In physics, a force is any interaction that, when unopposed, will
change the motion of an object.[1] A force can cause an object with
mass to change its velocity (which includes to begin moving from a
state of rest), i.e., to accelerate.
Contents 1 Development of the concept 2 Pre-Newtonian concepts 3 Newtonian mechanics 3.1 First law
3.2
4
5.1 Equilibrium 5.1.1 Static 5.1.2 Dynamic 5.2 Forces in quantum mechanics 5.3 Feynman diagrams 6 Fundamental forces 6.1 Gravitational 6.2 Electromagnetic 6.3 Strong nuclear 6.4 Weak nuclear 7 Non-fundamental forces 7.1 Normal force 7.2 Friction 7.3 Tension 7.4 Elastic force 7.5 Continuum mechanics 7.6 Fictitious forces 8 Rotations and torque 8.1 Centripetal force 9
10.1 Conservative forces 10.2 Nonconservative forces 11 Units of measurement
12
Development of the concept
Philosophers in antiquity used the concept of force in the study of
stationary and moving objects and simple machines, but thinkers such
as
Since antiquity the concept of force has been recognized as integral
to the functioning of each of the simple machines. The mechanical
advantage given by a simple machine allowed for less force to be used
in exchange for that force acting over a greater distance for the same
amount of work. Analysis of the characteristics of forces ultimately
culminated in the work of
Though Sir Isaac Newton's most famous equation is F → = m a → displaystyle scriptstyle vec F =m vec a , he actually wrote down a different form for his second law of motion that did not use differential calculus.
F → = d p → d t , displaystyle vec F = frac mathrm d vec p mathrm d t , where p → displaystyle vec p is the momentum of the system, and F → displaystyle vec F is the net (vector sum) force. If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time.[10] By the definition of momentum, F → = d p → d t = d ( m v → ) d t , displaystyle vec F = frac mathrm d vec p mathrm d t = frac mathrm d left(m vec v right) mathrm d t , where m is the mass and v → displaystyle vec v is the velocity.[4]:9-1,9-2
If
F → = m d v → d t . displaystyle vec F =m frac mathrm d vec v mathrm d t . By substituting the definition of acceleration, the algebraic version
of Newton's
F → = m a → . displaystyle vec F =m vec a . Newton never explicitly stated the formula in the reduced form
above.[11]
Newton's
F → 1 , 2 displaystyle scriptstyle vec F _ 1,2 is the force of body 1 on body 2 and F → 2 , 1 displaystyle scriptstyle vec F _ 2,1 that of body 2 on body 1, then F → 1 , 2 = − F → 2 , 1 . displaystyle vec F _ 1,2 =- vec F _ 2,1 . This law is sometimes referred to as the action-reaction law, with F → 1 , 2 displaystyle scriptstyle vec F _ 1,2 called the action and − F → 2 , 1 displaystyle scriptstyle - vec F _ 2,1 the reaction. Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies,[15][Note 3] and thus that there is no such thing as a unidirectional force or a force that acts on only one body. In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero: F → 1 , 2 + F → 2 , 1 = 0. displaystyle vec F _ 1,2 + vec F _ mathrm 2,1 =0. More generally, in a closed system of particles, all internal forces
are balanced. The particles may accelerate with respect to each other
but the center of mass of the system will not accelerate. If an
external force acts on the system, it will make the center of mass
accelerate in proportion to the magnitude of the external force
divided by the mass of the system.[4]:19-1[5]
Combining Newton's
p → 1 displaystyle scriptstyle vec p _ 1 is the momentum of object 1 and p → 2 displaystyle scriptstyle vec p _ 2 the momentum of object 2, then d p → 1 d t + d p → 2 d t = F → 1 , 2 + F → 2 , 1 = 0. displaystyle frac mathrm d vec p _ 1 mathrm d t + frac mathrm d vec p _ 2 mathrm d t = vec F _ 1,2 + vec F _ 2,1 =0. Using similar arguments, this can be generalized to a system with an
arbitrary number of particles. 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.[4][5]
