Question

In billiards, collisions occur between pool balls as they make contact with one another. In one particular collision, when all balls are initially at rest, a white ball is struck with a stick and makes contact with a red ball. The table below summarizes the motion of the white ball, with t = 0 when the white ball is initially struck by the pool stick.

Time (s) Speed (m/s) Kinetic Energy (J)
0 10 8
1 10 8
2 0 0
3 0 0

Assuming that the balls are on a surface with no friction, which table could summarize the motion of the red ball over the same time period?
A.
Time (s) Speed (m/s) Kinetic Energy (J)
0 0 0
1 0 0
2 10 8
3 10 8
B.
Time (s) Speed (m/s) Kinetic Energy (J)
0 0 0
1 10 8
2 5 2
3 0 0
C.
Time (s) Speed (m/s) Kinetic Energy (J)
0 10 8
1 10 8
2 0 0
3 0 0
D.
Time (s) Speed (m/s) Kinetic Energy (J)
0 10 16
1 10 16
2 5 8
3 5 8

Answer 1

Option B appears to describe the motion of the red ball consistent with the conservation of momentum and energy during the collision.

Conservation of momentum and energy

The conservation of momentum and energy applies to collisions where no external forces, such as friction, are present.

In an ideal scenario, the total momentum and total kinetic energy before the collision should be equal to the total momentum and total kinetic energy after the collision.

Looking at the given table for the white ball's motion:

At t = 0 and t = 1, the speed remains constant at 10 m/s, and the kinetic energy remains constant at 8 J.

At t = 2 and t = 3, both the speed and kinetic energy drop to 0.

Based on the conservation principles, the red ball, which is involved in the collision with the white ball, would experience a change in its motion accordingly.

Among the options provided, the table that seems to follow the conservation principles is:

B.

Time (s) | Speed (m/s) | Kinetic Energy (J)

0 | 0 | 0

1 | 10 | 8

2 | 5 | 2

3 | 0 | 0

This table implies that initially (at t = 0), the red ball is at rest with zero speed and kinetic energy. As the collision occurs, the red ball gains speed and kinetic energy, reaching a maximum speed of 10 m/s and a kinetic energy of 8 J at t = 1.

Subsequently, the red ball gradually loses speed and kinetic energy, coming to a stop at t = 3.

Therefore, option B appears to describe the motion of the red ball consistent with the conservation of momentum and energy during the collision.