
Concept explainers
The mass of the box which is held in place against a rough vertical wall by using a force directed upwards at an angle.

Answer to Problem 46P
Solution:
The mass of the box is found to be 1.9 kg.
Explanation:
The box of mass m is held in place when the net force on the box is zero. It starts to slide when the force acting downwards is more than the force acting in the upward direction.
Draw the free body diagram of the box.
The box is pushed against the wall by a force F acting at an angle to the horizontal. The weight of the box acts downwards. Since the box tends to slide down, the
Resolve the force F into two components , as shown in the figure.
For horizontal equilibrium,
…………(1)
For vertical equilibrium,
…………(2)
The force of friction and normal force are related as follows.
…………(3)
Substitute equations (1)and (3)in equation (2).
Simplify and write the expression for m.
Explanation of Solution
Given:
The coefficient of static friction
The coefficient of kinetic friction
The magnitude of the applied force
The angle made by the force to the horizontal
Formula used:
Calculation:
Substitute the given values of F, , , and 9.8 m/s2 for g in the formula used.
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Physics: Principles with Applications
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