LIST OF EQUIPMENT SET UP AND PROCEDURE 3B SCIENTIFIC PHYSICS EXPERIMENT

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Eleanore Bradley
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2 UE (3) T J D D: Tosional coefficient of coil spings The means that the peiod of oscillation T will be geate when the moment of inetia J is lage. Fom equation (3) it is possible to obtain a fomula fo detemining the moment of inetia: T (4) J D 4 The tosional coefficient of the coil spings can be detemined with the help of a sping dynamomete: F (5) D α: Deflection fom equilibium state LIST OF EQUIPMENT 1 Tosion Axle U Photo Gate U Digital Counte U /3 1 Bael Foot, 1000 g U Tipod Stand 185 mm U Pecision Dynamomete 1 N U Set of Test Bodies fo Tosion Axle U SET UP AND PROCEDURE Set up the expeiment as shown in Fig. 1. Align the otational axis to be hoizontal to the stand base with the help of the spiit level and the levelling scews. Connect the photo gate to channel A of the digital counte. Set the opeating mode selecto switch on the digital counte to the symbol fo measuing the peiods of a pendulum. Notes: When deflecting the ba, do so in such a way that the coupling spings ae foced togethe and do not bend outwads. At the stat of the oscillation, it is ecommended that a deflection angle of 180 be used (max. 360 ). Detemining tosional coefficient D fo coupling spings Suspend the sping dynamomete at distances = 5, 10, 15, 0, 5 and 30 cm fom the cente of the otational axis in sequence on the dumbbell ba and deflect them by an angle = 180 =. Make sue that the dynamomete hangs down at ight angles to the dumbbell ba. Read off the foce values needed to deflect the ba at the vaious distances fom the dynamomete. Ente all the esults into Table 1. Detemining the moment of inetia J0 fo the ba without weights Deflect the dumbbell ba without any weights attached by an angle of 180 and use the digital counte to measue the peiod of oscillation T0. Detemination of moment of inetia J as a function of the distance of weights fom the axis of otation Attach the two weights to the ba symmetically at distances = 5, 10, 15, 0, 5 and 30 cm to the left and ight of the axis of otation. Do not touch the scews which pess the atchet balls against the dumbbell ba. They ae adjusted in such a way that the weights can be moved but can also be secued against centifugal foce. Deflect the ba by 180 and use the digital counte to measue the peiods of oscillation T fo each distance. Ente the esults into Table. Detemine the moments of inetia J fo a wooden disc, a wooden sphee, a solid cylinde and a hollow cylinde Attach the sample bodies to the tosion axle one afte the othe. Use the pan fo the solid cylinde and the hollow cylinde. In ode to measue the length of a peiod of oscillation, use a suitable method to attach a pape flag to each of the samples in ode to beak the photo gate beam. Fist deflect the wooden disc by 180 then fit the wooden sphee and do the same. In each case, measue the peiod of oscillation and ente the esults into Table 3. Use the white makings on the samples to help you with the oientation fo the deflection. Deflect the pan by 180 and measue the peiod of oscillation. Ente the value into Table 3. Put the solid cylinde on the pan, deflect it by 180 and measue the peiod of oscillation. Do the same fo the hollow cylinde and ente all the esults into Table 3. Use the white makings on the samples to help you with the oientation fo the deflection. Veification of Huygen-Steine theoem Fasten the bolt though the boeholes at distances a = 0,, 4, 6, 8, 10, 1 and 14 cm fom the cente of the disc Fo each of the vaious positions of the bolt, mount the disc onto the axis, deflect it by 180 in each case and measue the peiod of oscillation. Use a suitable method to attach a pape flag to the disc. Ente the values into Table 4. / 5

