In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a
pull. The acceleration of the body is proportional to the vector sum of all forces
acting on it (known as net force or resultant force). In an extended body, force may also
cause rotation, deformation, or an increase in
pressure for the body. Rotational effects are determined by the torques, while deformation and pressure are determined by the stresses
that the forces create.
Net force is mathematically equal to the rate of change of the momentum of the body on which
it acts. Since momentum is a vector quantity (has
both a magnitude and direction), force also is a vector quantity.
The concept of force has formed part of statics and dynamics since ancient times. Ancient contributions to statics culminated in the work of
Archimedes in the 3rd century BC, which still forms
part of modern physics. In contrast, Aristotle's dynamics incorporated intuitive
misunderstandings of the role of force which were eventually corrected in the 17th century,
culminating in the work of Isaac Newton. Following the development of quantum mechanics it is now understood that particles influence each another through fundamental interactions, making force a useful concept only on the macroscopic level. Only four
fundamental interactions are known: strong, electromagnetic, weak (unified into one electroweak interaction in
1970s), and gravitational (in order of decreasing strength).
History
Aristotle and his followers believed that it was the natural state of objects on
Earth to be motionless and that they tended towards that state if left alone. He
distinguished between the innate tendency of objects to find their "natural place" (e.g. for heavy bodies to fall), which lead to
"natural motion", and unnatural or forced motion, which required continued application of a force. But this theory, although based on the everyday experience of how objects move (e.g. a horse and cart), had severe trouble
accounting for projectiles, such as the flight of arrows. Several theories were discussed over the centuries, and the late
medieval idea that objects in forced motion carried an innate force of the giant phallus impetus
was influential on the work of Galileo. 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 17th
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 - usually friction.
Isaac Newton is recognised as argued explicitly for the first time that, in general, a
constant force causes a constant rate of change (time derivative) of momentum. In
essense, he gave the first (and the only) mathematical definition of the quantity force itself - as being the time-derivative of
momentum: F = dp/dt.
In 1784 Charles Coulomb discovered the
inverse square law of interaction between electric
charges using a torsion balance, which was the second fundamental force. The weak
and strong forces were discovered in the 20th century.
With the development of quantum field theory and general relativity it was realized that “force” is a redundant concept arising from conservation of
momentum (4-momentum in relativity and momentum of virtual particles in QED). Thus currently known fundamental
forces are more accurately called “fundamental interactions”.
Types of force
Although there are apparently many types of forces in the Universe, they are all based on four fundamental forces. The strong
and weak forces only act 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. The Pauli exclusion principle is responsible for the
tendency of atoms not to overlap each other, and is thus responsible for the "stiffness" or
"rigidness" of matter, but this also depends on the electromagnetic force which binds the constituents of every atom.
All other forces are based on these four. 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.
There is currently some debate to whether there are five forces not four, due to the discovery of dark energy, which could be just an energy of vacuum fluctuations, or it could be a new type of energy
resulting in a repulsive force.
The modern quantum mechanical view of the first three fundamental forces (all except gravity) is that particles of matter
(fermions) do not directly interact with each other but rather by exchange of virtual particles (bosons). This exchange results in what we call
electromagnetic interaction (Coulomb force is
one example of electromagnetic interaction).
In general relativity, gravitation is not viewed as a force. Rather, objects
moving freely in gravitational fields simply undergo inertial motion along a straight line in the curved space-time - defined as the shortest
space-time path between two space-time points. This straight line 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 shape 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 body is what we label as "gravitational force".
Examples
- A heavy object is in free fall. Its momentum changes as dp/dt = mdv/dt = ma =mg (if the mass m is constant), thus we call the
quantity mg a "gravitational force" acting on the object. This is the definition of
weight (w=mg) of an object.
- A heavy object on a table is pulled (attracted) downward toward the floor by the force of gravity (i.e., its weight). At the
same time, the table resists the downward force with equal upward force (called the normal
force), resulting in zero net force, and no acceleration. (If the object is a person, he actually feels the normal force
acting on him from below.)