F → = d p → d t displaystyle vec F = frac mathrm d vec p mathrm d t remains valid because it is a mathematical definition.[17]:855–876 But for relativistic momentum to be conserved, it must be redefined as: p → = m 0 v → 1 − v 2 / c 2 , displaystyle vec p = frac m_ 0 vec v sqrt 1-v^ 2 /c^ 2 , where m 0 displaystyle m_ 0 is the rest mass and c displaystyle c the speed of light. The relativistic expression relating force and acceleration for a particle with constant non-zero rest mass m displaystyle m moving in the x displaystyle x direction is: F → = ( γ 3 m a x , γ m a y , γ m a z ) , displaystyle vec F =left(gamma ^ 3 ma_ x ,gamma ma_ y ,gamma ma_ z right), where γ = 1 1 − v 2 / c 2 . displaystyle gamma = frac 1 sqrt 1-v^ 2 /c^ 2 . is called the Lorentz factor.[18] In the early history of relativity, the expressions γ 3 m displaystyle gamma ^ 3 m and γ m displaystyle gamma m were called longitudinal and transverse mass. Relativistic force does not produce a constant acceleration, but an ever-decreasing acceleration as the object approaches the speed of light. Note that γ displaystyle gamma approaches asymptotically an infinite value and is undefined for an object with a non-zero rest mass as it approaches the speed of light, and the theory yields no prediction at that speed. If v displaystyle v is very small compared to c displaystyle c , then γ displaystyle gamma is very close to 1 and F = m a displaystyle F=ma is a close approximation. Even for use in relativity, however, one can restore the form of F μ = m A μ displaystyle F^ mu =mA^ mu , through the use of four-vectors. This relation is correct in relativity when F μ displaystyle F^ mu is the four-force, m displaystyle m is the invariant mass, and A μ displaystyle A^ mu is the four-acceleration.[19] Descriptions Free body diagrams of a block on a flat surface and an inclined plane. Forces are resolved and added together to determine their magnitudes and the net force. Since forces are perceived as pushes or pulls, this can provide an
intuitive understanding for describing forces.[3] As with other
physical concepts (e.g. temperature), the intuitive understanding of
forces is quantified using precise operational definitions that are
consistent with direct observations and compared to a standard
measurement scale. Through experimentation, it is determined that
laboratory measurements of forces are fully consistent with the
conceptual definition of force offered by Newtonian mechanics.
Forces act in a particular direction and have sizes dependent upon how
strong the push or pull is. Because of these characteristics, forces
are classified as "vector quantities". This means that forces follow a
different set of mathematical rules than physical quantities that do
not have direction (denoted scalar quantities). For example, when
determining what happens when two forces act on the same object, it is
necessary to know both the magnitude and the direction of both forces
to calculate the result. If both of these pieces of information are
not known for each force, the situation is ambiguous. For example, if
you know that two people are pulling on the same rope with known
magnitudes of force but you do not know which direction either person
is pulling, it is impossible to determine what the acceleration of the
rope will be. The two people could be pulling against each other as in
tug of war or the two people could be pulling in the same direction.
In this simple one-dimensional example, without knowing the direction
of the forces it is impossible to decide whether the net force is the
result of adding the two force magnitudes or subtracting one from the
other. Associating forces with vectors avoids such problems.
Historically, forces were first quantitatively investigated in
conditions of static equilibrium where several forces canceled each
other out. Such experiments demonstrate the crucial properties that
forces are additive vector quantities: they have magnitude and
direction.[3] When two forces act on a point particle, the resulting
force, the resultant (also called the net force), can be determined by
following the parallelogram rule of vector addition: the addition of
two vectors represented by sides of a parallelogram, gives an
equivalent resultant vector that is equal in magnitude and direction
to the transversal of the parallelogram.[4][5] The magnitude of the
resultant varies from the difference of the magnitudes of the two
forces to their sum, depending on the angle between their lines of
action. However, if the forces are acting on an extended body, their
respective lines of application must also be specified in order to
account for their effects on the motion of the body.
Free-body diagrams can be used as a convenient way to keep track of
forces acting on a system. Ideally, these diagrams are drawn with the
angles and relative magnitudes of the force vectors preserved so that
graphical vector addition can be done to determine the net force.[20]
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.[21]
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.
