Body force

 ( Force ) 

In physics, a body force is a force that acts throughout the volume of a body.Springer site - Book 'Solid mechanics'. preview paragraph 'Body forces'. Forces due to gravity, electrostatics and magnetic fields are examples of body forces. Body forces contrast with or which are exerted to the surface of an object. Fictitious forces such as the centrifugal force, Euler force, and the Coriolis effect are other examples of body forces.

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Definition

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Qualitative A body force is simply a type of force, and so it has the same dimensions as force, MLT⁻². 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 gradients 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,
• acting on an object charged throughout its volume,
• acting on currents within an object, such as the braking force that results from eddy currents,

(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 accelerating reference frame. (Gravity can also be considered a fictitious force in the context of General Relativity.)

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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;

$\backslash mathbf\{F\}\_\{\backslash mathrm\{body\}\}\; =\; \backslash int\backslash limits\_\{V\}\backslash mathbf\{f\}(\backslash mathbf\{r\})\; \backslash mathrm\{d\}\; V\; \backslash ,,$

where d V is an infinitesimal volume element, and f is the external body force density field acting on the system.

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Acceleration 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

$\backslash mathbf\{f\}\; (\backslash mathbf\{r\})=\backslash rho\; (\backslash mathbf\{r\})\backslash mathbf\{a\}\; (\backslash mathbf\{r\})$,

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

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The case of gravity In the case of a body in the gravitational field on a planet surface, a( r) is nearly constant ( g) and uniform. Near the Earth

$g\; =\; 9.81\; \backslash text\{\; \}\backslash mathrm\{ms\}^\{-2\}$.

In this case simply

$\backslash mathbf\{F\}\_\{\backslash mathrm\{body\}\}\; =\; \backslash int\backslash limits\_\{V\}\backslash rho\; (\backslash mathbf\{r\})\backslash mathbf\{g\}\backslash mathrm\{d\}\; V\; =\; \backslash int\backslash limits\_\{V\}\backslash rho\; (\backslash mathbf\{r\})\backslash mathrm\{d\}\; V\; \backslash cdot\; \backslash mathbf\{g\}\; =\; m\; \backslash mathbf\{g\}$

where m is the mass of the body.

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See also

• Action at a distance
• Fictitious force
• Force density
• Non-contact force
• Normal force
• Surface force

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