Concept explainers
The magnitude of the tension in the string which connects two blocks, one of which hangs vertically down and the other resting on an inclined plane.
Answer to Problem 79QAP
The tension in the string is found to be 3.92 N.
Explanation of Solution
Given info:
Mass of the block placed on the incline
Mass of the hanging block
Angle made by the plane with horizontal
Coefficient of static friction
Coefficient of kinetic friction
Formula used:
Free body diagrams are drawn for the two blocks and the tension in the string is determined using the force equations for both the blocks.
The free body diagram for the block of mass
The weight of the block is
The total force acting along the +x direction is given by,
Draw the free body diagram for the block of mass
The weight
Resolve the weight
The force equation along the +x direction is given by,
The force equation along the +y direction is given by,
Since the block is in equilibrium in the y direction,
Hence,
The force of friction and the normal force are related as follows:
The value of the coefficient of friction
Calculation:
The system would be at rest, if the following conditions are satisfied:
and
If
Since
Substitute the values of the variables in the above equation,
To check whether the system is at rest, use the expression
Therefore,
Calculate the value of
The component
Therefore,
Use the values of the variables in the equation.
If the system is at rest, assume the maximum force of static friction to act on the block.
Then,
From equation (4),
The component
Calculate the maximum force of static friction acting on the block.
It can be seen that
Conclusion:
Since the system is at rest, the force of tension in the string is equal to 3.92 N.
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Chapter 5 Solutions
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