Concept explainers
(a)
The minimum acceleration so that box will not fall to the ground.
(a)
Explanation of Solution
Given:
Mass of box is
Coefficient of friction between the box and the wall is
Formula used:
Draw free body diagram of the box.
Write expression for net force in x -direction.
Here,
Substitute
Here,
Write expression for net force in y -direction.
Substitute
Here,
Here,
Substitute
Here,
Substitute
Solve above expression for
Calculation:
Substitute
Conclusion:
Thus, the minimum acceleration is
(b)
The magnitude of frictional force.
(b)
Explanation of Solution
Given:
Mass of box is
Coefficient of friction between the box and the wall is
Formula used:
Draw free body diagram of the box.
Write expression for net force in y -direction.
Substitute
Here,
Rearrange above expression for
Calculation:
Substitute
Conclusion:
Thus, the magnitude of frictional force is
(c)
The
(c)
Explanation of Solution
Given:
Mass of box is
Coefficient of friction between the box and the wall is
Formula used:
Draw free body diagram of the box.
Write expression for net force in y -direction.
Substitute
Here,
Rearrange above expression for
Calculation:
Substitute
Conclusion:
The friction force is independent of minimum acceleration. Thus, the magnitude of frictional force is
(d)
To show that the box will not fall if the acceleration is greater or equal to
(d)
Explanation of Solution
Given:
Mass of box is
Coefficient of friction between the box and the wall is
Introduction:
Draw free body diagram of the box.
Write expression for net force in x -direction.
Here,
Write expression for net force in y -direction.
Substitute
Here,
Here,
Substitute
Here,
Substitute
Solve above expression for
The minimum acceleration required for the box to not fall in the ground is
If the acceleration is greater than
Conclusion:
Thus, the box will not fall if the acceleration is greater or equal to
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Chapter 5 Solutions
Physics for Scientists and Engineers
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