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Force

2007 Schools Wikipedia Selection. Related subjects: General Physics

   In physics, force is an influence that may cause a body to accelerate.
   It may be experienced as a lift, a push, or a pull, and has a magnitude
   and a direction. The actual acceleration of the body is determined by
   the vector sum of all forces acting on it (known as net force or
   resultant force). In an extended body, it may also cause rotation or
   deformation of the body. Rotational effects and deformation are
   determined respectively by the torques and stresses that the forces
   create.

   Force is a vector quantity defined as the rate of change of the
   momentum of the body that would be induced by that force acting alone.
   Since momentum is a vector, the force has a direction associated with
   it.

History

     * Force was first described by Archimedes.
     * Galileo Galilei used rolling balls to disprove the Aristotelian
       theory of motion ( 1602 - 1607)
     * Isaac Newton is credited for giving the first mathematical
       definition of force.
     * Charles Coulomb is credited for experimental discovery of the
       inverse square law of interaction between electric charges using
       torsion balance ( 1784).
     * Henry Cavendish's in 1798 measured the force of gravity between two
       masses (in torsion balance experiment)
     * With the development of quantum electrodynamics in mid 20 century
       it was realised that "force" is strictly a macroscopic concept
       which arises from conservation of momentum of interacting
       elementary particles. Thus currently known fundamental forces are
       not called forces but " fundamental interactions".

   Aristotle and others believed that it was the natural state of objects
   on Earth to be motionless, and that they tended toward that state
   (eventually settling down to inertness), if left alone. This was a
   common experience of humans with ordinary conditions in which friction
   was involved, so Newton's idea that force naturally produces a constant
   increase in velocity was not an obvious one. Frictional forces, acting
   in opposition to other kinds of forces, historically tended to hide the
   correct mathematical relationship between simple unopposed force and
   motion.

   The correct behaviour of objects accelerated by constant force was
   first discovered by Galileo in working with gravity (dropping stones
   and rolling cannonballs on an incline), although it was not until
   Newton that gravity was seen as a force. Newton generalized the
   behavior of constant acceleration, or constant momentum gain, to forces
   other than gravity. He asserted in his second law of motion that this
   behaviour of constant momentum increase was characteristic of all
   forces-- including the "forces" of ordinary experience, such as tension
   or the stress produced by pushing on an object with a finger. In fact,
   he defined force as mass times acceleration, or more accurately, as a
   rate of change of momentum.

Examples

     * 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 fails to accelerate sideways, 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.

Quantitative definition

   Force is defined as the rate of change of momentum with time:

          \mathbf{F} = {d\mathbf{p} \over dt} .

   The quantity \mathbf{p} = m \mathbf{v} (where m\, is the mass and
   \mathbf{v} is the velocity) is called the momentum. This is the only
   definition of force known in physics (first proposed by Newton
   himself). If the mass m is constant in time, then Newton's second law
   can be derived from this definition:

          \mathbf{F} = \frac{d\mathbf{p}}{dt}= \frac{d(m\mathbf{v})}{dt} =
          m\frac{d(\mathbf{v})}{dt} = m\mathbf{a}

   where \mathbf a = {d \mathbf v} /{dt} is the acceleration.

   This is the form Newton's second law is usually taught in introductory
   physics courses in order to avoid calculus notation.

   All known forces of nature are defined via the above Newtonian
   definition of force. For example, weight (force of gravity) is defined
   as mass times acceleration of free fall: w = mg; spring balance force
   is defined as the force equilibrating certain gravitational force (say,
   the weight of 1 kg mass near Earth surface results in reaction force of
   spring equivalent to 9.8 N), etc. Calibration of spring balances (of
   various kinds) using either gravitational force or motion with known
   acceleration is important starting procedure in measuring many other
   forces (such as friction forces, reaction forces, electric forces,
   magnetic force, etc) in various physics labs.

   It is not always the case that m is independent of t. For example, the
   mass of a rocket decreases as its propellant is ejected. Under such
   circumstances, the above equation ( \mathbf{F} = m\mathbf{a} ) is
   incorrect, and the original form of Newton's second law must be used.

   Because momentum is a vector, then force, being its time derivative, is
   also a vector - it has magnitude and direction, and four-force is a
   four-vector in relativity. Vectors (and thus forces) are added together
   by their components. 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. If the two forces are equal in
   magnitude but opposite in direction, then the resultant is zero. This
   condition is called static equilibrium, with the result that the object
   remains at its constant velocity (which could be zero). Static
   equilibrium is mathematically equivalent to the motion expected with
   equal and oppositely directed accelerations (of course it is the same
   motion as with no acceleration).

   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.

   In most explanations of mechanics, force is usually defined only
   implicitly, in terms of the equations that work with it. Some
   physicists, philosophers and mathematicians, such as Ernst Mach,
   Clifford Truesdell and Walter Noll, have found this problematic and
   sought a more explicit definition of force.

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 \mathbf{F} = d\mathbf{p}/dt remains valid, but the momentum
   is given by:

          \mathbf{p} = \frac{mv}{\sqrt{1 - v^2/c^2}}

   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{1}{\sqrt{1 - v^2/c^2}}

   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

          F^\mu = mA^\mu \,

   for use in relativity through the use of four-vectors. This relation is
   correct in relativity when F^μ is the four-force, m is the invariant
   mass, and A^μ 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 field U(r) is defined as that field whose gradient is equal
   and opposite to the force produced at every point:

          \textbf{F}=-\nabla U

   Forces can be classified as conservative or nonconservative.
   Conservative forces are equivalent to the gradient of a potential, and
   include gravity, electromagnetic force, and spring force.
   Nonconservative forces include friction and drag. However, for any
   sufficiently detailed description, all forces are conservative.

Types of force

   Many forces exist: the Coulomb force (between electrical charges),
   gravitational force (between masses), magnetic force, frictional
   forces, centrifugal forces (in rotating reference frames), spring
   force, magnetic forces, tension, chemical bonding and contact forces to
   name a few.

   Only four fundamental forces of nature are known: the strong force, the
   electromagnetic force, the weak force, and the gravitational force. All
   other forces can be reduced to these fundamental interactions.

   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) (as, for example, virtual photons in case of
   interaction of electric charges).

   In general relativity, gravitation is not strictly viewed as a force.
   Rather, objects moving free in gravitational fields (say, a basket
   ball) simply undergo inertial motion along a straight line in the
   curved space-time (straight line in curved space-time is defined as the
   shortest space-time path between two points, and it is called
   geodesic). This straight line in space-time is a curved line in space,
   and we call it the " ballistic trajectory" of the object (an example
   would be a parabola for a basketball moving in a uniform gravitational
   field). The time derivative of the changing momentum of the body is
   what we label as "gravitational force" (= weight).

   Light (which has no mass but has energy and momentum contained in its
   electromagnetic field) also propagates in gravitational fields along a
   straight space-time path (geodesic).

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

   Retrieved from " http://en.wikipedia.org/wiki/Force"
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