PARTICLE IMPINGING ON A FIXED SURFACE 241 



notice that resilience depends on the nature of the contact between 

 two bodies, being in this respect similar to the coefficient of fric- 

 tion. The resilience does not arise partly from one body and partly 

 from the other, for if it did the value of e for iron impinging on 

 lead would be intermediate between the values for iron on iron 

 and for lead on lead. 



As examples of bodies for which the coefficient of elasticity is 

 large, it is found that the value of e for the impact of two ivory 

 billiard balls is about .81, while for glass impinging on glass it is 

 .94. The most perfect elasticity conceivable is that of two bodies 

 for which e = 1, in which case the impulse of restitution is equal 

 to the impulse of compression. The bodies in this case are spoken 

 of as perfectly elastic. The peculiarity of perfectly elastic bodies is 

 that no energy is lost on impact. It is clear that the value of e can- 

 not exceed unity, for if the value of e were greater than unity, the 

 kinetic energy set up by the impulse of restitution would be greater 

 than that absorbed by the impulse of compression, so that the total 

 energy would be increased. 



We shall now apply these principles to some important cases 

 of impact. 



PARTICLE IMPINGING ON A FIXED SURFACE 

 Direct Impact 



198. Suppose first that the impact is direct i.e. that, at the 

 instant of collision, the particle is moving along the normal to the 

 surface at the point at which it strikes. Let m be its mass, and v 

 its velocity before impact. At the moment of greatest compression, 

 the particle will be at rest relatively to the plane, so that its 

 momentum is reduced by the impulse of compression from mv 

 to 0. Thus we must have 



/= mv. 



If e is the coefficient of elasticity, 



/' = e I = emv. 



