# User Contributed Dictionary

### Pronunciation

#### Translations

Troops

### Verb

forces- third-person singular of force

## French

### Noun

forces- Plural of force

### Verb

forces- Second-person singular simple present form of forcer.

# Extensive Definition

In physics, a force is a push or
pull that can cause an object with mass to accelerate. Force has both
magnitude and
direction, making it a vector
quantity. According to Newton's
Second Law, an object will accelerate in proportion to
the net
force acting upon it and in inverse proportion to the object's
mass. An equivalent
formulation is that the net force on an object is equal to the
rate
of change of momentum it experiences. Forces
acting on three-dimensional objects may also cause them to rotate or deform, or result in a
change in pressure. The
tendency of a force to cause rotation about an axis is termed
torque. Deformation and
pressure are the result of stress
forces within an object.

Since antiquity, scientists have used the concept
of force in the study of stationary and moving
objects. These studies culminated with the descriptions made by the
third century BC philosopher Archimedes of
how simple
machines functioned. The rules Archimedes determined for how
forces interact in simple machines are still a part of modern
physics. Earlier descriptions of forces by Aristotle
incorporated fundamental misunderstandings, which would not be
resolved until the seventeenth century when Isaac Newton
correctly described how forces behaved. This theory, based on the
everyday experience of how objects move, such as the constant
application of a force needed to keep a cart moving, had conceptual
trouble accounting for the behavior of projectiles, such as the
flight of arrows. The place where forces were applied to
projectiles was only at the start of the flight, and while the
projectile sailed through the air, no discernible force acts on it.
Aristotle was aware of this problem and proposed that the air
displaced through the projectile's path provided the needed force
to continue the projectile moving. This explanation demands that
air is needed for projectiles and that, for example, in a vacuum, no projectile would move
after the initial push. Additional problems with the explanation
include the fact that air
resists the motion of the projectiles.

These shortcomings would not be fully explained
and corrected until the seventeenth century work of Galileo
Galilei, who was influenced by the late medieval idea that
objects in forced motion carried an innate force of impetus.
Galileo constructed an experiment in which stones and cannonballs
were both rolled down an incline to disprove the
Aristotelian theory of motion early in the seventeenth century.
He showed that the bodies were accelerated by gravity to an extent
which was independent of their mass and argued that objects retain
their velocity unless
acted on by a force, for example friction.

## Newtonian mechanics

Isaac Newton is the first person known to explicitly state the first, and the only, mathematical definition of force—as the time-derivative of momentum: F = dp/dt. In 1687, Newton went on to publish his Philosophiae Naturalis Principia Mathematica, which used concepts of inertia, force, and conservation to describe the motion of all objects.- \vec = \frac = \frac

where \vec is the momentum of the system. The
\vec in the equation represents the net (vector
sum) force; in equilibrium there is zero net force by
definition, but (balanced) forces may be present nevertheless. In
contrast, the second law states an unbalanced force acting on an
object will result in the object's momentum changing over time.
Newton never stated explicitly the F=ma formula for which he is
often credited.

Newton's second law asserts the proportionality
of acceleration and mass to force. Accelerations can be defined
through kinematic
measurements. However, while kinematics are well-described through
reference
frame analysis in advanced physics, there are still deep
questions that remain as to what is the proper definition of mass.
General
relativity offers an equivalence between space-time and
mass, but lacking a coherent theory of quantum
gravity, it is unclear as to how or whether this connection is
relevant on microscales. With some justification, Newton's second
law can be taken as a quantitative definition of mass by writing
the law as an equality, the relative units of force and mass are
fixed.

The use of Newton's second law as a definition of
force has been disparaged in some of the more rigorous textbooks,
because it is essentially a mathematical truism. The equality between the
abstract idea of a "force" and the abstract idea of a "changing
momentum vector" ultimately has no observational significance
because one cannot be defined without simultaneously defining the
other. What a "force" or "changing momentum" is must either be
referred to an intuitive understanding of our direct perception, or
be defined implicitly through a set of self-consistent mathematical
formulas. Notable physicists, philosophers and mathematicians who
have sought a more explicit definition of the concept of "force"
include Ernst Mach,
Clifford
Truesdell and Walter
Noll.

Newton's second law can be used to measure the
strength of forces. For instance, knowledge of the masses of
planets along with the
accelerations of their orbits allows scientists to
calculate the gravitational forces on planets.

### Newton's third law

Newton's third law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. For any two objects (call them 1 and 2), Newton's third law states that- \vec_=-\vec_.

