CHAPTER II. 



WORK AND ENERGY. 



55. 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 resolved 

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

 geometrical product of the force and the displacement ( 7), is called 

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

 components of the force F are X, F, Z, and those of the displace- 

 ment s are s x , s yt s z , the work W is 



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



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

 dimensions, 



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 



(2) 



ds ds ds 



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

 line integral 



f*\ 



(3) 



