Collision ofunelastic Bodies. 



Application of the Principles of Collision ofunelastic Bodi 



es 



292. The principles which we have laid down respecting the 

 collision of unelastic bodies are applicable, whether the bodies im- 

 pinge directly upon each other, as we have supposed, or whether 

 they act upon each other by means of a rod which joins their 

 centres of gravity, or whether one draws the other by a thread, 

 provided the action is immediately and perfectly transmitted to 

 the centre of gravity of each. 



If, for example, the two bodies m and n act upon each other Fig.146. 

 by means of a thread passing over a pulley P, and we would de- 

 termine the motion that they would receive in virtue of their 

 gravity, we observe that gravity tends to impress the same veloc- 

 ity upon each of the two bodies at each instant. Now as one 

 cannot move without drawing the other, the same thing will take 

 place with regard to the two bodies at each new action of gravi- 

 ty, as if the two bodies drew each other in opposite directions 

 with equal velocities ; therefore, in order to find the resulting 

 velocity, it is necessary, calling u the velocity produced by 

 gravity at each instant in a free body, to take the difference 

 mu nit of the quantities of motion, and to divide it by the 

 sum m -f- n of the masses ; we have accordingly 



mu nu m n 

 or ; u 



m -f- n m -j- n 



for the actual velocity that each new action of gravity would 

 give to the body m. We see, therefore, since m, n, and w, are 

 constant quantities, that the body m is carried with a motion uni- 

 formly accelerated, and that the force which actually accelerates 

 it, is to free gravity 



m n m n 



u : u : : : 1 : : m n : m -\- n. 



m -f- n m -{ n 



Consequently, if we call g the velocity which gravity communi- 

 cates to a free body in one second, we shall have that which it 

 would communicate in the same time to the body m, impeded by 

 the body n, by the proportion 