This law implies that forces always occur in
action-reaction pairs. If object 1 and object 2 are considered to
be in the same system, then the net force on the system due to the
interactions between objects 1 and 2 is zero since

- \vec_+\vec_=0.

This means that in a closed
system of particles, there are no internal
forces that are unbalanced. That is, action-reaction pairs of
forces shared between any two objects in a closed system will not
cause the center of
mass of the system to accelerate. The constituent objects only
accelerate with respect to each other, the system itself remains
unaccelerated. Alternatively, if an external
force acts on the system, then the center of mass will
experience an acceleration proportional to the magnitude of the
external force divided by the mass of the system. Using the similar
arguments, it is possible to generalizing this to a system of an
arbitrary number of particles. This shows that exchanging momentum
between constituent objects will not affect the net momentum of a
system. In general, as long as all forces are due to the
interaction of objects with mass, it is possible to define a system
such that net momentum is never lost nor gained.

As well as being added, forces can also be
resolved into independent components at right angles
to each other. A horizontal force pointing northeast can therefore
be split into two forces, one pointing north, and one pointing
east. Summing these component forces using vector addition yields
the original force. Resolving force vectors into components of a
set of basis
vectors is often a more mathematically clean way to describe
forces than using magnitudes and directions. This is because, for
orthogonal
components, the components of the vector sum are uniquely
determined by the scalar addition of the components of the
individual vectors. Orthogonal components are independent of each
other; forces acting at ninety degrees to each other have no effect
on each other. Choosing a set of orthogonal basis vectors is often
done by considering what set of basis vectors will make the
mathematics most convenient. Choosing a basis vector that is in the
same direction as one of the forces is desirable, since that force
would then have only one non-zero component. Force vectors can also
be three-dimensional, with the third component at right-angles to
the two other components.

The simplest case of static equilibrium occurs
when two forces are equal in magnitude but opposite in direction.
For example, any object on a level surface is pulled (attracted)
downward toward the center of the Earth by the force of gravity. At
the same time, surface forces resist the downward force with equal
upward force (called the normal
force) and result in the object having a non-zero weight. The situation is one of
zero net force and no acceleration. When particle A emits (creates)
or absorbs (annihilates) particle B, a force accelerates particle A
in response to the momentum of particle B, thereby conserving
momentum as a whole. This description applies for all forces
arising from fundamental interactions. While sophisticated
mathematical descriptions are needed to predict, in full detail,
the nature of such interactions, there is a conceptually simple way
to describe such interactions through the use of Feynman diagrams.
In a Feynman diagram, each matter particle is represented as a
straight line (see world line)
traveling through time which normally increases up or to the right
in the diagram. Matter and anti-matter particles are identical
except for their direction of propagation through the Feynman
diagram. World lines of particles intersect at interaction
vertices, and the Feynman diagram represents any force arising
from an interaction as occurring at the vertex with an associated
instantaneous change in the direction of the particle world lines.
Gauge bosons are emitted away from the vertex as wavy lines
(similar to waves) and, in the case of virtual
particle exchange, are absorbed at an adjacent vertex. When the
gauge bosons are represented in a Feynman diagram as existing
between two interacting particles, this represents a repulsive
force. When the gauge bosons are represented in a Feynman diagram
as existing surrounding the two interacting particles, this
represents an attractive force.

The utility of Feynman diagrams is that other
types of physical phenomena that are part of the general picture of
fundamental
interactions but are conceptually separate from forces can also
be described using the same rules. For example, a Feynman diagram
can describe in succinct detail how a neutron decays into an
electron, proton, and neutrino: an interaction
mediated by the same gauge boson that is responsible for the
weak
nuclear force. While the Feynman diagram for this interaction
has similar features to a repulsive interaction, the decay is more
complicated than a simple "repulsive force". But in order to be
conserved, momentum must be redefined as:

- \vec = \frac

where

- v is the velocity and

- c is the speed of light.

The relativistic expression relating force and
acceleration for a particle with non-zero rest mass m\,
moving in the x\, direction is:

- F_x = \gamma^3 m a_x \,

- F_y = \gamma m a_y \,

- F_z = \gamma m a_z \,

where the Lorentz
factor

- \gamma = \frac

Here a constant force does not produce a constant
acceleration, but an ever decreasing acceleration as the object
approaches the speed of light. Note that \gamma is undefined
for an object with a non zero rest mass
at the speed of light, and the theory yields no prediction at that
speed.

