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: