The Principle of Conservation of Momentum in Billiard Ball Collisions

What is the final velocity of the combined mass system in a perfectly inelastic collision between Billiard Ball A and B?

Given that Billiard Ball A is moving at a speed of 53.4 m/s and collides with stationary Billiard Ball B of the same mass.

Answer:

The final velocity of the combined mass system of Billiard Balls A and B, following a perfectly inelastic collision in which they stick together, is 26.7 m/s.

In the scenario of a perfectly inelastic collision between two billiard balls, momentum is conserved based on the law of conservation of momentum. When Billiard Ball A, moving at 53.4 m/s, collides and sticks with stationary Billiard Ball B of the same mass, the final velocity of the combined mass system can be calculated.

During a perfectly inelastic collision, both objects stick together after collision, making them move with a common velocity. The total momentum before collision equals the total momentum after collision. To find the final velocity, we use the formula:

(mass of A)*(velocity of A) + (mass of B)*(velocity of B) = (total mass)*(final velocity)

By substituting the values into the equation and solving for the final velocity, we get:

Final Velocity = 53.4 m/s / 2 = 26.7 m/s

Therefore, the final velocity of the combined mass system of Billiard Balls A and B is 26.7 m/s following the perfectly inelastic collision.