3.5.1 Resultant of Two Like Coplanar Parallel Forces –
F1 and F2 are the two similar parallelforces that result in R = F1 + F2. Therefore we apply Varignon’s principle, and the following is obtained:
Or -F1 x AO +F2 x BO =R X CO =(F1+F2) CO
Or -F1 X AO +F2 X BO =F1 X CO +F2 X CO
Or F1 X (AO+CO) = F 2 (BO-CO)
Or F1 X AC =F2 X BC
Alternatively, F1/F2 =BC/AC.
Thus the conclusion is that C is the point the resultant point where the force acts.
3.5.2 Resultant of Two Coplanar Unlike Parallel Forces
Hence we relate the principle of moments to the equation given below:
O- F l X AO – F 2 X BO = -R X CO
= -R X CO
= – (F1-F2) CO
-F1 X AO –F2 X BO = – F1 XCO +CO +F2 X CO
F1 (CO –AO)
F1 X AC =F= X BC
F1 /F2 =BC/AC .
Thus the point C which is the fixed point of force application.