2 forces are acting on two different corners of a block that are diagonally oppo

Question

2 forces are acting on two different corners of a block that are diagonally opposite of each other (corners B and D). F1 is 12N and is directed parallel to the horizontal axis of the block. F2 is 12N and is directed parallel to the vertical axis of the block. The axis is in the center of the block. The length of the block is twice as long as the width. Find the magnitude and direction of the F3 that would have to be exerted on corner A in order to cancel out F1 and F2, and bring bring the block to equilibrium.

Explanation / Answer

Let L be the length of the short side of the rectangle, so that the length of the long side is 2L. Remembering that counterclockwise torques are positive and that the torque at corner A is counterclockwise, we can write the zero net torque as follows:

               = FA lA + FB*lB - FD*lD = 0

                    FA(L) + (12N)(L/2) - 12(L) = 0

                     FA = 12 - 6 = 6N (pointing toward point B)

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