PASCO Specialty & Mfg. ME-6694 User's Manual
Contents
1. Qa P RMS to computer upper wire interface clamp wire with bent ends Figure 1 Bend the ends of the wires to 90 angles 4 lower wire clamp Support Rod Table Clamp a upper wire Figure 2 clamp Assembly of the Torsion Pendulum and the Rotary Motion Sensor grooves 2 Slip the lower wire clamp onto the Support Rod Ws Ec 3 Clamp the RMS at the top of the Support Rod 4 Clamp one end of the wire under the washer of the upper wire clamp by firmly tightening the thumbscrew being sure to seat the wire in the grooves Figure 3 Figure 3 Securing the wire to the upper wire clamp 2 PASC QU 012 06339A Torsion Pendulum 5 Clamp the other end of the wire under the washer of the lower wire 10 clamp by tightening the thumbscrew firmly Be sure that the elbow of the bend in the wire fits snugly against the axle of the thumbscrew Figures 4a and 4b Support Rod thumbscrew and washer N lower wire clamp side view Figure 4 b thumbscrew wire and washer lower wire clamp front view Lateral a and front b views of attaching the bent wire to the lower clamp Adjust the height of the lower wire clamp to about 18 inches below the shaft of the RMS Align the guide of the upper wire clamp with the slot of the shaft of the RMS Slide the upper wire clamp onto the shaft Figure 4 Adjust height of2. from part A I using mass and radius measurements 1 4 x 10 14 012 06339A Torsion Pendulum Part C T 0 032 in wire 0 062 in wire Figure TN1 3 Typical data for determining the period of rotation T for the three wire diameters disk plus cylinder Table TN1 3 Calculation of f uk piis cylinder FOM torsional spring constants x of wires mass of cylinder 0 468 kg wire diameter I TTT inches em R of cylinder _ 0 027 m 0 032 6 8 x 104 0 047 6 8 x 104 R of cylinder 0 039 m j 8x 107 2 0 062 72 x 104 may vary somewhat from part A I using mass and radius measurements 6 7 x 10 kg m isk plus cylinder T 1 4x 10 kg m disk 5 3 x 10 kg m cylinder 176 7 x 10 kg m from Part B erentifre Torsion Pendulum 012 06339A Questions 16 J The experiment demonstrated that the magnitude of the moment of inertia of a disk can be determined two ways using the torsional spring constant of a wire K and the period of 2 T oscillation of the Torsion Pendulum T applying the relationship 2n K and by 1 measuring the mass and diameter of the disk and applying the relationship QR 2 The calculated magnitude of is approximately the same using either method However some experimental error is to be expected particularly since some portions contributing to I the pulley axle etc were not included in the calculation o
3. 6 FAS CC 012 06339A Torsion Pendulum Collect the Data J Put your safety glasses on 2 Wind the string around the large pulley in a clockwise direction Force Sensor Figure 1 1 Hold the Force Sensor 90 to the pulley a and 90 to the support rod b 3 Hold the Force Sensor parallel to the table at the height of large pulley and prepare to pull it straight out Figure 1 1 4 Start recording data and pull the Force Sensor straight out until about 5 N of force is exerted 5 Stop recording data This will be Run 1 6 Change the wire to the 0 47 inch diameter wire 7 Repeat steps 2 5 Run 2 8 Change the wire to the 0 62 inch diameter wire 9 Repeat steps 2 5 Run 3 Save the file Torsion Pendulum 012 06339A Analyze the Data 1 Use the following formula to calculate the torsional spring constant x for each wire and record in Table 1 1 where the length of the lever arm in meters the distance from the axis of the pulley to the groove of the pulley and F force in expressed in newtons and 81n the angular displacement at a force F Table 1 1 Calculation of torsional spring constants of the wires x wire diameter inches slope of F vs angPos gt Note Click the Autoscale button on each Graph display if necessary 012 06339A Torsion Pendulum Part B Determining the Moment of Inertia I of a
4. we Instruction Manual and 012 06339A and Experiment Guide for the T Typical Experiment Results PASCO scientific WS Model ME 6694 TORSION PENDULUM 1997 PASCO scientific D f 2 4 amp er 6 Se eee ee ee eer USE Scientific Phone 916 786 3800 FAX 916 786 8905 web www pasco com Torsion Pendulum 012 06339A IPASC Oe cl rire 3 012 06339A Torsion Pendulum Table of Contents Section Page Copyright Warranty and Equipment Return sese ii Titrod cO ET 1 WORT 1 AssembiywiththeRotaryMotionSensor 2 3 Suggested Experiment i m titer este d esed loser sa a Ee e eae ee uae 4 Experiment Experiment 1 Determining of the Magnitude of the Moment of Inertia Using Two Methods ciere ttt ore Re eda 5 12 Part A Determining the Spring Constants of the Wires K 6 8 Part B Determining the Moment of Inertia 7 of a Disk Using Two hn d 9 10 Part C Determining the Moment of Inertia of a Disk and Cylinder Using Two Methods ertet toten 11 12 Teacher s Notes erre nnnnnnes 13 16 Technical Suppott serer edic rre rete ee Deer s ayni i l EN Back Cover 00 i qf Ee gt Mi HE cle U Copyright Warranty and Equipment Return Please Feel free to duplicate this manual subje
