38 



THE HUMAN MOTOR 



because MB = MA cos a 

 (fig. 62). 



For a displacement / 

 the work will be : 



T =,F'/ cos a. 



Consider a curvilineal 

 displacement MM' (fig. 

 63), the fctoe having the 

 direction mm' ; the work 

 will be the same as if the 

 force had displaced the 



m 



m' 



Fio. 63. 



projection of the point M in the direction mm' from m to m'. 



Then 



T = F X mm 



Fio. 64 



Therefore the work done by a force that is constant in magni- 

 tude and direction, depend? only on the 

 initial and final position of the moving 

 body. If the force is tangential at each 

 point of the curve, the work done will be 

 T = F X MM'. 



If not, it will form an angle a with the tan- 

 gent at each point of the curve (fig. 64) ; 

 if the element of length traversed is de- 

 noted, dl, the work done is F dl cos a for such element of length. 

 The sum of the work done is the integral 



T =J Fdl cos a. 



o 



j. This general expression of work done applies equally to forces 

 of constant and variable intensity. 



If we plot the values of F cos a as ordinates and the lengths 



dl as abscissae, we obtain the 

 curve AB. The area ABO/ is the 

 value of the total work as repre- 

 sented by the above integral (fig. 

 65) Such areas as the above, 

 which are bounded by a curve, 

 can be measured by means of a 

 planimeter or by the method of 

 ** quadrature ( 218). 



It is essential to remember that 

 work does not consist of force 

 alone. If, for example, water is drawn out of a well, the effort 

 put forth is in proportion to the weight to be lifted, but that 



Fie. -05. 