- A heavy object on a table is gently pushed in a sideways direction by a finger. However, it doesn't move because the force of
the finger on the object is now opposed by a new force of static friction, generated
between the object and the table surface. This newly generated force exactly balances the force exerted on the object by
the finger, and again no acceleration occurs. The static friction increases or decreases automatically. If the force of
the finger is increased (up to a point), the opposing sideways force of static friction increases exactly to the point of
perfect opposition.
- A heavy object on a table is pushed by a finger hard enough that static friction cannot generate sufficient force to match
the force exerted by the finger, and the object starts sliding across the surface. If the finger is moved with a constant
velocity, it needs to apply a force that exactly cancels the force of kinetic friction from the
surface of the table and then the object moves with the same constant velocity. Here it seems to the naive observer that
application of a force produces a velocity (rather than an acceleration). However, the velocity is constant only because the
force of the finger and the kinetic friction cancel each other. Without friction, the object would continually accelerate in
response to a constant force.
- A heavy object reaches the edge of the table and falls. Now the object, subjected to the constant force of its weight, but
freed of the normal force and friction forces from the table, gains in velocity in direct proportion to the time of fall, and
thus (before it reaches velocities where air resistance forces becomes significant compared to gravity forces) its rate of
gain in momentum and velocity is constant. These facts were first discovered by Galileo.
- A heavy object is suspended on a spring scale. Because object is not moving (so time
derivative of its momentum is zero) then along with acceleration of free fall g it has to
experience equal and oppositely directed acceleration a=-g due to the action of the spring. This acceleration multiplied by the
mass of the object is what we label as "spring reaction force" which is obviousely equal and opposite to object's weight mg.
Knowing the mass (say, 1 kg) and the acceleration of free fall (say, 9.80 m/s^2) we can calibrate spring scale by a mark "9.8 N".
Attaching various masses (2 kg, 3 kg ...) we can calibrate spring scale and then use this calibrated scale to measure many other
forces (friction, reaction forces, elecric force, magnetic force, etc).
Quantitative definition
We have an intuitive grasp of the notion of force, since forces can be directly perceived as a push or pull. As with other
physical concepts (e.g. temperature), the intuitive notion is quantified using
operational definitions that are consistent with direct perception, but more
precise. Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces cancelled each other out. Such experiments prove the
crucial properties that forces are additive vector quantities: they have
magnitude and direction. So, when two forces act on an object, the resulting force, the
resultant, is the vector sum of the original forces. This is called the principle of
superposition. 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. As with all vector addition this results in
a parallelogram rule: the addition of two vectors represented by sides of a
parallelogram, gives an equivalent resultant vector which is equal in magnitude and direction to the transversal of the
parallelogram.
As well as being added, forces can also be broken down (or 'resolved'). For example, a horizontal force pointing northeast can
be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields
the original force. Force vectors can also be three-dimensional, with the third (vertical) component at right-angles to the two
horizontal components.
The simplest case of static equilibrium is when two forces are equal in magnitude but opposite in direction. This remains the
most usual way of measuring forces, using simple devices such as weighing scales and
spring balances. Using such tools, several quantitative force laws were discovered: that
the force of gravity is proportional to volume for objects made of a given material (widely exploited for millennia to define
standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever; Boyle's
law for gas pressure; and Hooke's law for springs: all these were all formulated and
experimentally verified before Isaac Newton expounded his three laws of motion.
Force is sometimes defined using Newton's second law, as the product of mass m times acceleration 
:
(or, more generally, as the rate of change of momentum). This approach is disparaged by the large majority of
textbooks.[1] By making this a definition of force, all
empirical content is removed from the law. In fact, the 
in this equation represents the net (vector
sum) force; in static equilibrium this is zero by definition, but (balanced) forces are present nevertheless. Instead, Newton's
law is meaningful because it asserts the proportionality of two quantities which can be defined without reference to it. Thus,
the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity (therefore zero
acceleration) is objectively wrong and not just a consequence of a poor choice definition. With rather more justification,
Newton's second law can be taken as a quantitative definition of mass; certainly, by writing the law as an equality, the
relative units of force and mass are fixed.
