitude and direction of the equilibrant E are measured rather than those of the resultant R and R E EXPERIMENTAL PROCEDURE 1 Setup the force table with strings and suspended weights and perform the following cases of vector addition 2 Vector addition I Given two vectors with magnitudes F 0 2000 N and F 0 200 g N at 30 and 120 respectively find their vector sum or resultant F F F by each of the following procedures Note Orientation angles of vectors are given relative to the 0 reference line or positive x axis a Graphical Using the triangle method of vector addition draw a vector diagram to scale Use a scale such that the finished vector diagram fills about half a sheet of graph paper Measure the magnitude and direction of the resultant with ruler and protractor and record the results in the data table Save your graphical sheets to attach to the Laboratory Report b Analytical Compute the magnitude of the resultant force Also compute the angle of orientation from the relationship tan 0 F F Why can you use tan 0 Remember that 0 is the angle between F and F Record the results in the data table c Experimental On the force table clamp pulleys at 30 and 120 and add enough weights to each weight hanger to total 0 200 kg
521. tion for the SHM of a mass suspended on a spring when the mass is initially a released 10 cm above the equilibrium position b given an upward push from the equilibrium position so that it undergoes a maximum displacement of 8 cm c given a downward push from the equilibrium position so that it undergoes a maximum displacement of 12 cm Hint Sketch the curve for the motion as in TI Fig 14 2 and fit the appropriate trigonometric function to the curve 7 For case a in Question 6 only what is the displacement y of the mass at times a t 7 2 b t 37 2 c t 3T 230 www ATIBOOK ir C I EX P E RI MENT 14 Simple Harmonic Motion S courpment NEEDED e Rotary Motion Sensor PASCO CI 6538 Mini rotational accessory PASCO CI 6691 This set includes a brass mass and a light rod to make the pendulum Support rods and clamps ED mory In this experiment the simple harmonic motion of a pen dulum will be investigated by examining the energy con versions that occur during the motion Simple harmonic motion is the motion executed by an object of mass m subject to two conditions The object is subject to a force that is proportional to the displacement of the object that attempts to restore the object to its equilibrium position No dissipative forces act during the motion so there is no energy loss Notice that as it is described in theory simple harmonic motion is an idealization because of the
522. tion in a material depends 2 Explain the linear absorption coefficient half thickness and stopping range 3 Explain the mass absorption coefficient EQUIPMENT NEEDED Geiger counter rate meter or scaler type Calibrated mounting board or meter stick Beta gamma source Cs 137 suggested Set of cardboard aluminum and lead sheets about mm thick 10 sheets of each Laboratory timer or stopwatch Micrometer caliper 3 sheets of Cartesian graph paper or optional 2 sheets of Cartesian graph paper and 1 sheet of semi log graph paper 3 cycle THEORY The three types of nuclear radiation alpha beta and gamma are absorbed quite differently by different materials The electrically charged alpha and beta particles interact with the material and produce ionizations along their paths The greater the charge and the slower the particle the greater the linear energy transfer LET and ionization along the path and this determines the degree of penetration of the radiation The absorption or degree of penetration of the radiation also depends on the density of the material Alpha particles are easily absorbed A few centime ters of air and even a sheet of paper will almost completely absorb them Hence alpha particles do not generally pen etrate the walls or window of an ordinary Geiger tube and so are not counted by this method Beta particles can travel a few meters in air or a few millimeters in a
523. tion of simple har monic motion After performing this experiment and analyzing the data you should be able to RV OBJECTIVES 1 Tell how Hooke s law is represented graphically and cite an example of an elastic object that does not follow Hooke s law 2 Explain why simple harmonic motion SHM is simple and harmonic 3 Better understand how the period of a mass oscillat ing on a spring varies with the mass and the spring constant A osusectives 1 Explain the energy conversion that happens during the simple harmonic motion of a pendulum 2 Experimentally verify the law of conservation of mechanical energy 221 www A TIBOOK ir This page intentionally left blank www A TIBOOK ir TI EXPER IMENT 14 Simple Harmonic Motion RV EQUIPMENT NEEDED Coil spring Wide rubber band Slotted weights and weight hanger Laboratory timer or stopwatch Meter stick Laboratory balance 2 sheets of Cartesian graph paper RV THEORY A Hooke s Law The fact that for many elastic substances the restor ing force that resists the deformation is directly pro portional to the deformation was first demonstrated by Robert Hooke 1635 1703 an English physicist and contemporary of Isaac Newton For one dimension this relationship known as Hooke s law is expressed math ematically as F kAx k x x TI 14 1 or F kx with x 0 where Ax is the linear
524. tional considerations Consider the schematic diagram of a ballistic pendu lum shown in Fig 8 2 A projectile of mass m with an initial horizontal velocity of is v fired into and becomes embedded in a stationary pendulum of mass M 131 To a good approximation the horizontal momentum is conserved during collision over the time interval of the collision Therefore the horizontal component of total momentum is taken to be the same immediately before and after collision The velocity of the pendulum bob is initially zero and the combined system m M has a velocity of magnitude V just after collision Hence by the conserva tion of linear momentum for the horizontal direction mv m M V before after Cn After collision the pendulum with the embedded projectile swings upward momentum of the system no longer conserved why and stops The center of mass of the pendulum ball system is raised a maximum vertical distance h h h By the conservation of mechanical The center of mass of the system is used because this represents the point where all the mass is considered concentrated www ATIBOOK ir 132 EXPERIMENT 8 Projectile Motion The Ballistic Pendulum d Figure 8 1 Ballistic pendula Types of ballistic pendula Photos Courtesy of a and b Sargent Welch c Bernard O Beck Co and d Reprinted courtesy of PASCO Scientific energy the increase in potential energy is equal
525. tions 1 Directions of the fields are indicated on field lines Why are no directions indicated on equipotential lines 2 For the dipole configuration in what region s does the electric field have the greatest intensity Explain how you know from your map and justify Don t forget units continued 289 www A TIBOOK ir EXPERIMENT 19 Fields and Equipotentials Laboratory Report 3 Comment on the electric field of the parallel plates a between the plates and b near the edges of the plates 4 Sketch the electric field for a a negative point charge near a positively charged plate and b two positive point charges TEEEEBEBEBBBERBBERERERAABBBBBBRGRGR BB A a b 5 Compare the electric fields and magnetic fields of the experimental arrangements Comment on any field similarities and differences 6 Explain how a gravitational field might be mapped Sketch the gravitational field for two point masses a short distance apart 290 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 20 Ohm s Law RWV Advance Study Assignment Read the experiment and answer the following questions 1 What is the definition of electrical resistance 2 What is an ohmic resistance Are all resistances ohmic in nature 3 In what ways are liquid and electrical circuits analogous 4 For a series circuit what is the terminal voltage of a battery or power supply equal to in term
