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# Body force

A body force is a force that acts on the volume of a body and also can be defined as an external force acting throughout the mass of a body. Gravity is a body force, the forces associated with a non-inertial reference frame may be viewed as body forces.

The units on a body force are force per volume; though sometimes force per mass is used. Force per mass is not favorable since some body forces are naturally written on a per volume bases instead of per mass, such as electric forces. The utility of body forces is seen in continuum mechanics, where it's difficult to make sense of a force applied to a point.

Examples of common body forces include::*Gravity (including bouyancy):*Centrifugal force:*Coriolis force:*Centripetal force:*Acceleration felt when a vehicle changes velocity (as in braking).:*A pressure gradient (but not pressure alone).

In general, any acceleration that a body undergoes will cause a body force given by:

:$f = ho a,$

Where $ho$ is the density of the substance at a given point and (lowercase) f is the body force. This result may be derived by applying Newton's law to a small volume and then taking the appropriate limit.

A body force doesn't necessarily involve acceleration, though. A prime example of such a body force is the action of gravity on an immobile object, other examples include the divergence of various stresses in solids and pressure gradient of a steady fluid flow.

The Navier-Stokes equations and Navier-Cauchy equations are written in terms of body forces.

ee also

*Surface force
*Fictitious force

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