Billiards Game: Conservation of Momentum

What principle can be used to find the final speed of the cue ball in a billiards game?

A. Conservation of Energy

B. Newton's First Law

C. Conservation of Momentum

Answer:

The principle that can be used to find the final speed of the cue ball in a billiards game is Conservation of Momentum.

When playing a game of billiards, understanding the concept of conservation of momentum is crucial in determining the final speed of the cue ball after a collision. This principle states that the total momentum before a collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system.

In the scenario described, the cue ball with a mass of 0.50 kg and an initial speed of 1.9 m/s collides with a stationary billiard ball weighing 0.30 kg. After the collision, the billiard ball moves off at 1.3 m/s at an angle of 32º clockwise from the cue ball's original path. By applying the conservation of momentum, we can calculate the final speed of the cue ball.

To solve this problem, we first break down the cue ball's velocity into horizontal and vertical components. The horizontal component remains unchanged after the collision, while the vertical component becomes zero. By calculating the final horizontal and vertical speeds of the cue ball and using the Pythagorean theorem, we find that the final speed of the cue ball is approximately 1.4 m/s.