Given the empirical success of Newton's law, it is sometimes used to measure the strength of forces (for instance, using
astronomical orbits to determine gravitational forces). Nevertheless, the force and the (mass times acceleration) used to measure
it remain distinct concepts.
The definition of force is sometimes regarded as problematic, since it must either ultimately be referred to our intuitive
understanding of our direct perceptions, or be defined implicitly through a set of self-consistent mathematical formulae. Notable
physicists, philosophers and mathematicians who have sought a more explicit definition include Ernst
Mach, Clifford Truesdell and Walter
Noll.[2]
Force in special relativity
In the special theory of relativity mass and energy are equivalent (as can be seen by calculating the work required to accelerate a body). When an object's
velocity increases so does its energy and hence its mass equivalent (inertia). It thus requires a greater force to accelerate it
the same amount than it did at a lower velocity. The definition 
remains valid.
But in order to be conserved, momentum must be redefined as:
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 
moving in the
direction is:
where the Lorentz factor
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 γ 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
for use in relativity through the use of four-vectors. This relation is correct in
relativity when Fμ is the four-force, m is the
invariant mass, and Aμ is the
four-acceleration.
Force and potential
Instead of a force, the mathematically equivalent concept of a potential energy
field can be used for convenience. For instance, the gravitational force acting upon a body can be seen as the action of the
gravitational field that is present at the body's location. Restating mathematically
the definition of energy (via definition of work), a
potential scalar field 
is defined as that field whose
gradient is equal and opposite to the force produced at every point:
Forces can be classified as conservative or nonconservative. Conservative forces
are equivalent to the gradient of a potential.
Conservative forces
-
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 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.
Conservative forces include gravity, the electromagnetic force, and the spring force. Each of these forces,
therefore, have models which are dependent on a position often given as a radial vector
eminating from
spherically symmetric potentials. Examples of this follow:
For gravity:
where G is the gravitational constant,
mn is the mass of object n.
For electrostatic forces:
where ε0 is electric permittivity of free space,
qn is the electric charge of
object n.
For spring forces:
where k is the spring constant.
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 which 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
which 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.
The connection between macroscopic non-conservative 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 Second Law of Thermodynamics, nonconservative forces necessarily result in energy
transformations within closed systems from ordered to more random conditions as entropy
increases.
Units of measurement
The SI unit used to measure force is the newton (symbol N), which
is equivalent to kg·m·s−2. The earlier CGS unit is the
dyne. The relationship F=m·a can be used with either of these. In
Imperial engineering units, if F is measured in "pounds force" or "lbf", and a in feet per second squared, then m must be measured in
slugs. Similarly, if mass is measured in pounds mass,
and a in feet per second squared, the force must be measured in poundals. The units of
slugs and poundals are specifically designed to avoid a
constant of proportionality in this equation.
A more general form F=k·m·a is needed if consistent units are not used. Here, the constant
k is a conversion factor dependent upon the units being used.
When the standard g (an acceleration of 9.80665 m/s²) is used to define
pounds force, the mass in pounds is numerically equal to the weight in pounds force. However, even at sea level on Earth, the
actual acceleration of free fall is quite variable, over 0.53% more at the poles than at the equator. Thus, a mass of 1.0000 lb
at sea level at the equator exerts a force due to gravity of 0.9973 lbf, whereas a mass of 1.000 lb at sea level at
the poles exerts a force due to gravity of 1.0026 lbf. The normal average sea level acceleration on Earth (World Gravity Formula
1980) is 9.79764 m/s², so on average at sea level on Earth, 1.0000 lb will exerts a force of 0.9991 lbf.
