lab exercise 4

Lab Exercise 4: Pendulum and Calculation of g Table 1- Effect of oscillation amplitude Length 100 cm Mass of bob 24.4 g Initial Bob Angle (degrees) Horizontal amplitude Displacem ent trial 1 trial 2 trial 3 average 5 cycles St. Dev. 5 cycles Estimated period (1 cycle) 5 4 cm 9.9 9.41 9.72 9.68 .06145 1.94 10 6.5 cm 10.03 9.81 9.88 9.91 .01265 1.98 15 9 cm 10.1 10 9.91 10 .00905 2 20 11.5 cm 10.14 9.81 9.90 9.97 .03945 1.99 25 14 cm 10.06 10.2 10.03 10.10 .00825 2.02 30 16.5 cm 9.78 9.94 9.97 9.9 .01045 1.98 QUESTION 1 What initial angle yields the smaller standard deviation? 25 degrees QUESTION 2 Does the period of the pendulum’s oscillation change with the initial bob angle? Justify your answer. No the period stays very close no matter what initial bob angle is used. The estimated cycles are all very close to 2 seconds for every different angle. The greater the initial angle causes for the bob to travel a larger distance but this increased distance comes with increased speed. Table 1.a Initial angle estimated value of g % error 5 9.29 5.3 10 9.67 1.4 15 9.87 0.6 20 9.77 0.4 Copyright © 2017 by Thomas Edison State University. All rights reserved.

25 10.07 2.7 30 9.67 1.4 QUESTION 3 For what initial angle do you obtain the lowest relative error? What about the highest relative error? What can you conclude from your data? The 20 degree angle gave the lowest relative error for gravity. The 5 degree initial angel provided the largest relative error for gravity. The larger initial angles appear to provide a smaller percentage of error in gravity. Table 2 - Effect of mass Target bob mass actual bob mass trial 1 trial 2 trial 3 average 5 cycles St. Dev. 5 cycles Estimated Period (1 cycle) 15 g 16.2 g 9.72 9.59 9.62 9.64 .00465 1.93 25 g 24.4 g 10.03 9.81 9.88 9.91 .01265 1.98 50 g 49.4 g 9.84 9.69 9.81 9.78 .0126 1.96 QUESTION 4 What is the effect of the bob’s mass on the period of the pendulum’s amplitude? Did you expect these results? Explain. The change in mass did not have much of an effect at all on the pendulum. I expected this because the rotational inertia of the pendulum remained the same no matter the weight of the mass. When the rotational inertia remains the same a change in rotational speed is not allowed to happen. Table 3 - Effect length of pendulum Length of string (cm) Length of string (m) trial 1 trial 2 trial 3 Average 5 cycles St. Dev. 5 Cycles Estimated Period (1 cycle) 100 1.0 10.03 9.81 9.88 9.91 .01265 1.98 75 .75 8.63 8.84 8.75 8.74 .0111 1.75 50 .5 7.19 7.05 7 7.08 .0097 1.42 Copyright © 2017 by Thomas Edison State University. All rights reserved.

Copyright © 2017 by Thomas Edison State University. All rights reserved.