5. Disk Using Two Methods Set Up Science Workshop 1 Use the setup detailed in Part A Save As a different file name and delete all data sets Runs 1 3 and the Graph display Note The Force Sensor will not be used in Parts B and C 2 Click the Sampling Options button and set the sampling rate to 200 Hz 3 Click and drag a Graph display to the RMS icon and choose Angular Position ang Pas from the pop up menu This will set input for the y axis Set Up the Equipment 1 Attach the disk from the Mini Rotational Accessory to the 3 step pulley with the thumbscrew Figure 1 2 Check the thumbscrews holding the wire to be sure they are tight Collect the Data J Put your safety glasses on 2 Twist the disk 1 4 turn clockwise 3 Begin recording data release the disk and record for about 3 5 seconds 4 Stop recording data 5 Click on the Autoscale button to resize the graph if necessary 6 Use the Smart Cursor to determine the time for each period of oscillation T of the pendulum measure the time between adjacent maxima of the angular position vs time graph Record in Table 1 2 7 Change the wire to the 0 047 inch diameter wire and repeat steps 2 6 ETAO disk from Mini Rotational Accessory EM 3 step pulley OH a Mi Figure 1 2 Experimental setup Torsion Pendulum 012 06339A 8 Change the w
6. cylinder calculated by 1 using a torsional spring constant K and the period of oscillation of the Torsion Pendulum T and 2 with 7 calculated using mass and radius measurements Materials and Equipment Required Torsion Pendulum ME 6694 Force Sensor CI 6537 Rotary Motion Sensor CI 6538 Table Clamp ME 9376B Mini Rotational Accessory CI 6691 Support Rod 90 cm ME 8738 Science Workshop 2 1 or higher mass balance PASCO computer interface 500 or 700 metric ruler computer sturdy non stretching string 18 inches e pages 2 and 3 of the manual Theory The magnitude of the moment of inertia of a disk can be determined with the Torsion Pendulum using the following relationship TY I 2 K where T the time s for a period of oscillation of the Torsion Pendulum and K the torsional spring constant of the wire The magnitude of the moment of inertia of a disk can also be determined by measuring the mass m and radius R of the disk and using the relationship I 1 nR 2 Therefore in the case ofa uniform disk rotating about its cylinder axis the following relationship 1 Ty mR x 2 2x In the case of a disk plus a cylinder Part C of the experiment the following relationship can can be shown be demonstrated 2 T 1 2 1 2 2 k 2 mR m R R z 2 7 1 R where R the inner radius of the cylinder and R the outer radius of the cylinder PASC QU 5 eren
7. the lower wire clamp as necessary to position to top of the upper wire clamp approximately half way up the shaft Figure 5 If necessary adjust the lower wire clamp so the wire is perpendicular to the table Recheck all screws on the clamps to be sure each part is firmly secured upper wire clamp Support Rod Figure 5 Sliding the upper wire clamp onto the shaft of the Rotary Motion Sensor 3 Torsion Pendulum 012 06339A gt Note The manual has been written with the assumption that the user has a basic familiarity with Science Workshop and has access to the User s Guide for Science Workshop Users can gain basic skills with Science Workshop by viewing the training video and by doing the tutorial within Science Workshop Another useful resource is the Quick Reference Card for Science Workshop Suggested Experiment The following experiment will help students build skills in using the Torsion Pendulumusing Science Workshop for data acquisition Students may want to experiment further with varying lengths thickness or composition of wire or with effects of variations of temperature on the torsional spring constant K 012 06339A Torsion Pendulum Experiment 1 Determining the Magnitude of the Moment of Inertia 1 Using Two Methods Purpose The purpose of the experiment is compare the magnitude of the moment of inertia of a disk and
