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# Potential and Kinetic Energy

Moving objects, without friction, represent a constant transformation between potential and kinetic energy.

#### What is kinetic energy?

Kinetic energy is the energy of motion. All moving things have kinetic energy, and the faster they’re moving the more energy they have.

#### What is potential energy?

Potential energy is a little more difficult to envision. It is the energy that is stored because of the position of an object. The potential energy we’ll be discussing here is stored because of the forces of gravity at work (there are other types of potential energy, but not that are used in Chaos). When you move an object upward on Earth, it gains potential energy. The higher an object is, the more force it will be able to fall with if let go. In other words, potential energy is the amount of kinetic energy that could be gained if the object traveled all the way to the ground.

Let’s look at a couple of examples of potential and kinetic energy. You should build these two structures side by side, with the ends of B at exactly the same height. You should then release the balls from A at different times from exactly the same height. Look at the velocity of the outgoing balls. The velocity should be the same. That’s because starting the balls at the same height at A with no initial speed gives them the same amount of potential energy. When they travel to B, even though one makes a lower trip by a different route, they end up with the same amount of potential energy because they are at the same height. Because they have both lost the same amount of potential energy, they should have both gained the same amount of kinetic energy, and therefore the same speed.

#### Why do they actually have slightly different speeds?

You may have already guessed yourself. Friction is at fault here. If you look closely, you’ll see that the second route has more track to move over. This means that it has a greater opportunity to slow down from friction.

Next example: This setup is very similar to the one before, except instead of looking at the ball moving lower than the final height, this studies the ball accelerating at a different angle. At first it might seem like track B would make the ball move faster than the less steep track A. In fact, all that happens is that track B makes it accelerate faster, but they both end up with the same speed. You can prove this to yourself with what you already know about potential and kinetic energy. If both balls start out at the same height, with neither one moving, they have the same potential energy. If they end up at the same lower height, they have lost the same amount of potential energy. Since that energy is transferred into the same amount of kinetic energy, they end up at the same speed.

Another example: Set up a steep, long track with as many bells as you have on the end, lined up close together. It takes energy to ring a bell, and some kinetic energy of the ball is lost when each bell rings. Therefore, the more bells that ring, the more kinetic energy the ball had when it hit them. You know how to give a ball more kinetic energy. Just start it at a greater height, and therefore with more potential energy.

Problems

7. An airplane flying at 200 m/s passes below another airplane of the same size and weight flying at 100 m/s.

a) Which airplane has more kinetic energy?

b) Which has more potential energy?

8. Imagine you’re swinging on a playground swing.

a) At what point in your swing are you going to have the most kinetic energy?

b) At what point will you have the most potential energy?

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