physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, a body force is a force that acts throughout the volume of a body.Springer site - Book 'Solid mechanics'
preview paragraph 'Body forces'.
/ref> Forces due to

gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

, electric fields and

magnetic fields A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

are examples of body forces. Body forces contrast with ''

contact force A contact force is any force that occurs because of two objects making contact with each other. Contact forces are very common and are responsible for most visible interactions between macroscopic The macroscopic scale is the length scale on ...

s'' or '' surface forces'' which are exerted to the surface of an object. Fictitious forces such as the

centrifugal force Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axi ...

, Euler force, and the Coriolis effect are other examples of body forces.

Definition

Qualitative

A body force is simply a type of force, and so it has the same dimensions as

force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...

, L] sup>−2. However, it is often convenient to talk about a body force in terms of either the

per unit

volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...

or the force per unit

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

. If the

per unit

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 In physics and electrical engineering, a conductor is an object or type of material that allows the flow of Electric charge, charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. The flow ...

and convective heat transmission are not body forces as they require contact between systems to exist.

Radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...

heat transfer, on the other hand, is a perfect example of a body force. More examples of common body forces include; *

Gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

, * Electric forces acting on an object charged throughout its volume, * Magnetic forces acting on currents within an object, such as the braking force that results from eddy currents, Fictitious forces (or inertial forces) can be viewed as body forces. Common inertial forces are, *

Centrifugal force Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axi ...

, *

Coriolis force In physics, the Coriolis force is a pseudo force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motio ...

, * 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 Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...

when it is formulated in an accelerating reference frame. (Gravity can also be considered a fictitious force in the context of

General Relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

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_ =  \int\limits_\mathbf(\mathbf) \mathrm V \,,

where d''V'' is an

infinitesimal In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " ...

volume element, and f is the ''external body force density field'' acting on the system.

Acceleration

Like any other force, a body force will cause an object to accelerate. For a non-rigid object,

applied to a small volume element is :

\mathbf (\mathbf)=\rho (\mathbf)\mathbf (\mathbf)

, where ''ρ''(r) is the

mass density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter rho), although the Latin letter ''D'' (or ''d'') ...

of the substance, ƒ the force density, and a(r) is

acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...

, all at point r.

The case of gravity

In the case of a body in the

gravitational field In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...

on a planet surface, a(r) is nearly constant (g) and uniform. Near the Earth :

g = 9.81 \text\mathrm^

. In this case simply :

\mathbf_ =  \int\limits_\rho (\mathbf)\mathbf\mathrm V = \int\limits_\rho (\mathbf)\mathrm V \cdot \mathbf = m \mathbf

where ''m'' is the mass of the body.

References