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 (?Fig. P11.78?). The pole is pivoted about a hinge at its base, is 1.75 m tall, and weighs 55.0 N. A thin wire connects the top of the pole to a vertical wall. The nail that holds this wire to the wall will pull out if an ?outward force greater than 22.0 N acts on it. (a) What is the greatest weight W that can be supported this way without pulling out the nail? (b) What is the ?magnitude? of the force that the hinge exerts on the pole?
Solution 82P Step 1: a) In this problem, we have to find out the maximum load which we can put on this system as W. So, we can draw a diagram Consider the hinge as the reference. Then, the maximum possible outward tension, T sin = 22 N Provided, = 37° Therefore, sin 37 = 0.602 That is, 0.602 T = 22 N Or, T = 22 N / 0.602 = 36.54 N We can write, the total moment is zero That is, Rearranging, we will get, Or, maximum weight, Or maximum weight,