146 WORK 



pounds. Thus we may say that the work done in moving a body 

 through any distance against a uniform force is the product of the 

 distance and the force. 



Suppose, for instance, that it is found that the force required to drag a 

 railway train along a level track is equal to the weight of 10,000 pounds, 

 then the work done in hauling this train a distance of 100 miles 



= 100 x 5280 x 10,000 foot pounds. 



110. Rate of performing work. Work frequently has to be done 

 within a given time, so that it is often necessary to measure the 

 rate at which work is being done. The rate of doing work in 

 which 33,000 foot pounds are done per minute is called one horse 

 power (I H. P.). 



This unit was introduced by Watt, and was supposed to measure the 

 rate of working of an ordinary horse. It is found, however, that very few 

 horses are capable of working continuously at one horse power for any 

 length of time. 



As an example of the calculation of horse pow r er, let us find the horse 

 power required of an engine to haul a train at 30 miles an hour, the fric- 

 tional resistance being equal to the weight of 10,000 pounds. A velocity 

 of 30 miles an hour = 44 feet per second, so that the work done per second 

 = 44 x 10,000 foot pounds. Since one horse power = 550 foot pounds per 

 second, we see that the horse power required 



44 x 10,000 



550 



= 800 horse power. 



This gives the horse power required to haul the train at a steady speed 

 of 30 miles per hour. We shall find that if the speed is not constant the 

 horse power will be different, part of the work being used up in producing 

 the acceleration of the motion. For the present, however, we confine our 

 attention to motion with uniform velocity. 



ABSOLUTE UNIT OF WORK 



111. We have already seen that besides the practical unit of 

 force, which is the weight of a unit mass, there is also a second 

 unit of force, known as the absolute unit, which is denned as being 

 a force capable of producing unit acceleration in unit mass. As 

 the practical unit produces acceleration g in unit mass, where g is 



