# Potential energy

Energy stored in an object or substance. Examples may include

• gravitational potential energy 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
• elastic potential energy stored as the result of a deformed solid such as a stretched spring
• chemical potential energy stored in a molecular substance such as a hydrocarbon, which may be released by a chemical reaction (see oxidation)
• electrical potential energy

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

A --> B --> A = (b-a)+(a-b) = 0

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 = a+c and the PE at B to be b+c [where c can be any number, positive or negative, but it must be the same number for all points] then the work done going from

A --> B = (b+c)-(a+c)= b-a as before.

In practical terms, this means that you can set the zero of PE 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 --> B does not depend on the route taken. If it did then it would be pointless to define a PE 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 PE associated with friction.

All the examples above are actually force field stored energy (sometimes in disguise). For example in elastic PE, 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 PE is actually electromagnetic PE. 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 PE as being derived from force or you can think of force as being derived from PE.