526. tive sources are solids and are encapsulated to prevent contact Others are in liquid form and are transferred during an experiment so there is a danger of spillage Proper handling is therefore important In general necessary precautions will be given in the experiment descriptions Note them well When you see the arrow symbol in the margin as illustrated here you should take extra care to follow the procedure carefully and adhere to the precautions described in the text As pointed out earlier experiments are designed to be done safely Yet a common kitchen match can be dangerous if used improperly Another good rule for the laboratory is If you have any questions about the safety of a procedure ask your instructor before doing it The physics lab is a place to learn and practice safety Equipment Care The equipment provided for the laboratory experiment is often expensive and in some instances quite delicate If used improperly certain pieces of apparatus can be dam aged The general rules given above concerning personal safety also apply to equipment care Even after familiarizing oneself with the equipment it is often advisable or required to have an experimental setup checked and approved by the instructor before put ting it into operation This is particularly true for electrical experiments Applying power to improperly wired circuits can cause serious damage to meters and other pieces of apparatus If a piece of equi
527. tly that you accidentally cause the rotor to lose contact with the rotor gear When you are satisfied with your technique record the initial counter reading in Data Table 5 Then using a laboratory timer or stopwatch mea sure count the number of rotations for a 1 minute in terval One lab partner should engage the counter for the timing interval while the other adjusts the rotor speed Repeat this procedure for four more 1 minute in 13 14 EXPERIMENT 9 Centripetal Force 147 Also share the action One lab partner should be the speed controller who constantly watches and adjusts the rotor speed as described in Procedure 3 Another partner should be the timer who engages the counter and times the interval If there are three lab partners the third may handle the counter engage ment and disengagement in response to the timer s instructions Rotate team responsibilities periodically Why might such rotation produce better experimen tal results Subtract the counter readings to find the number of ro tations for each timed interval They should be simi lar Then compute the average number of rotations of the five 1 minute intervals average rotations per minute Divide the average value by 60 1 min 60 s to obtain the average rotation frequency in rotations cycles per second or hertz Hz Without altering the spring tension setting remove the centripetal force apparatus from the rotor and su
528. to Channel A and works as a voltmeter The signal generator of the Science Workshop interface is used as the voltage source that produces a positive square wave function 4 Calculate the approximate time needed to consider the series The voltage source is the output source of the capacitor fully charged See CI Eq 26 4 Enter the value in CI Data Table 1 As explained in the CI Theory section the frequency of the square wave needs adjusting so that the voltage source remains ON for enough time to charge the capacitor fully before it automatically turns OFF and discharges as shown in CI Fig 26 3 This is accomplished by following these steps a The time to charge calculated in step 4 is half the required period of the square wave See CI Fig 26 3 Calculate the required period and enter it in CI Data Table 1 b Calculate the frequency remembering that the frequency is the inverse of the period Report the frequency in Data Table 1 c Enter the required frequency in the Signal Genera tor window and set the generator to AUTO Set up the circuit shown in CI Fig 26 2 The resistor the capacitor and the voltage source are connected in 750 Interface set to 3 V 7 Connect the voltage sensor across the capacitor as shown in CI Fig 26 2 8 Press the START button The capacitor will begin to charge and discharge Press the STOP button after two cycles have been completed Press the Scale to Fit but
529. to an exhaust hood or outdoors Mercury fumes are highly toxic The boiler should be about half full of water Keep steam or water from dampening the dry metal by shielding the cup with a cardboard lid with a hole for the thermometer While the boiler is heating determine and record the mass of the inner calorimeter cup and the stirrer without the ring Record the total mass m Also note and record the type of metal and specific heat of the cup and stirrer which is usually stamped on the cup The specific heat may be found in Appendix A Table A4 if it is not stamped on the cup Fill the calorimeter cup about one half to two thirds full of cold tap water and weigh the cup stirrer and water to determine the mass of the water my If a solid piece of metal is used which usually has less mass than the recommended amount of shot less water should be used so as to obtain an apprecia ble AT temperature change This may also be the case at high elevations where the temperature of boiling water is substantially less than 100 C EXPERIMENT 17 Specific Heats of Metals 263 Start with the water and stirrer in the cup at a tem perature T several degrees below room temperature T Adjust the temperature of the inner calorimeter cup and its contents by placing it in a beaker of ice water Measure and record the temperature T Remove the thermometer from the metal Then re move the lid from the calorimeter and quick
530. to the reflecting surface at the point of incidence e Fig 27 2 Also the incident and reflected rays and the normal lie in the same plane The rays from an object reflected by a smooth plane surface appear to come from an image behind the surface as shown in the figure From congruent triangles it can be seen that the image distance d from the reflecting surface is the same as the object distance d Such reflection is called regular or specular reflection The law of reflection applies to any reflecting surface If the surface is relatively rough like the paper of this page the reflection becomes diffused or mixed and no image of the source or object will be produced This type of reflec tion is called irregular or diffuse reflection 395 B Refraction When light passes from one medium into an optically dif ferent medium at an angle other than normal to the sur face it is bent or undergoes a change in direction as illustrated in Fig 27 3 for two parallel rays in a beam of light This is due to the different velocities of light in the two media In the case of refraction 0 is the angle of incidence and 6 is the angle of refraction Figure 27 1 Refraction Because of refraction the pencil appears to be bent Charles D Winters Cengage Learning www ATIBOOK ir 396 EXPERIMENT 27 Reflection and Refraction Normal 4 I l Xl fe VA NT a NI B Object lium Figure 27
