Potential energy

Potential energy can be thought of as energy stored within a physical system. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός It is called potential energy because it has the potential to be converted into other forms of energy, such as kinetic energy, and to do work in the process. The kinetic energy of an object is the extra Energy which it possesses due to its motion In Physics, mechanical work is the amount of Energy transferred by a Force. The standard (SI) unit of measure for potential energy is the joule, the same as for work, or energy in general. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity

1 Overview
2 Gravitational potential energy
3 Elastic potential energy
- 3.1 Calculation of elastic potential energy
4 Chemical potential energy
5 Electrical potential energy
6 Thermal potential energy
7 Rest mass energy
8 Relation between potential energy and force
9 References

Overview

Potential energy is the energy which is stored. Potential energy exists when there is a force that tends to pull an object back towards some original position when the object is displaced. In Physics, a force is whatever can cause an object with Mass to Accelerate. This force is often called a restoring force. Restoring force, in a Physics context is a variable Force that gives rise to an equilibrium in a physical system The phrase 'potential energy' was coined by William Rankine. William John Macquorn Rankine FRS ( July 5, 1820 &ndash December 24, 1872) was a Scottish engineer and ^[1] For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, un-stretched position. Or, suppose that a weight is lifted straight up. The force of gravity will try to bring it back down to its original position. Gravitation is a natural Phenomenon by which objects with Mass attract one another The initial steps of stretching the spring and lifting the weight both require energy to perform. According to the principle of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may Instead it is stored as potential energy. If the spring is released or the weight is dropped, this stored energy will be converted into kinetic energy by the restoring force — elasticity in the case of the spring, and gravity in the case of the weight. The kinetic energy of an object is the extra Energy which it possesses due to its motion Restoring force, in a Physics context is a variable Force that gives rise to an equilibrium in a physical system A material is said to be elastic if it deforms under stress (e Gravitation is a natural Phenomenon by which objects with Mass attract one another

The more formal definition is that potential energy is the energy of position, that is, the energy an object is considered to have due to its position in space. There are a number of different types of potential energy, each associated with a particular type of force. In Physics, a force is whatever can cause an object with Mass to Accelerate. More specifically, every conservative force gives rise to potential energy. A conservative force is defined as a Force with the following property when an object moves from one location to another the force changes the Potential energy of For example, the work of elastic force is called elastic potential energy; work of gravitational force is called gravitational potential energy, work of the Coulomb force is called electric potential energy; work of 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. A material is said to be elastic if it deforms under stress (e Gravitation is a natural Phenomenon by which objects with Mass attract one another ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature Baryons are the family of Subatomic particles with a Baryon number of 1 In Physics, Chemistry, and Biology, intermolecular forces are forces that act between stable Molecules or between functional groups of Chemical potential energy, such as the energy stored in fossil fuels, is the work of Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Fossil fuels or mineral fuels are fossil source Fuels that is Hydrocarbons found within the top layer of the Earth’s crust. Thermal energy usually has two components: the kinetic energy of random motion of particles and potential energy of their mutual positions. The kinetic energy of an object is the extra Energy which it possesses due to its motion

As a general rule, the work done by a conservative force F will be

$\,W = -\Delta PE$

where $Δ P E$ is the change in the potential energy associated with that particular force. The most common notations for potential energy are PE and U. It is important to note that electric potential (commonly denoted with a V for voltage) is not the same as electric potential energy. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field

Gravitational potential energy

Gravitational energy is the potential energy associated with gravitational force. Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass If an object falls from point A to point B 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.

The gravitational force keeps the planets in orbit about the Sun.

For example, consider a book, placed on top of a table. When the book is raised from the floor to the table, the gravitational force does negative work. If the book is returned back to the floor, the exact same (but positive) work will be done by the gravitational force. Thus, if the book is knocked off the table, this work (called potential energy) goes to accelerate the book (and is converted into kinetic energy). The kinetic energy of an object is the extra Energy which it possesses due to its motion When the book hits the floor this kinetic energy is converted into heat and sound by the impact.

The factors that affect an object's gravitational potential energy are its height relative to some reference point, its mass, and the strength of the gravitational field it is in. Thus, a book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard, and less gravitational potential energy than a heavier book lying on the same table. An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height on Earth because the Moon's gravity is weaker. (This follows from Newton's law of gravitation because the mass of the moon is much smaller than that of the Earth. Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass ) It is important to note that "height" in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. The following sections provide more detail.

The strength of a gravitational field varies with location. However, within a small range of distances from the center of the source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is constant. Near the surface of the Earth, for example, we assume that the acceleration of gravity is a constant g=9. 8 m/s². If we assume that the force of gravity is constant, a simple expression for gravitational potential energy can be derived using the W = Fd equation for work, and the equation

$\, W_F = -\Delta PE_F$ . In Physics, mechanical work is the amount of Energy transferred by a Force.

If h is the height above an arbitrarily assigned reference point, then

$\, PE = mgh$

where PE is the gravitational potential energy of an object of mass m at that point. Hence, the potential difference is

$\,\Delta PE = mg \Delta h$ .

