Concept explainers
(a)
The work done by the gravitational force on the statue.
Answer to Problem 43QAP
The work done by the gravitational force on the statue is
Explanation of Solution
Given:
Mass of the crate
Angle made by the inclined plane with the horizontal
Displacement of the crate along the plane
Coefficient of kinetic friction between the crate and the plane
Formula used:
Draw a free body diagram representing the forces and apply the condition for dynamic equilibrium. Work done by a force is given by the product of the force and the displacement along the direction of force.
Calculation:
Draw the free body diagram for the forces and assume the positive direction of the x axis down the plane.
Figure 1
The gravitational force
The magnitude of the gravitational force is given by,
Resolve the gravitational force
Therefore,
The work done by the x component of the gravitational force is given by,
Substitute the known values of the variables in the above equation.
The work done by the y component of the gravitational force is given by,
Substitute the known values of the variables in the above equation.
Therefore the work done by the gravitational force is given by,
Conclusion:
Thus the work done by the gravitational force on the statue is
(b)
Work done by the Curator in pushing the statue up the incline.
Answer to Problem 43QAP
The work done by the Curator in pushing the statue up the incline is
Explanation of Solution
Given:
Mass of the crate
Angle made by the inclined plane with the horizontal
Displacement of the crate along the plane
Coefficient of kinetic friction between the crate and the plane
Calculation:
The crate moves with a constant velocity, hence it is in dynamic equilibrium. The sum of the forces along the x and the y directions, independently add up to zero.
Use Fig 1, and apply the condition of equilibrium along the y axis.
From equation (3)
The magnitude of the force of friction and the normal force are related as follows:
From equation (4),
The force of friction acts along the − x axis.
Therefore,
Apply the condition of equilibrium along the x direction.
Therefore,
Use equations (2)
Substitute the known values of the variables in the above equation.
Write the expression for the work done by the Curator.
Substitute the values of the variables in the above equation.
Conclusion:
Thus the work done by the Curator in pushing the statue up the incline is
(c)
The work done by the friction force on the crate
Answer to Problem 43QAP
The work done by the friction force on the crate is
Explanation of Solution
Given:
Mass of the crate
Angle made by the inclined plane with the horizontal
Displacement of the crate along the plane
Coefficient of kinetic friction between the crate and the plane
Formula used:
The work done by the
Calculation:
Use equation (5)
Substitute the known values of the variables in the equation.
Conclusion:
Thus, the work done by the friction force on the crate is
(d)
The work done by the normal force between the crate and the incline.
Answer to Problem 43QAP
The work done by the normal force between the crate and the incline is 0.
Explanation of Solution
Given:
The expressions for normal force and displacement.
Formula used:
The work done by the normal force is given by,
Calculation:
Substitute the given values of the vectors in the formula.
Conclusion:
Thus the work done by the normal force between the crate and the incline is 0.
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Chapter 6 Solutions
COLLEGE PHYSICS
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