260 



MECHANICS 

 sin Mi = 





Resolution of Forces. A given force may have an innumer- 

 able number of combinations of components. The problem 

 is, however, determinate when the directions of the components 



are given. 



f Z 2 Let OC, Fig 2, repre- 

 sent in magnitude and 

 direction the force R 

 acting at O, and let it 

 be required to find its 

 components in the direc- 

 tions OXz and OXi. 

 Draw from C, lines 

 parallel to these directions meeting OXi at A and OXz at B. 

 Then, OA and OB are the required components Fi and Fi. 

 They may be determined also analytically by the formulas, 



R sin Mi 

 1 = sin (Mi+Mi) 



R sin Mi 

 2 ~sin (Mi+Mz) 

 are perpendicular to each other, then Mi 



Fi = RsinMi 

 Ft = R sin Mi 



and 



When Fi and 

 +M2 = 90 

 and 



MOMENTS OF FORCES 



The moment of a force about a point is the product obtained 

 by multiplying the magnitude of the force by the perpendicular 

 distance from the point to the line of action of the force. In 

 Pig. 3, the moment of F about the point C is Fp\ and about 

 the point Ci it is Fpi. 



The point to which a moment is referred, or about which a 

 moment is taken, is called the center of moments, or origin of 

 moments. The perpendicular p or pi from the origin of moments 



