PQR is a rigid equilateral triangular frame of side length 'L'. Forces F_(1), F_(2) and F_(3) are acting along PQ, QR and PR. Find the relation between the forces if system is in equilibrium.

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

1.	PQR is a rigid equilateral triangular frame of side length 'L'. Forces F_(1), 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 thhe relation between the forces. Perpendicular DISTANCE of any force shown in the figure from centroid .C. of triangle is `(L)/(2sqrt(3))` 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)/(2sqrt(3))+F_(2)xx(L)/(2sqrt(3))F_(3)xx(L)/(2sqrt(3))=0` Hence `F_(1)+F_(2)-F_(3)=0` `:.F_(3)=F_(1)+F_(2)`