Passage VI

A teacher described the procedure of a study to students in a science class:

A 1 kg sphere, Sphere X, and a 2 kg sphere, Sphere Y, were released from rest, one at a time, from Point P on the right side of a frictionless, U-shaped incline. Hp was the height of Point P above Point L, the lowest point on the incline (see Figure 1).

Each sphere was allowed to slide as far up the left side of the incline as it could go.

Next, the teacher gave the students the following definitions:

1. GPE_p, the gravitational potential energy of a sphere at Point P, equaled mgH_p, where m was the sphere's mass and g was the acceleration of the sphere due to Earth's gravity.

2. KE_L, the kinetic energy of a sphere at Point L, equaled mV_L², where V_L was the sphere's speed at Point L.

3. MO_L, the amount of momentum of a sphere at Point L, equaled mV_L.

Then the teacher asked 3 students to predict (giving their reasons) which sphere, if either, slid farther up the left side of the incline.

Student 1

As a sphere slid down the incline, its GPE_p was converted to kinetic energy. By the time it reached Point L, all of its GPE_p had been converted. Based on Definition 1, because Sphere Y had a greater m than did Sphere X, but the same g and Hp as Sphere X, Sphere Y had a greater GPE_p than did Sphere X. As a result, Sphere Y had a greater KE_L than did Sphere X. Thus, Sphere Y slid farther up the left side of the incline than did Sphere X.

Student 2

Because the 2 spheres had the same g and Hp, they had the same V_L. Based on Definition 3, because Sphere Y had a greater m than did Sphere X, Sphere Y had a greater MO_L than did Sphere X. Thus, Sphere Y slid farther up the left side of the incline than did Sphere X.

Student 3

Because the 2 spheres had the same g and Hp, they had the same V_L. Thus, they slid the same distance up the left side of the incline.

After hearing the students' predictions, the teacher gave them the results of the study (see Table 1).