(a)
The average power of the elevator motor.
(a)
Answer to Problem 38P
The average power of the elevator motor is
Explanation of Solution
Write the expression for average power
Here,
Consider the elevator as an isolated system.
Write the expression for work done by the motor on the elevator
Simplify the above expression.
Here,
Since the direction of force and displacement is same, hence the angle
Substitute
Simplify the above equation
Substitute
Write the expression for total force when the system is moving with an acceleration.
Here,
Write the expression for total force acting on the system
Here,
Substitute
Consider the elevator as an isolated system and the motion of elevator is by force acting by motor, the elevator starts from rest when a force is applied by motor against the gravitational force of the elevator.
The gravitaional force is negative because it is in opposite to the direction of acceleration.
Write the expression for force due to gravity.
Here,
Substitute
Simplify the above equation.
Consider the motion of elevator from rest to the speed of its cruising speed.
Write the equation of motion for velocity in terms of acceleration and time
Here,
Since the initial speed is zero.
Substitute
Simplify the above equation to find the expression for
Write the equation of motion for distance travelled in terms of acceleration, time and initial speed.
Here,
Since the initial speed is zero.
Substitute
Substitute
Simplify the above equation.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the average power of the elevator motor is
(b)
The comparison between average power and the power when elevator moves with cruising speed.
(b)
Answer to Problem 38P
The instantaneous power required is
Explanation of Solution
Write the expression for instaneous power when the elevator is moving at a constant cruising speed
Simplify the above expression
Here,
Since the force and velocity are in same direction, hence the angle between
Substitute
Simplify the above equation.
Here,
Since the elevator moves at constant speed when it reaches cruising speed, hence the acceleration will be zero.
Write the expression for comparison in both powers
Here,
Since the elevator is moving at constant speed hence the acceleration is zero.
Substitute
Simplify the above equation
Conclusion:
Substitute
Substitiute
Substitute
Thus, the instantaneous power required is
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Chapter 8 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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