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Power: Definition and Mathematics

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  • 0:01 What Is Power?
  • 1:51 Calculating Power
  • 4:30 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Work involves moving an object with a force, but power tells us how quickly that work is done. In this lesson, you will learn about how power depends on both work and time as well as see examples of how to calculate power.

What Is Power?

In the time before cars, people rode around in horse-drawn vehicles. But why have horses pull the carts instead of dogs? A dog would not be anywhere near as effective as a horse, but even worse might be something like a cat. It seems unlikely that you'd get very far in a cat-drawn vehicle if you were lucky enough to move at all!

We know that the horse-drawn vehicle is the best option because a horse is much more powerful than a dog, which of course is much more powerful than a cat. But what do we mean by 'power?' Well, power is the amount of work done in the time it takes to do it.

In another lesson, we learned that work is the displacement of an object due to force. We calculate work by multiplying the amount of force by the distance the object is moved. In equation form, work = force x distance.

Lifting a barbell over your head and pushing a box across the floor are both examples of work because a force is applied to the object, and the object moves some distance. How much work done depends on the amount of force and how far the object is moved. But you know that pushing that box across the floor quickly is more difficult than pushing it slowly. This is because the power is different - the amount of time in which that work is done.

So our horse is more powerful because, in the same amount of time, it can do more work than either the dog or the cat. It would also take the dog or cat a much longer time to do the same amount of work - pulling the vehicle - than it does the larger, more powerful horse.

You can see how power depends on both the amount of work done and the time it takes to do that work. Twice the power may come from the same work done but twice as fast, or it may be twice the work done in the same amount of time.

Calculating Power

Since power is the amount of work done over the time it takes to do it, we can easily put this concept into a workable equation: power = work done / time interval. For power, we use the unit of watt (W), which is named after Scottish engineer James Watt. You've heard of 'horsepower?' Well, you can thank Watt for that! He determined that a horse could pull with a force of about 180 pounds and coined this amount of work done '1 horsepower.'

A watt is also a joule/second (J/s) since we are dividing work done (which is in the unit of joules) by time. Therefore, 1 watt of power is used when 1 J of work is done in 1 s. Because this is a fairly small measurement, you're likely more familiar with a kilowatt (kW), which is 1000 W, or a megawatt (MW), which is 1,000,000 W.

Let's look at some examples of how we calculate power. Say you move a 10 N object 5 m in a time of 1 s, and you want to know how much power is needed for this activity. Have no fear! You can easily calculate this using both our work and our power equations.

We know that work = force x distance and that power = work done / time interval. So to start, let's figure out how much work was done. In this case, the force is 10 N and the distance is 5 m. So our work done is 10 N x 5 m, or 50 joules (because 1 J is 1 N*m). Using this information, we can now solve for power. Here, the power is 50 J/1 s, so 50 W.

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