Navigation Links

HOME >> BIOLOGY >> DEFINITION |

Potential energy

**Potential energy** (**U**, or **E _{p}**), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. For example a mass released above the Earth has energy resulting from the gravitational attraction of the Earth which is transferred in to kinetic energy.

Contents |

This energy is stored as a result of the elevated position of an object such as a rock on top of a hill or water behind a dam. It is written as

where *m* is the mass of the object, *g* the acceleration due to gravity and *h* the height above a chosen reference level (typical units would be kilograms for *m*, metres/second^{2} for *g*, and metres for *h*).

In relation to spacecraft and astronomy *g* is not constant and the formula becomes an integral. In the case of a sphere of uniform mass (such as a planet), with *h* measured above the surface, the integral takes the form:

Where *h*_{0} is the radius of the sphere, *M* is the mass of the sphere, and *G* is the gravitational constant.

If *h* is instead taken to be the distance from the center of the sphere, then outside the sphere the potential energy relative to that at the center has two terms:

which evaluates to:

[We may also want to link to an explanation of that second term (the gravitational forces created by hollow spherical shells)]

A frequently adopted convention is that an object infinitely far away from an attracting source has zero potential energy. Relative to this, an object at a finite distance *r* from a source of gravitation has negative potential energy. If the source is approximated as a point mass, the potential energy simplifies to:

See also Gravitational binding energy.

This energy is stored as the result of a deformed solid such as a stretched spring. As a result of Hooke's law, it is given by:

where *k* is the spring constant (a measure of the stiffness of the spring), expressed in N/m, and *x* is the displacement from the equilibrium position, expressed in metres *(see Main Article: Elastic potential energy)*.

Chemical energy is a form of **potential energy** related to the breaking and forming of chemical bonds.

Albert Einstein's famous equation, derived in his special theory of relativity, can be written:

where *E _{0}* is the rest mass energy,

The rest mass energy is the amount of energy inherent in the mass when it is at rest. This equation quantifies the equivalence of mass and energy: A small amount of mass is equivalent to a very large amount of energy. (i.e., 90 petajoule/kg ≈ 21 megatons/kg)

The electrical potential energy per unit charge is called electrical potential. It is expressed in volts. The fact that a potential is always relative to a reference point is often made explicit by using the term potential difference. The term voltage is also common.

The electrical *potential energy* between two charges *q*_{1} and *q*_{2} is:

The electric *potential* generated by charges *q*_{1} (denoted *V*_{1}) and *q*_{2} (denoted *V*_{2}) is:

Potential energy is closely linked with forces. If the work done going around a loop is zero, then the force is said to be conservative and it is possible to define a numerical value of potential associated with every point in space. A force field can be re-obtained by taking the vector gradient of the potential field.

For example, gravity is a conservative force. The work done by a unit mass going from point A with *U* = *a* to point B with *U* = *b* by gravity is (*b* - *a*) and the work done going back the other way is (*a* - *b*) so that the total work done from

The nice thing about potential energy is that you can add any number to all points in space and it doesn't affect the physics. If we redefine the potential at A to be *a* + *c* and the potential at B to be *b* + *c* [where *c* can be any number, positive or negative, but it must be the same number for all points] then the work done going from

as before.

In practical terms, this means that you can set the zero of *U* anywhere you like. You might set it to be zero at the surface of the Earth or you might find it more convenient to set it zero at infinity.

A thing to note about conservative forces is that the work done going from A to B does not depend on the route taken. If it did then it would be pointless to define a potential at each point in space. An example of a non-conservative force is friction. With friction, the route you take does affect the amount of work done, and it makes no sense at all to define a potential associated with friction.

All the examples above are actually force field stored energy (sometimes in disguise). For example in elastic potential energy, stretching an elastic material forces the atoms very slightly further apart. Powerful electromagnetic forces try to keep the atoms at their optimal distance and so elastic potential is actually electromagnetic potential. Having said that, scientists rarely talk about forces on an atomic scale. Everything is phrased in terms of energy rather than force. You can think of potential energy as being derived from force or you can think of force as being derived from potential energy.

A graph of a 1D or 2D potential function with the function value scale increasing upward is useful to visualize the potential field: a ball rolling to the lowest part corresponds to a mass or charge, etc. being attracted.

E.g. a mass, being an area of attraction, may be called a gravitational well. See also potential well.

'"/>

(Date:12/5/2014)... 4, 2014 Tute Genomics, a leader in cloud-based ... Series A1 funding led by UK-based Eurovestech. Peak Ventures ... the investment round. "We are at a ... next-generation sequencing and seeks new approaches for the diagnosis, ... , MD MBA, and CEO of Tute Genomics. "One ...

(Date:11/21/2014)... According to a new market research report ... Control, Intrusion Detection, Parking Management, Under Vehicle Inspection), End ... - Global Forecasts to 2020", published by MarketsandMarkets, The ... $25 Billion in 2014 and is expected to reach ... 8.69%. Browse 116 market data Tables and ...

(Date:11/21/2014)... , Nov. 20, 2014 Atmel® Corporation ... in microcontroller (MCU) and touch technology solutions, today launched ... sensors with the widest V cc range ... temperature accuracy and faster I 2 C bus communication ... serial EEPROM memory making them ideal for consumer, industrial, ...

Breaking Biology News(10 mins):Tute Genomics Raises $2.3 Million to Scale Up Cloud-Based Genome Analytics and Accelerate Personalized Medicine 2Tute Genomics Raises $2.3 Million to Scale Up Cloud-Based Genome Analytics and Accelerate Personalized Medicine 3Industrial Security Systems Market Worth $38 Billion by 2020 2Industrial Security Systems Market Worth $38 Billion by 2020 3Atmel Launches Industry's First Wide-V(cc) Low-Power Temperature Sensor Family 2Atmel Launches Industry's First Wide-V(cc) Low-Power Temperature Sensor Family 3Atmel Launches Industry's First Wide-V(cc) Low-Power Temperature Sensor Family 4... . . People with tomorrow,s prosthetic ... cold and touch through a series of developments by ... different ORNL research groups, Ilia Ivanov and Dave Geohegan ... John Simpson of the superhydrophobic materials group, are combining ...

... -- If projected increases in the use of corn ... could be considerable, and water supply problems at the ... new report from the National Research Council. The ... identified opportunities for new agricultural techniques and technologies to ...

... found in the environment may be interacting with the ... easier because of a new field of science called ... National Academies of Sciences (NAS) recognizes the importance of ... the integration of toxicogenomics into regulatory decision making. ...

Cached Biology News:Story tips from the Department of Energy's Oak Ridge National Laboratory, October 2007 2Increase in ethanol production from corn could significantly impact 2Increase in ethanol production from corn could significantly impact 3NAS report offers new tools to assess health risks from chemicals 2Affinity chromatographyAlcoholAlbuminAlexander FlemingAlleleAlfred Russel WallaceAllosteryAlgaAllele frequencyAllosteryAlpha helixAlternative splicingAmineAmes test

Other Tags