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A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F 1 and the other hand holding it up at .500 m from the end of the plank with force F 2 . If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F 1 and F 2 ?

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College Physics

1st Edition
Paul Peter Urone + 1 other
Publisher: OpenStax College
ISBN: 9781938168000

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College Physics

1st Edition
Paul Peter Urone + 1 other
Publisher: OpenStax College
ISBN: 9781938168000
Chapter 9, Problem 9PE
Textbook Problem
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A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at .500 m from the end of the plank with force F2. If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F1 and F2?

To determine

The magnitudes of the forces if a person F1 and F2 carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F1  and the other hand holding it up at .500 m from the end of the plank with force F2 , the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank?

    College Physics, Chapter 9, Problem 9PE

Explanation of Solution

Given:

Mass of plank = 20kg

Length of plank = 2.00 m

Distance between F1 and F2 = 0.5 m

Formula used:

Torque is given by the formula,

  T=F×r , where F is the force and r is the perpendicular distance.

Weight, W = mg

Calculation:

For keeping the system in balance, the net torque at CG of plank must be zero.

Net torque in CG of plank

  T = F1r1−F2r2 =F1×1−F2×0.5

Equating to zero,

  F1×1−F2×0.5=0F1−0

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