Question

The drawing shows a rectangular piece of wood. The forces applied to corners B and D have the same magnitude of 18 N and are directed parallel to the long and shortsides of the rectangle. The long side of the rectangle is twice as long as the short side. An axis of rotation is shown perpendicular to the plane of the rectangle atits center. A third force (not shown in the drawing) is applied to corner A, directed along the short side of the rectangle (either toward B or away from B), such thatthe piece of wood is at equilibrium. Find the magnitude and direction of the force applied to corner A.

Answer 1

Let L be the length of the short side of the rectangle, so that the length of the long side is 2L. The counterclockwise torques arepositive and that the torque at corner A is counterclockwise,

when the system is under equilibrium the net torque is zero

so Στ = FAlA + FBlB - FDlD = 0

then FAlA = FDlD - FBlB

FA = F(L - L/2) /L

= 18/2 = 9.0 N

which is pointing towards the corner B