164 WOKK 



A small amount of reflection will show that a system of forces 

 is conservative if the only forces which come into play are some 

 or all of the following : 



(a) gravity; 



(b) reactions in which the contact is perfectly smooth ; 



(c) tensions of strings, extensible or inextensible. 



On the other hand, if any one or more forces of the following 

 types come into play (so that work is performed against them), 

 the system of forces is non-conservative : 



(a) reactions in which the contact is rough ; 



(b) resistance of the air. 



131. THEOKEM. The work done on a system of bodies acted on 

 by conservative forces, in moving from one configuration P to a 

 Q second configuration Q, is independent of the series of 



configurations through which the system moves in 

 passing from P to Q. 



To prove this, let us denote the work done in pass- 

 ing from P to Q through one series of configurations 

 by W l , that done in passing through any second series 

 by W z , and that done in returning from Q to P by any 

 P third series of configurations by W 3 . If we pass from 



FIG. 95 p t Q by the first series and back from Q to P by 

 the third, the total work done is nil, so that 



So, also, if we pass from P to Q by series 2 and back from Q to 

 P by series 3, 



Thus W l =W z , which proves the theorem. 



132. DEFINITION. Taking any configuration P as standard, the 

 work done in moving a system of bodies from the configuration 

 P to the configuration Q is spoken of as the potential energy of 

 configuration Q. 



