Question

What is the coefficient of restitution?

Answer 1

It is used to determine the type of collision between two objects and is defined as the ratio between relative velocities of the two bodies before and after the collision. The value of the coefficient of the restitution between 0 and 1 and cannot exceed 1.

Complete step by step answer:
The coefficient of restitution is defined as the ratio of the final velocity to the initial velocity between two objects after the collision. The coefficient of restitution is essentially a measure of the restitution of a collision between two objects that is how much of the energy remains after the two bodies collide.
e = $\dfrac{V_{r-after}}{ V_{r-before}}$
For example, if we Bounce a rubber ball on a wooden floor it will bounce back in our hands and if you use a metal ball it won't bounce back in our hands this is because of the material of the ball we used. If we use a rubber ball the kinetic energy of the ball almost remains the same after the collision but in the case of metal ball loss of kinetic energy happens. This property of the material is explained using the term coefficient of restitution. In the first case V coefficient of restitution can be obtained as taking the ratio between the relative velocity of the ball and the ground before and after the collision and as the velocity, the ball is almost the same, we get the coefficient of restitution is one. In the second case, the relative velocity of two bodies after the collision becomes zero and hence the coefficient of restitution becomes zero in the second case.
Hence the coefficient of restitution is a measure of the loss of energy after the collision.
The collisions in which relative velocity before and after the collision are the same for the collision in which the loss of energy is zero are called elastic collisions.
For the elastic collisions we get the value of the coefficient of restitution as 1.
Another type of collisions in which the relative velocity of the two bodies after the collision becomes zero are called inelastic collisions.
The value of the coefficient of restitution in this type of collisions is 0
We know the relative velocity of the two bodies after the collision cannot exceed the relative velocity of the two bodies before the collision and hence the maximum value of the coefficient of the restitution becomes one which we obtained in case of Elastic collisions and the minimum value of the coefficient of restitution becomes zero which we obtain in case of inelastic collisions.

Note:
There is a possibility of making mistakes understanding the concept of coefficient of restitution as the ratio between the velocities of two bodies before and after the collision which is wrong, we need to consider only the relative velocity between the two bodies and not the velocity of the bodies relative velocity is different from the velocity of the two bodies.