Billiard Ball Elastic Collision
What is the scenario involving the collision of two billiard balls?
A billiard ball with mass 8.0 kg is shot due west at 8.8 m/s. It collides elastically with another billiard ball of the same mass. After the collision, the second ball travels due west in the same direction as the first ball. What can we determine from this scenario?
Scenario Explanation:
The scenario presented involves an elastic collision between two billiard balls of equal mass. The first ball is initially moving westward with a velocity of 8.8 m/s, and after the collision, the second ball also moves westward. To analyze the outcome of the collision, we can apply the principles of conservation of momentum.
Conservation of Momentum in Elastic Collisions:
When two objects collide elastically, the total momentum of the system before the collision is equal to the total momentum after the collision. In this scenario, the initial momentum of the system is the mass of the first ball (8.0 kg) multiplied by its velocity (8.8 m/s).
Since the collision is elastic and the table is assumed to be frictionless, we can calculate the final velocity of the second ball by equating the initial total momentum to the final momentum of the system. The final velocity of the second ball moving westward is equal to the initial velocity of the first ball, which is 8.8 m/s.
Therefore, the final velocity of the second billiard ball after the elastic collision is 8.8 m/s due west. This outcome is obtained by applying the principles of conservation of momentum in elastic collisions.