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Coefficient of Restitution of a superball

The coefficient of restitution, e, for a ball hitting a stationary surface with a velocity v1 and rebounding with a velocity v2 is:

e = - v2/v1

The value of e is positive, because v1 and v2 have opposite directions, and can be any number from 0 to 1 for a passive collision with the surface(no explosive type energy release in the collision). If e = 1 the kinetic energy of rebound is equal to the kinetic energy of the ball before it hits. If e = 0 the ball stops when it hits and all the kinetic energy is lost. Note that e has no units.

A ball dropped from a height y1 onto a floor surface will have a hit velocity v1 that can be determined by setting the gravitational potential energy at height y1 equal to the kinetic energy when hitting the floor. The rebound velocity v2 can be determined by setting the kinetic energy due to v2 equal to the potential energy at the rebound height y2.

initial potential energy PE1 = mgy1

kinetic energy when hitting the floor KE1 = 1/2 mv12

kinetic energy of rebound KE2 = 1/2 mv22

final potential energy PE2 = mgy2

Mass of the ball is 19g
Drop height 50cm Rebound height is 35 cm
drop height 100cm rebound height 73cm
drop height 150cm rebound height 109cm
drop height 180 cm rebound height 121 cm

Calculate Impact energy, Impact velocity, Rebound energy and Rebound Velocity and Coefficient of Restitution for each height.

2 Questions

1. What can be said about the impact if the coefficient of restitution is greater than one?

2. Solve for e algebraically by solving the energy equations for v1 and v2 in terms of y1 and y2 and taking the ratio.

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