v MATTER IN RELATION TO MOTION 57 



Weight of cannon = 10 tons = 22, 400 Ibs. 



Velocity of recoil = v= ? 



Weight of shot = 28 Ibs. 



Velocity of shot = 200 feet per second. 



We know that 



Momentum of cannon momentum of shot 

 Or, 22,400 x v = 28 x 200 

 Therefore v = 5,600-7-22,400 



= J foot per second. 



The Conservation of Momentum. It is convenient in many 

 problems to consider momentum from another point of view, 

 namely, that of the conservation of momentum, by which is 

 meant that though momentum can be transferred from one 

 body to another, none of it is lost by the transference. For 

 instance, if a number of inelastic bodies collide with one another, 

 and then move on together, the total momentum of the moving 

 mass is equal to the sum of the momenta of the separate 

 bodies. In other words, the total momentum of several moving 

 masses remains unaltered by impact. Expressed as an equation, 

 in which M and M are different masses moving with velocities 

 y and v', while the velocity after impact is F, we have 



(M + M') V = Mv + MV. 



The use of this equation will be best illustrated by a few 

 arithmetical examples. 



EXAMPLE. Two inelastic balls, having masses of 4 Ibs. and 



7 Ibs., and moving in opposite directions with velocities of 



8 and 10 feet per second respectively, collide with one another. 

 What is the velocity of the joint mass after impact I 



As the velocities are in opposite directions, one of them must 

 be distinguished by the sign - . The equation thus becomes 



(M+M') V = Mv-M'v' 



(4 + 7) V = (4x8) -(7x10) 



11 V = 32-70 



= -38 



Therefore V -38-j-ll 



= - 3 fi feet per second 



