There is only one form of kinetic energy, but there are many forms of potential energy. For example there is a potential energy stored in the gravitational field. If you lift a body up, then you are putting energy in the body. Anytime a body is lifted higher than it was earlier then is has potential energy. Physicists refer to gravitational potential as energy of position or energy of height. A body has zero potential when it is as the lowest height of its motion. It has the most at the highest point of its motion. Where the potential energy equal to "zero" is a relative thing. What is the same about each of the potential energies in the two animations?

Potential energy due to gravity is determined by the following math expression:

A system is made from the bodies that trade energy. Kinetic energy is associated with the object moving. The graviatinal potential energy comes from the Earth's gravitational.

What is the system for a ball rolling off a table?

What is the system for a roller coaster train that coasts up to the top of a roller coaster track?

What is the system for a student who trips and falls to the ground?

Thermal energy is the term given to the energy that is lost and is not stored anywhere mechanically. This energy goes into a collection of unorganized molecules. A block of wood, a car, and a person are examples of organized collections of molecules. Air is an example of unorganized molecules. Example: A baseball player is running towards 2nd base. He decides to slide along the dirt into second base in order to avoid being tagged out. Unfortunately he starts to slide too early and comes to rest before reaching the base. When he was moving he had energy. As he slid into second base, he began to lose energy to the dirt and air.The energy went into heating up the dirt and then the dirt heated up the air above it. His energy cannot be recovered. Eventually the "lost" energy goes into moving the unorganized collection of molecules in the air. It has been transformed into thermal energy.

The term, "thermal energy," is a physicist's generic energy term used to describe when mechanical energy is lost. It can be accounted for by means beyond the scope of this text.

The first law of thermodynamics says that all energy is conserved. This is referred to as the law of conservation of energy. This means if you are sitting, at rest, at the top of a playground slide and then slide down to the bottom, all the forms of energy at the top and the bottom of the slide add up to give the same number. It is written like the the line shown below.

If this expression is applied to the slide example above, it would be written as

Since only two forms of energy are being considered, it could further be described as

Example

This video shows how to apply the law of conservation of energy to problem solving.

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The second law of thermodynamics (when applied to mechanical energies) says all mechanical energies are not conserved but it can be accounted for by the work of nonconservative forces. Mathematically it looks like this

Where the work is work by nonconservative forces. Conservative forces, such as gravity, springs and other elastic forces, have their own formula for calculating the energy and do not need to be described by these works. Other forces, such as those from motors, rockets, frictions, air resistance, etcetera, are non conservative forces. When work is done by a nonconservative force, energy is either added to subtracted from the body. the energy is accounted for through work.