531. to the string on the horizontal support arm and with the bob hanging freely spring unat tached adjust the support arm so that the bob is suspended directly over the pointer Attach the spring to the bob and practice rolling the rotor between your thumb and fingers so that the bob revolves in a circu lar path and passes over the pointer on each revolution in uniform circular motion Adjust the position of the counterbalance on the support arm if necessary for ease of operation Make sure the locking screws are tight and be careful of the rotating counterweight Caution Safety glasses should be worn This is always a good prac tice in a laboratory with moving equipment While one lab partner operates the rotor another lab partner with a laboratory timer or stopwatch times the interval for the bob to make about 25 revolutions The number of counted revolutions may have to be varied depending on the speed of the rotor Count enough revolutions for an interval of at least 10 s Record the data in Data Table 1 Practice the proce dure before making an actual measurement Repeat the counting timing procedure twice Com pute the time per revolution of the bob for each trial and determine the average time per revolution of the three trials From the data calculate the average speed of the bob Recall v c t 2zr T where c is the circum ference of the circular orbit r is the radius of the or bit and T is the average time per
532. ton leftmost button on the graph toolbar to scale all data to fit on the screen 9 Print the graph If no printer is available make a care ful drawing of the graph Paste the graph to the labo ratory report 10 Record the maximum voltage across the capacitor Then calculate 6346 of this value Report these values in CI Data Table 1 The voltage value of 3 V is suggested for the values of R and C specified before because it produces an easy to read plot The voltage sensor can measure a high range of voltages and you may use a different value www ATIBOOK ir 390 EXPERIMENT 26 The RC Time Constant Electronic Timing A Charging 13 11 Look at the charging part of the graph Use the graph tools to find the time at which the voltage reached 63 of the maximum This is the experimental time constant of the circuit Refer to CI Eq 26 5 Enter the value in the table and compare it to the theoretical value with a percent error B Discharging 12 Determine 37 of the maximum voltage and record this value in the table 14 From the graph determine how long after the start of the discharge the voltage was only 37 of the maxi mum This is again the time constant of the circuit Refer to CI Eq 26 7 Enter this value in the labora tory report and compare it to the theoretical value by calculating the percent error Repeat the experiment with a different value of resis tance keeping the capacitor and the vo
533. top view of the experimental arrangement and procedure for deter mining the index of refraction of a glass plate See text for description www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 27 Reflection and Refraction RWV Laboratory Report A Reflection Glass Plate as a Mirror 0 0 Ray 1 d Ray 2 di Plane Mirror Length of pin d Length of image d Rotation of a Mirror Angle of rotation 0 20 Percent differences between 0 and 0 Ray 1 Ray 2 Percent differences between d and d Percent difference between pin length and image length Percent difference between d and d Angle of deflection of ray Percent difference between and 20 Calculations show work Don t forget units 399 continued www ATIBOOK ir Laboratory Report EXPERIMENT 27 Reflection and Refraction B Refraction Index of Refraction of a Glass Plate 0 05 Computed n Ray ARA Ray BRB Ray CRC Average n General range of the index of refraction of glass Displacement d of ray C C Thickness of glass plate Calculations show work AY QUESTIONS 1 a Why are two images seen in the glass plate when it is viewed from position 2 in Part A of the experiment Why is only one image seen when it is viewed from position 1 400 www A TIBOOK ir Name Section Date Lab Partner s
534. tudy Assignment 5 Describe how the density of an object less dense than water can be determined using Archimedes principle How about the density of a liquid 6 Why is it important to make certain that no air bubbles adhere to objects during the submerged weighing procedures How would the experimental results be affected if bubbles were present Is this a random or systematic error See Experiment 1 270 www A TIBOOK ir EX PER MENT 1 8 Archimedes Principle Buoyancy and Density INTRODUCTION AND OBJECTIVES Some objects float and others sink in a given fluid a liquid or a gas The fact that an object floats means it is buoyed up by a force equal to its weight Archimedes 287 212 BCE a Greek scientist deduced that the upward buoyant force acting on a floating object is equal to the weight of the fluid it displaces Thus an object sinks if its weight exceeds that of the fluid it displaces In this experiment Archimedes principle will be studied in an application determining the densities and specific gravities of solid and liquid samples After performing this experiment and analyzing the data you should be able to 1 Tell whether an object will sink or float in a fluid knowing the density of each 2 Distinguish between density and specific gravity 3 Describe how the densities of objects that sink or float may be determined experimentally EQUIPMENT NEEDED Triple beam pan balance with
535. tural frequencies or resonant frequencies The resulting standing wave pat terns are called normal or resonant modes of vibration In general all systems that oscillate have one or more nat ural frequencies which depend on such factors as mass elasticity or restoring force and geometry boundary conditions Since the string is fixed at each end a standing wave must have a node at each end As a result only an integral number of half wavelengths may fit into a length L of the string L A 2 A 3A 2 2A and so on such that in general Setting n 1 in Eq 15 5 gives the lowest possible frequency which is known as the fundamental frequency 1 JF h aNu 15 5 fundamental frequency so Eq 15 4 may be written in terms of the fundamental frequency as y n fa n 2L F i79 n 1 2 3 15 6 L of n x or A 2 2L ue 15 2 n 1 2 3 4 Fig 15 2 illustrates the case for L 3A 2 The wave speed in a stretched string is given by v 1 15 3 H wave speed in a stretched string where F is the magnitude of the tension force in the string and yp is the linear mass density mass per unit length u m L of the string Using Eqs 15 2 and 15 3 in Af v Eq 15 1 yields y Sn n F JE n 1 2 3 2LN M n 15 4 Moreover only certain frequencies produce stand ing waves for a gi
