POR is a rigid equilateral triangular frame of side length .L.. Forces F_(p) F_(2) and F_(3) are acting along PQ, QR and PR. Find the relation between the forces if system is in equilibrium.

POR is a rigid equilateral triangular frame of side length .L.. Forces

1.	POR is a rigid equilateral triangular frame of side length .L.. Forces F_(p) F_(2) and F_(3) are acting along PQ, QR and PR. Find the relation between the forces if system is in equilibrium.
Answer» Solution :If the system is in rotational equilibrium find the relation between the FORCES, Perpendicular distance of any force shown in the figure from centroid .C. of triangle is `L//2SQRT3`. The forces `F_(1)` and `F_(2)` PRODUCE anti-clockwise turning effect where as `F_(3)` clockwise turning effect about .C.. Since the system is in rotational equilibrium the total TORQUE acting on the system about the centroid is zero. `:.F_(1)xx(L)/(2sqrt3)+F_(2)xx(L)/(2sqrt3)+F_(2)xx(L)/(2sqrt3)-F_(3)xx(L)/(2sqrt3)=0` Hence `F_(1)+F_(2)-F_(3)=0` `:.F_(3)+F_(1)-F_(2)`.