In the most general sense, force denotes the faculty of action or the power to overcome a resistance. In the physical sciences it is that entity that changes, or tends to change, the state of rest or of motion of a body. Consequently, it may also be defined as the cause of motion, or more precisely—assuming the validity of the principle of inertia, according to which unaccelerated motion and rest are dynamically and causally equivalent and correspond merely to different choices of the reference systems—as the cause of acceleration.
The metric unit of force in science is the dyne, which is the force necessary in order to give a mass of one gram an acceleration (increase of velocity) of one centimeter per second in each second. The British unit of force is the poundal, which is the force necessary to give a mass of one pound an acceleration of one foot per second each second. The practical unit is the gram force, that is, the force Earth exerts on one gram of mass at sea level and 45° latitude; it equals 980.616 dynes. Another common unit is the newton, which is the force necessary in order to give a mass of one kilogram an acceleration of one meter per second each second, and is therefore equivalent to 105 dynes.
Apart from being used in a figurative sense, such as "force of habit," "police force," or "economic forces," the word force, especially in the natural philosophy of the eighteenth and nineteenth centuries and in the early writings on the principle of conservation of energy (R. Mayer, H. von Helmholtz) signified action and energy. This homonymic use caused considerable confusion at the time.
Originally taken as an analogy to human will power, muscular effort, and spiritual influence, the concept early became projected into inanimate objects and played an important role in ancient thaumaturgy, occultism, and medieval sorcery.
Concept of Force in Ancient Philosophy
The early Greek hylozoism of the Milesian school (Thales, Anaximander, Anaximenes) conceived nature as a living, animated, and self-moving being, and consequently did not see a problem in the origin of motion. The concept of force gained prominence only with Heraclitus's doctrine of opposing tensions, according to which force is a primary constituent of physical reality and a regulative element in the universe. In Empedocles's philosophy of love (philia ) and strife (neikos ), forces, although still conceived in analogy to human affections, became efficient causes of change and motion. In spite of the fact that Plato's natural philosophy relegates the principle of motion ultimately to the existence of a world soul and corresponds in this respect to early hylozoism rather than to the dynamistic teachings of Empedocles and Anaxagoras, the term dynamis, signifying not only transitive activity but also passive susceptibility or receptibility, plays an important role in his doctrine. Although Aristotle, in his conception of nature as "physis," still recognized the Platonic notion of force as something inherent in matter, in De Caelo he also approached the formulation of a more mechanical conception of force as a physical emanation from one substance to another: through push and pull, bodies affect each other and generate motion in extraneous objects. This Aristotelian notion of emanating kinematic effects, although restricted to contiguous modes of action, is the first instance of the modern dynamical conception of force. In his Physics Aristotle subjected this cause of compulsory motion to a quantitative investigation: A force A that moves a mobile B through a distance D during the time T could move half the mobile (½B ) through twice the distance (2D ) during the same time (T ), or could move half the mobile (½B ) through the distance D during half the time (½T ), and so forth. In modern terminology Aristotle's dynamical law of motion may be stated as follows: The velocity of a mobile is proportional to the ratio of the motive force and the resistance of the medium. Nowhere did Aristotle employ units in which these quantities were to be measured. Although it is fairly obvious that forces were practically measured in terms of weight (the early use of the balance is an evidence of this), Aristotle's conception of weight as a manifestation of natural motion and not as a cause of compulsory motion precluded, on theoretical grounds, the possibility of using the units of weight as units of force. Since, according to Aristotle, contiguity between the motor and the mobile was an indispensable prerequisite for the occurrence of dynamical action, force as an action at a distance had no place in his conceptual scheme. Hence, an explanation of planetary motion required the assumption of an external agent or astral intelligence as a "motor" attached to the star, unless the star was thought to be endowed with a life of its own.
With Posidonius's investigations at Gades of the connection between the tides and the movements of the sun and the moon and his doctrine of a universal tension, the concept of force was generalized as something able to pervade all space. Stoic philosophy thus abandoned the Aristotelian restriction of an immediate linkage between the mover and the moved, and conceived force as a mutual correspondence of action between objects, even when the objects were separated in space. In fact, the Stoics were probably the first to formulate the idea of a field of forces and to regard the universe as a vast system ruled by the interaction of forces.
Arabian and Christian medieval philosophy, in general, adhered to the Aristotelian conception of force. The exceptions were mostly inspired by Neoplatonic ideas. Thus, in Abū-Yūsuf Yaʿqūb ibn Ishāq al-Kindī's treatise On the Tides (Fi-l-madd wal-jazr ), his notion of force is wholly Aristotelian except that he holds that force can be propagated by means of optical rays, a theory conducive to astrological exploitation. Roger Bacon's conception of forces as "species"—isolated entities, detached from their subject and spreading through space in accordance with specific laws of propagation—showed similar features.
