Deeper Understanding of Coefficient of Restitution
To define it in scientific terms, it is the ratio of the final velocities and initial velocities of two objects after they collide with each other. This ratio typically ranges from 0 to 1; where 1 would be a perfectly elastic collision and 0 would be a perfectly inelastic collision.

A perfectly elastic collision is one where there is no dissipation or loss of kinetic energy from the collision and, in a perfectly inelastic collision, the objects do not separate after a collision. While these are not completely practical scenarios, there are some cases where a collision can be nearly elastic or elastic. When two hard steel balls collide, the collision is nearly elastic.

This is the principle behind Newton’s Cradle; the hard steel balls that swing back and forth without any loss in momentum or energy.  Similarly, collisions such as the Rutherford scattering as well as the slingshot orbit of a satellite of a planet are both perfectly elastic collisions.

Why is it Important?
The coefficient of restitution is important because it is what determines whether a collision is elastic or inelastic in nature.

Determining whether a collision is elastic or not shows if there is any form of loss of kinetic energy as a result of the collision. During the collision, in a perfect system, the kinetic energy of one object would get transferred to the other object when it collides. This means that the other object, if it was previously stationary, now has the energy of the colliding object. If the two objects when colliding are not stationary, then they both transfer some of their kinetic energy to the other object.

However, in a perfectly elastic collision, the energy is only transferred and not lost in overcoming other factors like friction. Therefore, the average kinetic energy remains unchanged. The coefficient of restitution, therefore, plays an important role here.

What are its Applications?
The practical uses of the coefficient of restitution are many: 

In sports:
The coefficient of restitution can be used to determine the speed of a ball after it collides with the bat in a game of cricket. By determining the kinetic energy of the ball after being bowled and after it collides with the bat, the speed of the ball can be determined. Similarly, this can be done for other sports such as basketball.

In industry:
The ratios of the average kinetic energies are used in collision testing for various objects in industrial settings. This value can be used to study the nature of the objects and determine their uses in various kinds of equipment that could be exposed to collisions. For example, in car manufacturing industries it can be used to reduce the impact of a collision on the body of a car to prevent too many injuries to the passengers inside.

The coefficient of restitution is not the property of the material of an object because it changes with the object’s shape and the specifics of the collision. The most common test available for determining the value of this coefficient is the Leeb rebound hardness test which uses a tungsten carbide tip that is dropped on an object from a specific height. Since variable properties of the tip determine the value of the coefficient, this test does not give an objective result.

The coefficient of restitution is a value that is important in determining the nature of a collision, occurring between two bodies.