8. 700 computer interfaces Using the Torsion Pendulum students can collect experimental dataon rotational acceleration rotational position and rotational velocity for a variety experiments with the PASCO CI 6691 Mini Rotational Accessory Three wires with different diameters supplied with the Torsion Pendulum provide three different and repeatable torque magnitudes Equipment 18 inch wires 3 each diameters inches 0 032 0 047 0 063 upper wire clamp lower wire clamp thumbscrew and Fa washer 18 inch wires lower wire clamp Additional Equipment Required gt Safety Note Science Workshop version 2 1 or higher PASCO Computer Interface 500 or 700 computer Rotary Motion Sensor CI 6538 Mini Rotational Accessory CI 6691 Force Sensor CI 6537 Always wear safety glasses when experimenting with the Torsion Pendulum Replacement Wires Additional Equipment Suggested To order a set of wires call PASCO Table Clamp ME 9376B or Large Rod Stand ME 8735 800 772 8700 and order part number Support Rod 90 cm ME 8738 003 06354 PASC C 1 scientific Torsion Pendulum 012 06339A Assembly with the Rotary Motion Sensor RMS gt Note You will need bend the wires as illustrated in Figure I The direction of the bend is not 1 Usethe Table Clamp to secure the Support Rod to a table in close critical proximity to your computer interface Figure 2
9. ct to the copyright restrictions below Copyright Notice The PASCO scientific 012 06339A manual is copyrighted and all rights reserved However permission is granted to non profit educational institutions for reproduction of any part of the Torsion Pendulum manual providing the reproductions are used only for their laboratories and are not sold for profit Reproduction under any other circumstances without the written consent of PASCO scientific is prohibited Limited Warranty PASCO scientific warrants the product to be free from defects in materials and workmanship for a period of one year from the date of shipment to the customer PASCO will repair or replace at its option any part of the product which is deemed to be defective in material or workmanship The warranty does not cover damage to the product caused by abuse or improper use Determination of whether a product failure is the result of a manufacturing defect or improper use by the customer shall be made solely by PASCO scientific Responsibility for the return of equipment for warranty repair belongs to the customer Equipment must be properly packed to prevent damage and shipped postage or freight prepaid Damage caused by improper packing of the equipment for return shipment will not be covered by the warranty Shipping costs for returning the equipment after repair will be paid by PASCO scientific Credits Author Sunny Bishop ii Equipment Return Sh
10. f Z from using mass and radius measurements but were included in the calculation of using the torsional spring constant of the wire and period of oscillation of the Torsion Pendulum The same comments apply to Part C 012 06339A Torsion Pendulum Feedback If you have any comments about the product or manual please let us know If you have any suggestions on alternate experiments or find a problem in the manual please tell us PASCO appreciates any customer feedback Your input helps us evaluate and improve our product To Reach PASCO For technical support call us at 1 800 772 8700 toll free within the U S or 916 786 3800 fax 916 786 3292 e mail techsupp pasco com web WWW pasco com Technical Support Contacting Technical Support Before you call the PASCO Technical Support staff it would be helpful to prepare the following information gt f your problem is with the PASCO apparatus note Title and model number usually listed on the label Approximate age of apparatus A detailed description of the problem sequence of events in case youcan tcall PASCO rightaway you won t lose valuable data If possible have the apparatus within reach when calling to facilitate description of individual parts gt If your problem relates to the instruction manual note Part number and revision listed by month and year on the front cover Have the manual at hand
11. ire to the 0 062 inch diameter wire and repeat steps 2 6 9 Determine the mass and radius of the disk and record below mass of disk kg radius of disk m Table 1 2 Calculation of from torsional spring constants of wires x wire diameter K N m I inches from pt A kg m I using mass and radius measurements Compare the values of calculated 2 1 1 Calculate 7 using both formulas s K and I 2 mR 27 above 10 and record 012 06339A Torsion Pendulum Part C Determining the Moment of Inertia 1 of a Disk and Cylinder Using Two Methods cylinder from Mini 1 Place the ring of the Mini Rotational Rotational Accessory E E T Accessory on the disk Figure 1 3 disk from Mini s Rotational 3 step pulley Accessory M data in Table 1 3 2 Repeat steps 2 6 of Part B Record your EE c 3 Change the wire to the 0 047 inch diameter wire and repeat steps 2 6 4 Change the wire to the 0 032 inch diameter wire and repeat steps 2 6 5 Measure the mass and R and R of the cylinder and record below Figure 1 3 Experimental setup for Part C mass of cylinder kg R m R m Table 1 3 Calculation of and eyinder rom the torsional spring constants of wires x wire diameter K Nm disk and cylinder inches from part A kg m 0 032 0 047 0 062
