Editing Force (section)

=== Conservation ===
{{main|Conservative force}}
A conservative force that acts on a [[closed system]] has an associated mechanical work that allows energy to convert only between [[kinetic energy|kinetic]] or [[potential energy|potential]] forms. This means that for a closed system, the net [[mechanical energy]] is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space,<ref>{{cite web
|last=Singh
|first=Sunil Kumar
|title=Conservative force
|work=Connexions
|date=2007-08-25
|url=http://cnx.org/content/m14104/latest/
|access-date=2008-01-04}}</ref> and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the [[contour map]] of the elevation of an area.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner />

Conservative forces include [[gravity]], the [[Electromagnetism|electromagnetic]] force, and the [[Hooke's law|spring]] force. Each of these forces has models that are dependent on a position often given as a [[radius|radial vector]] <math> \mathbf{r}</math> emanating from [[spherical symmetry|spherically symmetric]] potentials.<ref>{{cite web
|last=Davis
|first=Doug
|title=Conservation of Energy
|work=General physics
|url=http://www.ux1.eiu.edu/~cfadd/1350/08PotEng/ConsF.html
|access-date=2008-01-04}}</ref> Examples of this follow:

For gravity:
<math display="block">\mathbf{F}_\text{g} = - \frac{G m_1 m_2}{r^2} \hat\mathbf{r},</math>
where <math>G</math> is the [[gravitational constant]], and <math>m_n</math> is the mass of object ''n''.

For electrostatic forces:
<math display="block">\mathbf{F}_\text{e} = \frac{q_1 q_2}{4 \pi \varepsilon_{0} r^2} \hat\mathbf{r},</math>
where <math>\varepsilon_{0}</math> is [[Permittivity|electric permittivity of free space]], and <math>q_n</math> is the [[electric charge]] of object ''n''.

For spring forces:
<math display="block">\mathbf{F}_\text{s} = -kr\hat\mathbf{r},</math>
where <math>k</math> is the [[spring constant]].<ref name="FeynmanVol1" />{{rp|at=ch.12}}<ref name="Kleppner" />

For certain physical scenarios, it is impossible to model forces as being due to a simple gradient of potentials. This is often due a macroscopic statistical average of [[Microstate (statistical mechanics)|microstates]]. For example, static friction is caused by the gradients of numerous electrostatic potentials between the [[atom]]s, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include other [[contact force]]s, [[Tension (physics)|tension]], [[Physical compression|compression]], and [[drag (physics)|drag]]. For any sufficiently detailed description, all these forces are the results of conservative ones since each of these macroscopic forces are the net results of the gradients of microscopic potentials.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner />

The connection between macroscopic nonconservative forces and microscopic conservative forces is described by detailed treatment with [[statistical mechanics]]. In macroscopic closed systems, nonconservative forces act to change the [[internal energy|internal energies]] of the system, and are often associated with the transfer of heat. According to the [[Second law of thermodynamics]], nonconservative forces necessarily result in energy transformations within closed systems from ordered to more random conditions as [[entropy]] increases.<ref name=FeynmanVol1 />{{rp|at=ch.12}}<ref name=Kleppner />