PASCO Specialty & Mfg. ME-6828 User's Manual
Contents
1. J Instruction Manual PASC AA Dynamics Cart Magnetic Damping ME 6828 2 Included Equipment Part Number 1 Magnetic Damping Accessory ME 6828 2 Keeper plate 648 10173 Required Equipment Part Number PAScar Plunger Cart or Collision Cart ME 6950 ME 9430 or ME 9454 Aluminum Dynamics Track ME 6953 or similar For other recommended equipment see experiments starting on page 3 Introduction Use the Magnetic Damping Accessory to add drag to a PASCO dynamics cart When the cart moves on an alumi num track the accessory s magnets generate eddy currents in the track which cause an opposing magnetic field The resulting drag force is proportional to the cart s velocity The amount of damping can be varied by changing the size of the gap between the magnets and the track This manual includes set up instructions three experiments starting on page 3 and sample data page 13 Set up The Magnetic Damping Accessory attaches to a cart magnetically using the magnets built into the cart s bumper If your cart does not have bumper magnets install them before using the Magnetic Damping Accessory See instructions included with your cart for bumper magnet installation 1 Remove the keeper plate from the Magnetic Damping Accessory and put it aside E 800 772 8700 www pasco com Dynamics Cart Magnetic Damping 2 Place the Magnetic Damping Accessory on the magnet equipped end of the cart as illustrated 32. Damping b the damping constant F4 amping Experiment 2 Critical Damping bv determined by the height of the magnets Oy Vk m the natural frequency of the system in the absence of damping y b m a quantity with units of frequency If m and k are held constant then the damping behavior of the system whether it is under over or critically damped depends on the value of b Under damping For the system to be under damped we must have a relatively low value of y Let Y Ya such that 0 y 4 gt 0 Then y t 2 x t Xoe 2 2 Where NO Y 74 Over damping Tia cos ot CD For over damping the value of y must be higher Let y Y such that Oy Yo 74 lt 0 Then y 2 B t x t ol5 ape y 2 B txl 2 Where B 4 0 Critical damping To Y 2 B t e 2 4 Critical damping occurs at a specific value of y Let y Y such that Do y7 4 0 Then x t a Modeling the cart s motion Y t 2 e 2 Graph the three equations above and compare them to your actual data Either mea sure or estimate your experimental values of Xo m and k or to put into the equa tions Estimate values of b for under over and critical damping TEIH ME 6828 Experiment 3 Predicting Terminal Velocity Experiment 3 Predicting Terminal Velocity Equipment Part Number Dynamics Cart Magnetic Damping ME 6828 Motion Sensor PS 2103A or similar Cart ME 69
3. This experiment requires a spring or combination of springs with constant between 1 0 N m and 1 5 N m If the spring constant is too high over damping will not be achievable Set up 1 Set up the equipment as illustrated Use two or three weak springs combined end to end end stop two or three springs end to end pivot clamp Magnetic Damping Accessory Vi table clamp f FA JA N Experiment set up for Critical Damping 2 Adjust the angle of the track or the position of the end stop so that the cart s equilibrium position is about 20 cm from the lower end of the track PASC 5 Dynamics Cart Magnetic Damping Use tape or a pencil to mark the track about 50 cm above equilibrium Pull the cart up the track to the mark Let the cart go and carefully observe it s movement as it comes to a stop If the cart overshoots equilibrium and comes back up the track it is under damped If it comes to a stop without overshooting it is either over damped or critically damped Adjust the height of the magnets to reduce or increase the amount of damping Repeat steps 4 through 6 several times to find the least amount of damping big gest gap that will make the cart stop without overshooting This is critical damp ing Method I using a stopwatch Skip to Method II if you will be using a motion sensor 1 2 8 Pull the cart up the track exactly to the mark Release the cart and start the stop