Dynamic equilibrium was first described by
V ( x , y , z ) → V ^ ( x ^ , y ^ , z ^ ) displaystyle V(x,y,z)to hat V ( hat x , hat y , hat z ) .
This becomes different only in the framework of quantum field theory,
where these fields are also quantized.
However, already in quantum mechanics there is one "caveat", namely
the particles acting onto each other do not only possess the spatial
variable, but also a discrete intrinsic angular momentum-like variable
called the "spin", and there is the
Feynman diagram for the decay of a neutron into a proton. The W boson is between two vertices indicating a repulsion. In modern particle physics, forces and the acceleration of particles
are explained as a mathematical by-product of exchange of
momentum-carrying gauge bosons. With the development of quantum field
theory and general relativity, it was realized that force is a
redundant concept arising from conservation of momentum (
The four fundamental forces of nature[26] Property/Interaction Gravitation Weak Electromagnetic Strong (Electroweak) Fundamental Residual Acts on:
Particles experiencing: All Quarks, leptons Electrically charged Quarks, Gluons Hadrons Particles mediating: Graviton (not yet observed) W+ W− Z0 γ Gluons Mesons Strength in the scale of quarks: 6959100000000000000♠10−41 6996100000000000000♠10−4 1 60 Not applicable to quarks Strength in the scale of protons/neutrons: 6964100000000000000♠10−36 6993100000000000000♠10−7 1 Not applicable to hadrons 20 Gravitational Main article: Gravity Images of a freely falling basketball taken with a stroboscope at 20 flashes per second. The distance units on the right are multiples of about 12 millimeters. The basketball starts at rest. At the time of the first flash (distance zero) it is released, after which the number of units fallen is equal to the square of the number of flashes. What we now call gravity was not identified as a universal force until
the work of Isaac Newton. Before Newton, the tendency for objects to
fall towards the Earth was not understood to be related to the motions
of celestial objects.
g → displaystyle scriptstyle vec g and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth.[27] 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 displaystyle m will experience a force: F → = m g → displaystyle vec F =m vec g For an object in free-fall, this force is unopposed and the net force
on the object is its weight. For objects not in free-fall, the force
of gravity is opposed by the reaction forces applied by their
supports. For example, a person standing on the ground experiences
zero net force, since a normal force (a reaction force) is exerted by
the ground upward on the person that counterbalances his weight that
is directed downward.[4][5]
Newton's contribution to gravitational theory was to unify the motions
of heavenly bodies, which
m ⊕ displaystyle scriptstyle m_ oplus ) and the radius ( R ⊕ displaystyle scriptstyle R_ oplus ) of the Earth to the gravitational acceleration: g → = − G m ⊕ R ⊕ 2 r ^ displaystyle vec g =- frac Gm_ oplus R_ oplus ^ 2 hat r where the vector direction is given by r ^ displaystyle hat r , is the unit vector directed outward from the center of the Earth.[10] In this equation, a dimensional constant G displaystyle G is used to describe the relative strength of gravity. This constant
has come to be known as Newton's Universal Gravitation Constant,[29]
though its value was unknown in Newton's lifetime. Not until 1798 was
G displaystyle G using a torsion balance; this was widely reported in the press as a measurement of the mass of the Earth since knowing G displaystyle 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,
m 1 displaystyle m_ 1 due to the gravitational pull of mass m 2 displaystyle m_ 2 is F → = − G m 1 m 2 r 2 r ^ displaystyle vec F =- frac Gm_ 1 m_ 2 r^ 2 hat r where r displaystyle r is the distance between the two objects' centers of mass and r ^ displaystyle scriptstyle hat r is the unit vector pointed in the direction away from the center of
the first object toward the center of the second object.[10]
This formula was powerful enough to stand as the basis for all
subsequent descriptions of motion within the solar system until the
20th century. During that time, sophisticated methods of perturbation
analysis[30] were invented to calculate the deviations of orbits due
to the influence of multiple bodies on a planet, moon, comet, or
asteroid. The formalism was exact enough to allow mathematicians to
predict the existence of the planet
Instruments like GRAVITY provide a powerful probe for gravity force detection.[32] Mercury's orbit, however, did not match that predicted by Newton's Law
of Gravitation. Some astrophysicists predicted the existence of
another planet (Vulcan) that would explain the discrepancies; however
no such planet could be found. When
E → = F → q displaystyle vec E = vec F over q where q displaystyle q is the magnitude of the hypothetical test charge.
