A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic, causing the ball to rebound to the same height and fall again. Determine the average force exerted by the ball on the floor over a long time interval.

Step-by-step solution

Let the ball be dropped from a height h . The velocity of the ball just before hitting the floor is v = 2gh . Since the collision is perfectly elastic, the ball rebounds with the same speed v . The change in momentum of the ball during one collision is p = mv - (-mv) = 2mv . The time interval between two successive collisions is the time taken by the ball to go up to height h and fall back to the floor, which is T = 2v g . The average force exerted by the floor on the ball is F_ avg = p T = 2mv 2v g = mg . By Newto