
Aim: to estimate the Coefficient of Restitution for
a ball bouncing on the laboratory bench 
When two objects collide, their coefficient of
restitution gives a measure of the elasticity of the
collision. 
An totally elastic collision is one in which kinetic
energy is conserved. 
In practice some k.e. is always
converted into other forms. 
Which other forms? 
If we compare the relative velocity of the two
objects just before the collision (velocity of approach,
v_{a}) with their relative velocity just after
the collision (velocity of separation, v_{s}) we
can see "how elastic" the collision was. 
We therefore define the quantity the coefficient
of restitution, e as follows 

To use a sophisticated technical term, we
are going to find out how bouncy the ball is! 
Notice that e = 1 corresponds to a
perfectly elastic and e = 0 a totally inelastic
collision (the objects stick together). 

Method 
In order to estimate the height h_{2} to
which the ball bounces, it is helpful to have two
horizontal bars of adjustable positions, as shown below. 


An alternative method might be to video the ball in
front of a background with some kind of grid marked on
it... 

By considering energy changes during the fall
of the ball (gravitational potential energy to kinetic
energy) and during the rebound of the ball (k.e. to
g.p.e.), you will see how a value for e can
be taken from a graph of h_{2} against h_{1}. 