Glencoe Physics: Principles and Problems, Student Edition
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN: 9780078807213
Author: Paul W. Zitzewitz
Publisher: Glencoe/McGraw-Hill
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Chapter 8, Problem 76A
To determine

The force exerted by the two personson the board.

Expert Solution & Answer
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Answer to Problem 76A

The force exerted by the person, near the box, on the board is 62.8N and the force exerted by the other person on the board is 37.65N .

Explanation of Solution

Given:

The mass of the wooden board is m=4.25kg .

The length of the wooden board is 1.75m .

The mass of the box is m=6.00kg .

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.

  Glencoe Physics: Principles and Problems, Student Edition, Chapter 8, Problem 76A

For the equilibrium of the forces acting on the board,

  FA+FBFgFcog=0FA+FB=Fg+FcogFA+FB=(mboardg)+(mboxg)FA+FB=(mboard+mbox)gFA+FB=(4.25kg+6.00kg)×9.80m/s2FA+FB=100.45kgm/s2×(1N1kgm/s2)FA+FB=100.45N

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(1.25m+0.50m)=[41.65N×1.25m]+[41.65N×1.25m]FB(1.75m)=[36.44Nm]+[73.5Nm]FB=(109.94Nm1.75m)FB=62.8N

The force exerted by the person A on the board is

  FA+FB=100.45NFA+62.8N=100.45NFA=37.65N

Conclusion:

Therefore, the force exerted by the person, near the box, on the board is 62.8N and the force exerted by the other person on the board is 37.65N .

Chapter 8 Solutions

Glencoe Physics: Principles and Problems, Student Edition

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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