The Aristotelian law of motion, already criticized by John Philoponus in the sixth century CE and by Avempace in the twelfth century, was shown by Thomas Bradwardine in the middle of the fourteenth century to contradict experience in the case of equality between the motive force and the resistance, so that the ratio is one but the velocity zero. Bradwardine consequently modified the law, claiming that the velocity, in modern terms, depends on the logarithm of the ratio between motive force and resistance.
In the fourteenth century the Stoic conception of a field of forces was also revived, probably independently of the ancient school. In his Quaestiones Super Libris Quattuor de Caelo et Mundo (Questions on the four books of the heaven and the Earth) John Buridan postulates a celestial force that permeates all space and exerts its influence on physical bodies, in contrast to the Peripatetic dictum, Causa agens est simul cum suo effectu proximo et immediato. However, the revolutions of celestial bodies, according to Buridan, are not the result of a constant activity of special intelligences, but rather of an original rotational impetus communicated to these bodies by the Creator at the beginning of time.
A decisive stage in the development of the concept of force was reached in Johannes Kepler's search for a quantitative determination of dynamic activity. In his early writings, such as the Mysterium Cosmographicum (1596), Kepler still refers to force as a soul animating the celestial bodies. His correspondence, however, and particularly his letters addressed to David Fabricius, show clearly that his use of the term anima ("soul") in his writings was merely a metaphor to express the immateriality of the principle that governs the mutual movements of celestial bodies. In 1605 Kepler was already convinced that the force of attraction could be subjected to a mathematical formalism. In the third part of his Astronomia Nova (1609), Kepler discusses the causes of planetary motion and insists for the first time on a mathematical definition of force, even if it is not a push or pull. "For we see that these motions take place in space and time and this virtue emanates and diffuses through the space of the universe, which are all mathematical conceptions. From this it follows that this virtue is subject also to other mathematical necessities." Having discovered that the planets move in their orbits with velocities that vary with the distance from the sun, Kepler inquired into the physical cause of this mathematical relation and was thus led to assume the existence of a regulative force whose magnitude decreases with the distance. However, attraction was not yet seen as a radial force, but rather as a tangential drag, and Kepler, under the influence of William Gilbert's De Magnete (1600), suggested an analogy with magnetism. But in spite of this, Kepler's conception of a gravitational force of attraction is a typical example of the fact that the existence of forces is, and has to be, inferred from the phenomenological aspects of regularities in the variations of motion. It also exemplifies the fact that the postulation of forces as causes of motions and their kinematic variations is a methodological process that finds its philosophical justification in the reduction of numerous cases of functional dependence to one single agency. Kepler's procedure thus became the prototype for the introduction of forces in the various branches of physics: gravitational, elastic, electromagnetic, nuclear forces, and so forth.
Isaac Newton's conception of force can be traced to two originally disparate classes of mechanical or dynamical phenomena which, however, finally found their logical unification in his Principia (1687), through its very definitions of force and mass. Documentary evidence seems to show that his earliest conception of force originated from the study of impact phenomena. Thus Newton's "Waste Book 1664" (Ms. Add. 4004, Portsmouth Collection, University Library, Cambridge, U.K.) starts with a definition of the quantity of motion of a body as the product of its "quantity" (mass) and its velocity, and continues: "Hence it appeares how & why amongst bodys moved some require a more potent or efficacious cause others a lesse to hinder or helpe their velocity. And ye power of this cause is usually called force. And as this cause useth or applyeth its power or force to hinder or change ye perseverance of bodys in theire state, it is said to Indeavour to change their perseverance." In another document (Ms. Add. 3965, Portsmouth Collection), force is implicitly defined by the statement: "The alteration of motion is ever proportional to ye force by wch it is altered." Considering the exact text of Newton's second law of motion in the Principia, "The change of motion is proportional to the motive force impressed," one is led to the conclusion that "force" in these statements denotes more or less what we mean today by "impulse" (which, in fact, is equal to the change of momentum). Newton's original conception of force was consequently that of a thrust, a kick, or a push, as exhibited in collision phenomena, which at that time were the subject of extensive studies by Galileo Galilei, Marcus Marci, John Wallis, and Christian Huygens. On the other hand, in his search for a derivation of the phenomenological aspects of planetary motions from the hypothesis of an inverse-square law, Newton needed the time rate of change of momentum as the primitive notion, and thus identified the change of momentum with its rate of change for astronomical applications. Later commentators, therefore, interpreted Newton as stating that force is measured by the product of mass and acceleration, a product that for constant mass equals the time rate of change of momentum. Thus, although not rigorously impeccable, Newton's definition of force led to a unified treatment of terrestrial and celestial mechanics, and the notion of force became a fundamental concept of physics. Whereas Newton's first law of motion or law of inertia, according to which every body, unaffected by a force, persists in a state of rest or of uniform motion, may be regarded as a qualitative definition of force (namely, as change of state of motion), the second law quantified the concept and provided a meaning for the notion of mass. The Newtonian characterization of force is completed with the third law, which states, in essence, that every force manifests itself invariably in a dual aspect: It has a mirror-image twin. For it claims that if A acts on B, then B acts on A with equal magnitude in the opposite direction; or in other words, to every action there is always opposed an equal reaction. Forces, consequently, arise only as the result of a combined interaction of at least two entities. In a universe composed of only one body, no forces are conceivable.
