## Non-fundamental forces::Force

### ::concepts

Force::forces    Object::first    Title::physics    Which::newton's    Motion::center    Velocity::constant

Non-fundamental forces Some forces are consequences of the fundamental ones. In such situations, idealized models can be utilized to gain physical insight.

### Normal force

FN represents the normal force exerted on the object.

{{#invoke:main|main}} The normal force is due to repulsive forces of interaction between atoms at close contact. When their electron clouds overlap, Pauli repulsion (due to fermionic nature of electrons) follows resulting in the force that acts in a direction normal to the surface interface between two objects.<ref name=Cutnell/>:93 The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of the normal force in action is the impact force on an object crashing into an immobile surface.<ref name=FeynmanVol1 /><ref name=Kleppner />

### Friction

{{#invoke:main|main}} Friction is a surface force that opposes relative motion. The frictional force is directly related to the normal force that acts to keep two solid objects separated at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction.

The static friction force ($F_{\mathrm{sf}}$) will exactly oppose forces applied to an object parallel to a surface contact up to the limit specified by the coefficient of static friction ($\mu_{\mathrm{sf}}$) multiplied by the normal force ($F_N$). In other words, the magnitude of the static friction force satisfies the inequality:

$0 \le F_{\mathrm{sf}} \le \mu_{\mathrm{sf}} F_\mathrm{N}.$

The kinetic friction force ($F_{\mathrm{kf}}$) is independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals:

$F_{\mathrm{kf}} = \mu_{\mathrm{kf}} F_\mathrm{N},$

where $\mu_{\mathrm{kf}}$ is the coefficient of kinetic friction. For most surface interfaces, the coefficient of kinetic friction is less than the coefficient of static friction.

### Tension

{{#invoke:main|main}} Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and unstretchable. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> By connecting the same string multiple times to the same object through the use of a set-up that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on the load. However, even though such machines allow for an increase in force, there is a corresponding increase in the length of string that must be displaced in order to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine.<ref name=FeynmanVol1 /><ref name=Kleppner /><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

### Elastic force

{{#invoke:main|main}}

Fk is the force that responds to the load on the spring

An elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If $\Delta x$ is the displacement, the force exerted by an ideal spring equals:

$\vec{F}=-k \Delta \vec{x}$

where $k$ is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to the applied load.<ref name=FeynmanVol1 /><ref name=Kleppner />

### Continuum mechanics

When the drag force ($F_d$) associated with air resistance becomes equal in magnitude to the force of gravity on a falling object ($F_g$), the object reaches a state of dynamic equilibrium at terminal velocity.

{{#invoke:main|main}} Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. However, in real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows:

$\frac{\vec{F}}{V} = - \vec{\nabla} P$

where $V$ is the volume of the object in the fluid and $P$ is the scalar function that describes the pressure at all locations in space. Pressure gradients and differentials result in the buoyant force for fluids suspended in gravitational fields, winds in atmospheric science, and the lift associated with aerodynamics and flight.<ref name=FeynmanVol1 /><ref name=Kleppner />

A specific instance of such a force that is associated with dynamic pressure is fluid resistance: a body force that resists the motion of an object through a fluid due to viscosity. For so-called "Stokes' drag" the force is approximately proportional to the velocity, but opposite in direction:

$\vec{F}_\mathrm{d} = - b \vec{v} \,$

where:

$b$ is a constant that depends on the properties of the fluid and the dimensions of the object (usually the cross-sectional area), and
$\scriptstyle \vec{v}$ is the velocity of the object.<ref name=FeynmanVol1 /><ref name=Kleppner />

More formally, forces in continuum mechanics are fully described by a stresstensor with terms that are roughly defined as

$\sigma = \frac{F}{A}$

where $A$ is the relevant cross-sectional area for the volume for which the stress-tensor is being calculated. This formalism includes pressure terms associated with forces that act normal to the cross-sectional area (the matrix diagonals of the tensor) as well as shear terms associated with forces that act parallel to the cross-sectional area (the off-diagonal elements). The stress tensor accounts for forces that cause all strains (deformations) including also tensile stresses and compressions.<ref name=uniphysics_ch2>University Physics, Sears, Young & Zemansky, pp.18–38</ref><ref name=Kleppner>{{#invoke:Footnotes|harvard_citation_no_bracket}}</ref>:133–134<ref name=FeynmanVol2>{{#invoke:Footnotes|harvard_citation_no_bracket}}</ref>:38-1–38-11

### Fictitious forces

{{#invoke:main|main}} There are forces that are frame dependent, meaning that they appear due to the adoption of non-Newtonian (that is, non-inertial) reference frames. Such forces include the centrifugal force and the Coriolis force.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> These forces are considered fictitious because they do not exist in frames of reference that are not accelerating.<ref name=FeynmanVol1 /><ref name=Kleppner /> Because these forces are not genuine they are also referred to as "pseudo forces".<ref name=FeynmanVol1 />:12-11

In general relativity, gravity becomes a fictitious force that arises in situations where spacetime deviates from a flat geometry. As an extension, Kaluza–Klein theory and string theory ascribe electromagnetism and the other fundamental forces respectively to the curvature of differently scaled dimensions, which would ultimately imply that all forces are fictitious.

Force sections
Intro  Development of the concept  Pre-Newtonian concepts  Newtonian mechanics  Special theory of relativity  Descriptions  Fundamental forces  Non-fundamental forces  Rotations and torque  Kinematic integrals  Potential energy  Units of measurement  Force measurement  See also  Notes  References  Further reading  External links

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