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U = ½ · k · x 2(elastic) U = ½ · C · V 2 (electric) U = - m · B (magnetic) In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these ...

There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of configurations of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from a potential are also called conservative forces. The work done by a conservative force is W = − Δ U {\displaystyle \,W=-\Delta U} w...

Potential energy is closely linked with forces. If the work done by a force on a body that moves from A to B does not depend on the path between these points (if the work is done by a conservative force), then the work of this force measured from A assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for an applied force is independent of the path, then the work done by the force is evaluated at the start and end of the trajectory of the point of application. This means that there is a function U ( x ), called a "potential," that can be evaluated at the two points x A and x B to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is W = ∫ C F ⋅ d x = U ( x A ...

For small height changes, gravitational potential energy can be computed using U g = m g h , {\displaystyle U_{g}=mgh,} where m is the mass in kg, g is the local gravitational field (9.8 metres per second squared on earth), h is the height above a reference level in metres, and U is the energy in joules. In classical physics, gravity exerts a constant downward force F =(0, 0, F z ) on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r (t) = ( x (t), y (t), z (t)), such as the track of a roller coaster is calculated using its velocity, v =( v x , v y , v z ), to obtain W = ∫ t 1 t 2 F ⋅ v d t = ∫ t 1 t 2 F z v z d t = F z Δ z . {\displaystyle W=\int _{t_{1}}^{t_{2}}{\boldsymbol {F}}\cdot {\boldsymbol {v}}\mathrm {d} t=\int _{t_{1}}^{t_{2}}F_{z}v_{z}\mathrm {d} t=F_{z}\Delta z.} where the integral of the vertical...

A horizontal spring exerts a force F = (− kx , 0, 0) that is proportional to its deformation in the axial or x direction. The work of this spring on a body moving along the space curve s ( t ) = ( x ( t ), y ( t ), z ( t )), is calculated using its velocity, v = ( v x , v y , v z ), to obtain W = ∫ 0 t F ⋅ v d t = − ∫ 0 t k x v x d t = − ∫ 0 t k x d x d t d t = ∫ x ( t 0 ) x ( t ) k x   d x = 1 2 k x 2 {\displaystyle W=\int _{0}^{t}\mathbf {F} \cdot \mathbf {v} \mathrm {\,} {d}t=-\int _{0}^{t}kxv_{x}\mathrm {\,} {d}t=-\int _{0}^{t}kx{\frac {\mathrm {d} x}{\mathrm {d} t}}dt=\int _{x(t_{0})}^{x(t)}kx\ \mathrm {d} x={\frac {1}{2}}kx^{2}} For convenience, consider contact with the spring occurs at t = 0, then the integral of the product of the distance x and the x -velocity, xv x , is x 2/2. The function U ( x ) = 1 2 k x 2 , {\d...

The gravitational potential function, also known as gravitational potential energy, is: U = − G M m r , {\displaystyle U=-{\frac {GMm}{r}},} The negative sign follows the convention that work is gained from a loss of potential energy. Derivation The gravitational force between two bodies of mass M and m separated by a distance r is given by Newton's law F = − G M m r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {GMm}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} } is a vector of length 1 pointing from M to m and G is the gravitational constant. Let the mass m move at the velocity v then the work of gravity on this mass as it moves from position r (t 1 ) to r (t 2 ) is given by W = − ∫ r ( t 1 ) r ( t 2 ) G M m r 3 r ⋅ d r = − ∫ t 1 t 2 G M m r 3 r ⋅ v d t . {\displayst...

The electrostatic force exerted by a charge Q on another charge q separated by a distance r is given by Coulomb's Law F = 1 4 π ε 0 Q q r 2 r ^ , {\displaystyle \mathbf {F} ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} } is a vector of length 1 pointing from Q to q and ε 0 is the vacuum permittivity. This may also be written using Coulomb constant k e = 1 ⁄ 4πε 0 . The work W required to move q from A to any point B in the electrostatic force field is given by the potential function U ( r ) = 1 4 π ε 0 Q q r . {\displaystyle U({r})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r}}.}

The potential energy is a function of the state a system is in, and is defined relative to that for a particular state. This reference state is not always a real state; it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces. Any arbitrary reference state could be used; therefore it can be chosen based on convenience. Typically the potential energy of a system depends on the relative positions of its components only, so the reference state can also be expressed in terms of relative positions.

Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth's gravity. The potential energy due to elevated positions is called gravitational potential energy, and is evidenced by water in an elevated reservoir or kept behind a dam. If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. Consider a book placed on top of a table. As the book is raised from the floor to the table, some external force works against the gravitational force. If the book falls back to the floor, the "falling" energy the book receives is provided by the gravitational force. Thus, if the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy. When the book hits the floor this kinetic energy is convert...

Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. As an example, when a fuel is burned the chemical energy is converted to heat, same is the case with digestion of food metabolized in a biological organism. Green plants transform solar energy to chemical energy through the process known as photosynthesis, and electrical energy can be converted to chemical energy through electrochemical reactions. The similar term chemical potential is used to indicate the potential of a substance to undergo a change of configuration, be it in the form of a chemical reaction, spatial transport, particle exchange with a reservoir, etc.