However, if the force of gravity varies too much for this approximation to be valid, then we have to use the general, integral definition of work in order to determine gravitational potential energy. In order to derive the following formula, the reference point where PE = 0 is set at an infinite distance away from the source of the gravitational field provided by mass m₂. Thus, unlike the PE = mgh approximation formula, this formula assumes a preset reference point that cannot be arbitrarily defined. In order for the equation to be valid, m₂ must remain practically stationary so that its gravitational field does not change over time.

The gravitational potential energy of a mass m₁ at a distance R from another mass m₂ is

$PE = -G \frac{m_1 m_2}{R}$ .

This equation is found by integrating the gravitational force (whose magnitude is given by Newton's law of gravitation) with respect to the distance of the object r from the gravitating body from r = R to $r = \infty$ . The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass

Elastic potential energy

A catapult works due to elastic potential energy. A catapult is any one of a number of non-handheld mechanical devices used to throw a Projectile a great distance without the aid of an explosive substance—particularly various

Main article: Elastic potential energy

Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (often termed under the word stress by physicists). The elastic Potential energy is defined as a work (force x distance needed to compress or expand an elastic body A material is said to be elastic if it deforms under stress (e A bow is a Weapon that projects arrows powered by the elasticity of the bow Stress is a measure of the average amount of Force exerted per unit Area. It arises as a consequence of a force that tries to restore the object to its original shape, which is most often the electromagnetic force between the atoms and molecules that constitute the object. In Physics, the electromagnetic force is the force that the Electromagnetic field exerts on electrically charged particles

Calculation of elastic potential energy

In the case of a spring of natural length l and modulus of elasticity λ under an extension of x, elastic potential energy can be calculated using the formula:

$E = \frac{\lambda x^2}{2l}$

This formula is obtained from the integral of Hooke's Law:

$U_e = \int {k x}\, dx = \frac {1} {2} k x^2$

The equation is often used in calculations of positions of mechanical equilibrium. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the

In the general case, elastic energy is given by the Helmholtz potential per unit of volume f as a function of the strain tensor components ε_ij:

$f(\epsilon_{ij}) = \lambda \left ( \sum_{i=1}^{3} \epsilon_{ii}\right)^2+2\mu \sum_{i=1}^{3} \sum_{j=1}^{3} \epsilon_{ij}^2$

Where λ and μ are the Lamé elastical coefficients. The connection between stress tensor components and strain tensor components is:

$\sigma_{ij} = \left ( \frac{\partial f}{\partial \epsilon_{ij}} \right)_S$

For a material of Young's modulus, Y (same as modulus of elasticity λ), cross sectional area, A₀, initial length, l₀, which is stretched by a length, $Δ l$ :

$U_e = \int {\frac{Y A_0 \Delta l} {l_0}}\, dl = \frac {Y A_0 {\Delta l}^2} {2 l_0}$

where U_e is the elastic potential energy.

The elastic potential energy per unit volume is given by:

$\frac{U_e} {A_0 l_0} = \frac {Y {\Delta l}^2} {2 l_0^2} = \frac {1} {2} Y {\varepsilon}^2$

where $\varepsilon = \frac {\Delta l} {l_0}$ is the strain in the material.

Chemical potential energy

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. A chemical bond is the physical process responsible for the attractive interactions between Atoms and Molecules and which confers stability to diatomic and polyatomic Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called For 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. Solar energy is the Light and radiant heat from the Sun that powers Earth 's Climate and Weather and sustains Life Photosynthesis is a Metabolic pathway that converts Light Energy into Chemical energy. Electrochemistry is a branch of Chemistry that studies Chemical reactions which take place in a Solution at the interface of an electron conductor

The similar term chemical potential is used by chemists to indicate the potential of a substance to undergo a chemical reaction. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical

Electrical potential energy

Main article: electrical energy

An object can also have potential energy by virtue of its electric charge and several forces related to their presence. Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. There are three main kinds of this kind of potential energy; electrostatic potential energy, electrodynamic potential energy (also sometimes called magnetic potential energy), and nuclear potential energy.

Strong (sparks) in gas inside a plasma lamp. Plasma lamps (also variously plasma globes balls domes spheres or orbs are Novelty items which were most popular in the 1980s

Electrostatic potential energy

Main article: Electrostatic potential energy

In case the electric charge of an object can be assumed to be at rest, it has potential energy due to its position relative to other charged objects. Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where

The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where It is defined as the work that must be done to move it from an infinite distance away to its present location, in the absence of any non-electrical forces on the object. In Physics, mechanical work is the amount of Energy transferred by a Force. This energy is non-zero if there is another electrically charged object nearby.

