56 ELEMENTARY GENERAL SCIENCE CHAP. 



Momentum. The preceding paragraph has introduced the 

 student to the idea of a condition involving both motion and 

 mass. This condition is known as momentum, and is denned as 

 follows : 



The momentum of a body is the quantity of motion it has, 

 and is equal to the product of its mass and its velocity. 



Expressed as an equation we have 



Momentum = mass x velocity, 



or if momentum is represented by 3J, mass by m, and velocity 

 by v, all expressed in corresponding units, we can write 



M = mv. 



The unit of momentum is consequently that of a unit of mass 

 moving with a unit of velocity, or if the unit mass be that of the 

 imperial standard pound, the unit of momentum is the 

 quantity of motion in a mass of one pound moving with a 

 velocity of one foot per second. The meaning of momentum 

 will be better grasped after a concrete example. 



Suppose a shot fired from a cannon, the momentum generated 

 in both the cannon and the shot will be the same ; but since the 

 mass of the cannon is immensely greater than that of the shot, it 

 will be evident that the velocity of the shot must be corre- 

 spondingly greater than that of the cannon in order that the 

 product of the two quantities may be the same. This we know 

 is the case, the velocity of the "kick " or "recoil " of the cannon 

 is very much less than the velocity with which the shot is sent on 

 its journey. 



The motions of the shot and of the cannon are in opposite 

 directions, and it is usual to distinguish the two directions by 

 the signs + and - . If the mass of the cannon is represented 

 by M, and the mass of the shot by m, while the velocities of the 

 two are v and F respectively, then the momentum after the 

 explosion is expressed by the equation 



Mv tnV. 



EXAMPLE. A cannon weighing 10 tons fires a shot weighing 

 28 Ibs. The shot leaves the gun with a velocity of 200 feet 

 per second. With what velocity would the cannon recoil if it 

 were free to move ? 



