Potential energy Totally Explained

Everything about Potential Energy totally explained

Potential energy can be thought of as energy stored within a physical system. 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 standard (SI) unit of measure for potential energy is the joule, the same as for work, or energy in general.

Overview

Potential energy is the energy which is stored. Potential energy exists when there's a force that tends to pull an object back towards some original position when the object is displaced. This force is often called a restoring force. The phrase 'potential energy' was coined by William Rankine. 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. 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 can't be created or destroyed; hence this energy can't disappear. Instead it's 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 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. More specifically, every conservative force gives rise to potential energy. 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. 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. Thermal energy usually has two components: the kinetic energy of random motion of particles and potential energy of their mutual positions.
As a general rule, the work done by a conservative force F will be ť

,W = -Delta PE

where

Delta PE

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) isn't the same as electric potential energy.

Gravitational potential energy

Gravitational energy is the potential energy associated with gravitational force. 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.
   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). 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's 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.) It is important to note that "height" in the common sense of the term can't be used for gravitational potential energy calculations when gravity isn't 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 ť

, W_F = -Delta PE_F

.

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

, PE = mgh

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

,Delta PE = mg Delta h

.

However, if the force of gravity varies too much for this approximation to be valid, then we've 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 doesn't change over time.
The gravitational potential energy of a mass m₁ at a distance R from another mass m₂ is ť

PE = -G frac = (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.
   A thing to note about conservative forces is that the work done going from A to B doesn't 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. Scientists rarely talk about forces on an atomic scale. 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's independent from force which doesn't currently exist).
   A conservative force can be expressed in the language of differential geometry as a closed form. Because Euclidean space is contractible, its de Rham cohomology vanishes, so every closed form is exact, for example, 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.

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