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A weight W is supported by attaching it to a vertical
Chapter 5, Problem 82P(choose chapter or problem)
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?
Questions & Answers
QUESTION:
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?
ANSWER:
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,