Explanation Given data: Refer to the Figure P8.1 in the textbook for the standing of a student on a very light, rigid board. Given that, the student, and the board stand on a 10 kg mass board. Consider the mass of the board ( m B ) as 10 kg. Mass of the student ( m S ) is 54 kg. From the Figure, the distance between the two scales is 2.0 m and the distance between student and left scale is 1.5 m. Therefore, the distance of the student from the left scale ( d left ) is 1.5 m. The distance between the two scales ( d ) is 2.0 m. 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 weight of the object as follows. w = m g (2) Here, m is the mass of the object, and g is the acceleration due to gravity, which is 9.8 m s 2 . Write the expression for torque in terms of force and distance as follows. τ = F d (3) Here, F is the force, and d is the distance. Explanation: From the given data, the student and the board stand on a 10 kg mass. As the distance between the two scales is 2.0 m, consider the 10 kg mass board is at the center of two scales. Therefore, the distance between the left scale and the 10 kg mass board ( d left-B ) is 1.0 m. Calculation of weight of the student: Substitute 54 kg for m , and 9.8 m s 2 for g in equation (2), w S = ( 54 kg ) ( 9.8 m s 2 ) = 529.2 kg ⋅ m s 2 = 529.2 N { ∵ 1 kg ⋅ m s 2 = 1 N } Calculation of weight of the 10 kg mass board: Substitute 10 kg for m , and 9.8 m s 2 for g in equation (2), w B = ( 10 kg ) ( 9.8 m s 2 ) = 98 kg ⋅ m s 2 = 98 N Modify the expression in equation (1) by using the equation (3) to find the torques relative to the left scale as follows. − w B d left-B − w S d left + n right d = 0 (4) Here, w B is the weight of the 10 kg mass board, d left-B is the distance between left scale to the 10 kg mass board, w S is the weight of the student, d left is the distance between the left scale and the student, n right is the reading on the right scale, and d is the distance between the two scales

16th Edition

ISBN: 9781323515303

Author: Knight

Publisher: PEARSON C

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Question

Chapter 8, Problem 2P

To determine

To find: The reading on each of the scales.

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Chapter 8 Solutions

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The reading on each of the scales.

Solution Summary: The author explains how the student and the board stand on a 10 kg mass board. The distance between the two scales is 2.0 m.

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To find: The reading on each of the scales.

Chapter 8 Solutions