One can however restore the form of

- F^\mu = mA^\mu \,

for use in relativity through the use of four-vectors.
This relation is correct in relativity when F^\mu is the four-force, m is
the invariant
mass, and A^\mu is the four-acceleration.

## Fundamental models

All the forces in the universe are based on four fundamental forces. The strong and weak forces act only at very short distances, and are responsible for holding certain nucleons and compound nuclei together. The electromagnetic force acts between electric charges and the gravitational force acts between masses. All other forces are based on the existence of the four fundamental interactions. For example, friction is a manifestation of the electromagnetic force acting between the atoms of two surfaces, and the Pauli Exclusion Principle, which does not allow atoms to pass through each other. The forces in springs, modeled by Hooke's law, are also the result of electromagnetic forces and the Exclusion Principle acting together to return the object to its equilibrium position. Centrifugal forces are acceleration forces which arise simply from the acceleration of rotating frames of reference. This standard model of particle physics posits a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory subsequently confirmed by observation. The complete formulation of the standard model predicts an as yet unobserved Higgs mechanism, but observations such as neutrino oscillations indicate that the standard model is incomplete. A grand unified theory allowing for the combination of the electroweak interaction with the strong force is held out as a possibility with candidate theories such as supersymmetry proposed to accommodate some of the outstanding unsolved problems in physics. Physicists are still attempting to develop self-consistent unification models that would combine all four fundamental interactions into a theory of everything. Einstein tried and failed at this endeavor, but currently the most popular approach to answering this question is string theory. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of m will experience a force:- \vec = m\vec

In free-fall, this force is unopposed and
therefore the net force on the object is the force of gravity. For
objects not in free-fall, the force of gravity is opposed by the
weight of the object. For
example, a person standing on the ground experiences zero net
force, since the force of gravity is balanced by the weight of the
person that is manifested by a normal force
exerted on the person by the ground.

Newton came to realize that the effects of
gravity might be observed in different ways at larger distances. In
particular, Newton determined that the acceleration of the moon
around the Earth could be ascribed to the same force of gravity if
the acceleration due to gravity decreased as an inverse
square law. Further, Newton realized that the mass of the
gravitating object directly affected the acceleration due to
gravity. though it was of an unknown value in Newton's lifetime.
Not until 1798 was Henry
Cavendish able to make the first measurement of G using a
torsion
balance; this was widely reported in the press as a measurement
of the mass of the Earth since knowing the G could allow one to
solve for the Earth's mass given the above equation. Newton,
however, realized that since all celestial bodies followed the same
laws of
motion, his law of gravity had to be universal. Succinctly
stated,
Newton's Law of Gravitation states that the force on an object
of mass m_ due to the gravitational pull of mass m_2 is

- \vec=-\frac \hat

where r is the distance between the two objects'
centers of
mass and \hat is the unit vector pointed in the direction away
from the center of the first object toward the center of the second
object. were invented to calculate the deviations of orbits due to the influence of
multiple bodies on a planet, moon, comet, or asteroid. These techniques are
so powerful that they can be used to predict precisely the motion
of celestial bodies to an arbitrary precision at any length of time
in the future. The formalism was exact enough to allow
mathematicians to predict the existence of the planet Neptune before it
was observed.

It was only the orbit of the planet Mercury
that Newton's Law of Gravitation seemed not to fully explain. Some
astrophysicists predicted the existence of another planet (Vulcan)
that would explain the discrepancies; however, despite some early
indications, no such planet could be found. When Albert
Einstein finally formulated his theory of general
relativity (GR) he turned his attention to the problem of
Mercury's orbit and found that his theory added
a correction which could account for the discrepancy. This was
the first time that Newton's Theory of Gravity had been shown to be
less correct than an alternative.

Since then, and so far, general relativity has
been acknowledged as the theory which best explains gravity. In GR,
gravitation is not viewed as a force, but rather, objects moving
freely in gravitational fields travel under their own inertia in
straight lines through
curved
space-time – defined as the shortest space-time path
between two space-time events. From the perspective of the object,
all motion occurs as if there were no gravitation whatsoever. It is
only when observing the motion in a global sense that the curvature
of space-time can be observed and the force is inferred from the
object's curved path. Thus, the straight line path in space-time is
seen as a curved line in space, and it is called the ballistic
trajectory of the
object. For example, a basketball thrown from the
ground moves in a parabola, as it is in a uniform
gravitational field. Its space-time trajectory (when the extra ct
dimension is added) is almost a straight line, slightly curved
(with the radius
of curvature of the order of few light-years).
The time derivative of the changing momentum of the object is what
we label as "gravitational force". The properties of the
electrostatic force were that it varied as an inverse
square law directed in the radial
direction, was both attractive and repulsive (there was
intrinsic polarity),
was independent of the mass of the charged objects, and followed
the law of
superposition. Coulomb's
Law unifies all these observations into one succinct
statement.

