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{{Unreferenced|date=March 2007}}
A '''body force''' is a force that acts throughout the volume of a body, in contrast to [[contact force]]s. [[Gravity]] and [[electromagnetic force]]s are examples of body forces. [[Centrifugal force]] and [[Coriolis force]] can also be viewed as body forces. 

This can be put into contrast to the classical definition of [[surface force]]s which are supposed to be exerted to the surface of an object. [[Shear stress|Shear force]]s and [[normal force]]s occurring in physical and engineering circumstances are supposed to be '''surface forces''' and exerted to the surface of an object. All [[Cohesion (chemistry)|cohesive]] surface attraction and contact forces between objects are also considered as surface forces.

==Definition==

===Qualitative===
A body force is simply a type of force, and so it has the same [[dimensional analysis|dimensions]] as [[force]], [M][L][T]<sup>−2</sup>. However, it is often convenient to talk about a body force in terms of either the [[force]] per unit [[volume]] or the force per unit [[mass]]. If the [[force]] per unit [[volume]] is of interest, it is referred to as the [[force density]] throughout the system.

A body force is distinct from a contact force in that the force does not require contact for transmission. Thus, common forces associated with [[pressure gradient]]s and [[conductive]] and [[convective]] heat transmission are not body forces as they require contact between systems to exist. [[Radiation]] heat transfer, on the other hand, is a perfect example of a body force.

More examples of common body forces include;
*[[Gravity]],
*[[Electric force]]s acting on an object charged throughout its volume,
*[[Magnetic force]]s acting on currents within an object, such as the braking force that results from [[eddy currents]],

[[Fictitious force]]s (or inertial forces) can be viewed as body forces. Common inertial forces are,

*[[Centrifugal force]],
*[[Coriolis force]],
*[[Euler force]] (or transverse force), which occurs in a rotating reference frame when the rate of rotation of the frame is changing

However, fictitious forces are not actually forces. Rather they are corrections to [[Newton's second law]] when it is formulated in an [[Non-inertial reference frame|accelerating reference frame]].

===Quantitative===

The body force density is defined so that the [[volume integral]] (throughout a volume of interest) of it gives the total force acting throughout the body;

:<math>\mathbf{F}_{\mathrm{body}} =  \int\limits_{V} \mathbf{f}(\mathbf{r}) \mathrm{d} V \,,</math>

where d''V'' is an [[Differential (infinitesimal)|infinitesimal]] [[volume element]] and '''f''' is the force density within the system.

==Acceleration==
{{main|Newton's second law}}
Like any other force, a body force will cause an object to [[accelerate]]. For a non-rigid object, [[Newton's second law]] applied to a small volume element is

:<math>\mathbf{f} (\mathbf{r})=\rho (\mathbf{r})\mathbf{a} (\mathbf{r})</math>,

where ''ρ''('''r''') is the [[mass density]] of the substance, '''ƒ''' the force density, and '''a'''('''r''') all at point '''r'''.  

In the case of gravity, '''a'''('''r''') is simply the acceleration due to gravity, that is the [[gravitational field]] '''g'''.

==See also==
*[[Fictitious force]]
*[[Force density]]
*[[Normal force]]
*[[Surface force]]

{{DEFAULTSORT:Body Force}}
[[Category:Force]]