Potential Energy Formula

Energy is the most important concept to grasp in fundamental physics. Every change that occurs in a physical system is an energy change. The different forms of energy can all be classified into two forms primarily - potential and kinetic energy.

What is Potential Energy?

It is the dormant stored energy in any system. It is a type of energy that a system possesses on account of its configuration and position of various constituents of that system in presence of a force. This is the energy stored in an object when work is done on it against a force. Depending on the configuration of a system and the forces operational in it, there are various forms of potential energy. Motion occurs when this stored energy is converted into kinetic energy.

The formula for potential energy of an object in a force field depends on its position and other inherent factors like mass and charge. For example, when an object is lifted up, work is done against the gravitational force that pulls it down. This work done on the object is stored as potential energy. When such an object is released from the height to which it has been lifted and it falls freely, gravitational potential energy gets converted into kinetic energy. So one can say that objects at higher altitudes on Earth have a higher potential energy.

To solve a problem in dynamics, one must know the equation of motion of a system. There are various ways in which you could derive the equation of motion. One of them is by solving the Lagrangian equations of motion. The Lagrangian is the difference of potential and kinetic energy. You need to know the formulas for particular systems along with the kinetic energy expressions, to set up the Lagrangian. Potential energy is measured in SI unit of 'Joule'.

Different Formulas

The formula for potential energy of a system depends on the forces at work and the constituents of a system. All macroscopic systems outside the atomic nucleus are either governed by the electromagnetic or gravitational forces. So each one of the formulas are related to these two forces. Here are some of them.

Gravitational potential energy is a function of the position of the object in a gravitational field, force of gravity at that point and the mass of the object. The formula is as follows:

Gravitational Potential Energy = mgh
where m is the mass, g is the acceleration due to gravity (9.81 m/s²) and h is the height above the surface of earth.

The formula for a test charge 'q' that has been placed in the presence of a source charge 'Q', is as follows:

Electric Potential Energy = qQ/4πε_oR
where ε_o is the permittivity of free space and R is the distance between the two point charges.

The formula for a spring with a spring constant k is as follows:

Elastic Potential Energy = ½ kx²
where x is the displacement parameter for a spring.

Using the formulas provided above is all about plugging in the right values and getting the answers. Make a list of physics formulas, which includes all the relevant ones that you need. It comes in handy when you need a quick reference and revision before an exam.