In a game of billiards, a cue ball hits a stationary 8-ball and then stops moving after the collision. If the momentum is conserved, what is the final momentum of the cue ball?(1 point)

Question

Responses

It is less than its initial momentum but greater than zero.
It is less than its initial momentum but greater than zero. - incorrect

It is equivalent to the final momentum of the 8-ball.
It is equivalent to the final momentum of the 8-ball. - no response given

It is zero.
It is zero. - no response given

It is greater than its initial momentum.

Answer 1

In this scenario, the cue ball comes to a stop after colliding with the stationary 8-ball. According to the law of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision.

Let’s denote:

• \( m_1 \) as the mass of the cue ball,
• \( v_1 \) as its initial velocity,
• \( m_2 \) as the mass of the 8-ball (stationary initially),
• \( v_2 \) as its initial velocity (which is 0).

Before the collision, the total momentum is: \[ p_{\text{initial}} = m_1 v_1 + m_2 \cdot 0 = m_1 v_1. \]

After the collision, the cue ball stops (so its final momentum is 0) and the 8-ball moves with some final velocity \( v_f \). The total momentum after the collision is: \[ p_{\text{final}} = 0 + m_2 v_f = m_2 v_f. \]

Since momentum is conserved, we have: \[ p_{\text{initial}} = p_{\text{final}}, \] which gives us: \[ m_1 v_1 = m_2 v_f. \]

From this relationship, we can deduce that since the cue ball comes to a stop, all of its initial momentum is transferred to the 8-ball. Therefore, the final momentum of the cue ball is:

It is zero.

The correct response is, therefore: "It is zero."