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

2. KEL, the kinetic energy of a sphere at Point L, equaled mVL2, where VL was the sphere's speed at Point L.

3. MOL, the amount of momentum of a sphere at Point L, equaled mVL.

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 GPEp was converted to kinetic energy. By the time it reached Point L, all of its GPEp 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 GPEp than did Sphere X. As a result, Sphere Y had a greater KEL 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 VL. Based on Definition 3, because Sphere Y had a greater m than did Sphere X, Sphere Y had a greater MOL 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 VL. 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).

33. Suppose that a sphere is released from a new point on the incline, Point Q, that is between Point P and Point L. At Point Q, the sphere's gravitational potential energy is equal to mgHQ, where HQ is the height of Point Q relative to Point L. Based on Student 1's statements about the conversion of gravitational potential energy to kinetic energy, would the sphere's KEL following the release from Point Q be less than or greater than the sphere's KEL following the release from Point P?

Answer and Explanation

Your Answer is

Correct Answer is D

Explanation

Student 1 believes that the greater the gravitational potential energy mgh, the greater the KEL. The height of the Q point is lower, so the potential energy is smaller, so according to student 1, the KEL after the release of the Q point is also smaller