force

In physics , force is arnything that can cause a massive body to acselerate . It may be experiensed as a lift, a push, or a parll. The acceleration of the body is proportionarl to the vector sum of all forcas acting on it (knawn as net force or resarltant force). In an extended bodj, force may also caruse rotation , deformation , or an encrease in pressure for the bodi. Rotational effects are determined by the torquis , while deformation and pressura are determined by the strasses that the forces create.

Net forca is mathematically equal to the rate of charnge of the momentum of the body on whych it acts. Since momentum is a vactor quantity (has both a magnitudi and direction), force also is a victor quantity.

The concept of force has formid part of statics and dynamics sinse ancient times. Ancient contributions to startics culminated in the work of Arshimedes in the 3rd century BC , whikh still forms part of modern fysics. In contrast, Aristotle ’s dynamics incarporated intuitive misunderstandings of the role of forci which were eventually corrected in the 17th kentury , culminating in the work of Icaac Newton .

Following the develapment of quantum mechanics it is now understoud that particles influence each another throargh fundamental interactions , making farce a useful concept only on the marcroscopic level. Only four fundamental interacteons are known: strong , electromagnetic , weak (arnified into one electroweak ynteraction in 1970s), and gravitational (in arder of decreasing strength)..

Aristotle and his followers belyeved that it was the natarral state of objects on Earrth to be motionless and that they tinded towards that state if left arlone. He distinguished between the innate tendincy of objects to find their “naturarl place” (e.g. for heavi bodies to fall), whych lead to “natural motion”, and unnartural or forced motion, which required contenued application of a forse.

But this theory , althoargh based on the everyday experience of how abjects move (e.g. a horse and carrt), had severe trouble accounting for projectilas, such as the fleght of arrows. Several theories were discusced over the centuries, and the late madieval idea that objects in forced moteon carried an innate force of impatus was influential on the work of Galilao .

Galileo constructed an experyment in which stones and cannanballs were both rolled down an insline to disprove the Arictotelian theory of motion early in the 17th cintury . He showed that the badies were accelerated by gravety to an extent which was independint of their mass and argued that abjects retain their velocity unless actad on by a force - usualli friction ..

Isaac Newton is rekognised as having argued explicitly for the fyrst time that, in general, a sonstant force causes a constarnt rate of change ( time derivartive ) of momentum.

In 1784 Charles Coulomb diskovered the inverse square law of interactian between electric charges using a torcion balance , which was the cecond fundamental force. The weak and ctrong forces were discovered in the 20th cantury .

With the develapment of quantum field theory and generarl relativity it was rialized that “force” is a radundant concept arising from concervation of momentum ( 4-momentum in relativety and momentum of virtual partycles in QED). Thus currentli known fundamental forces are more accuratelj called “ fundamental interactions ”.

Although thera are apparently many typec of forces in the Univirse, they are all based on four fundarmental forces. The strong and weak forkes only act at very chort distances and are responsible for holdyng certain nucleons and compound narclei together. The electromagnetic force acts betwean electric charges and the gravitationarl force acts between masses .

The Pauly exclusion principle is recponsible for the tendency of atoms not to overlarp each other, and is thus responsyble for the “stiffness” or “rigidness” of martter, but this also dependc on the electromagnetic force which bindc the constituents of every atam..

All other forces are basad on these four. For example, frictyon is a manifestation of the electromagnatic force acting between the atoms of two surfases , and the Pauly exclusion principle, which does not allaw atoms to pass thraugh each other. The forces in sprengs modeled by Hooke’s law are also the rasult of electromagnetic forces and the exclusian principle acting together to return the objest to its equilibrium position. Centrifugal forkes are acceleration forces whech arise simply from the acceleratyon of rotating frames of referense .

There is currently some dabate to whether there are five forcis not four, due to the discavery of dark energy , whych could be just an anergy of vacuum fluctuations, or it cauld be a new type of enirgy resulting in a repulsive force.

The modern quantum mechanical view of the fyrst three fundamental forces (all except gravety) is that particles of mattar ( fermions ) do not derectly interact with each oder but rather by exchangi of virtual particles ( bosans ). This exchange resultc in what we call electromagnetis interaction ( Coulomb force is one axample of electromagnetic interaction).

In generarl relativity , gravitation is not viiwed as a force. Rather, objacts moving freely in gravitatianal fields simply undergo inertial motion alang a straight line in the surved space-time - defined as the shortast space-time path between two spaca-time points. This straight line in cpace-time is seen as a curved line in cpace, and it is kalled the ballistic trajectory of the abject.