Meanwhile, the
B = F I ℓ displaystyle B= F over Iell where I displaystyle I is the magnitude of the hypothetical test current and ℓ displaystyle scriptstyle 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 a magnetic field.[35] The connection between electricity and magnetism allows for the description of a unified electromagnetic force that acts on a charge. This force can be written as a sum of the electrostatic force (due to the electric field) and the magnetic force (due to the magnetic field). Fully stated, this is the law: F → = q ( E → + v → × B → ) displaystyle vec F =q( vec E + vec v times vec B ) where F → displaystyle scriptstyle vec F is the electromagnetic force, q displaystyle q is the magnitude of the charge of the particle, E → displaystyle scriptstyle vec E is the electric field, v → displaystyle scriptstyle vec v is the velocity of the particle that is crossed with the magnetic field ( B → displaystyle scriptstyle vec B ).
The origin of electric and magnetic fields would not be fully
explained until 1864 when
FN represents the normal force exerted on the object. Main article: Normal force
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.[17]: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.[4][5]
Friction
Main article: Friction
F s f displaystyle 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 ( μ s f displaystyle mu _ mathrm sf ) multiplied by the normal force ( F N displaystyle F_ N ). In other words, the magnitude of the static friction force satisfies the inequality: 0 ≤ F s f ≤ μ s f F N . displaystyle 0leq F_ mathrm sf leq mu _ mathrm sf F_ mathrm N . The kinetic friction force ( F k f displaystyle F_ mathrm kf ) is independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals: F k f = μ k f F N , displaystyle F_ mathrm kf =mu _ mathrm kf F_ mathrm N , where μ k f displaystyle 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
Main article: Tension (physics)
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.[39] 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.[4][5][40]
Elastic force
Main articles:
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.[41] This linear
relationship was described by
Δ x displaystyle Delta x is the displacement, the force exerted by an ideal spring equals: F → = − k Δ x → displaystyle vec F =-kDelta vec x where k displaystyle 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.[4][5] Continuum mechanics When the drag force ( F d displaystyle F_ d ) associated with air resistance becomes equal in magnitude to the force of gravity on a falling object ( F g displaystyle F_ g ), the object reaches a state of dynamic equilibrium at terminal velocity. Main articles: Pressure, Drag (physics), and Stress (mechanics)
Newton's laws and
F → V = − ∇ → P displaystyle frac vec F V =- vec nabla P where V displaystyle V is the volume of the object in the fluid and P displaystyle P is the scalar function that describes the pressure at all locations
in space.
F → d = − b v → displaystyle vec F _ mathrm d =-b vec v , where: b displaystyle b is a constant that depends on the properties of the fluid and the dimensions of the object (usually the cross-sectional area), and v → displaystyle scriptstyle vec v is the velocity of the object.[4][5] More formally, forces in continuum mechanics are fully described by a stress–tensor with terms that are roughly defined as σ = F A displaystyle sigma = frac F A where A displaystyle 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.[3][5]:133–134[35]:38-1–38-11
Fictitious forces
Main article: Fictitious forces
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.[42] These forces are considered fictitious because they do not
exist in frames of reference that are not accelerating.[4][5] Because
these forces are not genuine they are also referred to as "pseudo
forces".[4]:12-11
In general relativity, gravity becomes a fictitious force that arises
in situations where spacetime deviates from a flat geometry. As an
extension,
Relationship between force (F), torque (τ), and momentum vectors (p and L) in a rotating system. Main article: Torque Forces that cause extended objects to rotate are associated with torques. Mathematically, the torque of a force F → displaystyle scriptstyle vec F is defined relative to an arbitrary reference point as the cross-product: τ → = r → × F → displaystyle vec tau = vec r times vec F where r → displaystyle scriptstyle vec r is the position vector of the force application point relative to the reference point.
