Why Is the Coefficient of Restitution Less Than 1 in a Tennis Racket Collision?

[charlie1990]

1. calculate the coefficient of restitution when a player hits a ball traveling into a racket at 10m/s and the racket is stationary before the ball hits it. after the ball hits it, the ball has a velocity of 5m/s and the racket is moving in the opposite direction at 1 m/s (Velocity before a - velocity before b)/(Velocity after a - velocity after b)
I know this is what's used to get the answer normally, but I am getting the wrong answer (above 1).

I think it has something to do with racket going opposite direction but not sure what to do?

 

[Doc Al]

(Velocity before a - velocity before b)/(Velocity after a - velocity after b)

You have that a bit backwards (or upside down). You want the relative speed after the collision over the relative speed before the collision.

 

[charlie1990]

You have that a bit backwards (or upside down). You want the relative speed after the collision over the relative speed before the collision.

cheers, poor mistake

 

[haruspex]

cheers, poor mistake

... and the sign reverses.

 

[HalfLostAndSearching]

The coefficient of restitution is a measure of the elasticity of a collision between two objects. It is calculated by taking the ratio of the relative velocity before and after the collision.

In this scenario, the relative velocity before the collision is 10m/s (ball) - 0m/s (racket) = 10m/s. The relative velocity after the collision is 5m/s (ball) - (-1m/s) (racket) = 6m/s.

Thus, the coefficient of restitution would be 6m/s / 10m/s = 0.6. This means that the collision between the ball and the racket is not perfectly elastic, as some of the kinetic energy was lost in the collision and converted into other forms of energy such as heat and sound.

The fact that the racket is moving in the opposite direction does not affect the calculation of the coefficient of restitution, as it is still a measure of the elasticity of the collision between the two objects. I hope this helps clarify the concept of coefficient of restitution for you.