concept

potential energy

Potential energy is the stored energy a system possesses due to its position or configuration, which can be released under certain conditions.
9 related articles · 6 formulas · 1 who worked here

Description

The energy hidden in stationary objects is called potential by physicists. It comes in different forms: gravitational (associated with height in a gravitational field), elastic (compression or stretching of materials), electrical (charges in a field). All these types share a principle: the work that a system can perform is determined by its configuration. When a stone falls down, its potential melts away, turning into speed. On cosmic scales, gravitational potential energy is the main source of starlight: as a gas-dust cloud contracts, it heats up and ignites a thermonuclear furnace.

History

The term 'potential energy' was introduced in 1853 by the Scottish engineer and physicist William Rankine. However, the roots of the idea go back to Galileo and Leibniz, who spoke of 'living force' (vis viva) and 'dead force'. Lagrange and Hamilton embedded potential into analytical mechanics, making it the foundation of describing motion. In 1915, Emmy Noether proved that the law of conservation of energy (and hence the rigorous definition of potential function) follows from the homogeneity of time. Today, potential energy remains a key concept from quantum mechanics to cosmology.

How it works

In mechanics, the change in potential energy dU is related to the work dA done by a conservative force: dU = -dA = -F·dr. The potential is defined up to an arbitrary constant; only potential differences have physical meaning. In the Earth's gravitational field, U = mgh, where h is measured from a chosen reference level. In general, the gravitational potential of a point mass M is φ = -GM/r, and the potential energy of a test body of mass m is U = mφ. In electrodynamics, the scalar potential φ and vector potential A form a four-dimensional potential that determines field strengths. Quantum mechanics uses the potential energy operator in the Schrödinger equation. The gravitational potential energy of a uniform sphere (e.g., a star) determines its internal thermal history and stability.

In practice

Hydroelectric power plants convert water's potential energy into electricity. Any object at height stores energy ready to do work — from a clock weight to a hanging chandelier.

Fun fact

A tablespoon of neutron star matter, if it fell to Earth, would release as much energy as a powerful atomic bomb — thanks to the enormous gravitational potential energy.

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Formulas

$$V(z) = \phi - eFz - \frac{e^2}{4\pi\epsilon_0 z}$$
Potential energy for electron emission including work function and field.
What is in the formula
Vvariablepotential energy of electron — potential energy joule
zvariabledistance from the metal surface — position metre
φvariablework function of the metal — work function joule
Fvariableapplied electric field strength — electric field volt per metre
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
ε0constantability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre
m(φ,f,z)=φ-efz-\frac{e^{2}}{16πε_{0}z} · 2505.00872v4
$$K > (\gamma - 1) m c^2$$
Particle kinetic energy exceeds rest mass energy threshold.
What is in the formula
Kvariablekinetic energy — kinetic energy joule
γvariableLorentz factor — lorentz factor
mvariablerest mass — mass kilogram
cvariablespeed of light — speed of light metre per second
cconstantThe speed of light in vacuum, a fundamental constant of nature. — speed of light = 299792458 metre per second
v>2mc^2 · 2604.14378
$$V = \frac{1}{\sqrt{f}} \frac{d^2 \sqrt{f}}{dx^2}$$
An effective potential is defined from a function's second derivative.
What is in the formula
Vvariableeffective potential — potential energy joule
fvariablefunction whose curvature defines the potential
xvariableindependent variable — position metre
d²/dx²operatorsecond derivative with respect to x — second derivative
v=\frac{1}{\sqrt{v}}\frac{d^2\sqrt{v}}{d\eta_*^2} · 2605.11565v1
$$f( ext{mix}) = rac{ ext{component A}}{N_A} ext{ln} ext{component A} + rac{ ext{component B}}{N_B} ext{ln} ext{component B} + ext{interaction term}$$
Describes the free energy of mixing for polymer solutions.
What is in the formula
f(mix)variableFree energy of mixing per lattice site — free energy density joule per cubic metre
component AvariableVolume fraction of component A — volume fraction
component BvariableVolume fraction of component B — volume fraction
N_AvariableDegree of polymerization of component A — degree of polymerization
N_BvariableDegree of polymerization of component B — degree of polymerization
interaction termvariableInteraction contribution (typically χ φ_A φ_B)
lnoperatorComputes the natural logarithm of the argument — natural logarithm
f(φ)=\frac{φ}{n_a}\logφ+\frac{1-φ}{n_b}\log(1-φ)+χφ(1-φ) · 2606.31786
$$U = E_{\text{pair}} < 0$$
Pairing energy must be negative for favorable pair formation.
What is in the formula
UvariablePairing energy — energy joule
E_{\text{pair}}variablePairing energy contribution — energy joule
u=e_2+e_0-e_1-e_{1'}<0 · 2607.03022
$$E_{\text{ads}} = E_{\text{system}} - (E_{\text{surface}} + E_{\text{adsorbate}})$$
Energy released when a molecule adsorbs on a surface.
What is in the formula
E_{\text{ads}}variableAdsorption energy — energy joule
E_{\text{system}}variableTotal energy of the system with adsorbate — energy joule
E_{\text{surface}}variableEnergy of the clean surface — energy joule
E_{\text{adsorbate}}variableEnergy of the isolated adsorbate — energy joule
e_{{ads}}=e_{{system}}-(e_{{surface}}+e_{{molecule}}) · 2607.05321

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