144 STATICS. [233, 



product of the displacement into the projection of the force on 

 the displacement ; for we have 



Fscos<t> = F-PQ = s>PR. 



The work of a force is evidently positive or negative accord- 

 ing as the angle </> is less or greater than Tr/2, provided we 

 select for < always that angle between F and s which is not 

 greater than TT. 



233. The above definition of work assumes that the force F 

 remains constant, both in magnitude and direction, while the dis- 

 placement s takes place, and that this displacement is recti- 

 linear. If either, or both, of these conditions be not fulfilled, 

 the definition can be applied only to infinitesimal displacements 

 ds. As the work done by a finite force F during such a dis- 

 placement ds is infinitesimal, we have 



and the total work done by any variable force F while its point 

 of application is displaced along any straight or curvilinear patl 

 ?, is obtained by integrating from P to Q : 



234. Since work can always be regarded as the product of 

 force into a length, its dimensions are found by multiplying 

 those of force, MLT~ 2 (Art. 64), by L ; hence, the dimensions oj 

 work are 



The unit of work is the work of a unit force (poundal, dyne) 

 through a unit distance (foot, centimetre). The unit of work ii 

 the F.P.S. system is called the f oot-poundal ; in the C.G.S. sy 

 tern, the erg. Thus, the erg is the amount of work done by 

 force of one dyne acting through a distance of one centimetre. 

 These are trie absolute units. 



