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Torque and static equilibrium of a uniform metal rod: find tension, force exerted

A uniform metal rod, with a mass of 3.1 kg and a length of 1.2m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25 degrees above the horizontal. The wire is attached to the top of the rod.

(a) Find the tension in the wire.
(b) Find horizontal and vertical components of the force exerted on the rod by the hinge

Solution Preview

See attached file.

Because the weight of the rod will act at its center and it's vertical line of action will cut the horizontal wire at i's center.
hence, for equilibrium three ...

Solution Summary

With good explanations and calculations, the problem is solved.