Body force

# Body force

Discussion

Encyclopedia
A body force is a force that acts throughout the volume of a body, in contrast to contact force
Contact force
In physics, a contact force is a force that acts at the point of contact between two objects, in contrast to body forces. Contact forces are described by Newton's laws of motion, as with all other forces in dynamics....

s.
Gravity and electromagnetic
Electromagnetic
Electromagnetic may refer to:* Electromagnetism* Electromagnetic field* Electromagnetic force* Electromagnetic radiation* Electromagnetic induction* Electromagnetic spectrum...

forces are examples of body forces. Centrifugal and Coriolis forces can also be viewed as body forces.
This can be put into contrast to the classical definition of surface force
Surface force
Surface force denoted fs is the force that acts across an internal or external surface element in a material body. Surface force can be decomposed in to two perpendicular components: pressure and stress forces....

s which are supposed to be exerted to the surface of an object. Shear force
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

s and normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

s 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

A body force is simply a type of force, and so it has the same dimensions as force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

(mass times length per time squared). However, it is often convenient to talk about a body force in terms of either the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

per unit volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

or the force per unit mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

. If the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

per unit volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

is of interest, it is referred to as the force density
Force density
In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid...

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
In atmospheric sciences , the pressure gradient is a physical quantity that describes in which direction and at what rate the pressure changes the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pressure per unit length...

s and conductive and convective heat transmission are not body forces as they require contact between systems to exist. Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

heat transfer, on the other hand, is a perfect example of a body force.

Examples of common body forces include:
• Gravity
• An electric force acting on an object that is charged throughout its volume
• Magnetic forces acting on currents within an object, such as the braking force that results from eddy currents

Inertial forces (often called "fictitious forces") can be viewed as body forces. Common inertial forces are
• Centrifugal force
Centrifugal force
Centrifugal force can generally be any force directed outward relative to some origin. More particularly, in classical mechanics, the centrifugal force is an outward force which arises when describing the motion of objects in a rotating reference frame...

• Coriolis force
• transverse force or Euler force
Euler force
In classical mechanics, the Euler acceleration , also known as azimuthal acceleration or transverse acceleration is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes...

, which occurs in a rotating reference frame when the rate of rotation of the frame is changing

It is worth noting that inertial forces are not actually forces. Rather they are corrections to Newton's second law when it is formulated in an accelerating reference frame.

## Acceleration

Like any other force, a body force will cause an object to accelerate. For a non-rigid object the acceleration of a volume element would be found by
,

where is the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the substance at point and (lowercase) f is the force density. This is simply Newton's second law formulated to apply to a small volume element.

In the case of gravity a(r) is simply the gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

.

The entirety of the body force acting upon a system can be found by integrating the force density throughout a volume of interest.
,

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

• Fictitious force
Fictitious force
A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

• Force density
Force density
In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid...

• Normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

• Surface force
Surface force
Surface force denoted fs is the force that acts across an internal or external surface element in a material body. Surface force can be decomposed in to two perpendicular components: pressure and stress forces....