LVI.<i>Theory of collision of spheres of soft metals</i>

Abstract

Abstract Beginning with the fact that when two spheres of soft metal collide, permanent deformation is produced when the velocity of approach exceeds a definite critical value ; and with the aid of the assumption that over the permanently deformed region the pressure remains constant at all points, a theory of collision is worked out. This theory is found capable of accounting for the variation with the velocity of approach v, of 1. (a) The duration of contact t of the spheres,2. (b) the diameters d of the permanent deformations, and3. (c) the coefficient of restitution e. The detailed character of the experimental results is explained. At high speeds of approach, the duration of contact and the quantity e 2 v 2 are linear functions of 1/v and of v respectively; while it appears that a definite quantity of energy is required per unit mass of the material apparently removed during deformation. A latent heat of deformation for a number of substances is calculated. Finally, the influence of viscous resistance and of time-effects, such as the elastic after-effect etc., is considered.