56 THE HUMAN MOTOR 



Impact deforms bodies at the point of contact and this defor- 

 mation can be permanent as in the contact of two plastic bodies 

 such as two balls of lead. In this case, a diminution of energy 

 is produced, because after the shock : 



MV 2 , mv* (M + m) u* 



-g- + -3-; is changed to ^ -^ ; the 



difference, or the loss of energy, being : 



(MV 2 + tnv 2 (M + m) u z ). 

 Replace u by the above value. The loss of energy 



This is equal to the energy of a mass -^ moving with a 



speed equal to the difference of the speeds of the two bodies 

 prior to the impact. If the two bodies are of the same mass, 

 M = m ; then the loss of energy 



or 



If one of the bodies is at rest, i.e., v = O ; then the loss will be : 

 J MV 2 , and the moving body will lose half its energy. It was 

 a propos of " live " force thus transformed into vibratory energy, 

 and then into heat, that Leibnitz made the comparison of 

 sovereigns which could be changed into silver ( 32). 



Consider two bodies, which, after the deformation due to 

 impact, return to their initial form, owing to their elasticity. 

 For example, two ivory balls. At the moment of contact the mass 

 M loses a speed V u, and the elasticity of m causes it to lose 

 the same, in all, 2V - - 2, which reduces V to the final value : 



V, = V (2V 2) = 2u V. 



The mass m had gained (u v), and by the reaction caused by 

 its elasticity it will gain as much again, that is, in all 2 V 2u, 

 its final speed being therefore : 



(2 u 2 v) -f v, or v l = 2 u v. 



And the two elastic bodies will part, the reaction being of as 

 short duration as the action. 



Replace u by its value, as before, the speeds V and v l are 

 obtained as functions of V, v, M and m, and it will be seen that 



\ MV* + i mv* = MV 2 + J m*, 



