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Potential energy or potential is energy stored in an object or substance. In most scientific circles, potential energy is symbolized by .

 Table of contents 1 Gravitational potential energy 2 Elastic potential energy 3 Chemical potential energy 4 Electrical potential energy 5 Relation between potential energy and force

Gravitational potential energy

This energy is stored as a result of the elevated position of an object such as a rock on top of a hill or water behind a dam. It is written as
where is the mass of the object in kilograms, the acceleration due to gravity in m/s2 and the height in meters above a chosen reference level.

In relation to spacecraft and astronomy g is not constant and the formula becomes an integral. In the case of a sphere of uniform mass (such as a planet), with h measured above the surface, the integral takes the form:

Where is the radius of the sphere, M is the mass of the sphere, and G is the gravitational constant.

If h is instead taken to be the distance from the center of the sphere, then outside the sphere the potential energy relative to that at the center has two terms:

,

which evaluates to:

[We may also want to link to an explanation of that second term (the gravitational forces created by hollow spherical shells)]

A frequently adopted convention is that an object infinitely far away from an attracting source has zero potential energy. Relative to this, an object at a finite distance r from a source of gravitation has negative potential energy. If the source is approximated as a point mass, the potential energy simplifies to:

Elastic potential energy

where is the spring constant, expressed in N/m, and is the displacement from the relaxed position, expressed in meters.

Chemical potential energy

This energy is stored in a molecular substance such as a hydrocarbon, which may be released by a chemical reaction (see oxidation)

Electrical potential energy

The electrical potential energy per unit charge is called electrical potential. It is expressed in volt. The fact that a potential is always relative to a reference point is often made explicit by using the term potential difference. The term voltage is also common.

Relation between potential energy and force

Potential energy is closely linked with forces. If the work done going around a loop is zero, then the force is said to be conservative and it is possible to define a numerical value of potential associated with every point in space. A force field can be re-obtained by taking the vector gradient of the potential field.

For example, gravity is a conservative force. The work done by a unit mass going from point A with to point B with by gravity is and the work done going back the other way is so that the total work done from

The nice thing about potential energy is that you can add any number to all points in space and it doesn't affect the physics. If we redefine the potential at A to be and the potential at B to be [where can be any number, positive or negative, but it must be the same number for all points] then the work done going from
as before.

In practical terms, this means that you can set the zero of anywhere you like. You might set it to be zero at the surface of the Earth or you might find it more convenient to set it zero at infinity.

A thing to note about conservative forces is that the work done going from A to B does not depend on the route taken. If it did then it would be pointless to define a potential at each point in space. An example of a non-conservative force is friction. With friction, the route you take does affect the amount of work done, and it makes no sense at all to define a potential associated with friction.

All the examples above are actually force field stored energy (sometimes in disguise). For example in elastic potential energy, stretching an elastic material forces the atoms very slightly, further apart. Powerful electromagnetic forces try to keep the atoms at their optimal distance and so elastic potential is actually electromagnetic potential. Having said that, scientists rarely talk about forces on an atomic scale. Everything is phrased in terms of energy rather than force. You can think of potential energy as being derived from force or you can think of force as being derived from potential energy.  