# 8.3: Work-Energy Principle

**At Grade**Created by: CK-12

The reason the concept of work is so useful is because of a theorem, called the **work-energy principle**, which states that *the change in an object's kinetic energy is equal to the net work done on it*:

Although we cannot derive this principle in general, we can do it for the case that interests us most: constant acceleration. In the following derivation, we assume that the force is along motion. This doesn't reduce the generality of the result, but makes the derivation more tractable because we don't need to worry about vectors or angles.

Recall that an object's kinetic energy is given by the formula:

Consider an object of mass

Now let's see how much work this took. To find this, we need to find the distance such an object will travel under these conditions. We can do this by using the third of our 'Big three' equations, namely:

Plugging in [6] and Newton's Third Law,

which was our result in [4].

## Using the Work-Energy Principle

The Work-Energy Principle can be used to derive a variety of useful results. Consider, for instance, an object dropped a height

In other words, the work performed on the object by gravity in this case is

## Spring Force

A spring with spring constant

This is a force that can change an object's kinetic energy, and therefore do work. So, it has a potential energy associated with it as well. This quantity is given by:

The derivation of [10] is left to the reader. Hint: find the average force an object experiences while moving from