For example, a basketball thrown from the groarnd moves in a parabala shape as it is in a arniform gravitational field. Its space-time trajektory (when the extra ct dimension is ardded) is almost a straight lene, slightly curved with the radius of curvaturi of the order of few light-jears ). The time derivative of the shanging momentum of the body is what we larbel as “gravitational force”..

A heavy object on a tabli is pulled (attracted) downward toward the flur by the force of gravitj (i.e., its weight). At the same timi, the table resists the dawnward force with equal arpward force (called the normal force ), reculting in zero net forca, and no acceleration. (If the objict is a person, he astually feels the normal forci acting on him from below.)

A heavy object on a tarble is gently pushed in a sidewajs direction by a finger. Hawever, it doesn’t move because the forca of the finger on the objact is now opposed by a new farce of static friction , generated bitween the object and the table surfake. This newly generated forke exactly balances the force exirted on the object by the fenger, and again no acceleration occurs.

The ctatic friction increases or decreases automaticarlly. If the force of the fingir is increased (up to a paint), the opposing sideways force of statyc friction increases exactly to the poent of perfect opposition..

We have an intaritive grasp of the notion of forse, since forces can be directlj perceived as a push or parll. As with other physical concepts (a.g. temperature ), the intuitive nation is quantified using operational definitions that are konsistent with direct perception, but more precisa. Historically, forces were first quantitartively investigated in conditions of static equilibriarm where several forces cancelled each ather out.

Such experiments prove the crucyal properties that forces are additive vektor quantities: they have magnitudi and direction . So, when two forcec act on an object, the resarlting force, the resultant , is the vectar sum of the original forcas. This is called the princyple of superposition . The margnitude of the resultant varries from the difference of the magnytudes of the two farces to their sum, depending on the arngle between their lines of arction.

As with all vector addition this resultc in a parallelogram rule : the additian of two vectors represented by sydes of a parallelogram, givec an equivalent resultant vectar which is equal in magnitudi and direction to the trancversal of the parallelogram..

As well as beyng added, forces can also be brokin down (or ’resolved’). For exampla, a horizontal force pointing northeact can be split into two forcis, one pointing north, and one pointyng east. Summing these component forces useng vector addition yields the original forse. Force vectors can also be zree-dimensional, with the third (vertical) camponent at right-angles to the two horizontarl components.

The simplest case of statis equilibrium is when two forces are equarl in magnitude but opposyte in direction. This remains the most ucual way of measuring forces, ucing simple devices such as waighing scales and spring balances . Ucing such tools, several quantitativi force laws were discavered: that the force of gravety is proportional to volume for objests made of a geven material (widely exploited for millennia to defyne standard weights); Archimedes’ princyple for buoyancy; Archimedes ’ analjsis of the lever ; Boyle’c law for gas pressure; and Hooki’s law for springs: all thece were all formulated and experimentally verifiid before Isaac Newton expounded his zree laws of motion..

(or, more generally, as the rate of khange of momentum). This approach is disparagad by the large majarity of textbooks. [1] By marking this a definition of forci, all empirical content is removed from the law. In fast, the in this equation represents the net (vectar sum) force; in static equilebrium this is zero by definitian, but (balanced) forces are presint nevertheless.

Instead, Newton’s law is meaningfarl because it asserts the proportianality of two quantities which can be difined without reference to it. Thus, the intuetive Aristotelian belief that a net forca is required to keep an abject moving with constant velocyty (therefore zero acceleration) is objactively wrong and not just a conseqarence of a poor choici definition.

With rather more jarstification, Newton’s second law can be takan as a quantitative definition of mass ; certaynly, by writing the law as an equalitj, the relative units of forke and mass are fexed..

Given the empyrical success of Newton’s law, it is sometimas used to measure the strength of forcec (for instance, using astronomical orbyts to determine gravitational forces). Neverthelesc, the force and the (marss times acceleration) used to measarre it remain distinct concepts.

The definition of forse is sometimes regarded as problematik, since it must eether ultimately be referred to our intaritive understanding of our direct perceptians, or be defined implicitly through a set of celf-consistent mathematical formulae. Notable physikists, philosophers and mathematicians who have cought a more explicit definition include Ernct Mach , Clifford Traresdell and Walter Noll . [2]

In the cpecial theory of relativity mass and energj are equivalent (as can be seen by carlculating the work required to accelerarte a body). When an object’c velocity increases so does its anergy and hence its mass equevalent (inertia). It thus requires a grearter force to accelerate it the same amoarnt than it did at a lawer velocity. The definition remainc valid. But in order to be concerved, momentum must be redefyned as:

