Solved: A horizontal boom is supported at its left end by

Chapter 11, Problem 11.84

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A horizontal boom is supported at its left end by a frictionless pivot. It is held in place by a cable attached to the righthand end of the boom. A chain and crate of total weight w hang from somewhere along the boom. The booms weight cannot be ignored and the boom may or may not be uniform. (a) Show that the tension in the cable is the same whether the cable makes an angle or an angle with the horizontal, and that the horizontal force component exerted on the boom by the pivot has equal magnitude but opposite direction for the two angles. (b) Show that the cable cannot be horizontal. (c) Show that the tension in the cable is a minimum when the cable is vertical, pulling upward on the right end of the boom. (d) Show that when the cable is vertical, the force exerted by the pivot on the boom is vertical.