56 HI. GENERAL PRINCIPLES. WORK AND ENERGY. 



CHAPTER HI, 



GENERAL PRINCIPLES. WORK AND ENERGY. 



24. Work. If a point be displaced in a straight line, under 

 the action of a force which is constant in magnitude and direction, 

 the product of the length of the displacement and the component 

 of the force in the direction of the displacement, that is, the geometric 

 product of the force and the displacement 4, 10), is called the work 

 done by the force in producing the displacement. If the components 

 of the force F are X, Y, Z, and those of the displacement s are 

 s x > s^ s z , the work W is 



1) W=sFcos (Fs*) = Xs x + Ys y + Zs z . 



It is at once evident that if a force is resolved into components, the 

 sum of the works of the components is equal to the work of the 

 resultant, for if 



W 2 = X 2 s x + Y 2 s y + Zts g , 



Since work is denned as force x distance, we have for its dimensions, 

 [Work] = [L] [^j = [ML 2 T~*]. 



The C. G. S. unit of work is the work done when a force of 

 one dyne produces a displacement of one centimeter in its own 

 direction. This unit is called the erg = gm cm 2 sec~ 2 . 



If the displacement be not in a straight line, and the force be 

 not constant, the work done in an infinitesimal displacement ds is 



and the work done in a displacement along any path AS is the 

 line integral 



3 ) ^' 



The components of the force are supposed to be given as func- 

 tions of s and the derivatives -f-> -A -. *- are known as functions of s 



as as as 



from the equations of the path. 