Subsequent mathematicians and physicists found
the construct of the electric
field to be useful for determining the electrostatic force on
an electric charge at any point in space. The electric field was
based on using a hypothetical "test charge"
anywhere in space and then using Coulomb's Law to determine the
electrostatic force. Thus the electric field anywhere in space is
defined as

- \vec =

where q is the magnitude of the hypothetical test
charge.

Meanwhile, the Lorentz
force of magnetism
was discovered to exist between two electric
currents. It has the same mathematical character as Coulomb's
Law with the proviso that like currents attract and unlike currents
repel. Similar to the electric field, the magnetic
field can be used to determine the magnetic force on an
electric current at any point in space. In this case, the magnitude
of the magnetic field was determined to be

- B =

where I is the magnitude of the hypothetical test
current and \ell is the length of hypothetical wire through which
the test current flows. The magnetic field exerts a force on all
magnets including, for
example, those used in compasses. The fact that the
Earth's magnetic
field is aligned closely with the orientation of the Earth's
axis causes compass
magnets to become
oriented because of the magnetic force pulling on the
needle.

Through combining the definition of electric
current as the time rate of change of electric charge, a rule of
vector
multiplication called Lorentz's
Law describes the force on a charge moving in an magnetic
field.

However, attempting to reconcile electromagnetic
theory with two observations, the photoelectric
effect, and the nonexistence of the ultraviolet
catastrophe, proved troublesome. Through the work of leading
theoretical physicists, a new theory of electromagnetism was
developed using quantum
mechanics. This final modification to electromagnetic theory
ultimately led to quantum
electrodynamics (or QED), which fully describes all
electromagnetic phenomena as being mediated by wave particles known
as photons. In QED,
photons are the fundamental exchange particle which described all
interactions relating to electromagnetism including the
electromagnetic force.

It is a common misconception to ascribe the
stiffness and rigidity of solid
matter to the repulsion of like charges under the influence of
the electromagnetic force. However, these characteristics actually
result from the Pauli
Exclusion Principle. Since electrons are fermions, they cannot occupy the
same quantum mechanical
state as other electrons. When the electrons in a material are
densely packed together, there are not enough lower energy quantum mechanical states
for them all, so some of them must be in higher energy states. This
means that it takes energy to pack them together. While this effect
is manifested macroscopically as a structural "force", it is
technically only the result of the existence of a finite set of
electron states.

### Nuclear forces

There are two "nuclear forces" which today are usually described as interactions that take place in quantum theories of particle physics. The strong nuclear force is the force responsible for the structural integrity of atomic nuclei while the weak nuclear force is responsible for the decay of certain nucleons into leptons and other types of hadrons. The strong force is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves. The strong interaction is the most powerful of the four fundamental forces.The strong force only acts directly upon
elementary particles. However, a residual of the force is observed
between hadrons (the best
known example being the force that acts between nucleons in atomic nuclei) as
the nuclear
force. Here the strong force acts indirectly, transmitted as
gluons which form part of the virtual pi and rho mesons which classically transmit
the nuclear force (see this topic for more). The failure of many
searches for free quarks
has shown that the elementary particles affected are not directly
observable. This phenomenon is called colour
confinement.

The weak force is due to the exchange of the
heavy W and Z
bosons. Its most familiar effect is beta decay (of
neutrons in atomic
nuclei) and the associated radioactivity. The word
"weak" derives from the fact that the field strength is some 1013
times less than that of the strong
force. Still, it is stronger than gravity over short distances.
A consistent electroweak theory has also
been developed which shows that electromagnetic forces and the weak
force are indistinguishable at a temperatures in excess of
approximately 1015 Kelvin. Such
temperatures have been probed in modern particle
accelerators and show the conditions of the universe in the early moments
of the Big
Bang.

## Non-fundamental models

Some forces can be modeled by making simplifying assumptions about the physical conditions. In such situations, idealized models can be utilized to gain physical insight.### Normal force

The normal force is the surface force which acts
normal to
the surface interface between two objects. 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 of an object crashing into an
immobile surface. This force is proportional to the square of that
object's velocity due to the conservation
of energy and the work
energy theorem when applied to completely inelastic
collisions. 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. 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 is equal to:

- \vec=-k \Delta \vec

where k is the spring constant (or force
constant), which is particular to the spring. The minus sign
accounts for the tendency of the elastic force to act in opposition
to the applied load.