4. assistance with any PASCO product contact PASCO at Address PASCO scientific 10101 Foothills Blvd Roseville CA 95747 7100 Phone 916 786 3800 worldwide 800 772 8700 U S Fax 916 786 7565 Web WWW pasco com Email support pasco com Limited Warranty For a description of the product warranty see the PASCO catalog Copyright The PASCO scientific 012 10242A Dynamics Cart Magnetic Damping Instruction Manual is copyrighted with all rights reserved Per mission is granted to non profit educational institutions for reproduction of any part of this manual providing the reproductions are used only in their laboratories and classrooms and are not sold for profit Reproduction under any other circumstances without the written consent of PASCO scientific is prohibited Trademarks PASCO PASCO scientific DataStudio PASPORT and ScienceWorkshop are trademarks or registered trademarks of PASCO scien tific in the United States and or in other countries All other brands products or service names are or may be trademarks or service marks of and are used to identify products or services of their respective owners For more information visit www pasco com legal LEIHO 15
5. the sample rate at the motion sensor s default of 10 Hz Data Collection 1 Place the Magnetic Damping Accessory on the end of the cart with a gap of 10 mm between the magnets and the track 2 Tap the cart a few times so that it moves to its equilibrium position 3 Pull the cart up the track and hold it 20 0 cm from equilibrium 4 Release the cart and start data recording at the same time 5 Allow the cart to oscillate until it comes to a stop 6 Stop data recording 7 Repeat steps 3 through 6 to record data runs with the gap set to 8 mm 6 mm 4 mm and 2 mm Record a final data run with the magnets as close as possible to the track without touching Question What is the effect of moving the magnets closer to the track Motion sensor at end of track TEIH ME 6828 Experiment 2 Critical Damping Experiment 2 Critical Damping Equipment Part Number Dynamics Cart Magnetic Damping ME 6828 Stopwatch for Method l ME 1234 or similar ee Sensor for Method II PS 2103A or similar Carn ME 6950 ME 9430 or ME 9454 Aluminum Track ME 6953 or similar Harmonic Springs ME 9803A or similar Adjustable End Stop ME 8971 or similar IDS Pivot Clamp ME 9810 Large Table Clamp ME 9472 90 cm Rod ME 8738 or similar These items are components of many PASCO dynamics systems Either a plastic or aluminum cart will work however the lighter plastic cart allows a relatively greater amount of damping
6. 50 ME 9430 or ME 9454 Aluminum Track ME 6953 or similar IDS Pivot Clamp ME 9810 Large Table Clamp ME 9472 90 cm Rod ME 8738 or similar Angle Indicator ME 9495 These items are components of many PASCO dynamics systems 2Or other way to measure track angle Introduction In this experiment you will study the motion of a magnetically damped cart First you will discover the relationship between the velocity and acceleration as it comes to a stop after being pushed on a level track Using this relationship you will predict the cart s terminal velocity on a inclined track Finally you will test your prediction Part Acceleration versus Velocity eq eq eq PASC O Theory The magnetic drag force fp is proportional to and in the opposite direction of velocity V 1 fa bv where b is a positive constant On a level track assuming no other sources of friction fm is the only force along the axis of movement acting on the cart Therefore by Newton s second law 2 fo ma where m is the mass of the cart and a is the acceleration Note that f and a are not necessarily constant over time The combination of equations and 2 gives the relationship between a and v 3 v In a graph of v versus a the slope will equal m b Dynamics Cart Magnetic Damping Experiment 3 Predicting Terminal Velocity Equation 3 assumes that magnetic drag is the only source of friction A real cart is also
7. Place the cart on an aluminum track 4 Slide the Magnetic Damping Accessory up or down to adjust the amount of damping The magnets should not touch the track To set a gap size that can be measured or reproduced use a stack of cards as a gauge Place the cards between the magnets and track as illustrated Slide the Magnetic Damping Accessory down until the magnets contact the top card then remove the cards Use calipers to measure the thickness of the stack For maximum damping use a single card Storage and Safety e The Magnetic Damping Accessory is shipped with a keeper plate attached to the magnets The keeper protects the magnets and reduces