coefficient of restitution

Question

A ball is dropped from a height of 1.6 m onto a hard floor. It bounces to a height of 1.45 m. Calculate

the coefficient of restitution between the ball and the floor.

Answer 1

The coefficient of restitution is the ratio of the velocity after impact to the velocity before impact.

The velocity before impact can be found by conservation of energy; all the potential energy at the drop height will be converted to kinetic energy at the moment of impact

PE = KE

mgh = ¹/₂mv²

gh = ¹/₂ v²

9.8*1.6 = ¹/₂ v²

5.6 = v

Similarly, the velocity after impact can be found by conservation of energy; all the kinetic energy after impact is converted to potential energy at the height after the impact

PE = KE

mgh = ¹/₂mv²

gh = ¹/₂ v²

9.8*1.45 = ¹/₂ v²

5.33 = v

Find the ratio of the velocities after and before impact for your answer.