A 607-kg elevator starts from rest and moves upward for 4.40 s with constant acceleration until it reaches its cruising speed, 1.73 m/s.
(a) What is the average power of the elevator motor during this period?
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(b) How does this amount of power compare with its power during an upright trip with constant speed?
W
To find the average power of the elevator motor, we need to use the formula:
Average Power = Work / Time
To calculate the work done by the elevator motor, we first need to find the distance it traveled. We can use the formula of motion:
Distance = (Initial velocity * Time) + (0.5 * Acceleration * Time^2)
Given:
Initial velocity (u) = 0 (since the elevator starts from rest)
Time (t) = 4.40 s
Acceleration (a) = ?
To find the acceleration, we can use the formula:
Final velocity (v) = u + (a * t)
Given:
Final velocity (v) = 1.73 m/s
Substituting the given values into the equation, we can solve for the acceleration:
1.73 = 0 + (a * 4.40)
1.73 = 4.4a
a = 1.73 / 4.4
a = 0.393 m/s^2
Now we can calculate the distance traveled by substituting the acceleration into the distance formula:
Distance = (0 * 4.40) + (0.5 * 0.393 * 4.40^2)
Distance = 0 + (0.5 * 0.393 * 19.36)
Distance = 1.904 m
Now that we have the distance, we can calculate the work:
Work = Force * Distance
The force can be calculated using the formula:
Force = Mass * Acceleration
Given:
Mass (m) = 607 kg
Acceleration (a) = 0.393 m/s^2
Substituting the values into the equation, we get:
Force = 607 * 0.393
Force = 238.551 N
Now we can calculate the work:
Work = 238.551 * 1.904
Work = 454.638 J
Finally, we can calculate the average power using the work done and the time taken:
Average Power = 454.638 / 4.40
Average Power = 103.324 W
So, the average power of the elevator motor during this period is 103.324 Watts.
To answer part (b), comparing this amount of power with its power during an upright trip with constant speed, we can assume that during an upright trip, the elevator is moving at a constant speed, which means there is no acceleration involved. In this case, the average power will be zero because no work is being done to change the elevator's speed or altitude. The power only comes into play when there is a change in velocity or altitude.