Concept explainers
(a)
The average power of each elevator’s motor during the acceleration.
(a)
Answer to Problem 82PQ
The average power of each elevator’s motor during the acceleration is
Explanation of Solution
Write the expression for the distance travelled during acceleration.
Here,
Write the expression for average velocity.
Here,
Substitute
The forces acting on the elevator car are gravitational force and the force applied by elevator motor.
According to work-energy theorem, net work done by gravitational force and elevator motor is equal to change in kinetic energy.
Write expression for the change in kinetic energy.
Here,
Write the expression for the work done by gravity.
Here,
Since gravitational force acts in downward direction and elevator moves in upward direction, angle
Substitute
Write the expression for change in kinetic energy of elevator.
Initially elevator is at rest. Substitute
Substitute
Write the expression for the power of the motor.
Here,
Conclusion:
It is given that mass of elevator full of passenger is
Substitute
Substitute
Substitute
Therefore, the average power of each elevator’s motor during the acceleration is
(b)
The average power of each elevator’s motor during the cruising phase of its motion.
(b)
Answer to Problem 82PQ
The average power of each elevator’s motor during the cruising phase of its motion is
Explanation of Solution
The elevator attained a cruising speed of
Write the expression for the average power during cruising motion.
Here,
Write the expression for
Conclusion:
Substitute
Substitute
Therefore, The average power of each elevator’s motor during the cruising phase of its motion is
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Chapter 9 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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