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, the electric potential energy of an electric charge in an electric field; the unit for energy in the International System of Units 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 forces on the body depends only on the initial and final positions of the body in space; these forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work. 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. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy has two components: the kinetic energy of random motions of particles and the potential energy of their mutual positions. Forces derivable from a potential are called conservative forces; the work done by a conservative force is W = − Δ U where Δ U is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy.
Common notations for potential energy are PE, U, V, Ep. Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity; the action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. This work is stored in the force field, said to be stored as potential energy. If the external force is removed the force field acts on the body to perform the work as it moves the body back to the initial position, reducing the stretch of the spring or causing a body to fall. Consider a ball whose mass is m and whose height is h; the acceleration g of free fall is constant, so the weight force of the ball mg is constant. Force × displacement gives the work done, equal to the gravitational potential energy, thus U g = m g h The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.
Potential energy is 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 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 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, called a "potential," that can be evaluated at the two points xA and xB 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, W = ∫ C F ⋅ d x = U − U where C is the trajectory taken from A to B; because the work done is independent of the path taken this expression is true for any trajectory, C, from A to B.
The function U is called the potential energy associated with the applied force. Examples of forces that have potential energies are spring forces. In this section the relationship between work and potential energy is presented in more detail; the line integral that defines work along curve C takes a special form if the force F is related to a scalar field φ so that F = ∇ Φ = ( ∂ Φ ∂ x, ∂ Φ
Dusty Hughes is an English playwright and screenwriter of television. In the early seventies he was Theatre Editor of Time Out and helped to establish that magazine’s theatre coverage as an alternative voice, he joined the Bush Theatre as Artistic Director and with Simon Stokes and Jenny Topper developed it as a venue for new writing and directed new plays by Snoo Wilson, Tony Bicat, Julia Kearsley, Kurt Vonnegut, Howard Barker, Ron Hutchinson and Ken Campbell. Hughes was born in Boston, Lincolnshire the son of Harold Hughes a schoolmaster and Peggy a marriage guidance counsellor and youth theatre producer. Hughes was educated at Queen Elizabeth Grammar School and Trinity Hall, Cambridge. At Cambridge he was a member of Footlights where he appeared in the revue “Supernatural Gas” as Tsar Nicolas II and a seven foot high HP Sauce bottle, he is thinly disguised in James's autobiography. In 1980 his first play Commitments won him the London Theatre Critics Most Promising Playwright Award, his subsequents plays have been seen at the National Theatre, The Royal Shakespeare Company in Stratford and London, The Royal Court, Hampstead Theatre, The Traverse Theatre, The Bush, the Donmar and in the West End as well as in Europe and America.
He has worked extensively in television. He was joint winner of the Writer’s Guild Award for Best Drama Series for Between The Lines and created The Brief for ITV as well as adapting Joseph Conrad’s The Secret Agent for BBC1, he has written for many other series including Silent Witness and most the BBC’s swashbuckling series The Musketeers. Grrr Edinburgh, 1968 In At The Death, Bush Theatre, London, 1978 Commitments Bush Theatre, London, 1980 Heaven and Hell Edinburgh, 1981 Breach Of The Peace, Bush Theatre, London, 1982 Moliere. Published script ISBN 0-571-13778-4 Jenkin's Ear Royal Court Theatre, London. 1987, Published script ISBN 0-571-14565-5 Metropolis Piccadilly Theatre, London, 1989, A Slip of the Tongue Steppenwolf Theatre, Chicago, 1992 Helpless Donmar Warehouse Theatre, London, 2000, directed by Robin Lefevre. Commitments The Secret Agent, Silent Witness The Brief, Lewis The Musketeers Futurists and commitments and Faber, 1986, ISBN 978-0-571-13778-7 Dusty Hughes on IMDb John Stanley Bull and Irish dramatists since World War II.: Second series, Gale Group, 2001
The 2011–12 CEV Challenge Cup was the 32nd edition of the European Challenge Cup volleyball club tournament, the former CEV Cup. The final of 2011–12 CEV Challenge Cup became Polish derby, because of Tytan AZS Częstochowa and AZS Politechnika Warszawska meetings. Tytan AZS Częstochowa won the first match and lost the next one after tie-break, but their victory was decided by the golden set; the Most Valuable Player of final matches was chosen captain of winner team, Polish player Dawid Murek. 1st leg 22–23 October 2011 2nd leg 29–30 October 2011 1st leg 13–15 December 2011 2nd leg 20–22 December 2011 1st leg 10–12 January 2012 2nd leg 17–19 January 2012 1st leg 31 January – 2 February 2012 2nd leg 7–9 February 2012 1st leg 21–23 February 2012 2nd leg 28 February – 1 March 2012 Official site