Force

For other senses of this word, see force (disambiguation).

In physics, a force is anything that causes a free body with mass to accelerate. The net (or resultant) force is the sum of all the different forces acting on a body.

Force is a vector quantity defined as the rate of change of momentum induced in a free body by the force, and therefore has a direction associated. The SI unit for force is the newton.

Examples

A pitcher of water on a table is pushed downward toward the floor by its weight. However, the table pushes upward with equal force, resulting in zero net force, and no motion. Failure of the ancient writers (such as Aristotle) to appreciate that most ordinary objects do not move because they are in the grip of opposing but equal forces, is the cause of a long misunderstanding, up tot he time of Newton, of the natural effects of force. Aristotle and others, for example, 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.
A pitcher of water on a table is gently pushed sideways by a finger. It fails to move sideways because the force of the finger is now opposed by a new force of friction, generated between the pitcher bottom and the table surface. This newly generated force exactly balances the force produced on the pitcher by the finger, and again no motion occurs. Moreover, the new force increases or decreases automatically. If the force of the finger is doubled (up to a point), the opposing sideways force of friction INCREASES exactly to the point of perfect opposition, and stops all motion. Again, what is happening here is not obvious by simple inspection, and failure to appreciated it, contributed to the long historical misunderstanding of the opperation of, and nature of, force.
A pitcher of water on a table is pushed by a finger hard enough that the pitcher begins to slide on the surface at a constant rate. Here it is apparent that application of a constant force produces a constant velocity. This was a common experience of humans with ordinary objects under conditions in which friction was involved, so the idea that unopposed forces naturally produce increases in velocities was again not an obvious one. Frictional forces acting in opposition to other kinds of forces, tended to hide the correct relationship between simple force and motion.
A pitcher of water reaches the edge of the table and falls. Now the pitcher gains in velocity in proportion to the square of the the time of fall, and thus its rate of gain in momentum and velocity is constant. These facts were first discovered by Galileo. Although this is the correct behavior for unopposed forces, it was not until Newton that gravity was seen as simply an unopposed "force" in such circumstances. Moreover, Newton generalized the behavior of constant acceleration (constant momentum gain) to forces other than gravity as well, and asserted (see his second law of motion) that this behavior of constant momentum increase was characteristic of all "forces" (the forces of ordinary experience such as weight and the tension produced by pushing on an object with a finger).

Quantitative definition

Newton was first to mathematically define force as the rate of change of momentum: F=dp/dt. Here Newton provides an accurate definition of force, and moreover asserts that the forces of ordinary experience produce motions of a type which is usually NOT seen in ordianary experience (which is sullied by frictional forces which are hidden). The law is historically regarded as "Newton's second law":

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

.

The quantity mv is called the momentum. Thus, the net force on a particle is equal to the rate change of momentum of the particle with time. Typically, the mass m is constant in time, and Newton's law can be written in the simplified form

\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. 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 is incorrect and the full form of Newton's second law must be used.

The relation F=ma also fails to hold as velocity approaches the speed of light, in accordance with the special theory of relativity, although the basic definition F= dp/dt is still valid.

Because momentum is a vector, then force, being its time derivative, is also a vector - it has magnitude and direction. Vectors (and thus forces) are added together by their components - this results in so called parallelogram rule - thus parallelogram of force rule of force addition. 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. If the two forces are equal but opposite, then the resultant is zero. This condition is called static equilibrium, with the result that the object remains at rest or moves with a constant velocity. Static equilibrium is mathematically equivalent to the motion with equal and oppositely directed accelerations.

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 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: Coulomb's force (the force between electrical charges), gravitational (force between masses), magnetic force, frictional forces, centrifugal, impact force, and spring force, magnetism, tension, chemical bonding and contact force to name a few.

Only four fundamental forces of nature are known: the strong nuclear force, the electromagnetic force, the weak nuclear force, and the gravitation. 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). According to general relativity gravity results from the curvatures of spacetime.

Units of measurement

The SI unit used to measure force is the newton (symbol N), which is equivalent to kg·m·s⁻². The relationship F=m·a can be used with any consistent units (SI or CGS). If these units are not consistent, a more general form, F=k·m·a, is needed, where the constant k is a conversion factor dependent upon the units being used.

For example, in imperial engineering units, F is measured in "pounds force" or "lbf", m in "pounds mass" or "lb", and a in feet per second squared. In this particular system, one needs to use the more general form above, usually written F=m·a/g_c with the constant normally used for this purpose g_c = 32.174 lb·ft/(lbf·s²) equal to the reciprocal of the k above.

As with the kilogram, the pound is colloquially used as both a unit of mass and a unit of force. 1 lbf is the force required to accelerate 1 lb at 32.174 ft per second squared, since 32.174 ft per second squared is the standard acceleration due to terrestrial gravity.

Another imperial unit of mass is the slug, defined as 32.174 lb. It is the mass that accelerates by one foot per second squared when a force of one lbf is exerted on it.

When the standard gee (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 gee 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 disintinguish 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 coversion factors between various mesurements of force:

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

Instruments to measure forces

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 to give first mathematical definition to force.
Henry Cavendish's torsion bar experiment measured the force of gravity between two masses (1798)

References

Halliday, David (2001). Physics v. 1. New York: John Wiley & Sons. ISBN 0471320579. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
Serway, Raymond A. (2003). Physics for Scientists and Engineers. Philadelphia: Saunders College Publishing. ISBN 0534408427.
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed. ed.). W. H. Freeman. ISBN 0716708094. {{cite book}}: |edition= has extra text (help)