τ → = I α → displaystyle vec tau =I vec alpha where I displaystyle I is the moment of inertia of the body α → displaystyle scriptstyle vec alpha is the angular acceleration of the body. This provides a definition for the moment of inertia, which is the
rotational equivalent for mass. In more advanced treatments of
mechanics, where the rotation over a time interval is described, the
moment of inertia must be substituted by the tensor that, when
properly analyzed, fully determines the characteristics of rotations
including precession and nutation.
Equivalently, the differential form of Newton's
τ → = d L → d t , displaystyle vec tau = frac mathrm d vec L mathrm dt , [43] where L → displaystyle scriptstyle vec L 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,[44] and therefore also directly implies the conservation of angular momentum for closed systems that experience rotations and revolutions through the action of internal torques. Centripetal force Main article: Centripetal force For an object accelerating in circular motion, the unbalanced force acting on the object equals:[45] F → = − m v 2 r ^ r displaystyle vec F =- frac mv^ 2 hat r r where m displaystyle m is the mass of the object, v displaystyle v is the velocity of the object and r displaystyle r is the distance to the center of the circular path and r ^ displaystyle scriptstyle hat r 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.[4][5]
I → = ∫ t 1 t 2 F → d t , displaystyle vec I =int _ t_ 1 ^ t_ 2 vec F mathrm d t , which by Newton's
W = ∫ x → 1 x → 2 F → ⋅ d x → , displaystyle W=int _ vec x _ 1 ^ vec x _ 2 vec F cdot mathrm d vec x , which is equivalent to changes in kinetic energy (yielding the work energy theorem).[4]:13-3 Power P is the rate of change dW/dt of the work W, as the trajectory is extended by a position change d x → displaystyle scriptstyle d vec x in a time interval dt:[4]:13-2 d W = d W d x → ⋅ d x → = F → ⋅ d x → , so P = d W d t = d W d x → ⋅ d x → d t = F → ⋅ v → , displaystyle text d W,=, frac text d W text d vec x ,cdot , text d vec x ,=, vec F ,cdot , text d vec x ,qquad text so quad P,=, frac text d W text d t ,=, frac text d W text d vec x ,cdot , frac text d vec x text d t ,=, vec F ,cdot , vec v , with v →
= d x → / d t displaystyle vec v text = text d vec x / text d t the velocity.
U ( r → ) displaystyle scriptstyle U( vec r ) is defined as that field whose gradient is equal and opposite to the force produced at every point: F → = − ∇ → U . displaystyle vec F =- vec nabla U. Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not.[4][5] Conservative forces Main article: Conservative force A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space,[47] 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.[4][5] Conservative forces include gravity, the electromagnetic force, and the spring force. Each of these forces has models that are dependent on a position often given as a radial vector r → displaystyle scriptstyle vec r emanating from spherically symmetric potentials.[48] Examples of this follow: For gravity: F → = − G m 1 m 2 r → r 3 displaystyle vec F =- frac Gm_ 1 m_ 2 vec r r^ 3 where G displaystyle G is the gravitational constant, and m n displaystyle m_ n is the mass of object n. For electrostatic forces: F → = q 1 q 2 r → 4 π ϵ 0 r 3 displaystyle vec F = frac q_ 1 q_ 2 vec r 4pi epsilon _ 0 r^ 3 where ϵ 0 displaystyle epsilon _ 0 is electric permittivity of free space, and q n displaystyle q_ n is the electric charge of object n. For spring forces: F → = − k r → displaystyle vec F =-k vec r where k displaystyle k is the spring constant.[4][5]
Nonconservative forces
For certain physical scenarios, it is impossible to model forces as
being due to gradient of potentials. This is often due to
macrophysical considerations that yield forces as arising from a
macroscopic statistical average of microstates. For example, friction
is caused by the gradients of numerous electrostatic potentials
between the atoms, but manifests as a force model that is independent
of any macroscale position vector. Nonconservative forces other than
friction include other contact forces, tension, compression, and drag.