the external magnetic field Always store the Magnetic Damping Accessory with the keeper in place e Use caution when replacing the keeper to avoid being pinched or chipping the magnets e Do not remove the magnets from the body of the Magnetic Damping Acces sory If the magnets are accidentally removed replace them with caution The poles of all three magnets should have the same orientation e Keep the Magnetic Damping Accessory away from computers and magnetic recording media Qualitative Demonstrations The effects of magnetic damping can be surprising Use these demonstrations illus trate the phenomenon e Place a strongly damped cart on a track and ask students to move it by hand When the cart is moved quickly the damping force 1s easily detected e Raise one end of the
8. ack Method without sensors Skip to Method II if you will be using a motion sensor 1 Place the Magnetic Damping Accessory on the end of the cart with a gap of 10 mm between the magnets and the track 2 Tap the cart a few times so that it moves to its equilibrium position Gap between magnets and track TEIH 3 3 Pull the cart up the track and hold it 20 0 cm from equilibrium Dynamics Cart Magnetic Damping Experiment 1 Damped Oscillation 4 Release the cart 5 Allow the cart to oscillate Count and write down the number of down up cycles that the cart completes before stopping 6 Repeat steps 3 through 5 with the gap set to 8 mm 6 mm 4 mm and 2 mm and with the magnets as close as possible to the track without touching Skip to the Questions section on page 4 Method II using a motion sensor Sensor Interface and Software Set up For detailed information about setting up your motion sensor interface and software refer to the instructions supplied with those products 1 Place a motion sensor at the lower end of the track 2 Adjust the angle of the track so that the cart s equilibrium position is about 40 cm from the sensor 3 Connect the sensor to your interface 4 Prepare a graph to display Position versus time 5 Take some test data and adjust the sensor so that it can measure the cart s position up to a distance of about 70 cm Delete the test data Leave
9. affected by friction that is not proportional velocity but is constant as long as the cart is moving If this additional frictional force is f then the net force on the cart is eq 4 Fea Ma bv fy for v gt 0 and __m _to eq 5 B aa The addition of f does affect the slope of the v versus a graph but it does add a ver tical offset or Y intercept equal to fp b In this part of the experiment you will use the motion sensor to record v and a as the cart slows down after you push it on a level track Set up 1 Make the track level 2 Attach a motion sensor to the left end of the track 3 Attach the Magnetic Damping Accessory to the cart 4 If you are using a plastic cart add about 250 g of mass so that the total mass is about 500 g Additional mass is not necessary with a metal cart 5 Place the cart on the track with the Magnetic Damping Accessory away from the motion sensor 6 Adjust the magnets to be about 1 mm above the track Check to make sure that the magnets do not touch the track when you push the cart swiftly Important After you have adjusted the magnets do not readjust them for the remainder of the experiment Ca A KO O LO i 10 Experiment set up for Terminal Velocity Part I Sensor Interface and Software Set up For detailed information about setting up your motion sensor interface and software refer to the instructions supplied with those pr
10. back on the track and hold it about 15 cm from the motion sensor with the magnets away from the sensor Note Before releasing the cart be prepared to stop it so that the Magnetic Damping Accessory is not knocked out of position 2 Start data recording 3 Release the cart stop it after it has rolled about 1 m 4 Stop data recording Analysis From your recorded data determine the terminal velocity At 8 3 0 vp __ measured Questions 1 How close was your prediction to your measured value of v If they were not exactly equal what might account for the difference 2 Would the terminal velocity change if you changed the mass of the cart 3 Did you have to measure the mass of the cart to predict the terminal velocity 12 LEIHO ME 6828 Sample Data Experiment 1 Damping increases as the magnets are moved closer to the track Experiment 2 Critical damp ing makes the cart stop in the shortest time Note that due to static fric tion the under damped cart stops at a slightly differ ent position PASC O Be iy SERENAN Ga n Sample Data Damped Oscillation AAS T E sm ona TE e aa ie cre Atti FTE hcoe ata fanned en nasa snid GT Anes nN See a EH EEE ERE A eet po a Tomm i betes cusazentasatastantataats a ae pom seh HHHH Cc Makan tT eee co T a Timet s 0 0 0 5 1 0 1 5 2 0 Dynamics Cart Magnetic Damping Sample Data Experiment 3 Pre