12. ould the product have to be returned to PASCO scientific for any reason notify PASCO scientific by letter phone or fax BEFORE returning the product Upon notification the return authorization and shipping instructions will be promptly issued gt NOTE NO EQUIPMENT WILL BE ACCEPTED FOR RETURN WITHOUT AN AUTHORIZATION FROM PASCO When returning equipment for repair the units must be packed properly Carriers will not accept responsibility for damage caused by improper packing To be certain the unit will not be damaged in shipment observe the following rules The packing carton must be strong enough for the item shipped Make certain there are at least two inches of packing material between any point on the apparatus and the inside walls of the carton Make certain that the packing material cannot shift in the box or become compressed allowing the instrument come in contact with the packing carton Address PASCO scientific 10101 Foothills Blvd P O Box 619011 Roseville CA 95678 9011 Phone 916 786 3800 FAX 916 786 3292 email techsupp pasco com web o www pasco com 012 06339A Torsion Pendulum Introduction The PASCO ME 6694 Torsion Pendulum an accessory for the PASCO CI 6538 Rotary Motion Sensor RMS facilitates the study of torque and the moment of inertia in a rotating body The apparatus uses the data acquisition capabilities of the RMS with Science Workshop through the PASCO 500 or
13. rani sinde USING mass and radius measurements PE Compare the values of calculated 1 Calculate using both formulas E d 2 T 1 1 I B K and QnR j G TOR and record above 1 I sr R pz Eee 11 Torsion Pendulum 012 06339A Questions 1 How closely did the calculations of J match 2 Whatare some possible sources of experimental error 12 012 06339A Torsion Pendulum Teacher s Notes General gt Safety Note Use safety glasses when operating the Torsion Pendulum Experimental data will vary somewhat from the typical data included here due to the differences in wire lengths and other variables but the overall data patterns will be the same a2 1 42996 slope of ohi 2 0 03058 the fitted iterations 20 line 2 0 3 0 Angular Position rad Figure TN1 1 Typical data for determining the torsional spring constant x 0 047 inch diameter wire Table TN1 1 Calculation of torsional spring constants of the wires x typical data wire diameter slope of inches F vs angPos PASC QU 13 Torsion Pendulum 012 06339A Part B Figure TN1 2 Typical data for determining the period of rotation T for the three wire diameters disk accessory Table TN1 2 Calculation of from torsional spring constants x of wires i wire diameter I mass of disk 0 126 kg 2 inches kg m radius of disk 0 047 m may vary somewhat
14. tifire Torsion Pendulum 012 06339A Part A Determining the Torsional Spring Constants of the Wires x Set Up the Equipment 1 Assemble the Torsion Pendulum and the RMS as directed on pages 2 and 3 of the manual using the 0 032 inch diameter wire 2 Securely tie the Force Sensor to the large pulley of the 3 step pulley on the RMS with a piece of sturdy string 0 5 m in length Set Up Science Workshop 1 Plug the digital plugs of the RMS into digital channels 1 amp 2 on the computer interface box 2 Plugthe DIN connector of the Force Sensor into analog channel 1 of the computer interface box 3 Turn on the interface box and start Science Workshop 4 Inthe Setup Window set up the RMS on digital channels 1 amp 2 and the Force Sensor on analog channel 1 gt Note Refer to the RMS and Force Sensor manuals for more detailed instructions on setting them up in Science Workshop 5 Double click the Force Sensor icon and set the sensitivity to Med 10X 6 Click the Sampling Options button and set the sampling rate to 50 s 7 Click and drag a Graph icon to the Force Sensor icon Click the Statistics button and select Curve Fit gt Linear Fit from the pop up menu Size and move the Graph display as is convenient 8 Double click the RMS icon and set Divisions Rotation to 1440 9 Click the x axis input button on the Graph display and select Digital 1 gt Angular Position angPos This will set the input for the x axis
15. to discuss your questions
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