536. ty is approximately constant with a common value of g 9 80 m s 980 cm s 32 2 fus Of course air resistance affects the acceleration of a falling object But for relatively dense objects over short dis tances of fall the effects of air resistance are negligible and objects fall with an acceleration of g In this experiment the acceleration due to gravity is used to investigate an object undergoing uniformly accelerated motion to see how its velocity and displacement change with time Conversely with displacement and time measurements the value of g can be determined The experimental data and their analyses will yield a better understanding of the kinetic equations describing the motion RV OBJECTIVES After performing this experiment and analyzing the data you should be able to do the following 1 Clearly distinguish between average and instanta neous velocity 2 Express how the velocity of a uniformly accelerated object changes with time 3 Express how the distance traveled by a uniformly accelerated object changes with time 4 Explain how the uniform acceleration of an object may be determined from distance and time measurements 51 A ossectives 1 Analyze the motion of an object that moves with con stant acceleration 2 Understand what it means to say that the position varies with the square of the time GENERAL THEORY TI Cl When an object moves with a uniform or constant accel eration the
537. type of ballistic pendulum Caution In either case be careful not to bruise or hurt your hand when cocking the gun Also keep your fingers away from the projectile end of the gun Fire the projectile into the pendulum to see how the apparatus operates If the catch mechanism does not catch on the notched track you should adjust the pendulum suspension to obtain the proper alignment 2 A preset pointer or a dot on the side of the pendulum bob indicates the position of the center of mass CM of the pendulum ball system With the pendulum hanging freely measure the height h of the pointer above the base surface Fig 8 2 and record it in Data Table 1 3 Shoot the ball into the freely hanging stationary pen dulum and note the notch at which the catch mecha nism stops on the curved track Counting upward on the curved track record the notch number in Data Table 1 Repeat this procedure four times and for each trial record the notch number in the data table Alternatively the height may be measured each time See Procedure 4 note 4 Determine the average of these observations which is the average notch position of the pendulum Place the catch mechanism in the notch corresponding most closely to the average and measure the height h of the CM dot above the base surface used for the h measurement Fig 8 2 Note To minimize frictional losses the catch mechanism may be disabled by tying it up with thread or using a rubb
538. ubricating powder 9 Plastic block with dry lubricating powder Answer the following questions on a separate sheet of paper and attach it to the TI Laboratory Report a Compare No 1 with TI Data Table 1 Is the inclined plane method valid for p b Compare No 2 with No 1 and No 3 with TI Data Table 4 Does u depend on area c Compare Nos 3 4 and 5 Does up depend on material d Compare No 5 with No 6 Does uy depend on velocity e Compare No 7 with anything How does rolling friction compare with other types of friction f Compare Nos 8 and 9 with Nos 5 and 4 What is the effect of adding the lubricant RV QUESTIONS 1 Explain why f uN that is why is f less than or equal to uN continued 165 www ATIBOOK ir EXPERIMENT 10 Friction Laboratory Report 2 Speculate in terms of the microscopic surface irregularities about why ju lt u and what effect a lubricant has on the coefficient of friction 3 a Prove that tan 0 is equal to ju when the block slides down the incline with a constant speed Use symbols not numbers b If 0 is the maximum angle of incline just before the block moves what is jz in terms of 0 4 Suppose that the block were made to move up the inclined plane with a uniform speed by suspending masses on a string over the pulley Derive an equation for the coefficient of kinetic friction for this case in terms of the suspended masses the mass of th
539. uctor s choice optional Your instructor may have a particular case he or she would like you to investigate If so the conditions will be given Space has been provided in the data table for reporting your findings B Apparatus Supported at Different Pivot Points In the previous cases the mass of the meter stick was not explicitly taken into account since the fulcrum or the posi tion of the support was at the meter stick s center of gravity or center of mass In effect the torques due to the mass of the meter stick on either side of the support position can celed each other The centers of gravity of the lengths of the stick on either side of the support are equidistant from the support for example at the 25 cm and 75 cm positions for a uniform stick and have equal masses and moment arms For the following cases the meter stick will not be sup ported at its center of gravity position x but at some other pivot points designated in general by x for example see Fig 12 5 In these cases the mass of the meter stick needs to be taken into account To illustrate this very vividly let s start off with a case with only one suspended mass 7 Case 5 Meter stick with one mass Suspend a mass m 100 g at or near the zero end of the meter stick Fig 12 5 Record the mass position x in Data Table 2 If a string loop is used a piece of tape to hold the string Xo i Center of lt if x ly gt gravity
540. ugh a given tempera ture interval AT as is needed to raise the temperature of 1 kg of lead by the same amount This material behavior is characterized quantitatively by specific heat which is the amount of heat necessary to raise the temperature of a unit mass of a substance by one unit temperature interval that is to raise 1 gram or 1 kilo gram of a substance 1 degree Celsius Thus in the previous example iron has a greater specific heat than does lead The specific heat of a material is specific or char acteristic for that material As can be seen from the definition the specific heat of a given material can be determined by adding a known amount of heat to a known mass of material and noting the corresponding temperature change It is the purpose of this experiment to determine the specific heats of some common metals by calorimetry methods After performing this experiment and analyzing the data you should be able to 1 Tell what is meant by the specific heat of a substance and compare the effects of different specific heats 2 Calculate the heat necessary to raise the temperature of a given mass of a substance a particular number of degrees 3 Describe and explain calorimetry and the method of mixtures EQUIPMENT NEEDED Calorimeter Boiler and stand Hot plate or Bunsen burner and striker Two thermometers 0 C to 110 C Two kinds of metal shot form or slugs with attached strings Laboratory balan
541. uish between nodes and antinodes 3 Tell what determines the natural frequencies of a vibrating string system EQUIPMENT NEEDED Electric string vibrator Clamps and support rod Pulley with rod support String Weight hanger and slotted weights Meter stick Laboratory balance sheet of Cartesian graph paper THEORY A wave is characterized by its wavelength A in meters the frequency of oscillation f in Hz or 1 s s and wave speed v m s See e Fig 15 1 These quantities are related by the expression Af v 15 1 Check to see whether the equation is dimensionally correct Waves in a stretched string are transverse waves that is the particle displacement is perpendicular to the di rection of propagation In longitudinal waves the particle y amplitude sak Displacement ra T Figure 15 1 Wave description The parameters involved in describing a wave See text for description displacement is in the direction of wave propagation for example in sound waves The maximum displacements of the particle oscillation are A and A The magnitude of the maximum displacement called the amplitude A is related to the energy of the wave The period of oscilla tion T is related to the frequency of oscillation T 1 f When two waves meet they interfere and the com bined wave form is a superposition of the two interfer ing waves The superposition of two waves of
