Explanation Given data: Refer to the Figure P8.53 in the textbook for the position of flagpole with the rope. Length of the flagpole ( L ) is 7.5 m. Mass of the flagpole ( m pole ) is 28 kg. From the figure, the angle between flagpole and the horizontal line ( θ horizontal-pole ) is 30 ° . The angle between rope and the flagpole ( θ rope-pole ) is 20 ° . Formula used: Write the expression for static equilibrium condition of the torque as follows. ∑ τ = 0 (1) Here, ∑ τ is the sum of the torques acting on any object. Write the expression for torque in terms of force and distance as follows. τ = F d (2) Here, F is the force, and d is the distance. Write the expression for force due to the weight of the object as follows. w = m g (3) Here, m is the mass of the object, and g is the acceleration due to gravity, which is 9.8 m s 2 . Explanation: Consider the flagpole has a uniform diameter. Therefore, the center of mass of the flagpole is at its center. As the length of the pole is 7.5 m, the center of mass of the pole is at 3.75 m from any end of the flagpole. The flagpole must be in equilibrium state in order to attain the pole in motionless condition. Therefore, the net torque in the system is zero. The following are torques exists in the given system. 1. The clockwise torque is due to the weight of the flagpole, and 2. The counterclockwise torques is due to the tension in the rope. Compute the sum of the torque by modifying the expression in equation (1) as follows. τ counter-clock + ( − τ clock ) = 0 (4) Here, τ counter-clock is the counterclockwise torque in the system, which is due to the tension in the rope, and τ clock is the clockwise torque in the system, which is due to the weight of the flagpole. Write the expression for counterclockwise torque in the system by using the equation (2) and given figure as follows. τ counter-clock = F rope L sin ( θ rope-pole ) (5) Here, F rope is the tension in the rope, L is the length of the flagpole, θ rope-pole is the angle between the rope and the flagpole. The tension in the rope is the force that the person required to pull on the pole to hole the pole motionless in the given position. Write the expression for clockwise torque in the system by using the equation (2) and given figure as follows. τ clock = w pole L center of mass of the pole sin ( θ w pole − pole ) (6) Here, w pole is the force due to weight of the flagpole, L center of mass of the pole is the distance between end of the flagpole to the center of mass of the flagpole, which is 3.75 m, and θ w pole − pole is the angle between direction of weight of the flagpole and the half of the flagpole. Calculation of angle θ w pole − pole : The weight of the flagpole acts in the downward direction from the center of the mass of the flagpole. Therefore, draw the perpendicular line from the center of the flagpole towards the horizontal line in vertical direction as shown in Figure 1. From Figure 1, write the expression to find the angle θ w pole − pole as follows. 30 ° + 90 ° + θ w pole − pole = 180 ° Rewrite and solve the expression as follows. θ w pole − pole = 180 ° − ( 30 ° + 90 ° ) = 60 ° Calculation of force due to weight of the flagpole: Modify the expression in equation (3) to find the force due to weight of the flagpole as follows

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Question

Chapter 8, Problem 53GP

To determine

To find: The force that the person required to pull on the rope to hold the pole motionless in the given position.

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Chapter 8, Problem 52GP

Chapter 8, Problem 55GP

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Chapter 8 Solutions

College Physics: A Strategic Approach (4th Edition)

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Ch. 8 - Take a spring and cut it in half to make two...Ch. 8 - A wire is stretched right to its breaking point by...Ch. 8 - Prob. 13CQ Ch. 8 - Prob. 14CQ Ch. 8 - Steel nails are rigid and unbending. Steel wool is...Ch. 8 - Two children hold opposite ends of a lightweight,...Ch. 8 - Prob. 19MCQ Ch. 8 - Prob. 20MCQ Ch. 8 - Prob. 21MCQ Ch. 8 - Prob. 22MCQ Ch. 8 - Prob. 23MCQ Ch. 8 - Prob. 24MCQ Ch. 8 - Prob. 25MCQ Ch. 8 - Prob. 26MCQ Ch. 8 - You have a heavy piece of equipment hanging from a...Ch. 8 - Prob. 1P Ch. 8 - Prob. 2P Ch. 8 - Prob. 3P Ch. 8 - Prob. 4P Ch. 8 - Youre carrying a 3.6-m-long, 25 kg pole to a...Ch. 8 - Prob. 6P Ch. 8 - Prob. 7P Ch. 8 - Prob. 9P Ch. 8 - Prob. 11P Ch. 8 - Prob. 13P Ch. 8 - Prob. 14P Ch. 8 - Prob. 15P Ch. 8 - The stability of a vehicle is often rated by the...Ch. 8 - Prob. 18P Ch. 8 - A car manufacturer claims that you can drive its...Ch. 8 - Prob. 20P Ch. 8 - An orthodontic spring, connected between the upper...Ch. 8 - Prob. 22P Ch. 8 - Experiments using optical tweezers measure the...Ch. 8 - Prob. 24P Ch. 8 - One end of a 10-cm-long spring is attached to the...Ch. 8 - Prob. 26P Ch. 8 - A spring has an unstretched length of 10 cm. It...Ch. 8 - A spring stretches 5.0 cm when a 0.20 kg block is...Ch. 8 - You need to make a spring scale to measure the...Ch. 8 - Prob. 30P Ch. 8 - A force stretches a wire by 1.0 mm. a. A second...Ch. 8 - Prob. 32P Ch. 8 - What hanging mass will stretch a 2.0-m-long,...Ch. 8 - An 80-cm-long, 1.0-mm-diameter steel guitar string...Ch. 8 - A mineshaft has an ore elevator hung from a single...Ch. 8 - The normal force of the ground on the foot can...Ch. 8 - A three-legged wooden bar stool made out of solid...Ch. 8 - Prob. 38P Ch. 8 - Prob. 39P Ch. 8 - Prob. 40P Ch. 8 - A glass optical fiber in a communications system...Ch. 8 - The Achilles tendon connects the muscles in your...Ch. 8 - Prob. 44P Ch. 8 - Prob. 47P Ch. 8 - Prob. 48P Ch. 8 - Prob. 49P Ch. 8 - Prob. 51GP Ch. 8 - Prob. 52GP Ch. 8 - Prob. 53GP Ch. 8 - Prob. 55GP Ch. 8 - Two identical, side-by-side springs with spring...Ch. 8 - Prob. 57GP Ch. 8 - Prob. 58GP Ch. 8 - Prob. 59GP Ch. 8 - A 25 kg child bounces on a pogo stick. The pogo...Ch. 8 - Prob. 61GP Ch. 8 - In the hammer throw, an athlete spins a heavy mass...Ch. 8 - There is a disk of cartilage between each pair of...Ch. 8 - Orb spiders make silk with a typical diameter of...Ch. 8 - Larger animals have sturdier bones than smaller...Ch. 8 - Prob. 67GP Ch. 8 - Prob. 68GP Ch. 8 - Prob. 69MSPP Ch. 8 - Prob. 70MSPP Ch. 8 - Prob. 71MSPP Ch. 8 - Prob. 72MSPP

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