Question

In order to determine the coefficient of restitution e experimentally, a ball is dropped from height h0 onto a horizontal rigid surface After the ball has hit the surface 7 times, it reaches only 20% of the original height h0. Calculate the coefficient of restitution.

Answer 1

With the positive direction of the velocity taken as upwards, the velocity of the ball immediately before the first impact is given by

of the coefficient of restitution in terms of the velocities yields the velocity ¯v immediately after the impact is given by

From the Conservation of Energy Law we obtain the height which the body reach

for the subsequent impacts. Thus