Force Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! === 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> \vec{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">\vec{F}_\text{g} = - \frac{G m_1 m_2}{r^2} \hat{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">\vec{F}_\text{e} = \frac{q_1 q_2}{4 \pi \varepsilon_{0} r^2} \hat{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">\vec{F}_\text{s} = - k r \hat{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 /> Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page