542. ulum when the maximum kinetic energy was reached From the potential energy graph look at the first clear complete cycle of the motion and find the maximum potential energy during that cycle Record it in the table Record also the position of the pendulum when the maximum potential energy was reached Repeat for the minimum values of kinetic and poten tial energies To further reinforce the idea of conversions between kinetic and potential energy create a new graph Graph 3 by dragging the kinetic energy data icon and dropping it on top of the Graph icon on the displays list Then drag the potential energy icon and drop it in the graph This graph will show both KE and PE as functions of time www ATIBOOK ir Name Section Date Lab Partner s C I EXPERIMENT 14 Simple Harmonic Motion Rd Laboratory Report Ly vata taste Purpose To examine the variations of kinetic and potential energy as a pendulum swings Mass of pendulum M________kg Max amplitude Length 2 m Period Position of pendulum Value deg KE max PE max KE min PE min Don t forget to attach the graphs to the laboratory report Don t forget units 237 continued www A TIBOOK ir EXPERIMENT 14 Simple Harmonic Motion Laboratory Report A ouestions 1 Compare the values of the maximum kinetic energy and the maximum potential energy Discuss them in terms of the
543. um 210 138 4 days 5 305 Potassium 42 12 4 hours 3 52 1 97 Radium 226 1600 years 4 781 0 186 4 598 Sodium 22 2 60 years 0 545 1 275 1 82 Strontium 90 28 1 years 0 546 Thallium 204 3 78 years 0 763 Uranium 238 4 5 X 106 years 4 195 0 48 Yttrium 90 64 0 hours 2 21 Zinc 65 243 6 days 0 329 1 116 515 www ATIBOOK ir 516 APPENDIX A Material Properties TABLE A10 Elements Atomic Numbers and Atomic Weights The atomic weights are based on C 12 0000 If the element does not occur naturally the mass number of the most stable isotope is given in parentheses Atomic Atomic Atomic Atomic Symbol number weight Symbol number weight Actinium Ac 89 227 Mercury Hg 80 200 59 Aluminum Al 13 26 9815 Molybdenum Mo 42 95 94 Americium Am 95 243 Neodymium Nd 60 144 24 Antimony Sb 51 121 75 Neon Ne 10 20 179 Argon Ar 18 39 948 Neptunium Np 93 237 Arsenic As 33 74 9216 Nickel Ni 28 58 71 Astatine At 85 210 Niobium Nb 41 92 9064 Barium Ba 56 137 34 Nitrogen N 7 14 0067 Berkelium Bk 97 247 Nobelium No 102 253 Beryllium Be 4 9 01218 Osmium Os 76 190 2 Bismuth Bi 83 208 9806 Oxygen O 8 15 9994 Boron B 5 10 81 Palladium Pd 46 106 4 Bromine Br 35 79 90 Phosphorus P 15 30 9738 Cadmium Cd 48 112 40 Platinum Pt 78 195 09 Calcium Ca 20 40 08 Plutonium Pu 94 224 Californium Cf 98 251 Polonium Po 84 209 Carbon C 6 12 011 Potassium K 19 39 102 Cerium Ce 58 140 12 Praseodymium Pr 59 140 9077 Cesium Cs 55 132 9055 Promethium
544. using a commonly available item Hint What is a common polarizing material or application of polarization 5 You hold two polarizing sheets in front of you and look through both of them How many times would you see the sheets lighten and darken a if one of them were rotated through 360 or one complete rotation and b if both of them were rotated through one complete rotation in opposite directions at the same rate 432 www A TIBOOK ir Cl EXPERIMENT 29 Malus s Law a EQUIPMENT NEEDED Diode laser PASCO OS 8525 eT Aperture bracket PASCO OS 8534 AA ASE OTTO AA Optics bench PASCO OS 8515 or OS 8541 Rotary motion sensor PASCO CI 6538 Polarization analyzer PASCO OS 8533 Polarizer with groove plastic belt and mounting screws are included in the kit a THEORY Notice that the transmitted intensity can vary from com STE plete transmission L to no transmission J 0 and See the methods of p olarization m the TI Theory section can take on any intermediate value between the maximum When unpolarized light is incident Upon ap olarizer and minimum depending on the angle between the polarizing the transmitted light Hs reduced PATENTLY and linearly planes of the polarizer and analyzer Here J is the maxi polarized as shown in TI Fig 29 3a When this polarized mum intensity of light through the analyzer when 0 0 light falls on a second polarizer usually referred ioi In this experim
545. value in the space pro vided in Data Table 3 and use Data Tables 3 and 4 for your findings B Wheatstone Bridge Method 7 Set up a slide wire Wheatstone bridge circuit as in Fig 21 4a using the previous small known resistance R as R Leave the switch open until the instructor checks the circuit The wires connecting the resistances and www ATIBOOK ir EXPERIMENT 21 The Measurement of Resistance Ammeter Voltmeter Methods and Wheatstone Bridge Method 315 the bridge should be as short as practically possible The decade resistance box is used for R This should be initially set for a value about equal to R Contact is made to the wire by sliding contact key C Do not slide the key along the wire while it is pressed down This will scrape the wire causing it to be nonuni form Have the instructor check your setup before acti vating the circuit Activate the circuit by closing the switch S and bal ance the bridge by moving the slide wire contact Open the switch and record R L and L in Data 10 11 Table 5 Leave the switch open except when you are actually making measurements Repeat Procedures 7 and 8 for R settings of a R 3R and b R 0 3R Compute the value of R for each case and find the av erage value Compare this value to the accepted value of R by finding the percent error Repeat the previous procedures with a large known resistance Record your findings in Data Table 6
546. ve spherical lenses Many of us wear lenses in the form of eyeglasses Cameras and projectors use lens systems to form images Cameras form reduced size images on film or a chip digital and projectors form magnified images on a screen In this experiment the fundamental properties of spherical mirrors and lenses will be investigated to learn the parameters that govern their use After performing this experiment and analyzing the data you should be able to 1 Distinguish among converging and diverging spheri cal mirrors and lenses 2 Determine the image characteristics for spherical mirrors graphically using ray diagrams and analytically using the mirror equation and magnification factor 3 Determine the image characteristics for spherical lenses graphically using ray diagrams and analytically using the thin lens equation and magnification factor EQUIPMENT NEEDED Concave and convex spherical mirrors Convex lens focal length 10 cm to 20 cm Concave lens focal length at least 5 cm longer than convex lens Meter stick optical bench or precision bench with lens holder screen and screen holder white card board can serve as the screen Light source candle and candle holder or electric light source with object arrow THEORY A Spherical Mirrors A spherical mirror is a section of a sphere and is char acterized by a center of curvature C Fig 28 1 The distance from the center of curvature to
