A 690 kg elevator starts from rest. It moves upward for 2.56 s with constant acceleration until it reaches its cruising speed, 1.84 m/s. What is the average power of the elevator motor during this period?,
What is the power of the elevator motor during an upward cruise with constant speed?
To find the average power of the elevator motor during the period of acceleration, we can use the formula:
Average Power = Work / Time
First, let's find the work done by the elevator. Since the elevator starts from rest and moves with constant acceleration, we can use the formula:
Work = Force * Distance
The force acting on the elevator is the weight of the elevator, given by:
Force = mass * acceleration due to gravity
Force = 690 kg * 9.8 m/s^2
Now, we need to find the distance traveled by the elevator during the acceleration phase. We can use the formula for distance traveled with constant acceleration:
Distance = (Initial velocity * Time) + (0.5 * Acceleration * Time^2)
Since the initial velocity is 0 m/s and the acceleration is unknown, we can rearrange the formula to solve for acceleration:
Acceleration = (Final velocity - Initial velocity) / Time
Acceleration = (1.84 m/s - 0 m/s) / 2.56 s
Now that we have both the force and the distance, we can calculate the work done by the elevator:
Work = Force * Distance
Finally, we can substitute the work and time values into the average power formula to find the average power of the elevator motor during the period of acceleration.
For the power of the elevator motor during the upward cruise with constant speed, no acceleration is involved. Thus, the power required is simply the force (weight of the elevator) multiplied by the constant speed of the elevator.
So, for the upward cruise, the power of the elevator motor is given by:
Power = Force * Speed
Let's calculate the average power of the elevator motor during the period of acceleration first and then the power during the upward cruise using the given values.