However, for any sufficiently detailed description, all these forces
are the results of conservative ones since each of these macroscopic
forces are the net results of the gradients of microscopic
potentials.[4][5]
The connection between macroscopic nonconservative forces and
microscopic conservative forces is described by detailed treatment
with statistical mechanics. In macroscopic closed systems,
nonconservative forces act to change the internal energies of the
system, and are often associated with the transfer of heat. According
to the
Units of force v t e newton (SI unit) dyne kilogram-force, kilopond pound-force poundal 1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl 1 dyn = 10−5 N ≡ 1 g⋅cm/s2 ≈ 1.0197 × 10−6 kp ≈ 2.2481 × 10−6 lbf ≈ 7.2330 × 10−5 pdl 1 kp = 9.80665 N = 980665 dyn ≡ gn ⋅ (1 kg) ≈ 2.2046 lbf ≈ 70.932 pdl 1 lbf ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kp ≡ gn ⋅ (1 lb) ≈ 32.174 pdl 1 pdl ≈ 0.138255 N ≈ 13825 dyn ≈ 0.014098 kp ≈ 0.031081 lbf ≡ 1 lb⋅ft/s2 The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units. See also Ton-force.
Orders of magnitude (force) Parallel force Notes ^ Newton's Principia Mathematica actually used a finite difference
version of this equation based upon impulse. See Impulse.
^ "It is important to note that we cannot derive a general expression
for
References ^ Nave, C. R. (2014). "Force". Hyperphysics. Dept. of
Further reading Corben, H.C.; Philip Stehle (1994). Classical Mechanics. New York:
Dover publications. pp. 28–31. ISBN 0-486-68063-0.
Cutnell, John D.; Johnson, Kenneth W. (2003). Physics, Sixth Edition.
Hoboken, New Jersey: John Wiley & Sons Inc.
ISBN 0471151831.
Feynman, Richard P.; Leighton; Sands, Matthew (2010). The Feynman
lectures on physics. Vol. I: Mainly mechanics, radiation and heat (New
millennium ed.). New York: BasicBooks. ISBN 978-0465024933.
Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (2010). The
Feynman lectures on physics. Vol. II: Mainly electromagnetism and
matter (New millennium ed.). New York: BasicBooks.
ISBN 978-0465024940.
Halliday, David; Resnick, Robert; Krane, Kenneth S. (2001).
External links Wikimedia Commons has media related to Forces (physics). Look up force in Wiktionary, the free dictionary. Video lecture on Newton's three laws by
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Linear/translational quantities Angular/rotational quantities Dimensions 1 L L2 Dimensions 1 1 1 T time: t s absement: A m s T time: t s 1 distance: d, position: r, s, x, displacement m area: A m2 1 angle: θ, angular displacement: θ rad solid angle: Ω rad2, sr T−1 frequency: f s−1, Hz speed: v, velocity: v m s−1 kinematic viscosity: ν, specific angular momentum: h m2 s−1 T−1 frequency: f s−1, Hz angular speed: ω, angular velocity: ω rad s−1 T−2 acceleration: a m s−2 T−2 angular acceleration: α rad s−2 T−3 jerk: j m s−3 T−3 angular jerk: ζ rad s−3 M mass: m kg ML2 moment of inertia: I kg m2 MT−1 momentum: p, impulse: J kg m s−1, N s action: 𝒮, actergy: ℵ kg m2 s−1, J s ML2T−1 angular momentum: L, angular impulse: ΔL kg m2 s−1 action: 𝒮, actergy: ℵ kg m2 s−1, J s MT−2 force: F, weight: Fg kg m s−2, N energy: E, work: W kg m2 s−2, J ML2T−2 torque: τ, moment: M kg m2 s−2, N m energy: E, work: W kg m2 s−2, J MT−3 yank: Y kg m s−3, N s−1 power: P kg m2 s−3, W ML2T−3 rotatum: P kg m2 s−3, N m s−1 power: P kg m2 s−3, W Authority control LCCN: sh85050452 GND: 4032651-2 NDL: 00926874 N |