📂Physics

Collision of Two Objects and the Coefficient of Restitution

Explanation

When two objects collide, there are three types of collisions.

1. Perfectly elastic collision (Elastic collision)
2. Inelastic collision
3. Perfectly inelastic collision

The classification is based on the coefficient of restitution $e$.

The coefficient of restitution is the ratio of the relative speed of the two objects before collision to the relative speed after collision. In other words, it’s defined as the ratio of the speed at which the two objects come together to the speed at which they move apart.

$$ e= \dfrac{ {v_2}^{\prime} - {v_{1}}^{\prime}} {v_{1} - v_2} = - \dfrac{ {v_{1}}^{\prime}- {v_2}^{\prime} } {v_{1} - v_2 } $$

The coefficient of restitution generally ranges from $0$ to $1$.

$$ 0 \le e \le 1 $$

Based on the coefficient of restitution, the collision of two objects can be further classified as follows.

1. Perfectly elastic collision (Elastic collision, when $e=1$)
2. Inelastic collision (when $0 \lt e \lt 1$)
3. Perfectly inelastic collision (when $e=0$)

There are two important features in a perfectly elastic collision, which are as follows.

• The kinetic energy is conserved before and after the collision.
• If the masses of the two colliding objects are equal, their velocities exchange after the collision.