Concept explainers
An object moves in the xy plane 111 Figure P7.43 and experiences a friction force with constant magnitude 3.00 N, always acting in the direction opposite the object's velocity. Calculate the work that you must do to slide the object at constant speed against the friction force as the object moves along (a) the purple path O to Ⓐ followed by a return purple path to O, (b) the purple path O to © followed by a return blue path to O, and © the blue path O to © followed by a return blue path to O. (d) Each of your three answers should be nonzero. What is the significance of this observation?
(a)
The work done by the frictional force on the particle as the particle moves along purple path
Answer to Problem 7.46P
The work done by the frictional force on the particle is
Explanation of Solution
Given info: The friction force with constant magnitude is
The particle moves along the
The expression for the work done of the particle along the path
Here,
Substitute
The expression for the work done of the particle along the return path
Substitute
Total work done by the frictional force along the path
Substitute
Conclusion:
Therefore, the work done by the frictional force on the particle is
(b)
The work done by the frictional force on the particle as the particle moves along purple path
Answer to Problem 7.46P
The work done by the frictional force on the particle is
Explanation of Solution
The position of particle is
From part (a), the work done of the particle along the path
The expression for the work done of the particle along the path
Here,
Substitute
The expression for the work done of the particle along the path
Here,
From the Pythagoras theorem, the value of
Substitute
Substitute
The total work done of the particle along the path
Substitute
Conclusion:
Therefore, the work done by the frictional force on the particle is
(c)
The work done by the frictional force on the particle as the particle moves along blue path
Answer to Problem 7.46P
The work done by the frictional force on the particle is
Explanation of Solution
From part (b), the work done of the particle along the return path
The work done of the particle along the path
Total work done by the frictional force along the path
Substitute
Conclusion:
Therefore, the work done by the frictional force on the particle is
(d)
The significance of the observation when all three answers should be nonzero.
Answer to Problem 7.46P
The frictional force is a non-conservative force.
Explanation of Solution
The expression for the work done by the frictional force on the particle is,
From part (a), the work done of the particle along the path
From part (b), the work done of the particle along the path
From part (b), the work done of the particle along the path
The above equations shows, the value of work done by the frictional force on the particle in all closed paths and that are non-zero because the particle pushes with a force
The value of
Conclusion:
Therefore, the frictional force is a non-conservative force.
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Chapter 7 Solutions
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