3 UE SAMPLE MEASUREMENT Detemining tosional coefficient D fo coupling spings Tab. 1: Measuements of foce F at a distance fom the cente of the axis of otation when the dumbbell ba is deflected and allowed to oscillate fom a static position = 180 = fom its est position. / m F / N Veification of Huygens-Steine theoem Tab. 4: Peiod of oscillation T fo oscillation of a wooden disc aound points at vaious distances a fom its cente of gavity. a / cm Detemination of moment of inetia J0 fo dumbbell ba without weights Peiod of oscillation T0: 460 ms Detemination of moment of inetia J as a function of the distance of weights fom the axis of otation Tab. : Peiod of oscillation T fo a dumbbell ba with weights attached at a distance fom the axis of otation / m EVALUATION Detemining tosional coefficient D fo coupling spings Fom equation (5), the following applies: 1 1 (6) F D C whee C D 1 Plot the foce measuements F fom Table 1 against the invese of the distances 1/ and daw a staight line though the measuement points. F / N Detemination of moment of inetia J fo a wooden disc, a wooden sphee, a solid cylinde and a hollow cylinde Tab. 3: Peiod of oscillation T fo vaious sample bodies Sample bodies Disc 1800 Sphee 1880 Pan 51 Solid cylinde + pan 917 Hollow cylinde + pan / m -1 Fig. : Foce F as a function of the invese of the distance of the weights fom the cente 1/. Detemine the tosional coefficient D fom the gadient C as indicated in equation (6): C Nm (7) C D D Nm. 3 / 5

4 UE Detemination of moment of inetia J0 fo dumbbell ba without weights Fom equation (4), the moment of inetia fo the dumbbell ba without weights is given by: (8).460 s 3 J Nm kgm. 4 Detemination of moment of inetia J as a function of the distance of weights fom the axis of otation Use equation (4) to calculate the moments of inetia J of the dumbbell ba with weights fom the values in Table and ente them into Table 5. Deteine the moments of inetia of the weights themselves Jm fom the following (9) Jm J J0 Ente the esults into Table 5 Tab. 5: Peiod T, moment of inetia J fo dumbbell ba with weights plus moment of inetia Jm fo weights at vaious distances fom the axis of otation. / m T / s J / 10-3 kg m Jm / 10-3 kg m Accoding to (): (10) J m m Plot the moments of inetia Jm fom Table 5 against the squae of the distance and confim the linea elationship expected fom equation (10) (Fig. 3). J m / 10-3 kg m / cm Fig. 3: Moment of inetia of weights Jm as a function of the distance of the weights fom the axis. Detemination of moment of inetia J fo a wooden disc, a wooden sphee, a solid cylinde and a hollow cylinde Using equation (4), calculate the moments of inetia J fo the vaious sample bodies and the measuements enteed into Table 3 and ente the esults into Table 6. In ode to detemine the moments of inetia of the solid cylinde and the hollow cylinde JV and JH, in each case subtact the moment of inetia of the pan JT fom the values of the moment of inetia fo the solid cylinde + pan o the hollow cylinde + pan JVT and JHT: JV JVT JT (11). J J J H HT T Calculate the theoetical values fo the moment of inetia Jth with the help of the data in the appendix. Ente them into Table 6 and compae them with the values detemined by measuement. Tab. 6: Moments of inetia J fo vaious sample bodies. Sample bodies T / s J / 10-3 kg m Jth / 10-3 kg m Disc / m =.57 Sphee /5 m =.54 Pan Solid cylinde + pan Solid cylinde / m = 0.43 Hollow cylinde + pan Hollow cylinde 0.77 m = 0.86 The values detemined by measuement ae well in ageement with those calculated in accodance with the theoy. Veification of Huygens-Steine theoem Detemine the moments of inetia Ja fo vaious distances a fom the measuements in Table 4 using equation (4) and ente these values into Table 7. Tab. 7: Moment of inetia Ja fo a disc oscillating about vaious axes at distance a fom its cente of gavity. a / cm T / s Ja / 10-3 kg m / 5

Unit 6 Test Review Gravitation & Oscillation Chapters 13 & 15

Unit 6 Test Review Gravitation & Oscillation Chapters 13 & 15 A.P. Physics C Unit 6 Test Review Gavitation & Oscillation Chaptes 13 & 15 * In studying fo you test, make sue to study this eview sheet along with you quizzes and homewok assignments. Multiple Choice