# Kinetic Energy and the Work Energy Theorem

Energy is the ability to do work. We will talk about several kinds of energy, but first we need to start with the energy associated with objects in motion. We call this Kinetic Energy We said that when a force is applied to an object through a distance, it does work. Let's do a quick derivation:

Recall that

Wnet= Fnet x d.

Also recall from Newton's 2nd Law that Fnet = mass x acceleration, or

F = ma.

Let's let d = Dx, or the change in distance. From our kinematics equations,

Solving for a,

Now we substitute this back into the 2nd Law and the Net Work equation to obtain

We will define a new term, Kinetic Energy (KE). Earlier, we said this was energy due to an object in motion. Specifically, we say

So the Work done is merely the change in Kinetic Energy of a system, or

This is the Work-Energy Principle: A change in Kinetic Energy is equal to the total work done on or by a system. Kinetic energy, like work, is measured in Joules.Important thing to note here: The change in Kinetic Energy, DKE, will ALWAYS be the final Kinetic Energy (KE) minus the initial Kinetic Energy (KEo).

Example: How much Kinetic Energy does a 2000 kg car traveling at 25 m/s have?

KE = 1/2 mv2 = (.5)(2000kg)(25 m/s) = 25,000 Joules.

How much work is done by the brakes of the car to bring the car to rest?

Since v = 0 m/s, the final KE of the car is 0 Joules. Therefore, W = DKE = 0J - 25,000J = -25,000 Joules.

Speed will have a greater effect on Kinetic Energy than mass. From the equation for KE above, we can see that if you double the mass, you double the kinetic energy. But if you double the velocity, since KE is a function of velocity squared, then you quadruple the KE. This is why an object such as a bullet, with very small mass but very large velocity can do so much damage.

Check your understanding: If you triple the velocity of an object, the Kinetic Energy goes up by a factor of ___? (Answer: A factor of 9)

Often it is helpful to see what someone else has to say on the topic. Be sure to check out:

http://www.physicsclassroom.com/Class/energy/u5l1c.html

and

http://hyperphysics.phy-astr.gsu.edu/hbase/ke.html

For Practice Problems, Try: From the University of Oregon:

Calculating Kinetic Energy

Giancoli Multiple Choice Practice Questions (Select "Practice Problems) and try some.
Don't worry - you won't be able to do all of them yet.