Coefficient of Restitution Explained

Inelastic Collision

The restitution coefficient is an important parameter relating to the objects’ collision. In English, the term restitution defines the act of reinstating something that was stolen or lost, while on the other hand, coefficient signifies a number that describes how much.

Hence, by definition, the restitution coefficient is a number that shows how much kinetic energy is restored following collision of two or more. This depends on a number of factors, which includes; the properties of the materials of the objects, their impact velocities, and their physique geometry.

On mathematical basis, the restitution is a number between zero and one. If this coefficient is high, it implies that a small amount of energy was lost in the course of the collision. Contrariwise, if the coefficient is low, it implies that a substantial amount of energy was converted into deformation force or into heat energy during the collision.

Types of Collisions

To comprehend the concept of restitution coefficient much better, let’s look again at the two types of collisions which we have learnt during our Physics tuition classes on Dynamics:

Elastic Collision: In an elastic type of collision, on collision of two bodies, most of the bodies’ kinetic energy, prior to the collision, and following the collision, stays the same. If all the energy is conserved, it’s referred to as a perfectly elastic collision. This can occur only when the colliding bodies’ kinetic energy is not converted into any other energy form in the course of the collision.

A great example of a perfectly elastic collision is when you toss a rubber ball against a wall. The ball bounces back from the wall at practically the exact same velocity you tossed it with. Hence, since most of its kinetic energy stays the same, this collision is regarded as an elastic collision.

Inelastic Collision: This is a collision where most of the colliding bodies’ kinetic energy is converted into different forms of energy in the course of the collision. A perfectly inelastic collision occurs when all the colliding bodies’ kinetic energy is converted into different forms of energy, and it’s lost as a result.

A good example of an inelastic collision is a head-on collision of two vehicles. Nearly all the colliding vehicles’ kinetic energy is used up for the heat generation due to friction, and for vehicles bodies’ deformation. This explains why vehicles get deformed on colliding with others. This collision can be regarded as a nearly perfectly inelastic collision.