547. vector quantity so is linear momentum Newton s second law of motion commonly ex pressed in the form F ma can also be written in terms of momentum TI 7 2 Recall a Av t If there is no net or unbalanced external force acting on the object F 0 then Ap F s At and Ap 0 That is the change in the momentum is zero or the mo mentum is conserved Conserved means that the momen tum remains constant in time Expanding Ap Ap py pj 0 and Pr Pi TI 7 3 and the final momentum p at any time f is the same as the initial momentum p at time f Notice that this is con sistent with Newton s first law of motion since pr pi or mw MV Boldface symbols indicate vectors see Expt 5 107 and Vr Vj That is an object remains at rest v 0 or in uniform motion v vj unless acted on by some external force The previous development also applies to the total mo mentum of a system of particles or objects For example the total linear momentum P of a system of two objects m and m is P p py and if there is no net external force acting on the system then AP 0 In the case of a collision between two objects of a system with only internal forces acting the initial total momen tum before the collision is the same as the final total mo mentum after the collision That is after Pi Po before Pi p TI 7 4
548. ven string tension linear density and length As noted above the lowest natural frequency fi Eq 15 5 is called the fundamental frequency All other natural frequencies are integral multiples of the fundamen tal frequency f nf for n 1 2 3 The set of frequencies fj f 2f f 3fi is called a harmonic series f the fundamental frequency is the first harmonic f the second harmonic and so on In this experiment the electrically driven string vibra tor has a fixed frequency so the driving frequency cannot be varied to produce different normal mode standing wave patterns However varying the string tension can vary the wave speed so as to produce different standing wave patterns Since v V F y Eq 15 3 resonant frequencies where f and A are the frequency and wavelength respec tively for a given integer n See Experiment 12 Theory B for a discussion of linear mass density v 1 F A 15 7 ae where f and u are constant Hence by varying F one can select the appropriate wavelengths that will fit into a given string length L to produce standing waves www A TIBOOK ir EXPERIMENTAL PROCEDURE 1 If one has not been provided cut a piece of string long enough to be used in the experimental setup long enough to be looped at each end so as to be attached to the vibrator and a weight hanger suspended from the end running over the pulley Fig
549. veral times and it is very unlikely that identical results will be obtained for all trials For a set of measurements with pre dominantly random errors that is the measurements are all equally trustworthy or probable it can be shown math ematically that the true value is most probably given by the average or mean value The average or mean value x of a set of N measure ments is N Sa 1 4 i 1 XQ xb xb xy 1 N N where the summation sign gt is a shorthand notation indi cating the sum of N measurements from x to xy x is com monly referred to simply as the mean Example 1 6 What is the average or mean value of the set of numbers 5 42 6 18 5 70 6 01 and 6 32 x x i Mz m Nj 1 5 42 6 18 5 70 6 01 6 32 5 5 93 There are other more advanced methods to express the dispersion or precision of sets of measurements Two of these are given in the appendices Appendix C Abso lute Deviation from the Mean and Mean Absolute Devia tion and Appendix D Standard Deviation and Method of Least Squares www ATIBOOK ir EXPERIMENT 1 Experimental Uncertainty Error and Data Analysis 9 F Graphical Representation of Data It is often convenient to represent experimental data in graphical form not only for reporting but also to obtain information GRAPHING PROCEDURES Quantities are commonly plotted using rectangular Cartesian axes X and Y The horizontal
550. w A TIBOOK ir Name Section Date Lab Partner s Ry The Transmission Diffraction Grating Measuring the T EX PERIMENT Wavelengths of Light RW Laboratory Report 2 Number of lines per millimeter on grating mm RV DATA TABLE 1 Purpose To determine the wavelength range of the visible spectrum Divided circle reading an A wavelength Spectrum limit 20 sind Right Left Violet end Red end Calculations show work Don t forget units 467 continued www ATIBOOK ir EXPERIMENT 32 The Transmission Diffraction Grating Laboratory Report RV DATA TABLE 2 Purpose To determine the wavelengths of spectral lines Mercury Lines Divided circle reading Computed Percent 7 20 0 sind Color Wavelength Right Left AC error First order spectrum Second order spectrum Calculations show work 468 www A TIBOOK ir Name Section Date Lab Partner s EXPERIMENT 32 The Transmission Diffraction Grating Laboratory Report RV QUESTIONS 1 If a grating with more lines per unit length were used how would the observed angles or spread of the spectra be affected 2 Was there any difference in the accuracy of the determination of the wavelengths of the mercury lines for the different order spectra If so give an explanation 3 Is it po
551. what conditions is the tension in the string pulling horizontally on the cart equal in magnitude to the frictional force 156 www A TIBOOK ir EX PER d Friction OVERVIEW Experiment 10 examines friction using complementary TI and CI approaches The TI procedures are concerned with determination of the coefficients of friction u and pa With an option of investigating the dependence of u MENT 1 0 on various parameters such as different materials lubrica tion and so on The CI procedures extend the investigation by exam ining the effect of speed on sliding friction INTRODUCTION AND OBJECTIVES In general the term friction refers to the force or resis tance to motion between contacting material surfaces Internal friction occurs in liquids and gases The friction between unlubricated solids is a broad and complicated topic because it depends on the contacting surfaces and the material properties of the solids Three general empiri cal rules are often used to describe friction between solid surfaces These are that the frictional force is 1 independent of the surface area of contact 2 directly proportional to the load or the contact force that presses the surfaces together 3 independent of the sliding speed Let s take a look at each of these rules 1 Intuitively one would think that friction depends on the roughness or irregularities of the surfaces and the greater the are
552. where d is the distance the car moves If the car moves approximately at the same constant speed in each case it might be assumed that the magni tude of the frictional force f would be the same in each case same angle of incline and load This will be investigated experimentally B Work of Friction Energy Method Another way of looking at the frictional work is in terms of energy CAR MoviING UP THE PLANE For the case of the car moving up the plane by the conser vation of energy the decrease in the potential energy of the descending weight on the weight hanger A U mgh is equal to the increase in the potential energy of the car A U m gh plus the energy lost to friction which is equal to the work done against the force of friction W Fig 11 1 That is AU AU W or W AU a AU and W mgh m gh 11 4 car moving up CAR MovinG DOWN THE PLANE Similarly for the case of the car moving down the plane by the conservation of energy the decrease in the potential energy of the descending car is equal to the increase in the potential energy of the ascending weight plus the work done against the force of friction Fig 11 1 AU AU W or W AU AU and W m gh mgh 11 5 car moving down In terms of the experimental parameters the methods for determining W are equivalent EXPERIMENTAL PROCEDURE Force Distance Method 1 Using a laboratory b
