What is Potential Energy? A 5 Minute Introduction

[Greg Bernhardt]

Definition/Summary
Potential energy is simply another name for (minus) the work done by a conservative force.
Since the work-energy theorem states that change in energy minus work done is constant, that means that for a conservative force, energy plus potential energy is constant.
For example, a object of mass $m$ moving a height $h$ and distance $s$ along a curved path up a slope loses energy $\int mg\,dh$ because of the force of gravity and $\int \mathbf{F}\cdot d\mathbf{s}$ because of the force $F$ of friction. Gravity is conservative (while friction is not) and so the first integral may be replaced simply by $mgh$
Potential energy is measured relative to an arbitrary level, which in each case may be taken to be whatever is most convenient (for example the starting level, or infinity).
Potential energy (commonly shortened to PE) is a scalar (an ordinary number), with the same dimensions as energy...

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[eljose79]

Potential energy is a term used to describe the energy that an object possesses due to its position or configuration in a system. It is often referred to as the energy that an object has stored within it, which can be released or converted into other forms of energy. This energy is associated with the concept of work done by a conservative force, which is a force that does not dissipate or lose energy as it acts on an object. According to the work-energy theorem, the change in energy of an object is equal to the work done on it minus the work done by it. In the case of a conservative force, this means that the sum of the object's energy and potential energy remains constant. Potential energy is measured relative to an arbitrary level, which can be chosen based on convenience. It is a scalar quantity with the same dimensions as energy and is often abbreviated as PE. Examples of potential energy include gravitational potential energy, elastic potential energy, and electric potential energy.