# Calculate the efficiency of the electric motor.

• 1irishman
In summary, the conversation was about calculating the efficiency of an electric motor pulling up an elevator at a constant velocity of 1m/s. The work done and work in can be expressed in terms of mass, gravity, velocity, and time. The book's answer is 83%, but the calculations done in the conversation resulted in 833%. It was suggested that the initial values may have been incorrect or there may have been a mistake in the question. The question of when to use power out/power in vs. work out/work in was also raised.
1irishman

## Homework Statement

An 8.5 X 10^3 kg elevator is pulled up at a constant velocity of 1m/s by a 10kW electric motor.
Calculate the efficiency of the electric motor.

## Homework Equations

P=w/t
%efficiency=work out/work in X 100%
W=mgh
d=vit+1/2at^2
v=d/t

## The Attempt at a Solution

In the meantime, this is how far I got (not too far):

vi=1m/s
m=8.5X10^3kg
vf=0

The work done can be expressed in gravitational terms: mass * g * height. The work in can be calculated by power * time. Height can be found with velocity * time.

mass * g * velocity * time / (power * time) * 100 = mass * g * velocity / power * 100
8.5X10^3kg * 9.81 * 1 m/s / ( 10000 W) * 100 = 833%. It's off by a multiple of ten, so you gave the wrong initial values, the book published a faulty question, or (i sure hope this isn't it) I'm partly wrong. I hope this helps.

Is the time 1 second? Is the height 1 metre? Yes, I got the mass wrong, it was suppossed to be to the power of 2 not to the power of 3.
How do I know whether to use power out/power in vs. work out/work in? Thanks!

## 1. How do you define efficiency for an electric motor?

Efficiency for an electric motor is defined as the ratio of the mechanical power output to the electrical power input. In other words, it measures how well the motor converts electrical energy into mechanical energy.

## 2. What is the formula for calculating the efficiency of an electric motor?

The formula for calculating the efficiency of an electric motor is efficiency = (mechanical power output / electrical power input) x 100%. This will give the efficiency as a percentage.

## 3. Can the efficiency of an electric motor be greater than 100%?

No, the efficiency of an electric motor cannot be greater than 100%. This would violate the law of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. Therefore, the output power of the motor cannot exceed the input power.

## 4. What factors can affect the efficiency of an electric motor?

There are several factors that can affect the efficiency of an electric motor, including the design and quality of the motor, the type of load it is powering, the temperature and humidity of the environment, and the maintenance and upkeep of the motor.

## 5. How can the efficiency of an electric motor be improved?

The efficiency of an electric motor can be improved by using high-quality materials and designs, minimizing friction and resistance, and ensuring proper maintenance and lubrication. Additionally, using a variable speed drive or controlling the motor's speed can also improve efficiency by reducing energy waste.

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