( 34 ) 



CHAITKI; in. 



RESULTANT OP TWO i\ i:\lM I. FORCES. COUPLES. 



To find the magnitude and direction of the rw 

 of two parallel force* acting on a rigid body. 



Let Pand Q be the forces; A and // their points of ap- 



plication: let P and Q act in the same direction, makinir 

 angles a with AB. The effect of the forces will not be 

 altered if we apply two forces equal in magnitude and acting 

 in opposite directions along th ; line Alt. Let 



each of these forces, and suppose one to act at A and the 

 other at B. 



Then Pand S acting at A arc equivalent t<> some force P 

 acting in some direction AP' inclined to AP (Art. 17); and 

 Q and S acting at B are equivalent to some force Q acting in 

 gome direction BQ' inclined to BQ. 



Produce FA, QB to cut each other at C, and draw 

 parallel to AP, meeting A /'; suppose C rigidly cou- 



rt with AB. 



Transfer P and Q to C (Art. 11), and resolve them almi- 

 CD and a straight line parallel to J//: th- latter parts will 

 each be equal to S but act in opposite directions, and the sum 

 of the former isP-f Q. Hence M, the resultant of /' and f t t. 

 = P-f Q and acts parallel to P and Q in the straight line CD. 

 We shall now determine the point where this straight line 

 cuts AB. 



