# Resultant of Two Coplanar Parallel Forces

RESULTANT OF TWO COPLANAR PARALLEL FORCES

3.5.1 Resultant of Two Like Coplanar Parallel Forces

F1 and F2 are two like parallel forces, their resultant R = F1 + F2. Applying Varignon’s principle, we have

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

Or                                                                    F1/F2 =BC/AC, Thus point C is located

C is the point through which the resultant acts.

3.5.2 Resultant of Two Coplanar Unlike Parallel Forces

Applying the principle of moments about we get

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)

=F2 (BO+CO)

F1 X AC =F= X BC

F1 /F2 =BC/AC . This point C which is the application point of resultant is fixed.