168 WORK 



KINETIC ENERGY 



138. Suppose that a moving particle is acted on by a force 

 of which the direction is opposite to that of the motion of the 

 particle. The effect of the force, according to the second law of 

 motion, is to produce a retardation in the velocity of the particle. 

 The velocity of the particle decreases so long as the force acts, so 

 that if the force continues to act for a sufficient time, the particle 

 must ultimately be reduced to rest. 



Consider, for example, a hammer striking a nail. The reaction between 

 the hammer and nail^ is a force in the direction opposite to that of the 

 motion of the hammer, and this ultimately brings the hammer to rest. 

 Again, when a particle is projected vertically upwards, its weight after a 

 time reduces it to rest, after which of course it falls back to the ground. 



By the time that the moving body has been reduced to rest 

 the point of application of the force, which has moved with the 

 moving body, has moved through a certain distance. Thus a cer- 

 tain amount of work has been done by the moving body. We are 

 thus led to the conception of the motion of a body possessing a 

 capacity for doing work. 



For instance, in the previous examples, the motion of the hammer has 

 driven the nail into position, and the motion of the particle projected into 

 the air has raised it to a certain height above the earth's surface. 



139. Let us suppose that a particle moving with velocity v is 

 opposed by a force P (in absolute units) acting in the direction 

 opposite to that of the motion of the particle. Let the particle 

 describe a distance ds in opposition to this force in time dt, an( 

 let its velocity change from v to v dv in this time. The particle 



then has a retardation in the direction of its motion, or, what is 

 dt , 



the same thing, an acceleration in the direction in which 



ctt 



is acting, so that by the second law of motion 



dv 



p = m 

 dt 



