CHAPTER VIII. 



THEORY OF WORK AND ENERGY. 



131. Work of a Force. Consider a force of magnitude P 

 applied to a particle at a point A. 



Let the particle be displaced to a point A' so that the dis- 

 placement A A and the line of action of P include an angle 6. 



The product P . A A . cos 6 is defined to be the work of the 

 force in the displacement of the particle. It is the product of the 

 magnitude of the force and the resolved part of the displacement 

 in the direction of the force, it is also the product of the magnitude 

 of the displacement and the resolved part of the force in the 

 direction of the displacement. 



Since the sum of the resolved parts in any direction of a set of 

 forces acting on a particle is the resolved part of their resultant in 

 that direction, it is clear that the sum of the works of the com- 

 ponents in any displacement is equal to the work of the resultant 

 in that displacement. 



132. Work done. When the displacement is infinitesimal, 

 the work is infinitesimal. The work of a force in any infinitesimal 

 displacement of the point at which it is localised is defined to be 

 the work done by the force in that displacement. 



Let X, Y, Z be the resolved parts of the force parallel to the 

 axes of reference, 8x, By, Sz the resolved parts of the displacement, 

 then the work done is 



XSx + YSy + ZSz. 



When the work done by a force is negative it is said to be 

 done " against " the force. 



