Concept explainers
To Calculate: The acceleration of each block and the tensions in the segments of string between each block and the pulley.
Answer to Problem 74P
The acceleration of each block is
The tension acting on the block of mass
The tension acting on the block of mass
The tension on the pulley is
Explanation of Solution
Given Information:
Mass of block resting on the ledge,
Mass of the block hanging from the pulley,
Coefficient of kinetic friction between ledge and block,
Mass of the pulley,
Radius of the disk of the pulley,
Formula used:
By Newton’s second law of motion, the net force acting on a system is:
Where, m is the mass and a is the acceleration.
Calculation:
Free body diagram can be drawn as follows:
By using the Newton’s second law of motion, horizontal component of force on block
Normal force on block
Substitute this value in the equation
Write the equation of motion for the pulley of mass
Moment of inertia
Angular acceleration
Substitute the equations of
Write the equation of motion for the hanging mass
Substitute the equations
Equation the equations
Substitute
The acceleration of each block is
Tension
Substitute
Hence the tension acting on the block of mass
Tension
Substitute
Hence the tension acting on the block of mass
Tension acting on the pulley of mass
Hence, the tension on the pulley is
Conclusion:
The acceleration of each block is
The tension acting on the block of mass
The tension acting on the block of mass
The tension on the pulley is
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