Passage II

Some students experimentally determined g, the acceleration due to gravity.

In each trial, the students suspended a spring from a stand and measured the spring's length, L. They attached a mass to the suspended spring, allowed the spring-mass system to come to rest, and measured the length, y, of the extended spring (see Figure 1).

Then they calculated the distance D = y - L.

Next, they pulled the mass down to the release point, R, and released it, allowing the mass and spring to oscillate. Using a sensor and a computer, they plotted the distance of the mass from Point R over time (see Figure 2).

The measured period, P, of the spring-mass system equaled the time that elapsed from the moment the mass left Point R until the moment the mass returned to Point R. Finally, the students used D and P to calculate g.

Study 1

In Trial 1, the students tested Spring 1 with a 0.50 kg mass. (Spring 1 had a spring constant [stiffness], k, of

100 newtons/meter, N/m.) In Trials 2 and 3, the students replaced the 0.50 kg mass with a 1.00 kg mass and a 1.50 kg mass, respectively. The results are shown in Table 1.

Study 2

The students followed the procedure from Study 1, except that they substituted Spring 2 (k = 200 N/m) for Spring 1. The results are shown in Table 2.

Study 3

The students followed the procedure from Study 1, except that they substituted Spring 3 (k = 300 N/m) for Spring 1. The results are shown in Table 3.