Calculating Power from Torque and Rotor Speed

In summary, the electric motor runs at 24 rev/s and supplies a torque of 50.3 Nm. The power delivered by this motor is P = (50.3Nm) (24rev/s).
  • #1
littlesohi
5
0

Homework Statement



An electric motor runs at 24 rev/s and supplies a torque of 50.3 Nm. What is the power P delivered by this motor?

Homework Equations





The Attempt at a Solution



I just know that power is work/second. I don't know how I can relate the torque, rotor speed and power! Pleaseee help :(
 
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  • #2
That is tricky! It should be okay to think of the motor lifting a weight of 50.3 N at a distance of 1 meter from the center of the shaft. Can you figure out how fast it is moving the weight from that 24 rev/s?

There is a way to do the rest more elegantly with formulas, but at what I think is your level of physics, I would recommend you consider a small time, say 0.1 second.
Figure out how far the weight is lifted in that time.
Figure out how much work is done in lifting it that far.
Then use your power formula on those figures.
 
  • #3
So basically by dividing the "weight" of the 50.3 by the rotos speed I will get how much speed it will actually take to move that weight? Is that right??
 
  • #4
"how much speed it will actually take to move that weight" doesn't make sense to me. The thing is, it makes 24 complete turns per second so it has a definite speed you must take into account. Think 24 times the circumference divided by one second. From that you can figure out how far it is lifted in the arbitrary time of 0.1 s. Maybe better to use 0.001 s so you don't get sidetracked thinking about non-vertical motion. This arbitrary time should cancel out in the whole calc.
 
  • #5
Instead of all this hand waving about lifting a weight in a certain amount of time, there is a simple formula which relates torque and angular velocity to power output. A simple Google search should find this formula.
 
  • #6
True, but is the only objective to find the answer?
I think the OP will have a much better learning experience figuring it out a step at a time with the familiar basic formulas. Then, perhaps, he or she will take time to derive the linear formula for power as a function of force and velocity using the same technique, only with algebra instead of numbers. The last step, using the formula you mentioned, I would say is simply going too far into the abstract. There are enough formulas to remember already!
 

1. How do you calculate power from a given torque?

To calculate power from a given torque, you can use the formula P = τω, where P is power, τ is torque, and ω is angular velocity. Alternatively, you can use the formula P = Fv, where F is force and v is linear velocity. Both of these formulas are derived from the definition of power as the rate of doing work.

2. What is the unit of measurement for power?

The unit of measurement for power is the watt (W), which is defined as one joule per second. Other commonly used units of power include horsepower (hp) and kilowatt (kW).

3. How does torque affect power?

Torque and power are directly proportional to each other. This means that as torque increases, power also increases. In other words, a greater torque will result in a greater power output.

4. Can you use torque and power interchangeably?

No, torque and power are not interchangeable terms. While they are related in the sense that torque affects power output, they are two distinct concepts. Torque is a measure of rotational force, while power is a measure of the rate at which work is done.

5. What are some real-world applications of calculating power from torque?

Calculating power from torque is important in many industries, including automotive, manufacturing, and aerospace. In the automotive industry, power is used to measure the performance of engines and motors. In manufacturing, power is used to determine the efficiency of machines. In aerospace, power calculations are crucial for designing and testing aircraft engines and other propulsion systems.

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