### What is the Coefficient of Restitution?

Posted:

**Thu Aug 13, 2009 3:13 pm**Q: What is the Coefficient of Restitution?

A: In a central collision (i.e., where the collision force acts directly through the centers of mass of the colliding bodies), the speed at which the centers of mass are moving toward each other at the instant of initial contact is called the

Subsequent to the initial contact, the centers of mass of the colliding bodies continue to approach each other, as deformations occur at the contact regions, until the relative motion has been stopped by the deceleration-acceleration action of the collision force between the two bodies. Thus, the speed of approach is reduced to zero during the collision.

If the collision force does not immediately vanish at the end of the approach period, the continued deceleration-acceleration of the collision partners will produce a

In the extreme case of a perfectly elastic recovery of the deformed contact regions, a separation speed equal and opposite to the approach speed will be produced.

At the other extreme, the case of a perfectly inelastic, or “plastic” behavior of the deformed contact regions, no separation speed will be generated and the colliding bodies will remain in contact until acted upon by external forces (i.e., forces external to the two-body system, such as tire-terrain forces in the case of an automobile collision).

The ratio of the speed of separation to the speed of approach is referred to as the

A: In a central collision (i.e., where the collision force acts directly through the centers of mass of the colliding bodies), the speed at which the centers of mass are moving toward each other at the instant of initial contact is called the

*speed of approach*.Subsequent to the initial contact, the centers of mass of the colliding bodies continue to approach each other, as deformations occur at the contact regions, until the relative motion has been stopped by the deceleration-acceleration action of the collision force between the two bodies. Thus, the speed of approach is reduced to zero during the collision.

If the collision force does not immediately vanish at the end of the approach period, the continued deceleration-acceleration of the collision partners will produce a

*separation speed*.In the extreme case of a perfectly elastic recovery of the deformed contact regions, a separation speed equal and opposite to the approach speed will be produced.

At the other extreme, the case of a perfectly inelastic, or “plastic” behavior of the deformed contact regions, no separation speed will be generated and the colliding bodies will remain in contact until acted upon by external forces (i.e., forces external to the two-body system, such as tire-terrain forces in the case of an automobile collision).

The ratio of the speed of separation to the speed of approach is referred to as the

**coefficient of restitution**.