The simplest example is the case of two point-like objects A₁ and A₂ with electrical charges q₁ and q₂. The work W required to move A₁ from an infinite distance to a distance d away from A₂ is given by:

$W=k\frac {q_1q_2} d$

where k is Coulomb's constant, equal to $\frac 1 {4\pi\epsilon_0}$ . ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form

This equation is obtained by integrating the Coulomb force between the limits of infinity and d. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form

A related quantity called electric potential is equal to electric potential energy of a unit charge. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field

Electrodynamic potential energy

In case a charged object or its constituent charged particles are not at rest, it generates a magnetic field giving rise to yet another form of potential energy, often termed as magnetic potential energy. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges This kind of potential energy is a result of the phenomenon magnetism, whereby an object that is magnetic has the potential to move other similar objects. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Magnetic objects are said to have some magnetic moment. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current Magnetic fields and their effects are best studied under electrodynamics. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently

Nuclear potential energy

Nuclear potential energy is the potential energy of the particles inside an atomic nucleus, some of which are indeed electrically charged. Nuclear Energy is released by the splitting (fission or merging together (fusion of the nuclei of Atom (s A subatomic particle is an elementary or composite Particle smaller than an Atom. The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom This kind of potential energy is different from the previous two kinds of electrical potential energies because in this case the charged particles are extremely close to each other. The nuclear particles are bound together not because of the coulombic force but due to strong nuclear force that binds nuclear particles more strongly and closely. In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and Weak nuclear forces provide the potential energy for certain kinds of radioactive decay, such as beta decay. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Nuclear physics, beta decay is a type of Radioactive decay in which a Beta particle (an Electron or a Positron) is emitted

Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured). The energy from the Sun, also called solar energy, is an example of this form of energy conversion. The Sun (Sol is the Star at the center of the Solar System. Solar energy is the Light and radiant heat from the Sun that powers Earth 's Climate and Weather and sustains Life In the Sun, the process of hydrogen fusion converts about 4 million metric tons of solar matter per second into light, which is radiated into space. The Sun (Sol is the Star at the center of the Solar System.

Thermal potential energy

Thermal energy of an object is simply a sum of average kinetic energy of random motion of particles constituting the object plus average potential energy of their displacement (from their equilibrium positions) as they oscillate/move around it. In case of ideal gas there is no potential energy due to interactions of particles, but kinetic energy may include rotational part too (for multiatomic gases) - if rotational levels are excited at given temperature T.

Solar updraft tower uses this kind of power. The solar updraft tower is a proposed type of renewable-energy Power plant.

Rest mass energy

Albert Einstein was the first to calculate the amount of work needed to accelerate a body from rest to some finite speed using his definition of relativistic momentum. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product To his surprise, this work contained an extra term which did not vanish as the speed of accelerated body approached zero:

$E_0 = m c^2. \,$

This term (E₀) was therefore called rest mass energy, as m is the rest mass of the body (c is the speed of light in a vacuum). Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. (The subscript zero is used here to distinguish this form of energy from the others that follow. In most other contexts, the equation is written with no subscript. )

So, the rest mass energy is the amount of energy inherent in the mass when it is at rest. If the mass changes, so must its rest mass energy which must be released or absorbed due to energy conservation law. Thus, this equation quantifies the equivalence of mass and energy.

Due to large numerical value of squared speed of light, even a small amount of mass is equivalent to a very large amount of energy, namely 90 petajoules per kilogram ≈ 21 megaton of TNT per kilogram. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity

Relation between potential energy and force

Potential energy is closely linked with forces. In Physics, a force is whatever can cause an object with Mass to Accelerate. If the work done moving along a path which starts and ends in the same location 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. In Vector calculus, the gradient of a Scalar field is a Vector field which points in the direction of the greatest rate of increase of the scalar

For example, gravity is a conservative force. A conservative force is defined as a Force with the following property when an object moves from one location to another the force changes the Potential energy of 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

$U_{A \to B \to A} = (b - a) + (a - b) = 0 \,$

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

$U_{A \to B} = (b + c) - (a + c) = b - a \,$

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. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001

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. Equilibrium between electromagnetic forces and Pauli repulsion of electrons (they are fermions obeying Fermi statistics) is slightly violated resulting in small returning force. In Physics, the electromagnetic force is the force that the Electromagnetic field exerts on electrically charged particles In Physics, the exchange interaction is a Quantum mechanical effect which increases or decreases the expectation value of the Energy or Distance In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Statistical mechanics, Fermi-Dirac statistics is a particular case of Particle statistics developed by Enrico Fermi and Paul Dirac that Scientists rarely talk about forces on an atomic scale. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny Often interactions are described 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 (though the latter approach requires a definition of energy that is independent from force which does not currently exist).

A conservative force can be expressed in the language of differential geometry as a closed form. Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry In Mathematics, especially Vector calculus and Differential topology, a closed form is a Differential form α whose differential is Because Euclidean space is contractible, its de Rham cohomology vanishes, so every closed form is exact, i. In Mathematics, a Topological space X is contractible if the Identity map on X is Null-homotopic, i In Mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to Algebraic topology and to Differential topology, capable e. , is the gradient of a scalar field. This gives a mathematical justification of the fact that all conservative forces are gradients of a potential field.

References

^ Smith, Crosbie (1998). The Science of Energy - a Cultural History of Energy Physics in Victorian Britain. The University of Chicago Press. ISBN 0-226-76420-6.

Serway, Raymond A. ; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed. ). Brooks/Cole. ISBN 0-534-40842-7.
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed. ). W. H. Freeman. ISBN 0-7167-0809-4.

Dictionary

-noun

the energy possessed by an object because of its position (in a gravitational or electric field), or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass)

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents