Solution Found!
Answer: A weight W is supported by attaching it to a
Chapter 11, 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
\(40.0 \mathrm{~cm}\) below the top and pulls horizontally on it (Fig. P11.82). The pole is pivoted about a hinge at its base, is \(1.75 \mathrm{~m}\) 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?
Equation Transcription:
°
Text Transcription:
40.0 cm
1.75 m
37.0^circ
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
\(40.0 \mathrm{~cm}\) below the top and pulls horizontally on it (Fig. P11.82). The pole is pivoted about a hinge at its base, is \(1.75 \mathrm{~m}\) 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?
Equation Transcription:
°
Text Transcription:
40.0 cm
1.75 m
37.0^circ
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 sin𝜃 = 22 N
Provided, 𝜃 = 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,