553. which can produce what is called a triangle wave voltage CI Fig 20 1 shows how the voltage from such a source varies with time Notice that it increases up to a maximum value then drops steadily back to zero and then with a change of polarity increases Voltage Vinax oy neared Voltage Voltage increasing decreasing Time Vmax CI Figure 20 1 A triangle wave voltage function With a triangle wave voltage function the voltage will increase up to a maximum value drop steadily back to zero and then change the polarity and increase in the opposite direction This will repeat with a certain fixed frequency 303 in the opposite direction This repeats with a certain fixed frequency SETTING UP DATA STUDIO 1 Open Data Studio and choose Create Experiment 2 The Experiment Setup window will open and you will see a picture of the Science Workshop interface There are seven channels to choose from and a signal gen erator Digital Channels 1 2 3 and 4 are the small buttons on the left analog Channels A B and C are the larger buttons on the right the signal generator is all the way to the right as shown in CI Fig 20 2 3 Click on the Channel A button in the picture A win dow with a list of sensors will open 4 Choose the Voltage Sensor from the list and press OK 5 Connect the sensor to Channel A of the interface as shown on the computer screen 6 Click on the picture of the signal generator The
554. www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 3 Simple Machines Mechanical Advantage RV Advance Study Assignment Read the experiment and answer the following questions 1 Why is the actual mechanical advantage AMA a force multiplication factor 2 Can work be multiplied by a machine Explain 3 Why is the theoretical mechanical advantage TMA theoretical or ideal 4 Which is larger the AMA or the TMA of a machine and why 207 continued www ATIBOOK ir EXPERIMEN TF 18 Advance Study Assignment 5 What factors comprise the ratio of the efficiency of a machine and how is efficiency related to the AMA and TMA 6 Why is efficiency always less that 100 208 www A TIBOOK ir EXP Es Rl Simple Machines ENT 1 3 Mechanical Advantage INTRODUCTION AND OBJECTIVES Machines are used daily to do work Upon analysis all mechanical machines however complex are combinations of simple machines of which there are six mechanical classes 1 inclined planes 2 levers 3 pulleys 4 wheel and axles 5 wedges and 6 screws Although used to perform work a simple machine is basically a device that is used to change the magni tude or direction of a force Essentially a machine is a force multiplier The magnitude of this multiplication is given by a machine s mechanical advantage that is the actual mechanical advantage AMA which takes into account
555. ximity The wires are too far apart for a spark to jump directly from one wire to TI Figure 4 1A Spark timers Sargent Welch right Harvard 67 the other However as the metal object falls between the wires the spark electrical current jumps from one wire to the metal object travels through the object and jumps to the other wire In so doing the spark burns a spot on the paper tape strip The spots on the tape are then a certain time inter val apart as selected and usually preset on the spark timer The series of spots on the tape gives the vertical distance of fall as a function of time from which can be measured the distance y that the object falls in a time f The instantaneous velocity v of a free falling object neglecting air resistance at a time f is given theoretically by TI 4 1A V V t gt Types of free fall spark timer apparatuses Photos left and center Photo Courtesy of www ATIBOOK ir 68 EXPERIMENT 4A Uniformly Accelerated Motion where downward is taken as the positive direction Hence a graph of v versus t is a straight line y mx b with a slope m Av At g and an intercept b v the initial velocity Recall that t in TI Eq 4 1A is really a time interval measured from an arbitrary starting time f 0 At this time the velocity of the object is vj which may or may not be zero The motion of the falling object as recorded on the experimental data tape is ana
556. xis See Appendix D for a discussion of graphing on semi log and log log graph paper www ATIBOOK ir This page intentionally left blank www A TIBOOK ir Name Section Date Lab Partner s EX PERIMENT 3 4 Radioactive Half Life RWV Laboratory Report Background count cpm DATA TABLE Purpose To determine the half life of Ba 137m t N Corrected for Calculations Elapsed time Observed background show work min activity cpm radiation cpm Time from full to 2 activity Time from j to 1 activity Average experimental half life Accepted half life Percent error Decay constant from average half life Decay constant from graph Percent difference Don t forget units 497 Half life Measurements for Ba 137m continued www ATIBOOK ir EXPERIMENT 34 Radioactive Half Life Laboratory Report RV QUESTIONS 1 In the experiment if the Ba 137m sample were placed closer to the Geiger tube the mea sured activity would be greater inverse square relationship Would this affect the result of the half life Explain how this would affect the N versus t graph on Cartesian graph paper or on semi log paper 2 A cobalt 60 source has a measured activity of 12 000 cpm After how long would the ob served activity be 750 cpm The half life of Co 60 is 5 27 y 3 An instructor buys a 10 uCi Cs 137 source for laboratory exp
557. xplain 4 When a mercury in glass thermometer is placed in hot water the thermometer reading first drops slightly and then rises Explain why 256 www ATIBOOK ir Name Section Date Lab Partner s EXPERIMENT 16 The Thermal Coefficient of Linear Expansion Laboratory Report 5 If flat strips of iron and brass were bonded together and this bimetallic strip were heated what would be observed Justify your answer and draw a sketch of the situation Hint See Appendix A Table A3 for a s 6 A Pyrex graduated cylinder has a volume of exactly 200 mL at 0 C If its temperature is increased to 100 C will its volume increase or decrease Compute the change in volume 7 Assume a metal rod with an initial length L is heated through a temperature increase of AT to a length L and then cooled to its initial temperature that is through a temperature decrease of AT same AT increase and decrease Call the final length of the rod L after this thermal cycle a Show that Eq 16 3 implies that L L 1 aAT that is L Le b What is the implication if the rod were taken through a number of such thermal cycles continued 257 www A TIBOOK ir EXPERIMENT 16 The Thermal Coefficient of Linear Expansion Laboratory Report c Obviously something is wrong Can you explain what it is Hint Think of basis or reference For example if you had an investment that appreciated 100 in value one day a