11. clined track its velocity will increase until the frictional forces acting against the direction of movement equal the gravitational force acting in the direction of movement At that point the net force on the cart is zero the acceleration is zero and the velocity remains constant This velocity is known as the terminal velocity v The gravitational force acting on the cart in the direction of movement is mgsin where g 9 81 m s and 9 is the angle of incline At terminal velocity the net force is eq 6 Faet 0 mg sinb bv fo for v gt 0 n The values of b and f are the same as they were on the level track Solving equation 6 gives eq 7 v Mg sino 2 Analysis In Part 1 you found the values of m b and f bD Use these values and equation 7 to predict the terminal velocity of your cart on a track inclined at 0 3 0 At 0 3 0 Vy __ prediction LEIHO 11 Dynamics Cart Magnetic Damping Experiment 3 Predicting Terminal Velocity Part Ill Measuring Terminal Velocity Set up 1 Take the cart off the track and set it aside Be careful not to let the Magnetic Damping Accessory shift on the cart 2 Use a table clamp rod and pivot clamp to raise the left end of the track with the motion sensor attached Adjust the incline to 3 0 lt 4 Qual o re Q E Experiment set up for Terminal Velocity Part III Data Collection 1 Place the cart
12. dicting Terminal Velocity 14 The graph below shows position versus time as the cart is coming to a stop on a level track O75 Positiont Timet s The graph below shows velocity versus acceleration for the cart on the level track 0 30 SSS Linear Fit _ Peete errr os bey ee 0 0326 0 0054 0 25 0 998 Wean AT Error 2 82E 5 Root MSE 0 00531 0 20 Velocity mis Co on So _ So 0 05 0 00 0 70 0 60 0 50 0 40 0 30 0 20 0 10 0 00 Acceleration misis 3 From the slope and intercept of the best fit line m b 0 52 s and f b 0 033 m s From these val ues and equation 7 the predicted terminal velocity is v 0 23 m s The graph below shows position versus time for the cart running down a 3 incline The slope of the linear por tion is the measured terminal velocity v 0 2225 m s T SSS E manm K ae co O 6 Linear Fit m i Slope TETE Ep4 bi Y Intercept 0 1830 4 5E 4 E f 1 0000 o 02 Mean Squared Error 0 0000 i p 9 0542E 4 0 0 Timet s In this case the predicted and measured values differ by about 0 01 m s or 4 The difference may be due to uncertainty in the values of m b f b and the angle of the inclined track The terminal velocity would be different if the cart s mass were changed In this experiment it is not necessary to know the mass of the cart to predict the terminal velocity TEIH ME 6828 Technical Support Technical Support For
13. oducts 1 Connect the sensor to your interface 2 Prepare a graph or graphs to display Position Velocity and Acceleration versus time 3 Take some test data and adjust the sensor so that it can measure the cart s position up to a distance of about 1 m Delete the test data Leave the sample rate at the motion sensor s default of 10 Hz TEIH ME 6828 Experiment 3 Predicting Terminal Velocity Data Collection You may need to try several times to complete the following steps successfully If you do not get it right delete your data and try again The recorded data should show the motion of the cart only after you release it and before it comes to a complete stop There should be about s of recorded data Use one hand to push the cart and the other hand to start and stop data recording 1 Using a smooth sweeping motion push the cart away from the motion sensor and release it Make sure that your hand does not prevent the motion sensor from detecting the cart 2 About 0 1 s after releasing the cart start data recording 3 Just before the cart stops stop data recording Analysis 1 Create a graph showing velocity on the vertical axis versus acceleration on the horizontal axis 2 Apply a linear fit to the data According to equation 5 the slope of the best fit line equals m b and the Y inter cept equals f b Part Il Predicting Terminal Velocity Theory If a cart is allowed to roll down an in
