ELASTICITY 239 



after impact it is receding. Hence at some instant during the 

 impact, its motion must have changed from one of approaching to 

 one of receding; at this instant the distance between the two 

 centers was a minimum. 



Suppose that, before the experiment, we had chalked the two 

 faces of the balls on which the collision takes place. On examin- 

 ing the balls after impact it will be found that the chalk has been 

 disturbed, not only at a single point, but all over a circle of con- 

 siderable size, perhaps of diameter half an inch for billiard balls 

 moving with a fair velocity. This shows that at the moment at 

 which the centers of the balls were closest to one another, their 

 distance was less than if they had been placed in contact and at 

 rest, the balls were compressed. 



The instant at which the two centers were nearest is called the 

 moment of greatest compression. 



In general, for any two surfaces in collision, the instant at which 

 the relative velocity along the common normal vanishes is called 

 the moment of greatest compression. Obviously this is the instant 

 at which the motion of the two surfaces changes from one of 

 approach to one of recession. 



195. By the time the moment of greatest compression is reached, 

 the velocities of both bodies will, in general, have been changed, 

 so that forces must have been at work to produce this change. The 

 whole time of action of these forces, the time from the instant at 

 which the bodies first touch to the instant of greatest compression, 

 is so small that these forces may be treated as impulsive. The 

 impulses acting on the two bodies, being action and reaction, must 

 be equal and opposite. If the surfaces are smooth, the direction of 

 these impulses will be along the common normal. If the surfaces 

 are rough, we cannot specify the direction until we know the direc- 

 tion of sliding, if any, of the surfaces over one another. In either 

 case, let us denote the component of the impulse along the com- 

 mon normal by /. The quantity / is called the impulse of com- 

 pression. Clearly it is the forces of which this impulse is composed 

 which reduce the relative normal velocity to zero. 



