# Elastic collision

From Mech

## Definition

A collision between two bodies is termed an **elastic collision** or **perfectly elastic collision** if it satisfies the following equivalent conditions:

- The total kinetic energy of the bodies after the collision equals the total kinetic enery of the bodies before the collision.
- The coefficient of restitution of the collision is , i.e., the velocity difference between the bodies after collision is equal in magnitude and opposite in sign to the velocity difference before the collision (this is the definition for head-on collisions; for oblique collisions, we consider the components of velocity in the normal direction).

Elastic collisions are an ideal approximation that may not occur in practice, hence the term *perfectly elastic* is sometimes used to describe such collisions.

## Related notions

- Coefficient of restitution: Usually denoted or , this number, which typically varies between and , measures the
*bounciness*of a collision. An elastic collision has coefficient of restitution equal to , and a perfectly inelastic collision has a coefficient of restitution equal to . - Perfectly inelastic collision: A collision after which the two bodies stick to each other, i.e., their relative position remains the same as their relative position at the time of the collision.