Concept explainers
(a)
The speed of the block.
(a)
Answer to Problem 53P
The speed of the block is
Explanation of Solution
The change in kinetic energy of the system is equal to the net work done on the system. Only friction on the block of mass
Write the expression for the conservation of energy.
Here,
Change in kinetic energy is sum of rotational kinetic energy and translational kinetic energy.
Write the expression for change in kinetic energy.
Here,
Write the expression for change in translational kinetic energy.
Here,
Write the expression for the change in potential energy.
Here,
Substitute
Write the expression for final kinetic energy.
Here,
Write the expression for initial kinetic energy.
Here,
Write the expression for change in rotational kinetic energy.
Here,
Write the expression for inertia of pulley.
Here,
Substitute
Write the expression for change in potential energy.
Here,
Write the expression for energy of the second block.
Here,
Substitute
Write the expression for frictionof second block.
Here,
Angular speed of the pulley is related to the speed of the objects.
Write the expression for the final angular speed.
Write the expression for the initial angular speed.
Substitute
Rearrange the above expression for
Conclusion:
Substitute
Thus, the speed of the block is
(b)
The angular speed of the pulley.
(b)
Answer to Problem 53P
The angular speed of the pulley is
Explanation of Solution
Write the expression for the angular speed of the pulley.
Conclusion:
Substitute
Thus, the angular speed of the pulley is
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Chapter 10 Solutions
Physics for Scientists and Engineers With Modern Physics
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