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

4th Edition

ISBN: 9780134899978

Author: Knight

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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