Question

A uniform beam of weight 520 N and length 3.4 m is suspended horizontally. On the left it is hinged to a wall; on the right is it supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N.

What value of D corresponds to that tension?

Answer 1

Set the cable tension T equal to 1200 N, the breaking point. Then solve for the value of D that makes the total moment about the hinge equal to zero. The moment due to the weight of the beam acts trhough the center, 1.7 m from the wall. The vertical component of the cable force is T sin A, where A = arctan D/3.4

Use the moment balance to solve for the angle A and then solve for D = 3.4 tan A