Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 8, Problem 107P

(a)

To determine

The maximum distance to the right hand edge of plank that the painter can walk before the tipping of plank.

(a)

Expert Solution
Check Mark

Answer to Problem 107P

The painter can move up to 0.96mfrom the right hand edge.

Explanation of Solution

Mass of painter is 61kg, length of uniform plank is 6.00m, mass of plank is 20.0kg, distance to sawhorse from an end of plank is 1.40m, mass of paint bucket is 4.0kg, and the diameter of bucket is 0.28m.

The axis of rotation is passing through the meeting point of plank with right sawhorse.

Write the equation for rotational equilibrium.

m3gd3m1gd1m2gd2=0

Here, m1 is the mass of painter, m2 is the mass of paint can , m3 is the mass of plank, g is the gravitational acceleration, d1 is the moment arm of weight due to painter, d2 is the moment arm of weight due to can, and d3 is the moment arm of weight due to plank.

Rewrite the above equation in terms of d1.

d1=m3d3m2d2m1 (I)

Write the equation to find the distance to painter from the right-hand edge.

d=1.40md1 (II)

Here, d is the distance to painter from the right-hand edge.

Conclusion:

Substitute 20.0kg for m3, (3.00m1.40m) for d3, 4.0kg for m2, (1.40m0.14m) for d2, and 61kg for m1 in equation (I) to find d1.

d1=((20.0kg)(3.00m1.40m))((4.0kg)(1.40m0.14m))61kg=26.96kgm61kg=0.44m

Substitute 0.44m for d1 in equation (II) to find d.

d=1.40m0.44m=0.96m

Therefore, the painter can move up to 0.96mfrom the right hand edge.

(b)

To determine

The maximum distance to the left hand edge of plank that the painter can walk before the tipping of plank.

(b)

Expert Solution
Check Mark

Answer to Problem 107P

The painter can move up to 0.58mfrom the left hand edge.

Explanation of Solution

Mass of painter is 61kg, length of uniform plank is 6.00m, mass of plank is 20.0kg, distance to sawhorse from an end of plank is 1.40m, mass of paint bucket is 4.0kg, and the diameter of bucket is 0.28m.

The axis of rotation is passing through the meeting point of plank with left sawhorse.

Write the equation for rotational equilibrium.

m1gd1m2gd2m3gd3=0

Rewrite the above equation in terms of d1.

d1=m2d2+m3d3m1 (III)

Write the equation to find the distance to painter from the right-hand edge.

dleft=1.40md1 (IV)

Here, dleft is the distance to painter from the left-hand edge.

Conclusion:

Substitute 20.0kg for m3, (3.00m1.40m) for d3, 4.0kg for m2, (1.40m0.14m) for d2, and 61kg for m1 in equation (III) to find d1.

d1=((4.0kg)(1.40m0.14m)+((20.0kg)(3.00m1.40m)))61kg=50.02kgm61kg=0.82m

Substitute 0.44m for d1 in equation (IV) to find d.

dleft=1.40m0.82m=0.58m

Therefore, the painter can move up to 0.58mfrom the left hand edge.

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Chapter 8 Solutions

Physics

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