- \vec = - \frac

where m is the mass of the object, v is the
velocity of the object and r is the distance to the center of the
circular path and \hat is the unit vector
pointing in the radial direction outwards from the center. This
means that the unbalanced centripetal force felt by any object is
always directed toward the center of the curving path. Such forces
act perpendicular to the velocity vector associated with the motion
of an object, and therefore do not change the speed of the object (magnitude of
the velocity), but only the direction of the velocity vector. The
unbalanced force that accelerates an object can be resolved into a
component that is perpendicular to the path, and one that is
tangential to the path. This yields both the tangential force which
accelerates the object by either slowing it down or speeding it up
and the radial (centripetal) force which changes its direction.
These forces are considered fictitious because they do not exist in
frames of reference that are not accelerating.

where \vec is the angular momentum of the
particle.

Newton's Third Law of Motion requires that all
objects exerting torques themselves experience equal and opposite
torques, and therefore also directly implies the
conservation of angular momentum for closed systems that
experience rotations and revolutions through the
action of internal torques.

## Kinematic integrals

Forces can be used to define a number of physical concepts by integrating with respect to kinematic variables. For example, integrating with respect to time gives the definition of impulse:- \vec=\int

which, by Newton's Second Law, must be equivalent
to the change in momentum (yielding the Impulse
momentum theorem).

Similarly, integrating with respect to position
gives a definition for the work done
by a force:

- W=\int

which, in a system where all the forces are
conservative (see
below) is equivalent to changes in kinetic
and potential
energy (yielding the
Work
energy theorem). The time derivative of the definition of work
gives a definition for power in
term of force and the velocity (\vec):

- P=\frac=\int

## Potential energy

Instead of a force, often the mathematically related concept of a potential energy field can be used for convenience. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field U(\vec) is defined as that field whose gradient is equal and opposite to the force produced at every point:- \vec=-\vec U.

Forces can be classified as conservative
or nonconservative. Conservative forces are equivalent to the
gradient of a potential while
non-conservative forces are not. and can be considered to be an
artifact of the potential field in the same way that the direction
and amount of a flow of water can be considered to be an artifact
of the contour map
of the elevation of an area. Examples of this follow:

For gravity:

- \vec = - \frac

where G is the gravitational
constant, and m_n is the mass of object n.

For electrostatic forces:

- \vec = \frac

where \epsilon_ is electric
permittivity of free space, and q_n is the electric
charge of object n.

For spring forces:

- \vec = - k \vec

where k is the spring
constant. The corresponding CGS unit is the
dyne, the force required to
accelerate a one gram mass by one centimeter per second squared, or
g•cm•s−2. 1 newton is thus equal to
100,000 dyne.

The foot-pound-second
Imperial
unit of force is the pound-force
(lbf), defined as the force exerted by gravity on a pound-mass in
the standard
gravitational field of 9.80665 m•s−2. The
pound-force provides an alternate unit of mass: one slug is the
mass that will accelerate by one foot per second squared when acted
on by one pound-force. An alternate unit of force in the same
system is the poundal,
defined as the force required to accelerate a one pound mass at a
rate of one foot per second squared. The units of slug and
poundal are designed to
avoid a constant of proportionality in Newton's
Second Law.

The pound-force has a metric counterpart, less
commonly used than the newton: the kilogram-force
(kgf) (sometimes kilopond), is the force exerted
by standard gravity on one kilogram of mass. The kilogram-force
leads to an alternate, but rarely used unit of mass: the metric slug
(sometimes mug or hyl) is that mass which accelerates
at 1 m•s−2 when subjected to a force of
1 kgf. The kilogram-force is not a part of the modern
SI system, and
is generally deprecated; however it still sees use for some
purposes as expressing jet thrust, bicycle spoke tension, torque
wrench settings and engine output torque. Other arcane units of
force include the sthène which is
equivalent to 1000 N and the kip which is
equivalent to 1000 lbf.

## References

## Bibliography

- Lectures on Physics, Vol 1

## External links

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# Synonyms, Antonyms and Related Words

armed force, armed service, army, array, career soldiers, fighting
force, fighting machine, firepower, ground forces,
ground troops, hands,
host, legions, men, military establishment,
occupation force, paratroops, personnel, rank and file,
ranks, regular army,
regulars, ski troops,
soldiery, standing
army, storm troops, the big battalions, the line, the military,
troops, units, work
force