IMPACT OF TWO MOVING BODIES 245 



From the first line u = V H > 



m 



i-V- 



m' 



so that uu'=I( 1 -\> 



\m m'/ 



an equation connecting / with the relative velocity before collision. 

 Similarly, from equations (86), 



The experimental relation I' = el is now seen to be exactly 

 equivalent to the relation 



v v r = e(u u r ), (87) 



or, in words : The normal component of relative velocity of the 

 centers of gravity after collision is equal to e times the relative 

 velocity before collision, and is in the opposite direction. 



This law is known as Newton's experimental law ; it expresses 

 the same property of matter as the relation /' = el. 



A second relation, connecting velocities before impact with 

 velocities after, is given by the conservation of momentum; we 



nave mv + m'v' = mu + m'u'. 



Combining this with equation (87), we can determine the 

 velocities v, v r after collision in terms of the velocities u, u f 

 before collision. 



Solving, we find that 



mu + raV em'(u u r ) oox 



V = - r- 5 - -> (00) 



m + m' 



f _ 



ra + ra' 



giving the normal velocities. 



If the bodies are rough, we find the tangential velocities in 

 the same way as in 200 ; while if the bodies are smooth, the 

 velocities in directions perpendicular to CP remain unaltered. 



