MECHANICS 259 



SOLUTION. In this case, W= 62.5 X. IX 10 = 62.5 Ib. The 

 kinetic energy is therefore, 



62.5X102 6,250 



COMPOSITION AND RESOLUTION OF 

 FORCES 



The resultant of two or several forces acting on a body is the 

 single force that, if acting alone, would produce the same effect 

 as the several forces combined. The latter forces are called 

 components with respect to the resultant. 



Composition of forces is the process of finding the resultant 

 when the components are known, and the converse process of 

 finding the components when 

 the resultant is given, is called 

 resolution offerees. 



Parallelogram of Forces. If 

 two forces, as Fi and Fz, Fig. 1, 

 are represented in magnitude 



and direction by two lines, as 



OA and OB, their resultant R A p IG j 



will be represented in magni- 

 tude and direction by the diagonal OC of the parallelogram O A CB 

 which is constructed by drawing BC and AC parallel to OA 

 and OB, respectively, and joining the intersection C with O. 



The resultant R can also be determined analytically; its 

 magnitude by the formula R= ^F^+F 2 z X2FiF 2 cos L, and 

 the angles Mi and Mi that R makes with Fi and Fz, respectively, 

 may be found by the formulas, 



Fz sin L 

 sin Mi 



and sin Mi = 



R 



Fi sin L 



R 



For rectangular components, L = 90. The formulas then 

 become: 



