Collinear Impact of Spheres

Consider a collinear collision of two rigid, frictionless, and nonrotating spheres, as shown in Fig. 2.1. Neither sphere has a tangential momentum component in this system. Therefore, conservation of the normal momentum component of the two-ball system yields 

The rebounding velocities of the colliding spheres can be expressed in terms of the coefficient of restitution as 

Therefore, the loss of the kinetic energy of the system is given by 

It is clear that e = 1 for the normal impact of perfect elastic spheres, while e = 0 for the normal impact of perfect plastic spheres. 

Equation (2.3) also provides a basis for the experimental determination of the coefficient of restitution. Consider the case where a ball at rest is dropped from a height h to a horizontal stationary massive rigid surface, rebounding back to a height of h . If we label the ball with the subscript 1 and the massive plane with 2, Eq. (2.3) can be rearranged to 

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