558. xt for description www ATIBOOK ir 398 EXPERIMENT 27 Reflection and Refraction line and the length of the object pin and record Also measure the object distance d and the image distance d from the mirror line and record Compute the percent differences of the respective measured quantities ROTATION OF A MIRROR 7 Place the mirror near the center of a sheet of paper as described above and draw a line along the length of the silvered side of the mirror Measure so as to find the center of the line and mark that location Stick two pins A and B in the board to one side and in front of and in line with the center of the mirror as in Fig 27 6 Viewing the aligned images of these pins from the other side of the page place two more pins C and D in alignment Label the locations of the pins 8 Leaving pins A and B in place rotate the mirror a small but measurable angle 0 approximately 10 to 15 about its center point and draw a line along the silvered side of the mirror Align two pins E and F with the aligned images of A and B and mark and label the locations of E and F 9 Remove the equipment from the paper and draw the incident ray and the two reflected rays Measure the angle of rotation 0 of the mirror and the angle of deflection between the two reflected rays and record in the laboratory report Double 0 and compute the percent difference between 20 and Make a conclusion about the rela tions
559. y current pulse which lasts on the order of microseconds the potential difference between the wire and the cylinder resumes its original value lonizing radiation lon electron pair Output to counter Geiger tube Figure 33 1 Geiger tube A schematic diagram of the Geiger tube and circuit See text for description www A TIBOOK ir 484 EXPERIMENT 33 Detection of Nuclear Radiation The Geiger Counter A finite time is required for the discharge to be cleared from the tube During this time the voltage of the tube is less than that required to detect other radiation that might arrive This recovery time is referred to as the dead time of the tube If a large amount of radiation arrives at the tube the counting rate counts per minute or cpm as indicated on the counting equipment will be less than the true value There are two common types of Geiger tubes a nor mal or side window tube and an end window tube The side window tube has a relatively thick wall that may not be penetrated by less penetrating radiation such as alpha particles Fig 33 2 The end window tube has a thin end window usually of mica and may be thin enough to be penetrated by very energetic alpha particles The brief change in the potential that occurs when a discharge takes place in the tube produces a voltage pulse that can be detected and counted by appropriate instrumen tation Common instruments used for counting are scalers a
560. y many ac circuit characteristics The screen display of voltage versus time makes it possible to observe a variety of measurements In particular in an RC resistance capacitance circuit the charging of the capacitor can be visually observed And using the horizontal time scale the time constant of the charging process can be readily determined In this experiment the oscilloscope will be used to determine the time constant of an RC circuit as the capaci tor is continually charged and discharged by an ac signal voltage RV OBJECTIVES After performing this experiment and analyzing the data you should be able to 1 Explain the charging characteristics of a capacitor with ac voltage 2 Appreciate how the oscilloscope can be used to moni tor electrical characteristics and to make electrical measurements 3 Describe how an RC time constant may be measured from an oscilloscope trace Rd ossectives The purpose of this experiment is to investigate the charging and discharging of a capacitor in a series RC circuit The time constant of the circuit will be determined experimen tally and compared to the theoretical value After perform ing this experiment and analyzing the data you should be able to 1 Describe the charging and discharging of a capacitor through a resistor 2 Explain how the time constant can be measured experimentally 3 Explain what the RC time constant means in terms of circuit characteristics
561. y mov ing the mirror rather than the object light source Move the screen along the side of the optical bench until an image is observed on the screen This is best observed in a darkened room The Tf a window is not available or it is a dark day use Procedure 3 to determine f experimentally In this case show first that d d R and M 1 Then d having been measured the focal length is f d 2 R 2 www A TIBOOK ir EXPERIMENT 28 Spherical Mirrors and Lenses 409 Figure 28 5 Experimental arrangements b spherical lenses Cengage Learning 5 6 mirror may have to be turned slightly to direct the rays toward the screen c Estimate the magnification factor M and measure and record the image distance d d Using the mirror equation compute the image distance and the magnification factor e Compare the computed value of d with the experi mental value by computing the percent difference Case 2 d R Repeat Procedure 3 for this case Case 3 f lt d lt R Repeat Procedure 3 for this case Case 4 d lt f Repeat Procedure 3 for this case CONVEX MIRROR 7 B Sketch ray diagrams for objects at 1 d gt R 2 f d lt R and 3 d lt f and draw conclusions about the characteristics of the image of a convex mirror Experimentally verify that the image of a convex mirror is virtual that is try to locate the image on the screen Spherical Lenses CONVEX LENS
562. ylinder 15 16 Using Eq 9 3 compute the magnitude of the centripetal force Compare this with the directly mea sured value given by the weight force required to pro duce the same extension of the spring by computing the percent difference Change the spring tension to a maximum setting about the 20 mark on the scale above the threaded collar and repeat Procedures 3 through 7 recording your results in Data Table 6 www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 9 Centripetal Force AY Laboratory Report A Manual Centripetal Force Apparatus DATA TABLE 1 Purpose To determine period of revolution for computation of centripetal force Mass of bob Trial 1 Trial 2 Trial 3 Radius of circular path Number of revolutions Average time per revolution Total time Average speed of bob v Time revolution Conia cane df centripetal force Computation of centripetal force Direct measurement of attach additional sheet centripetal force Percent difference DATA TABLE 2 Purpose To observe the effect of varying mass Trial 1 Trial 2 Trial 3 Mass of bob Number of revolutions Radius of circular path Average time per revolution Total time Average speed of bob v Time revolution Computed value of centripetal force Computation of centripetal force attach additional sheet Direc
563. you predict the position of the center of gravity x of the system would be if m were moved to the 90 cm position Record your prediction in the data table Using your prediction compute the counter clockwise and clockwise torques taking into account the mass of the meter stick as in Proce dure 7 c Compare the torques by computing the percent difference Experimentally determine the position of the center of gravity of the system and compute the percent difference between the experimental and predicted values www ATIBOOK ir Name Section Date Lab Partner s EX PERIMENT 1 2 Torques Equilibrium and Center of Gravity RWV Laboratory Report A Apparatus with Point of Support at Center of Gravity Mass of meter stick Total mass of clamps Average mass of one clamp m Balancing position center of gravity of meter stick x DATA TABLE 1 Values add m to masses Moment Diagram 5 lever Results if clamps used arms Case 1 k n 31 r m x 15cm Ti Tee i 1 i x k My X fg Tew i i 108 CA N La Percent diff Case 2 a m x 30cm Fa Te m x 70cm 72 Tow ms x r Percent diff Case 2 b m x 20cm ri r3 calculated My X 60 cm r3 m X measured Percent error Draw a diagram to

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