KINETIC ENEBGY 169 



The work done by the particle in moving the distance ds in 

 opposition to the force P is 



Pds = m ds, 



or, since is the same as the velocity v of the particle, 

 at 



Pds = mv dv. 



Integrating, we find that the whole work done by the particle 

 before being reduced to rest is 



(36) 



Since P has to be measured in absolute units (cf. 22), it 

 follows ( 111) that the work ^mv 2 will also be measured in 

 absolute units. 



Thus whatever the magnitude of the force opposing the motion 

 of a particle, the work performed by the particle before being 

 reduced to rest is the same, namely J- mv 2 absolute units of work. 



The quantity \mv 2 (measured in absolute units) is called the kinetic 

 energy of a moving particle. It is equal to the amount of work which 

 can be performed by the particle before being reduced to rest. 



Suppose, for instance, that the resistance offered by a nail to being 

 driven into a board is equal to the weight of 5000 pounds, i.e. that it would 

 require a weight of 5000 pounds to press it into the board. Suppose that 

 it is driven into the board by being struck with a hammer, of which the 

 head weighs 10 pounds, and hits the nail with a velocity of 50 feet per 

 second. Let s be the distance the nail is driven in at each stroke measured 

 in feet, then the work done by the hammer at each stroke is that of moving 

 a force of 5000 pounds weight or 5000 x g poundals through a distance 

 of s feet. It is therefore equal to 5000 gs foot poundals. The kinetic energy 

 of the hammer in striking the nail is 



mv 2 = I 10 50 2 = 12,500 



in absolute foot-pound-second units. Thus from the relation (36) we have 



the equation 



5000 gs = 12,500, 



in which, since the units are foot-pound-second units, we may take g = 32, 



and so obtain 



s = JU. feet = 44 inches. 