14. steps 1 through 4 Question What type of damping under over or critical makes the cart stop in the shortest time Further Study What factors affect critical damping You have already discovered that reducing the height of the magnets can change the system from under damped to critically damped to over damped What other factors can you adjust to change the system s damping behavior Starting with a critically damped system each time make the following changes to the system and observe the result e Release the cart from a different position on the track e Add about 20 g of mass to the cart e Change the angle of the track e Change the spring constant replace or remove one of the springs Further Study Theoretical model For the theoretical model of the cart s position as a function of time we will assume that the spring is massless and obeys Hooke s law that the damping force 1s propor tional to velocity and that there are no forces acting on the cart other than the spring force the damping force the force of gravity and the normal force of the track We will also set the condition that the initial velocity v 0 O attime t 0 The motion of the cart is determined with the following quantities x the position of the cart with x O at the equilibrium position Xo the initial position at time t 0 m the mass of the cart k the spring constant F kx pring E TEIH 7 Dynamics Cart Magnetic
15. track by a few centimeters Set the Magnetic Damping Accessory for maximum damping and allow the cart to run down the track With the track inclined just enough to overcome rolling friction the cart will creep very slowly at a constant velocity Storage and Safety stack of TEIH ME 6828 Experiment 1 Damped Oscillation Experiment 1 Damped Oscillation Equipment Part Number Dynamics Cart Magnetic Damping ME 6828 Motion Sensor optional for Method II PS 2103A or similar Cart ME 6950 ME 9430 or ME 9454 Aluminum Track ME 6953 or similar Harmonic Springs ME 9803A or similar Adjustable End Stop ME 8971 or similar IDS Pivot Clamp ME 9810 Large Table Clamp ME 9472 90 cm Rod ME 8738 or similar These items are components of many PASCO dynamics systems This experiment works best with a spring or combination of springs with a constant between 1 0 N m and 1 5 N m Set up 1 Set up the equipment as illustrated Use two or three weak springs combined end to end two or three springs end to end MEREEE 3 all cart 7 TELE eee eeeeeee A Ll ena stop CT ANS PF CS HO _ ANG Magnetic pivot clamp Damping Accessory rod Be W table f Sk A y Experiment set up for Damped Oscillation 2 Adjust the angle of the track or the position of the end stop so that the cart s equilibrium position is about 40 cm from the lower end of the tr
16. watch at the same time Stop the stopwatch when the cart stops Record the time Move the magnets up by about 1 mm to make the system under damped Repeat steps 1 through 4 Move the magnets down as close to the track as you can get them without touch ing to make the system over damped Repeat steps 1 through 4 Skip to the Question on page 7 Method Il using a motion sensor Sensor Interface and Software Set up For detailed information about setting up your motion sensor interface and software refer to the instructions supplied with those products L 2 Place a motion sensor at the lower end of the track Connect the sensor to your interface Set the sampling rate to 50 Hz Prepare a graph to display Position versus time Take some test data and adjust the sensor so that it can measure the cart s position up to a distance of about 70 cm Delete the test data Experiment 2 Critical Damping Motion sensor at end of track TEIH ME 6828 Experiment 2 Critical Damping Data Collection 1 Pull the cart up the track exactly to the mark 2 Release the cart and start data recording at the same time 3 Wait until the cart stops 4 Stop data recording 5 Move the magnets up by about 1 mm to make the system under damped 6 Repeat steps 1 through 4 7 Move the magnets down as close to the track as you can get them without touch ing to make the system over damped 8 Repeat
Download Pdf Manuals
Related Search