# What are some examples of a coefficient of restitution?

May 29, 2014

Golf ball, coefficient of restitution = 0.86, steel ball bearing, coefficient of restitution = 0.60.

#### Explanation:

Golf ball, coefficient of restitution, $C$ = 0.86. Steel ball bearing, $C$ = 0.60.

$C = {v}_{2} / {v}_{1}$
(where ${v}_{2}$ is the velocity immediately after the collision and ${v}_{1}$ is the velocity immediately before the collision).

You can also derive an expression for $C$ in terms of a height of drop and rebound (neglecting air resistance, as usual):
$C = \setminus \sqrt{\setminus \frac{h}{H}}$
(H is height of drop, h is height of rebound).

For the golf ball we can collect the following data:
H = 92 cm.
${h}_{1} = 67 , {h}_{2} = 66 , {h}_{3} = 68 , {h}_{4} = 68 , {h}_{5} = 70$ (all cm)

Find the average rebound height and then calculate the coefficient of restitution.

For the ball bearing we can collect the following data:
H = 92 cm.
${h}_{1} = 32 , {h}_{2} = 33 , {h}_{3} = 34 , {h}_{4} = 32 , {h}_{5} = 33$ (all cm)

Perform the same method as for the golf ball above.