World Library  
Flag as Inappropriate
Email this Article

Body force

Article Id: WHEBN0010092550
Reproduction Date:

Title: Body force  
Author: World Heritage Encyclopedia
Language: English
Subject: Cauchy momentum equation, Navier–Stokes equations, Capillary surface, Derivation of the Navier–Stokes equations, Deformation (mechanics)
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Body force

A body force is a force that acts throughout the volume of a body, in contrast to contact forces. Gravity and electromagnetic forces are examples of body forces. Inertial spin forces such as the Centrifugal force, Euler force, and the Coriolis effect are also examples of body forces.

This can be put into contrast to the classical definition of surface forces which are supposed to be exerted to the surface of an object. Shear forces and normal forces occurring in physical and engineering circumstances are supposed to be surface forces and exerted to the surface of an object. All 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 dimensions as force, [M][L][T]−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;

Fictitious forces (or inertial forces) can be viewed as body forces. Common inertial forces are,

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.

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;

\mathbf{F}_{\mathrm{body}} = \int\limits_{V} \mathbf{f}(\mathbf{r}) \mathrm{d} V \,,

where dV is an infinitesimal volume element and f is the force density within the system.

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

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

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

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.