If a weight of 90N is suspended from the hinge, what is the new tension T of the

Question

If a weight of 90N is suspended from the hinge, what is the new tension T of the rope, in Newtons? the rope connected at the midpoints to the two ladders is the needed tension. Also I know I need to find the new force at one of the reaction points. to answer but Im not sure how

Explanation / Answer

Moment about one side 0 = 393N(2mcos37) + 294N(5m - 1.5mcos57) + 5m A A = 371.5m All forces added = 0 B = 686N - 371.5N B = 315N so alternatively force at other side is A-B = 371.5-315=56.5 so now repeating B point===> Since the rope attaches the midpoints of the ladders, the triangle it forms at the right bottom is similar with (3/2) proportions to the entire ladder triangle, and therefore is horizontal. Isolate one side of the ladder-system and take a moment about the hinge. Free body diagrams are your friend. You have the force at the reaction point and the tension in the rop as forces.

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