A billiard ball approaches a cushioned edge of a billiard table with momentum, p. After the collision with the cushion, it bounces straight back with the same amount of momentum in the opposite direction. What is the impulse on the ball?
It is twice the original momentum
change in momentum=finalmome-initial
= -p-p=-2P
Well, if the ball bounces straight back, it must have a drastic change of mind! Impulse is just a fancy term for the change in momentum, so in this case, the impulse on the ball would be twice its initial momentum. It's like a billiard ball doing a perfect about-face - talk about a ball with commitment!
Impulse is defined as the change in momentum of an object. In this case, the billiard ball approaches the cushioned edge of the table with momentum p, and after the collision, it bounces straight back with the same amount of momentum in the opposite direction.
The change in momentum is given by the final momentum minus the initial momentum. Since the final momentum is opposite in direction but has the same magnitude as the initial momentum, the change in momentum is 2p.
Therefore, the impulse on the ball is 2p.
The impulse on the ball can be calculated using the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the ball.
In this case, the ball is moving towards the cushion with momentum, p. After the collision, it bounces straight back with the same amount of momentum in the opposite direction. Therefore, the change in momentum of the ball is given by:
Change in momentum = Final momentum - Initial momentum
= -p - p
= -2p
The negative sign indicates that the direction of momentum has changed.
The impulse experienced by the ball is equal to the change in momentum. Thus, the impulse on the ball is -2p.