A weight W is supported by attaching it to a vertical uniform metal pole by a thin cord passing over a pulley having negligible mass and friction. The cord is attached to the pole 40.0 cm below the top and pulls horizontally on it. The pole is pivoted about a hinge at it base, is 1.75 m tall, and weighs 55.0 N. A thin wire connects the top of the pole to a vertical wall at an angle of 37.0 degrees to the wall. The nail that holds this wire to the wall will pull out if an outward force greater than 22.0N acts on it.
a) What is the greatest weight W that can be supported in this way without pulling out the nail?
b) What is the magnitude of the force that the hinge exerts on the pole?