A ball is dropped from rest at a height of 20 m from the flo

A ball is dropped from rest at a height of 20 m from the floor. It rebounds straight up and reaches a maximum height of 14 m. What is the coefficient of restitution between the ball and floor?

Solution

Coefficient of restitution for any body is defined as the ratio of the speed after collision to the speed before collision.

Now, we will use conservation of energy to determine the speed of the ball right before the collision and right after the collision to determine the required ratio

For the fall:

m20*9.81 = 0.5mv^2

or V = sqrt(40g) = 19.809 m/s

For the rise: 0.5mu^2 = mg x 14

or, u = sqrt(28g) = 16.5735 m/s

Therfore the required ration = U /V = 16.5735 / 19.809 = 0.8367