GENERAL PRINCIPLES 



57 



in other words, in the impact of perfectly elastic bodies, the sum 

 of the energies is conserved, being the same after as before the 

 impact, In practice, the restored energy is less than the original 



energy, and there is often a very slight 

 dissipation into heat, a dissipation 

 which increases if the bodies are good 

 conductors of heat and if the impart 

 is of relatively long duration. 



ft..*.... 



r 



o 



B 



41. In impact the forces are of such 

 a brief duration that they have been 

 wrongly called instantaneous forces 

 which would presume infinitely hard 

 bodies. Hertz has shown that with 

 spheres of the same radius the duration 

 of the impact depends on the relative 

 speed and the elastic properties of the 

 substances. Between two cylinders of 

 steel Hamburger obtained an average 



duration of 



TOOOO 



of a second, and 



FIG. 72. 



Hopkinson obtained the same result. 



Mention must be made of the part played by the axis of 

 gravity (20) a? an axis of rotation of a body subjected to impact. 

 If I K is the moment of inertia of a body round its axis of gravity 

 OZ (fig. 72) , the moment in relation to a parallel axis AB will be 

 I g + M/' 2 , M being the mass of the body, and /', the distance 

 between the two axes. As I = Mp 2 , therefore : 



I = 



and finally, 



- M P ' 2 -j-M/' 2 , 



== M 



If the axis of rotation coincides with the axis of gravity, it is 

 clear that the moment of inertia will be the minimum. 



On the other hand, presuming that the body oscillates in 

 relation to the axis AB like a pendulum of a length /', then 



/ being the length of the equivalent simple pendulum. And in 

 consequence : 



Let the length CC' = I, the point C' will oscillate like a 

 simple pendulum attached to the fixed point C. The point 

 C' is the centre of percussion. And so that there may not 

 be percussion on the axis of rotation AB, that percussion. 



