# Work-Energy Theorem: Definition and Application

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• 0:01 Work Is a Change in Energy
• 1:34 Potential Energy Is…
• 2:25 Energy Can Increase or…
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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 and energy are closely related in physics. In this lesson, you'll learn what that relationship is as well as how we can apply it to various situations.

## Work Is a Change in Energy

'Work' means different things to different people because we all have very different jobs that we do every day. But in physics, work means something very specific: 'a change in energy.' This change in energy comes from a force that causes an object to move a certain distance.

So in order for work to be done on an object, a force must move that object. You can push on a wall all day, but you're not doing any work on the wall unless you get it moving. In other words, you don't do any work on an object unless you change its energy.

When we move an object (that is to say, when we do work on it), we increase its kinetic energy, which is known as 'energy of motion.' When we bring a moving object to rest, we also do work on the object, but in this case we are decreasing its kinetic energy. Regardless of whether we are increasing or decreasing an object's kinetic energy, the amount of work done is equal to the change in energy. This is an important relationship known as the work-energy theorem.

We can write this statement as an equation that makes it very easy to see the relationship: Work = Î” E, where E is energy, and the Greek letter Delta means 'change in.' So we read this as: work = change in energy.

This helps us understand why no work is done on a wall that isn't moved. You get tired because, on a biological level, some work is being done on your muscles as you push, but no work is done on the wall because there is no change in energy - it doesn't go anywhere!

## Potential Energy Is Stored Energy

The work-energy theorem can also be applied to an object's potential energy, which is known as 'stored energy.' When a skier waits at the top of the hill before taking off, they have potential energy because they have the potential to do work. Once they take off down the hill this gets converted to kinetic energy because the skier is now in motion.

If you raise a dumbbell over your head, you are doing work on the dumbbell as you raise it because you are moving it and therefore changing its kinetic energy. But you're also changing its potential energy because just like the skier, it is changing from a state of rest to a state of motion. However, once that dumbbell is above your head, if you simply hold it there you are no longer doing work on it because you aren't changing its energy - either potential or kinetic.

## Energy Can Increase or Decrease

Since the work-energy theorem describes a change in energy, this change can come in the form of either an increase or a decrease of energy. This is because the faster an object is traveling, the more kinetic energy it has, and the more work it will take to slow or stop that moving object.

It takes less distance to stop a car traveling at 25 mph than a car that is traveling at 70 mph, right? This is because, as mentioned before, work is done when a force acts over a given distance. So if you increase the distance, you increase the work. The car traveling at 70 mph has much more kinetic energy than the slower car, so more work is required to stop the faster car because a greater change in energy is required to reach the same state of rest.

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