Name Section Lab on Motion: Measuring Time and Gravity with a Pendulum Introduction: Have you ever considered what the word time means?

Transcription

1 Name Section Lab on Motion: Meaurin Time and Gravity with a Pendulum Introduction: Have you ever conidered what the word time mean? For example what i the meanin of when we ay it take two minute to boil an e? Can you define time without uin word like lenth or time in the definition? The econd that we meaure with a clock i related to the repeatin chane occurrin inide a clock which we aume to be reular and uniform, or periodic in rate and interval. Time involve the countin of periodic event uch a econd. The time period, T for repeated event can be obtained by comparin them to a clock; countin the number of econd for each event' beinnin to it end. To illutrate, imaine water droplet fallin at a rate of 200 drop every 15.0 econd; then the time period for each drop can be determined by T = 15.0 econd / 200 drop = 0.075, the time period per drop. A imple pendulum conit of a trin and a winin bob. In thi experiment you will compare and time the repeated win of the pendulum with a tandard time piece uch a a topwatch timer. Your roup will be able to anwer the followin quetion. I the motion of a imple pendulum periodic? What factor overn the motion of a imple pendulum? Some factor to conider include: 1) The ma of the bob; 2) The lenth of the trin a meaured from where the pendulum i held to the center of the pendulum bob; and 3) The acceleration of ravity on the Earth urface. By repeatedly uin the pendulum; varyin the ma of the bob, meaurin the lenth of the pendulum trin, and obervin the averae time period for each complete win, forth and back - the full cycle, we reveal how differin factor affect the pendulum. A plot of the meaured time period v. tin lenth hould reveal the law of motion for a imple pendulum. Once we know thi, the pendulum can be ued to accurately meaure the local acceleration of ravity,. Procedure: 1) Uin a mall loop connect at leat 0.8 meter of trin to a mall ma. Fix the other end of the trin into the pendulum clamp. Diplace the pendulum bob no more than 15 deree from the vertical and allow it to win freely back and forth a you time the trial. One full cycle i a complete out and back motion. If the pendulum i periodic, then different number of win hould be made up of different time which are made of multiple of an equal (inle) win period of time. Determine the time period, T for one full cycle in each cae by dividin the elaped time for the

2 iven number of win by the number of win counted. Enter and complete the data in table A. 2) Next tet if different pendulum bob alter the period of the pendulum. Record the ma of the bob in each cae. Be ure that the bob in each cae i held at the ame trin lenth to be ure that ma i the teted variable, do not let different bob win at different lenth to do thi properly. You will have a election of at leat three different bob of the ame ize, but of differin ma. Be ure to keep the pendulum bob at a contant lenth exactly equal to 60 cm meaured from the top of the trin to the center of the bob while varyin the bob (and the ma). Enter your data in table B below. To determine the averae period of one full cycle, divide the time for 10 cycle by 10 to obtain the averae period T for one full win. Graph the data obtained. Plot the bob' period, T (a the ordinate) v. the ma, M (a the abcia). Doe the plotted data how a variation of period with differin ma? Explain your anwer with reference to your raph. 3) To determine the effect that lenth, L of the pendulum trin ha on the pendulum' period, ue the ame metal bob throuhout thi part of the meaurement and vary the trin' lenth from 80.0 cm to 10.0 cm in 10 cm interval. Thi can be done uin the pendulum clamp. Looen the trin clamp to adjut the trin to the proper lenth and then tihtenin the trin clamp on the upport. Record the lenth ued in each trial carefully from the pendulum clamp upport to the center of the winin bob. Accurately meaure and et the tin lenth to et ood reult. Dicard any time meaurement that may be in error and repeat for ood reult. Be ure the rin tand rin holdin the pendulum doe not wobble or way and provide poor reult. Repeat each trial of ten win three time and take the averae. Determine the averae time period for one full cycle of the pendulum by dividin the averae time for ten win by 10. Place the data in table C below. Calculate the averae time and then the period of one full cycle. Do the calculation to complete table C. Analyi: 1) Plot the period of the pendulum - the ordinate v. the trin lenth - the abcia. Doe thi raph pa throuh the oriin? I the bet fit line of thi raph a traiht line? 2) To help uncover how a pendulum period and lenth are related, determine the period quared ( T 2 ) for each different trin lenth from the data your team obtained.

3 3) Now plot the period T 2 - the ordinate veru the L - the abcia. If the quare of the period of the pendulum i directly proportional to the pendulum' lenth; the plot of T 2 veru L hould be a traiht line. Draw a line that bet fit the plotted data point. I the bet fit line of thi plot a traiht line? Determine the lope of the traiht line that bet fit the plotted point for T 2 v. L. Show the calculation of lope on your raph paper and in your report. 4) The period of a imple pendulum can be determined from the equation T 2 = ( 4 π 2 / ) L where ( 4 π 2 / ) hould equal the lope of the bet fit line of T 2 v. L So with (4 π 2 / ) equal to m, the lope of thi line, = 4 π 2 / m. Solve for in thi way and report your reult in your lab report. Quetion: 1. Accordin to the data and your team obervation, i the motion of a imple pendulum periodic? Can a pendulum be ued a a clock? Refer to the firt procedure and the data in table A to anwer. 2. What hould be the unit for the lope of the bet fit line of T 2 v. L. Determine the value of the lope of thi raph. 3. Obtain a value for a determined at your location from the plot of your data (T 2 v. L) where the lope i m. Calculate the value for local ravity at BTHS uin the equation = 4 π 2 / m where m i the lope of the T 2 v. L plot.

4 TABLE A time trial Period for 1 cycle 10 win 10 win 20 win 20 win Trial 5 30 win Trial 6 30 win TABLE B bob ma bob ma bob ma bob ma time trial Period for 1 cycle

5 TABLE C Lenth (L) time trial averae period in meter ( T) for 1 cycle T 2 10 win 2 L = 0.80 m 10 win 2 L = 0.70 m 10 win 2 L = 0.60 m 10 win 2 L = 0.50 m Trial 5 10 win 2 L = 0.40 m Trial 6 10 win 2 L = 0.30 m Trial 7 10 win 2 L = 0.20 m Trial 8 10 win L = 0.10 m 2