Restitution, Coefficient of

a quantity in impact theory that depends on the elastic properties of bodies in collision and that determines what portion of the initial relative velocity of these bodies is regained after the impact. The coefficient of restitution defines the loss of mechanical energy for colliding bodies owing to the development in them of residual deformations and heat. In the case of direct impact of a body on an immovable obstacle (plate), it is k = u/v, where v and u are the velocities of the body with respect to the plate at the beginning and end of the impact, respectively. For wooden bodies k = 1/2; for steel, ~ 5/9; for ivory, ~ 8/9; and for glass, ~ 15/16.