What is the power input of a motor pulling up an elevator?

In summary, the problem involves an elevator being lifted at a steady speed, with a known mass and lift rate. The efficiency of the system is given and the goal is to calculate the power input into the motor unit.
  • #1
magnesium12
19
0

Homework Statement


Once under way at a steady speed, the 1100-kg elevator A rises at the rate of 1 story (2.74 m) per second. Determine the power input Pin into the motor unit M if the combined mechanical and electrical efficiency of the system is e = 0.76.

Here is a link to the diagram for the problem:
https://imgur.com/jf58KT6

Homework Equations


e = Pin/Pout
P = Fv
∑Fy = ma = 0

The Attempt at a Solution


First I tried finding the tension in the rope leading to the bottom two pullies:
∑F = 0 = -W +2T1
T1 = W/2

Then I tried finding T2 and T3:
∑F = 0 = T2 + T3 - T1 = 2T3 -T1

Assuming T2 = T3
0 = 2T3 -T1
T2 = T3 = T1/2 = W/4

So then the tension leading to the motor is W/4 = T2

Calculating the power output of the motor:
P = Tv = (W/4)(2.74m/s) = (1100/4 kg)(9.81m/s/s)(2.74m/s) = 7391.84 J/s = 7.39184 kW

Power input of the motor:
e = Pin/Pout
Pin = e(Pout) = 0.76(7.39184kW) = 5.618 kW (Incorrect answer)

I think I'm going wrong when calculating the tensions in the cables. Can someone please explain how to do this correctly?

Thank you!

 
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  • #2
magnesium12 said:
finding the tension in the rope leading to the bottom two pullies:
You don't need to worry about the tensions. Just think about the net force on the elevator.
magnesium12 said:
P = Tv = (W/4)(2.74m/s)
That's the velocity of the elevator, not of the cable.
 
  • #3
The problem may be easier to solve if the diagram is ignored. We have an elevator on which work is being done as it is lifted. We know its mass and how rapidly it is being lifted. We have a mechanism which is doing all of the work lifting the elevator. It has a known efficiency. We have a power source providing all of the energy to allow the mechanism to do its work.

Three black boxes -- elevator, mechanism, power source. Is the information already provided enough to solve the problem without peeking inside the black boxes?
 
  • #4
e = Pin/Pout

Check that.
 
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Related to What is the power input of a motor pulling up an elevator?

What is the power input of a motor pulling up an elevator?

The power input of a motor pulling up an elevator is the amount of energy required for the motor to lift the elevator. It is measured in watts (W) or horsepower (hp).

How is the power input of a motor calculated?

The power input of a motor can be calculated by multiplying the force applied by the motor with the velocity at which the force is applied. This is known as the power formula: Power = Force x Velocity.

What factors affect the power input of a motor pulling up an elevator?

The power input of a motor pulling up an elevator can be affected by various factors such as the weight of the elevator, the height it needs to be lifted, the speed at which it needs to be lifted, the efficiency of the motor, and any external forces acting on the elevator.

How does the efficiency of a motor affect the power input?

The efficiency of a motor is the ratio of output power to input power. A more efficient motor will require less input power to achieve the same output, while a less efficient motor will require more input power to achieve the same output. Therefore, a higher efficiency motor will have a lower power input while pulling up an elevator.

Is the power input of a motor constant while pulling up an elevator?

No, the power input of a motor can vary while pulling up an elevator. It will depend on the weight and height of the elevator, the speed at which it needs to be lifted, and the efficiency of the motor. As the elevator reaches higher floors, the power input may also increase due to the increased weight and height.

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