# Coefficient of Restitution – definition, formula, numerical

In this post, we will cover the definition and formula of the **coefficient of restitution**. We will also see how types of collision can be determined from the value of the **coefficient of restitution**. We will also solve a numerical problem using the formula of the **coefficient of restitution**.

## What is the **Coefficient of Restitution**? What is its formula?

For any collision between two bodies in one dimension, the **coefficient of restitution** is defined as **e = (v _{2 f} − v_{1 f}) / (v_{1i} − v_{2i})**where v

_{1i}and v

_{2i}are velocities before the collision.

And, v

_{1 f }and v

_{2 f}are velocities after the collision.

|v1i − v2i | is called the relative speed of approach and |v2 f −v1 f | is the relative speed of recession.

## Types of collision and values of Coefficient of Restitution

If Coefficient of Restitution e = 1 the collision is perfectly elastic.

• If e < 1 the collision is inelastic.

• If e = 0 the collision is perfectly inelastic (the two bodies stick together).

## Numerical problem based on Coefficient of Restitution – solved

Q1) Two blocks m1 = 2 kg and m2 = 1 kg collide head-on with each other on a frictionless surface (see Fig. 1).

If v_{1i} = −10 m/s and v_{2i} = 15 m/s and the coefficient of restitution is e = 1/4, determine the final velocities of the masses just after the collision.

Solution: