Definitions first: Kinetic energy is the energy of things moving. The faster something moves, the more kinetic energy it has. (The equation for kinetic energy is 1/2mv^2, where m is the object’s mass and v is its velocity.) Potential energy is a bit trickier - you can think of it as energy that’s stored up, giving something the potential to do something. For example, if you lift something up, you give it what’s called ’gravitational potential energy’, or the potential to move when you let go of it. (The equation for gravitational potential energy is mgh, where m is the mass, g is the acceleration of gravity, and h is how high up the object is.)
The thing about energy is that it’s always conserved - that is, between potential and kinetic, you always have the same total amount of energy all together. So when you drop the book, what used to be gravitational potential energy turns into kinetic energy as it falls.
A pendulum would also work very well for this. You could start by pulling the pendulum up some distance. This will give it a certain amount of potential energy due to the force of gravity. Then let go of the pendulum. As the pendulum moves down, the gravitational potential energy is turned into kinetic energy. All of the potential energy is turned into kinetic energy as the pendulum passes through the lowest point that it can go. On its way back up, gravity does work on the pendulum to turn the kinetic energy to potential energy again. The pendulum therefore goes to the exact same height from which you let it go. This is because all the potential energy that initailly was turned into kinetic energy is then turned back into potential energy without the energy being used anywhere else. This means that the total energy of the system is conserved. This shows the relation between kinetic and potential energy very well and can be used in most systems where there is some type of oscillation is taking place.
In cases where friction is present, the sum of kinetic and potential energy will not stay constant. If you are driving in a car, for example, and put on the brakes, then the car will eventually stop. The kinetic energy in this case goes from a large value to zero, and the potential energy does not change as long as the road is horizontal.
It is still true that the total energy is conserved, however. The "missing" energy in this case is just heat. (The breaks of a car get very hot when you stop). If we add up kinetic energy plus potential energy plus "heat" energy, then we would again find that energy is conserved.
Heat is really just the kinetic energy of the atoms inside jiggling around and the potential energy of them squashing together and pulling apart. Technically, scientists call this thermal energy and mean something a little different by "heat", but often we forget and use the word this way.
I hope that this helps you guys come up with ideas.
(republished on 07/13/06)