Pendulums and the Acceleration of Gravity

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1 GSCI Physical Science Laboratory Experiment # Name Partners Pendulums and the Acceleration of Gravity Date Section Background: The use of the pendulum for timing purposes was discovered by Galileo while sitting in church. The sermon must have been boring, because he was watching the swinging motion of one of the lights overhead when he noticed that it seemed to be swinging with a very well defined time. Using his pulse rate, he confirmed this. This discovery provided the basis for accurate timing devices like pendulum clocks. Today's experiment deals with the pendulum in its simplest form: a mass supported by a string. Part of the experiment will be to decide what it is that determines the period of the pendulum (i.e., the time for one complete swing). The other part is to use a given formula to calculate a value for g, the acceleration of gravity. Equipment: String ( m), brass ball, aluminum ball, supports ( posts, 1 bar, clamps), meter stick, timer, tape. Procedure: 1. Set up the support posts and clamp the bar to them.. Tie a string to each ball. 3. Measure the mass of each ball and record it on your data sheet. 3. Loop the string of each ball around the bar and tape it into place. Make sure the balls are separated from each other by at least 10 cm. 4. Adjust the length of each string so the ball is several centimeters above the table s surface. Make sure the two balls are at the same height. 5. Measure the length of each pendulum and record on your data sheet. The pendulum length is measured from the middle of the bar to the middle of the ball. I. Factors Affecting Time Period We want to determine what factors affect the time period of a pendulum. Try each of the following and record your observations on the data sheet. A. Pull both pendulums back a small distance and release at the same time. Record which pendulum takes the longest time to go through one oscillation (one full swing back and forth) or whether they oscillate at the same rate. The only physical difference in these two pendulums is that the brass ball has more mass than the aluminum ball. B. Pull the brass ball back a small distance and the aluminum ball back a large distance and release at the same time. Record which pendulum takes the longest time to go through one oscillation. C. Pull the brass ball back the same distance as the aluminum ball and release them at the same time. Release the brass ball as normal; however, give the aluminum

2 Physical Science Page Lab Experiment # ball a slight push to the side upon release so it moves in a circle instead of a line. Record which pendulum takes the longest time to go through one oscillation. D. Shorten the length of the aluminum pendulum by releasing the tape and adjusting the string at the bar. Make the length about 5 cm shorter than the brass pendulum. Pull each pendulum back and release at the same time. Record which pendulum takes the longest time to go through one oscillation. II. Period vs. Length We want to find the mathematical relationship between period (the time for one oscillation) and the length of the pendulum. As you did at the end of part I, shorten the aluminum pendulum further. A. Keep adjusting the length of the aluminum pendulum until it oscillates twice for one oscillation of the brass pendulum. To verify that you have the aluminum pendulum adjusted correctly the brass pendulum should oscillate 4 times while the aluminum pendulum oscillates 8 times. If this verification doesn t match, make slight adjustments in the length of the aluminum pendulum until you can get a match of 6 to 1. Measure the new length of the aluminum pendulum and record on your data sheet. B. Repeat the previous procedure but get the aluminum pendulum to oscillate 3 times for one brass pendulum oscillation. To verify accuracy fine tune your length so 4 brass oscillations match 1 aluminum oscillations. Measure the new length of the aluminum pendulum and record on your data sheet. C. Repeat again to get a 4 times oscilliation rate. To verify accuracy fine tune your length so 4 brass oscillations match 16 aluminum oscillations. Measure the new length of the aluminum pendulum and record on your data sheet. D. On the data sheet calculate the following products and ratios for each of the measurements performed above. Record these results on your data sheet. III. Measurement of gravity Pull the brass pendulum back a small distance and release. Start a timer as soon as the pendulum is released. After the pendulum has made a total of 30 oscillations, stop the timer. Record this time and repeat 4 more times. Average the results and record on your data sheet. The uncertainty of your average is the largest difference between the average and your 5 measurements. Record how many significant digits you have on your measurement of the average time. Using the average obtained above calculate the time for one oscillations and in turn the acceleration due to gravity. Find the percentage error between your measurement and the known value of gravity.

3 Physical Science Page 3 Lab Experiment # Ball Mass DATA SHEET -- Acceleration of Gravity Brass Ball Aluminum Ball Length of Pendulum Brass Ball Aluminum Ball Factors Affecting Time Period Indicate which ball has the longest oscillation time or whether they are the same. A. Mass of ball B. Distance pulled back C. Moving in a circle D. Shorter pendulum length Period vs. Length Record the length of the aluminum pendulum and calculate the products and ratios of period and length. A. oscillations (Period = 1/) Length = B. 3 oscillations (Period = 1/3) Length = C. 4 oscillations (Period = 1/4) Length = Period*Length A = B = C = Period/Length A = B = C = Period *Length A = B = C = Period*Length A = B = C = Period /Length A = B = C = Period/Length A = B = C =

4 Physical Science Page 4 Lab Experiment # Which combination of period and length gives the same answer for A, B, & C? Measurement of Gravity Record the time period for 30 oscillations and then average the results. Run #1 Run # Run #3 Run #4 Run #5 Average = Uncertainty = Signifant digits = Period for one oscillation Period = Average/30 = Gravity calculation Note: Convert your length from centimeters to meters before performing the gravity calculation. 4π Length gravity = = Period 9.81 gravity %error = 100% = 9.81

5 Physical Science Page 5 Lab Experiment # Conclusions: 1. What factors have an effect on the period of a pendulum and which don t?. Were any of the combinations of period and length constant for your aluminum pendulum? If so, is this combination consistent with our gravity calculation formula 4 Length of gravity = π? Explain why or why not. Period 3. How accurate was your measurement of the acceleration of gravity? Even if you got good results, what could you change in the experimental procedure and measurement to get even better results? 4. What does this experiment tell you about the validity of the work done by Galileo centuries ago? What does this tell you about the methods used by science to determine truth? 5. We often use demonstrations and illustrations to reinforce spiritual truths. How might you use a pendulum as part of a Sunday School lesson to do this. Include a Scripture reference that would support your spiritual application.

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