Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN: 9780078807213
Author: Paul W. Zitzewitz
Publisher: Glencoe/McGraw-Hill
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Question
Chapter 8, Problem 76A
To determine
The force exerted by the two personson the board.
Expert Solution & Answer
Answer to Problem 76A
The force exerted by the person, near the box, on the board is 62.8 N and the force exerted by the other person on the board is 37.65 N .
Explanation of Solution
Given:
The mass of the wooden board is m=4.25 kg .
The length of the wooden board is 1.75 m .
The mass of the box is m=6.00 kg .
Formula used:
The torque is the product of the lever arm and the applied force.
The expression for the torque as follows:
τ=Frsinθ
Here, F is the applied force, r is the radius of the wheel, and θ is the angle made by anobject with the vertical.
Calculation:
Consider the force exerted by the person A on the board is FA .
Consider the force exerted by the person B,near the box, on the board is FB .
Consider the force due to the weight of the box is denoted by Fg .
Consider the force due to the centre of gravity is denoted by Fcog .
Consider a crank is connected to a chained wheel.
The forces acting on the board are shown in the Figure below.
For the equilibrium of the forces acting on the board,
FA+FB−Fg−Fcog=0FA+FB=Fg+FcogFA+FB=(mboardg)+(mboxg)FA+FB=(mboard+mbox)gFA+FB=(4.25 kg+6.00 kg)×9.80 m/s2FA+FB=100.45 kg⋅m/s2×(1 N1 kg⋅m/s2)FA+FB=100.45 N
Consider the torque exerted on the board due to the forces FA,FB,Fg,Fcog are denoted by
τA,τB,τg,τcog .
For Equilibrium of the torque acting on the board,
τA+τB=τg+τcog0+τB=τg+τcogτB=τg+τcogFBrB=[Fgrg]+[Fcogrcog]FB(1.25 m+0.50 m)=[41.65 N×1.25 m]+[41.65 N×1.25 m]FB(1.75 m)=[36.44 N⋅m]+[73.5 N⋅m]FB=(109.94 N⋅m1.75 m)FB=62.8 N
The force exerted by the person A on the board is
FA+FB=100.45 NFA+62.8 N=100.45 NFA=37.65 N
Conclusion:
Therefore, the force exerted by the person, near the box, on the board is 62.8 N and the force exerted by the other person on the board is 37.65 N .
Chapter 8 Solutions
Glencoe Physics: Principles and Problems, Student Edition
Ch. 8.1 - Prob. 1PPCh. 8.1 - Prob. 2PPCh. 8.1 - Prob. 3PPCh. 8.1 - Prob. 4PPCh. 8.1 - Prob. 5PPCh. 8.1 - Prob. 6SSCCh. 8.1 - Prob. 7SSCCh. 8.1 - Prob. 8SSCCh. 8.1 - Prob. 9SSCCh. 8.1 - Prob. 10SSC
Ch. 8.2 - Prob. 11PPCh. 8.2 - Prob. 12PPCh. 8.2 - Prob. 13PPCh. 8.2 - Prob. 14PPCh. 8.2 - Prob. 15PPCh. 8.2 - Prob. 16PPCh. 8.2 - Prob. 17PPCh. 8.2 - Prob. 18PPCh. 8.2 - Prob. 19PPCh. 8.2 - Prob. 20PPCh. 8.2 - Prob. 21PPCh. 8.2 - Prob. 22PPCh. 8.2 - Prob. 23PPCh. 8.2 - Prob. 24PPCh. 8.2 - Prob. 25PPCh. 8.2 - Prob. 26PPCh. 8.2 - Prob. 27PPCh. 8.2 - Prob. 28PPCh. 8.2 - Prob. 29PPCh. 8.2 - Prob. 30PPCh. 8.2 - Prob. 31SSCCh. 8.2 - Prob. 32SSCCh. 8.2 - Prob. 33SSCCh. 8.2 - Prob. 34SSCCh. 8.2 - Prob. 35SSCCh. 8.2 - Prob. 36SSCCh. 8.2 - Prob. 37SSCCh. 8.3 - Prob. 38PPCh. 8.3 - Prob. 39PPCh. 8.3 - Prob. 40PPCh. 8.3 - Prob. 41PPCh. 8.3 - Prob. 42SSCCh. 8.3 - Prob. 43SSCCh. 8.3 - Prob. 44SSCCh. 8.3 - Prob. 45SSCCh. 8.3 - Prob. 46SSCCh. 8.3 - Prob. 47SSCCh. 8.3 - Prob. 48SSCCh. 8 - Prob. 49ACh. 8 - Prob. 50ACh. 8 - Prob. 51ACh. 8 - Prob. 52ACh. 8 - Prob. 53ACh. 8 - Prob. 54ACh. 8 - Prob. 55ACh. 8 - Prob. 56ACh. 8 - Prob. 57ACh. 8 - Prob. 58ACh. 8 - Prob. 59ACh. 8 - Prob. 60ACh. 8 - Prob. 61ACh. 8 - Prob. 62ACh. 8 - Prob. 63ACh. 8 - Prob. 64ACh. 8 - Prob. 65ACh. 8 - Prob. 66ACh. 8 - Prob. 67ACh. 8 - Prob. 68ACh. 8 - Prob. 69ACh. 8 - Prob. 70ACh. 8 - Prob. 71ACh. 8 - Prob. 72ACh. 8 - Prob. 73ACh. 8 - Prob. 74ACh. 8 - Prob. 75ACh. 8 - Prob. 76ACh. 8 - Prob. 77ACh. 8 - Prob. 78ACh. 8 - Prob. 79ACh. 8 - Prob. 80ACh. 8 - Prob. 81ACh. 8 - Prob. 82ACh. 8 - Prob. 83ACh. 8 - Prob. 84ACh. 8 - Prob. 85ACh. 8 - Prob. 86ACh. 8 - Prob. 87ACh. 8 - Prob. 88ACh. 8 - Prob. 89ACh. 8 - Prob. 90ACh. 8 - Prob. 91ACh. 8 - Prob. 92ACh. 8 - Prob. 93ACh. 8 - Prob. 94ACh. 8 - Prob. 95ACh. 8 - Prob. 96ACh. 8 - Prob. 97ACh. 8 - Prob. 98ACh. 8 - Prob. 99ACh. 8 - Prob. 100ACh. 8 - Prob. 101ACh. 8 - Prob. 102ACh. 8 - Prob. 103ACh. 8 - Prob. 104ACh. 8 - Prob. 105ACh. 8 - Prob. 106ACh. 8 - Prob. 107ACh. 8 - Prob. 108ACh. 8 - Prob. 109ACh. 8 - Prob. 110ACh. 8 - Prob. 1STPCh. 8 - Prob. 2STPCh. 8 - Prob. 3STPCh. 8 - Prob. 4STPCh. 8 - Prob. 5STPCh. 8 - Prob. 6STPCh. 8 - Prob. 7STP
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