Calculate Efficiency of 10.0 kW Motor for 8.5 kg Elevator

[petuniac]

Homework Statement

An 8.5 kg elevator is pulled at a constant velocity of 1.0 m/s by a 10.0 kW motor. Calculate the efficiency of the motor.

Homework Equations

W = change in E = Fd

e = Work out/Work in * 100 = energy out/energy in *100

Epotential = mgh
Ekinetic = 1/2mv^2

P = W/t

The Attempt at a Solution

Ekinetic = 1/2mv^2 = 8.5 J (Energy in)

I don't know how to get the Work from the motor as I don't have the time?

 

[Reshma]

I don't know how to get the Work from the motor as I don't have the time?

Power is also written as: Power = Force x Velocity. You have two known quantities viz. Power & velocity. Can you find the force?

 

[matheyrichs]

if you want to approach this using time and simply potential energy change, you can set an initial condition and a final condition:

ex)
initial condition:
height=0m
t=0

final condition:
height=10m
t=10s

Then play with (delta)E in a much simpler way.

 

[petuniac]

Sorry Reshma but I am still confused ... if I solve for F using the P = Fv equation what does this accomplish as I need to calculate the efficiency, and why would I use the 10 kW power given for the motor in that equation and the speed of the elevator?? Please help.

 

[matheyrichs]

petuniac, you should not be using 10kW and the elevator's speed in the same equation.

It sounds like 10kW is your Power in, the power supplied to the motor.

efficiency is also Pout/Pin.

So Pout is the amount of power used while lifting the elevator. For this calculation you can in fact use P=Fv. Your unknown here is NOT F, but rather P. If you're stuck on figuring out F, remember gravity's effect on the elevator's mass.

 

[petuniac]

Thank you Matheyrichs! You've made it much clearer to me!

I made an error in quoting the original question.. the elevator mass is 85 kg.

Ok, so for the solution I get...

Pout = Fv = mgh = (85*9.81*1) = 833.85 W

Pin = 10000 W

e = Pout/Pin = (833.85)/10000 *100 = 8.33%

The only issue is that the answer is 83.3% so I am off by an order of magnitude and can't seem to see why?

 

[matheyrichs]

are there any people in the elevator??

I'm not sure. 833/10,000 is certainly only 8.33%. I also did the problem a different way, substituting the initial start and end and got the same answer.

Check the problem again and make sure V_elevator and P_motor are actually 1 m/s and 10kW as well.

83% sounds like a reasonable efficiency, 10kW is ~13horsepower, and 85kg is ~187lbs.

I'd say that the most unreasonable piece of that is for an elevator to only weigh 85kg.

 

[petuniac]

Thanks again!