Question

A pool cue ball moving at 2.1 m/s east collides in a straight line with the eight ball at rest. (You may assume that the cue ball and the eight ball have the same mass.) Find the velocity of the eight ball after the collision if momentum is conserved and

the cue ball stops
the cue ball continues on in the same direction at 0.10 m/s
the cue ball continues on in the same direction at 0.70 m/s.

Answer 1

1. 2.1 m/s west.

2. 2.0 m/s west.

3. 1.4 m/s west.

Momentum is a conserved quantity, meaning that it is neither created nor destroyed. This means that the total momentum of the system (cue ball and eight ball) before and after the collision must stay the same. After the collision, the momentum of the system is equal to the momentum of the eight ball alone since the cue ball no longer has momentum after it stops (for option 1) or has a different momentum depending on its speed (for options 2 and 3).

Since momentum is mass times velocity, we can solve for the velocity of the eight ball by rearranging this equation:

Momentum = Mass x Velocity

Velocity = Momentum / Mass

Plugging in the given values:

1. Velocity = (2.1 m/s east) / (mass of both balls) = 2.1 m/s west

2. Velocity = (2.1 m/s east + 0.10 m/s east) / (mass of both balls) = 1.9 m/s west

3. Velocity = (2.1 m/s east + 0.70 m/s east) / (mass of both balls) = 1.4 m/s west