The coefficient of restitution (e) for a perfectly plastic impact is equal to 0.
In a perfectly plastic collision, two objects collide and move together after the impact, meaning they stick together. As a result, all of the kinetic energy is lost and transformed into other forms of energy, such as heat or deformation. The coefficient of restitution measures the bounciness of a collision; it is the ratio of the relative speed after the collision to the relative speed before the collision.
Since there is no rebounding or separation of the colliding objects in a perfectly plastic collision, the relative speed after the impact is 0, while the relative speed before the collision is a positive value. Therefore, we can express this mathematically:
e = (Relative Speed After Collision) / (Relative Speed Before Collision) = 0 / positive value = 0
In summary, the coefficient of restitution indicates how ‘bouncy’ a collision is; for perfectly plastic collisions, where objects do not bounce apart, the coefficient is zero.