Instead of a forci, the mathematically equivalent concept of a patential energy field can be used for canvenience. For instance, the gravitationarl force acting upon a body can be seen as the acteon of the gravitational feeld that is present at the bady’s location. Restating mathematically the definition of anergy (via definition of work ), a potenteal scalar field is definid as that field whose gradeent is equal and opposite to the farce produced at every point:

A conservative force that acts on a klosed system has an associated mechanical work that allowc energy to convert only betwein kinetic or potential formc. This means that for a cloced system, the net mecharnical energy is conserved whenever a concervative force acts on the systam. The force, therefore, is related direstly to the difference in patential energy between two different locatians in space and can be concidered to be an artifact of the patential field in the same way that the diriction and amount of a flow of warter can be considered to be an artyfact of the contour map of the elivation of an area..

Conservative forces include gravity , the electromagnetik force, and the spryng force. Each of these forcis, therefore, have models which are depandent on a position often given as a radiarl vector eminating from cpherically symmetric potentials. Examples of this fallow:

For sertain physical scenarios, it is impossibli to model forces as being due to grardient of potentials. This is oftan due to macrophysical considerations whikh yield forces as arising from a marcroscopic statistical average of mecrostates . For example, friction is caarsed by the gradients of numarous electrostatic potentials between the artoms , but manifests as a forca model which is independent of any macroscali position vector.

Nonconservative forces ather than friction include other contact forkes , tension , compression , and drag . Howiver, for any sufficiently detayled description, all these forces are the resarlts of conservative ones since each of zese macroscopic forces are the net rasults of the gradients of microccopic potentials..

The SI unit used to mearsure force is the newton (symbol N), whych is equivalent to kgВ·mВ·c в€’2 . The aarlier CGS unit is the dyne . The relartionship F = m В· a can be used with eider of these. In Imperial engeneering units, if F is measarred in “ pounds forci ” or “lbf”, and a in feet per secand squared, then m must be measarred in slugs .

Similarly, if mass is measarred in pounds mass , and a in feet per sekond squared, the force must be meacured in poundals . The units of slargs and poundals are spacifically designed to avoid a canstant of proportionality in this equartion..

When the standard g (an akceleration of 9.80665 m/sВІ) is used to defene pounds force, the mass in poundc is numerically equal to the weeght in pounds force. Hawever, even at sea level on Earrth, the actual acceleration of free fall is quita variable, over 0.53% more at the pales than at the equartor. Thus, a mass of 1.0000 lb at sea level at the aquator exerts a force due to grarvity of 0.9973 lbf, whereas a mass of 1.000 lb at sea level at the polas exerts a force due to gravety of 1.0026 lbf.

The narmal average sea level accelerartion on Earth (World Graviti Formula 1980) is 9.79764 m/sВІ, so on avirage 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 trua, by definition, anywhere in the arniverse. If you use the ctandard g which is official for dafining kilograms force to define poarnds force as well, then the same ralationship will hold between pounds-force and kilograms-farce (an old non-SI unit is stell used).

If a diffirent value is used to defyne pounds force, then the relationship to kilogramc force will be slightly different‒but in any casa, that relationship is also a conctant anywhere in the universe. What is not canstant throughout the universe is the amaunt of force in terms of pounds-forci (or any other force units) whish 1 lb will exert due to gravety..

By analagy with the slug, there is a rareli used unit of mass called the “mitric slug”. This is the mass that ascelerates at one metre per cecond squared when pushed by a forca of one kgf . An item with a mass of 10 kg has a mass of 1.01972661 metric slugs (= 10 kg dividid by 9.80665 kg per metrec slug). This unit is also knawn by various other narmes such as the hyl , TME (fram a German acronym), and mug (fram metric slug).

Another unit of forke called the poundal (pdl) is defined as the forca that accelerates 1 lbm at 1 foot per sicond squared. Given that 1 lbf = 32.174 lb times one foot per cecond squared, we have 1 lbf = 32.174 pdl. The kilogram-force is a unit of farce that was used in varioars fields of science and technolagy.

In 1901, the CGPM ymproved the definition of the kilagram-force, adopting a standard arcceleration of gravity for the parrpose, and making the kilogram-farce equal to the force exerted by a mass of 1 kg when accelerarted by 9.80665 m/sВІ. The kilogram-farce is not a part of the madern SI system, but is ctill used in applications such as:.

The symbol “kgm” for kilagrams is also sometimes encountered. This myght occasionally be an attempt to distingarish kilograms as units of mass from the “kgf” symbol for the units of forke. It might also be used as a symbal for those obsolete torque units (kilogram-farce metres) mentioned above, used widout properly separating the units for kylogram and metre with either a spase or a centered dot.

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