The forces applied to corners B and D of a rectangular piece of wood have the sa

Question

The forces applied to corners B and D of a rectangular piece of wood have the same magnitude of 15 N and are directed parallel to the long and short sides 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 at its 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 that the piece of wood is at equilibrium. Find the magnitude and direction of the force applied to corner A.

Explanation / Answer

ou need to specify the direction of the 18N forces NOT just which sides they are parallel to. OK...... Let length AD equal 2L and CD equal L The force B->D gives clockwise moment = 18*L about the centre. The force B->C gives anti-clockwise moment = 18*L/2 about the centre. The sum of these is 18*L/2 clockwise about the centre i.e. 9*L. To balance this moment, a force A->B of 9 N is required. This will provide the balancing moment 9*L anti-clockwise about the centre.

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