Passage VI

In each of 3 experiments, students studied the motion of pendulums. Each pendulum was a solid sphere on a string. Each pendulum had a mass, M, equal to the mass of its sphere and a length, L, equal to the length of its string plus the radius of its sphere (see the diagram).

The students performed the following steps for each pendulum tested in Experiments 1-3:

1. Student 1 moved the pendulum until its string made an angle, A, with the vertical and then released the pendulum from rest.

2. Student 1 timed the pendulum for 10 full swings (one full swing was from the starting point to the turning point and back). Student 1 then divided that time by 10 to obtain the average period, T, for the pendulum.

3. Student 2 solved the simple pendulum equation for the pendulum tested in Steps 1 and 2. (The simple pendulum equation is a relation that predicts the value of T for a pendulum based on its physical characteristics. )

Experiment 1

The students tested several pendulums: L was 100 cm for each, but M was different for each. Student 1 released each pendulum from A = 10°. Figure 1 shows the values of T, in seconds (s), that Student 1 measured and those that Student 2 calculated.

Experiment 2

The students tested several pendulums: M was 100 g for each, but L was different for each. Student 1 released each pendulum from A = 10°. Figure 2 shows the students' results.

Experiment 3

The students tested several pendulums: M was 100 g for each, and L was 100 cm for each. Student 1 released each pendulum from a different A. Figure 3 shows the students' results.