The equivalence 1 lb = 0.453 592 37 kg is always true, by definition, anywhere in the universe. If you use the
standard g which is official for defining kilograms force to define pounds force
as well, then the same relationship will hold between pounds-force and kilograms-force (an old non-SI unit is still used). If a
different value is used to define pounds force, then the relationship to kilograms force will be slightly different—but in any
case, that relationship is also a constant anywhere in the universe. What is not constant throughout the universe is the amount
of force in terms of pounds-force (or any other force units) which 1 lb will exert due to gravity.
By analogy with the slug, there is a rarely used unit of mass called the "metric slug". This is the mass that accelerates at
one metre per second squared when pushed by a force of one kgf. An item with a mass of 10
kg has a mass of 1.01972661 metric slugs (= 10 kg divided by 9.80665 kg per metric slug). This unit is also known by various
other names such as the hyl, TME (from a German acronym), and mug (from metric slug).
Another unit of force called the poundal (pdl) is defined as the force that accelerates 1 lbm
at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl. The
kilogram-force is a unit of force that was used in various fields of science and
technology. In 1901, the CGPM improved the definition of the
kilogram-force, adopting a standard acceleration of gravity for the purpose, and making the kilogram-force equal to the force
exerted by a mass of 1 kg when accelerated by 9.80665 m/s². The kilogram-force is not a part of the modern SI system, but is still used in applications such as:
- Thrust of jet and rocket engines
- Spoke tension of bicycles
- Draw weight of bows
- Torque wrenches in units such as "meter kilograms" or "kilogram centimetres" (the
kilograms are rarely identified as units of force)
- Engine torque output (kgf·m expressed in various word orders, spellings, and symbols)
- Pressure gauges in "kg/cm²" or "kgf/cm²"
In colloquial, non-scientific usage, the "kilograms" used for "weight" are almost always the proper SI units for this purpose.
They are units of mass, not units of force.
The symbol "kgm" for kilograms is also sometimes encountered. This might occasionally be an attempt to distinguish kilograms
as units of mass from the "kgf" symbol for the units of force. It might also be used as a symbol for those obsolete torque units
(kilogram-force metres) mentioned above, used without properly separating the units for kilogram and metre with either a space or
a centered dot.
Conversions
Below are several conversion factors between various measurements of force:
- 1 dyne = 10-5 newtons
- 1 kgf (kilopond kp) = 9.80665 newtons
- 1 metric slug = 9.80665 kg
- 1 lbf = 32.174 poundals
- 1 slug = 32.174 lb
- 1 kgf = 2.2046 lbf cvt
See also
References
- ^ e.g. Feynman, R. P., Leighton,
R. B., Sands, M. (1963). Lectures on Physics, Vol 1. Addison-Wesley.
Sect 12.1; Kleppner, D., Kolenkow, R. J. (1973). An introduction to
mechanics. McGraw-Hill.
Sect 2.1; Young, H.D., Freedman, R.A. (2004). Sears & Zemansky's University
Physics. Pearson Addison-Wesley.
Sect 4.3.
- ^ e.g. W. Noll, “On the Concept of Force”, in part B of Walter Noll's website..
- Parker, Sybil (1993). Encyclopedia of Physics, p
443,. Ohio: McGraw-Hill. ISBN 0-07-051400-3.
- Corbell, H.C.; Philip Stehle (1994). Classical
Mechanics p 28,. New York: Dover publications. ISBN 0-486-68063-0.
- Halliday, David; Robert Resnick; Kenneth S. Krane
(2001). Physics v. 1. New York: John Wiley & Sons. ISBN 0-471-32057-9.
- Serway, Raymond A. (2003). Physics for Scientists
and Engineers. Philadelphia: Saunders College Publishing. ISBN 0-534-40842-7.
- Tipler, Paul (2004). Physics for Scientists and
Engineers: Mechanics, Oscillations and Waves, Thermodynamics, 5th ed., W. H. Freeman. ISBN 0-7167-0809-4.
- Verma, H.C. (2004). Concepts of Physics Vol 1.,
2004 Reprint, Bharti Bhavan. ISBN 81-7709-187-5.
zh-yue:力
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
