Concept explainers
The motor applies a constant downward force
(a)
The velocity of the elevator.
Answer to Problem 13.22P
Explanation of Solution
Given information:
The constant downward force is equal to
Weight of elevator E is equal to
Counterweight is equal to
Elevator travels
In a dependent motion of particles such as the pulley system shown above,
The total length of the rope is a constant
For example,
The kinetic energy of a particle is defined as,
Principle of work and energy is defined as,
Above equation states “If a particle moves from A1 to A2 under an action of force F, the work of the force F is equal to the change in kinetic energy.”
Calculation:
Length of both cables is constant, therefore
For cable 1,
Differentiate,
For cable 2,
Differentiate,
For elevator E,
Apply principle of work and energy,
For counter weight,
Apply principle of work and energy,
But we know that,
Therefore,
Add both equations,
Therefore,
Conclusion:
The velocity of elevator E is equal to
(b)
The velocity of the counter weight.
Answer to Problem 13.22P
Explanation of Solution
Given information:
The constant downward force is equal to
Weight of elevator E is equal to
Counterweight is equal to
Elevator travels
In a dependent motion of particles such as the pulley system shown above,
The total length of the rope is a constant
For example,
The kinetic energy of a particle is defined as,
Principle of work and energy is defined as,
Above equation states “If a particle moves from A1 to A2 under an action of force F, the work of the force F is equal to the change in kinetic energy.”
Calculation:
According to sub part a,
We have found,
And,
Therefore, the velocity of counter weight is equal to,
Conclusion:
The velocity of counter weight is equal to
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Chapter 13 Solutions
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