Passage IV

Using the equipment shown in Figure 1, a group of students performed 3 experiments involving pendulums in motion. Each pendulum consisted of a bob of mass M sus­pended from a rigid support by a string of length L.

At the start of each trial, the students displaced the bob to a selected angle, θ, measured from the vertical, using a protractor fastened to the support. The students then released the bob from rest, allowing it to swing back and forth. They used a stopwatch to measure the period, T, of the pendulum, defined as the time required for the bob to complete 1 full swing (from Point A to Point B and back to Point A).

Before each experiment, the students derived an equa­tion, based on tbe laws of physics, to predict T for each trial of that experiment. Then, after obtaining their mea­surements, the students graphed their predicted T data and their measured T data.

Experiment 1

A pendulum with M = 100 g and L = 100 cm was released from rest at various values of θ, in degrees. The pendulum was timed for 10 full swings and the measured time was then divided by 10 to obtain a measured aver­age T, in seconds (sec), for each θ (see Figure 2).

Experiment 2

Pendulums with M = 100 g but various values of L were released from rest at θ = 10°. The measured average T for each pendulum was obtained as in Experiment 1 (see Figure 3).

Experiment 3

Pendulums with L = 100 cm but various values of M were released from rest at θ = 10°. The measured average Tfor each pendulum was obtained as in Experiment 1 (see Figure 4).