POTENTIAL ENERGY 163 



POTENTIAL ENERGY 



129. It will have been noticed that we are concerned with two 

 different kinds of work. The first is typified by the work done in 

 raising a weight in opposition to gravity, the second by the work 

 done against friction in hauling a train along a level road. The 

 essential difference between the two kinds is that work of the first 

 kind can be recovered from the system of bodies by making these 

 bodies themselves perform mechanical work, whereas work of the 

 second kind, when once expended, can never be regained. In rais- 

 ing a weight we may be said to be storing up work rather than 

 spending it, for the weight can at any time be made to yield back 

 all the work devoted to raising it. If we raise a weight w through 

 a distance h, the work done on the Weight is wh ; on letting the 

 weight descend to its original position, the work done for us by 

 the weight is wh, so that the total work performed on the weight 

 is nil. 



On the other hand, in hauling a mass a distance s against 

 a frictional force F the work performed is Fs. To bring the 

 mass back to its original position, we have to expend an addi- 

 tional amount of work Fs, so that the total work performed is 

 2 Fs. This brings out the essential difference between the two 

 types of work and between the two systems of forces against 

 which the work is performed. 



130. DEFINITION. When the forces acting on a system of bodies 

 are of such a nature that the algebraic total work done in perform- 

 ing any series of displacements which bring the system back to its 

 original configuration is nil, the system of forces is said to be a 

 conservative system. 



The algebraic work being nil, the work done on the system in taking 

 it to any configuration is equal and opposite in sign to the work done on 

 the system in allowing it to .resume its former configuration, so that all 

 the work spent can be regained. The work is accordingly stored up, or 

 conserved. 



