In this article we will discuss about coefficient of restitution. Coefficient of restitution is also known as coefficient of resilience.
Coefficient of restitution or coefficient of resilience
Most of the real collisions are neither perfectly elastic nor perfectly plastic. They are partially elastic collisions, in which the K.E. reduces and so the speed of separation is less than the speed of approach.
The coefficient of restitution gives a measure of the degree of restitution of a collision and is defined as the ratio of the magnitude of relative velocity of separation after collision to the magnitude of relative velocity of approach before collision. It is given by
The value of e depends on the materials of the colliding bodies. For two glass balls, e = 0.95 and for the lead balls, e = 0.20.
The coefficient of restitution can be used to distinguish between the different types of collisions as follows:
(i) For a perfectly elastic collision, e = 1 i.e., relative velocity of separation is equal to the relative velocity of approach.
(ii) For an inelastic collision, 0 < e < 1 i.e., the relative velocity of separation is less than relative velocity of approach.
(iii) For a perfectly inelastic collision, e = 0 i.e., the relative velocity of separation is zero. The two bodies move together with a common velocity.
(iv) For a superelastic collision, e >1 i.e., the kinetic energy increases.
Table: Different types of collisions
| Collision | Kinetic energy | Coefficient of restitution | Main domain |
| Elastic | Conserved | e = 1 | Between atomic particles |
| Inelastic | Not conserved | 0 < e < 1 | Between ordinary objects |
| Perfectly inelastic | Max. loss of K.E. | e = 0 | During shooting |
| Super elastic | K.E. increases | e > 1 | In explosions |