Energy

• An introduction to energy
• Example: Dropping a ball
• Example: Making heat with your hands
• Example: A boy on a swing
• Energy formulas
• Quiz yourself on energy

Energy is a quantity associated with the state of a system. There are many forms of energy: kinetic energy (energy of motion), potential energy (energy stored in the interaction of an object with another object), chemical energy (energy stored in your body and in molecules), and heat energy are some examples. Energy can easily change forms and locations. Sometimes it stored and becomes invisible. Stored energy can be later released to produce motion, like the chemical energy in your food gives your body the energy to move. Kinetic energy and potential energy are the two forms of energy that we work with most often.

Energy can be stored in the way an object interacts with another object. When this other object is the earth, we call this energy gravitational potential energy. Gravitational potential energy is one type of potential energy. For instance, if you hold a ball one meter above the ground then let it go, it will fall and move more and more quickly toward ground (earth). While moving, the ball has kinetic energy, but while it was in your hand, the energy was stored as gravitational potential energy between the ball and earth. Before you let it go, the potential energy between the ball and earth is invisible, but once you release the ball, the energy is quite obvious in the motion of the ball.

Since energy is conserved, we should be able to track all the energy as it changes forms. As the ball comes closer to the ground, the gravitational potential energy decreases and the kinetic energy increases. We see this increase in kinetic energy as an increase in speed. With the ball and earth system, we know all the forms that the energy can change into. As a result, we can predict how fast the ball will be moving at any position.

We use formulas to describe how much of each form of energy there is. Just as in the office building analogy, the formulas let us calculate the exact amount of energy present even if the energy is invisible. The security guard measured the temperature to know how many people were in the conference room; you can measure how high you hold the ball above the ground to know how much gravitational potential energy there is between the ball and the earth.

There are forms or energy that are difficult, if not impossible, to count up. One of these forms is heat energy. When you rub your hands together, they get warm. The energy of motion when you move your hands back and forth is changed into heat by friction. Quite often we don't know how much heat energy is produced by the interaction, but we do know that all the kinetic energy your hands put into the interaction (that is now gone) went toward producing the heat. In this case, energy is still conserved, but since we do not know how to count up the heat energy, we can not predict anything useful about this interaction.

We can still analyze a system that is being influenced by outside forces if we can describe how the outside forces are affecting the system. For example, a little boy is on a swing. He just sits on the swing and lets his mom push him. Each time his mom gives him a push, she is exerting a force on him and giving him energy. This energy changes the total energy of the system, where the system consists of just the boy and the swing. Once his mom has put in the energy, it changes into kinetic energy and potential energy. If his mom keeps pushing, the little boy will move faster and faster and go higher and higher.

When his mom stops pushing him, he should just keep swinging up to the same height, but in the real world, this doesn't happen. There is friction between the swing's chain and the pole that is supporting the swing. The metal rubs together. Energy is taken out of the system and converted to heat. Energy is also converted to heat through air resistance. Eventually, the boy will slow down to a stop.

The mom, the friction and the air resistance are examples of outside forces which influence the boy and swing system. We know how each of these is adding and subtracting energy from the system so we can still analyze the energy transfers as the boy swings back and forth. If the boy keeps going up to the same height, we know that his mom's pushing, the friction and the air resistance somehow balance and cancel each other out.

Notice that the energy conversion between kinetic and potential energy continues to occur while the boy is swinging. When the boy is at the highest point, he is not moving for a split-second and the potential energy is at a maximum. At the bottom, the boy is moving the fastest and the kinetic energy is at a maximum. Energy is constantly see-sawing between these two forms.

Gravitational potential energy is defined to be

In an isolated system, the value of this quantity, the total energy of the system, will always remain the same.