Question

if the coefficient of restitution be 0.5 what is the percentage loss of energy on each rebounding a ball dropped from a height?

Answer 1

Given, Coefficient of Restitution = e = 0.5

Velocity of the ball before collision with the floor = u
Velocity of the ball after collision with the floor = v
Velocity of floor = 0  (before or after collision)

          e = (velocity of separation after collision)
                      ÷ (velocity of approach before collision)
=>      e  = v / u
          e² = v² / u²  =  1/2 m v² / (1/2 m u²)
         0.5² = KE after collision / KE before collision
         KE after Collision = 1/4 * KE before collision

         Loss of KE = 3/4 * KE before collision
                            = 3/4 * 100 = 75%