MECHANICS 91 



In Fig. 4 the forces OE, EF, etc., all point in the same 

 direction; that is, a body at O acted on by these forces in 

 succession would move from O to L. The resultant therefore 

 acts from O to L, and not from L to O. This line of reason- 

 ing will give the direction of the resultant in a force diagram. 

 In Fig. 4, the forces were taken in the order AO, BO, CO, and 

 DO. However, the magnitude and direction of the resultant 

 OL would be the same, no matter in what order the forces 

 were taken. 



RESOLUTION OF FORCES 



Since two forces can be combined to form a single resultant 

 force, a single force may also be treated as if it were the 

 resultant of two forces whose joint action on a body will be 

 the same as that of a single force. Thus, in Fig. 5, the force 

 OA may be resolved into two forces, OB' and B'A. 



It will be observed that one resultant force may have an 

 innumerable number of combinations of components. 

 Instead of OB' and B'A, 

 Fig. 5, OB" orB"A or OB'" 

 and B'"A may be taken as 

 components. It is cus- 

 tomary, however, to make 

 OB' and B'A perpendicu- 

 lar to each other, as 

 shown in the illustia- 

 tion. F 'G. 5 



Frequently, the position, magnitude, and direction of u 

 certain force are known, and it is desired to know the effect 

 of the force in some direction other than that in which it 

 acts. Thus, in Fig. 6, suppose 

 that OA represents, to some 

 scale, the magnitude, direction, 

 and line of action of a force 

 acting on a body at A, and 

 that it is desired to know what 

 effect OA produces in the 

 direction BA. From A draw a 

 line AB in the required direction; from O draw a line per- 

 pendicular to AB. Then BA is the component required. 



