# Potential energy

A potential energy is the energy that an object has because of its position on a gradient of potential energy called a potential field.[1][2]

• An actual, or kinetic, energy (E = hf) is a nonzero‑frequency angular momentum.[3] It is the amount of work a moving body is capable of doing at any instant.[4] The actual energy is always positive.[5]
• A potential energy is the zero‑frequency angular momentum stored in a potential flux of the vacuum.[6][7] The potential energy is always negative.[8] It is not a mere convention but a consequence of conservation of energy in the zero-energy universe—as an object descends into a potential field, its potential energy becomes more negative, while its actual energy becomes more positive.

The potential fields are irrotationally radial ("electric") fluxes of the vacuum[6][7] and divide into two classes:

• The gravitoelectric fields;[9]
• The electric fields.[10]

Accordingly, the potential energy of the universe divides into two classes:

• The gravitoelectric potential energy, also known as rest mass;[11]
• The electric potential energy, also known as electric charge (a positive charge is a region of high electric potential energy, while a negative charge is a region of low electric potential energy).

In accordance with the minimum total potential energy principle, the universe's matter flows towards the minimum (i.e., the most negative) total potential energy. This cosmic flow is time.

## Simple examples

Bringing a rock uphill consumes (negates) actual energy but increases (i.e., makes less negative) its gravitoelectric potential energy.

Increasing the distance between two elementary electric charges of different signs (an electron and a proton) consumes (negates) external actual energy but increases (i.e., makes less negative) the electric potential energy of their mutual attraction.

Stretching a rubber band increases its elastic potential energy, which is a form of the electric potential energy. A mixture of a fuel and an oxidant has a chemical potential energy, which is another form of the electric potential energy. Batteries too have chemical potential energy.

## Gravitational potential energy

Hyrdroelectric power plants use the gravitational potential energy of water (in the form of a difference in height) to produce electricity.

Gravitational potential energy is experienced by an object when height and mass is a factor in the system. Gravitational potential energy causes objects to move towards each other. If an object is lifted a certain distance from the surface from the Earth, the force experienced is caused by weight and height. Work is defined as force over a distance, and work is another word for energy. This means Gl Potential Energy is equal to:

${\displaystyle U=F\Delta h}$
where
${\displaystyle F}$ is the force of gravity
${\displaystyle \Delta h}$ is the change in height

or

${\displaystyle U=mgh}$

Total work done by Gravitational Potential Energy in a moving object from position 1 to position 2 can be found by:

${\displaystyle \Delta W=U_{1}-U_{2}}$

or

${\displaystyle \Delta W=mgh_{1}-mgh_{2}}$
where
${\displaystyle m}$ is the mass of the object
${\displaystyle g}$ is the acceleration caused by gravity (constant)
${\displaystyle h_{1}}$ is the first position
${\displaystyle h_{2}}$ is the second position

## Electric potential energy

Electric potential energy is experienced by charges both different and alike, as they repel or attract each other. Charges can either be positive (+) or negative (-), where opposite charges attract and similar charges repel. If two charges were placed a certain distance away from each other, the potential energy stored between the charges can be calculated by:

${\displaystyle U={\frac {kQq}{r}}}$
where
${\displaystyle k}$ is 1/4πє (for air or vacuum it is ${\displaystyle 9x10^{9}Nm^{2}/C^{2}}$)
${\displaystyle Q}$ is the first charge
${\displaystyle q}$ is the second charge
${\displaystyle r}$ is the distance apart

## Elastic potential energy

Elastic potential energy is experienced when a rubbery material is pulled away or pushed together. The amount of potential energy the material has depends on the distance pulled or pushed. The longer the distance pushed, the greater the elastic potential energy the material has. If a material is pulled or pushed, the potential energy can be calculated by:

${\displaystyle U={\frac {1}{2}}kx^{2}}$
where
${\displaystyle k}$ is the spring force constant (how well the material stretches or compresses)
${\displaystyle x}$ is the distance the material moved from its original position

## References

1. Morrison, Faith A. An Introduction to Fluid Mechanics. CUP, 2013, p. 442. "Energy may be stored in the state of a system—for example, as kinetic energy stored in the speed of the system, as potential energy stored in the position of the system in a potential field, or as internal energy stored in the chemical state of a system."
2. Best, Myron G. Igneous and Metamorphic Petrology. John Wiley & Sons, 2013, p. 21. "Potential energy can be equated with the amount of work required to move a body from one position to another in a potential field, in this instance, the gravitational field of the Earth."
3. Biedenharn, L. C.; Louck, J. D. Angular Momentum in Quantum Physics. Addison-Wesley Pub. Co., Advanced Book Program, 1981. "The Planck quantum of action, h, has precisely the dimensions of an angular momentum, and, moreover, the Bohr quantization hypothesis specified the unit of (orbital) angular momentum to be ħ = h/2π. Angular momentum theory and quantum physics are thus clearly linked."
4. Skertchly, J. Alfred. Natural Philosophy. Part I. Mechanics. Thomas Murby, 1873, p. 145. "Kinetic, or Actual, Energy is the amount of work a moving body is capable of doing at any instant."
5. Semat, Henry; Baumel, C. Philip. Fundamentals of Physics. Holt, Rinehart and Winston, 1974, p. 83. "It must be emphasized that energy is a scalar; even though kinetic energy is a consequence of motion it has no direction and is a scalar quantity. Since the square of the speed is always positive and the mass of an object is always positive, the kinetic energy is always positive."
6. Ziegler, Franz. Mechanics of Solids and Fluids. Springer, 1995, p. 167. "Force in such a potential field is a flux in the sense of a mechanical driving agent."
7. Volovik, G. E. The Universe in a Helium Droplet. OUP, 2003, p. 60. "The non-viscous flow of the vacuum should be potential (irrotational)."
8. Why is the Potential Energy Negative? HyperPhysics
9. Grøn, Øyvind; Hervik, Sigbjørn. Einstein's General Theory of Relativity with Modern Applications in Cosmology. Springer, 2007, pp. 201, 203. "φ is the Newtonian or 'gravitoelectric' potential: φ = −Gm/r. ... In the Newtonian theory there will not be any gravitomagnetic effects; the Newtonian potential is the same irrespective of whether or not the body is rotating. Hence the gravitomagnetic field is a purely relativistic effect. The gravitoelectric field is the Newtonian part of the gravitational field, while the gravitomagnetic field is the non-Newtonian part."
10. Soviet Physics, Uspekhi. Vol. 40, issues 1–6, American Institute of Physics, 1997, p. 39. "From Maxwell equations (6.20) it follows that the electric field is potential: E(r) = −gradφ(r)."
11. Heighway, Jack. Einstein, the Aether and Variable Rest Mass. HeighwayPubs, 2011, p. 36. "Understanding why rest masses are reduced in a gravitational field only requires a simple insight: when an object is raised in a gravitational field, the gravitational potential energy increase is real, and exists as an increase, usually tiny, in the rest mass of the object."