Having thus explored the quantitative aspects of force, and of gravitational force in particular, Newton does not specify the metaphysical nature of force; as far as physical science is concerned, force is an ultimately irreducible notion. Newton's contribution may thus be regarded as the culmination of a conceptual development in a search for a quantitative determination of an otherwise obscure and indiscernible, yet necessary, notion—a development whose philosophical necessity had already been stressed by Bacon, Thomas Hobbes, and even René Descartes.
The scientific legitimacy of a force such as gravitation, which could act at a distance without the intermediacy of an intervening medium, was early called into question. Newton himself, particularly in his Opticks (1704), referred to certain speculations, primarily to the notion of an ether, in order to reduce such actions at a distance to contiguous effects compatible with the corpuscular-kinetic theory prevalent at that and later times. Yet, in spite of early opposition (as voiced particularly by Gottfried Wilhelm Leibniz, who rejected action at a distance as a scholastic obscure quality), the notion of force as conceived by Newton became the basic concept of classical theoretical mechanics. Pierre de Laplace, in his Mécanique céleste (1799–1805), considered the reduction of all mechanical phenomena to forces acting at a distance as the ultimate objective of the physical sciences, and Joseph Louis Lagrange's Mécanique analytique (1788), the highlight of classical mechanics, was written in the same spirit. The mechanics of action at a distance gained further support through its successful applications by Laplace, Siméon Denis Poisson, and Wilhelm Weber in the classical theories of electricity and magnetism. Even capillary phenomena—contact phenomena par excellence—were treated by Laplace and Karl Gauss as subject to actions at a distance.
Criticism of Action at a Distance
The great mathematical success of these theories of force as an action at a distance did not suppress doubts as to the philosophical legitimacy of such conceptions, and alternative mechanistic or kinetic-corpuscular theories, especially for gravitation, were proposed in great number. One of the earliest attempts in this direction, George Louis Lesage's theory of "ultramundane particles" (1747), was typical of similar hypotheses that gained great popularity in the nineteenth century. Particles were assumed to move in all directions through space and to be rebounded by macroscopic bodies; the resulting screening effects were supposed to produce the mutual "attractions" of "gravitating" bodies. The main criticism of the Newtonian conception of force from the philosophical point of view, however, was directed against the hypostatization of force as a metaphysical entity of an autonomous ontological status. George Berkeley, in his De Motu (On motion; 1721) opposed this approach and viewed the notion of force as a convenient auxiliary fiction with which to work; for the notion had the same status in science as the concept of epicycle has in astronomy. Such terms as force, gravity, and attraction, he admitted, are convenient for purposes of reasoning or computation; for an understanding of the nature of motion itself, however, Berkeley regards them as wholly irrelevant. They should not lead us to the fallacy that they could throw any light on the real efficient causes of motion, for the only objective of physical science is the establishment of the regularities and uniformities of natural phenomena; to account for particular phenomena means "reducing them under, and shewing their conformity to, such general rules" (Siris, 1744). David Hume, Pierre de Maupertuis, and especially the early proponents of modern positivism (Gustav Kirchhoff, Heinrich Hertz, Ernst Mach) followed Berkeley in asserting that force is merely a construct in the conceptual scheme of physics and that it should not be confounded with metaphysical causality. Most radical in this respect was Mach's antimetaphysical attitude, in accordance with which he tried to divest mechanics of all conceptions of cause and force and to adopt a purely functional point of view. Following Kirchhoff's Lectures on Mechanics (Vorlesungen über Meckanik, 1874–1876), Mach, in his Science of Mechanics (Die Mechanik in ihrer Entwicklung, historisch-kritisch dargestellt, 1883), identified force with the product of mass and acceleration and thus reduced it to a purely mathematical expression relating certain measurements of space and time.
But even after this process of purification and divestment of all causal or teleological implications, the concept of force was not eliminated from the conceptual scheme of physics. Its methodological justification lies in the fact that it enables us to discuss the general laws of motion irrespective of the particular physical situation with which these motions are associated. In contemporary physics the concept plays somewhat the same role as does the middle term in the traditional syllogism; it is a methodological intermediate in terms of which we can study the kinematical behavior of a physical body independent of the particular configuration in which it is found.
Psychological Origins of the Concept of Force
The advancement of the critical attitude toward the concept of force, initiated by Berkeley and Hume and culminating in the logical and metaphysical point of view held by Kirchhoff and Mach, brought in its wake a study of the psychological origin of the notion. The first to deal at length with this problem was Thomas Reid, Hume's immediate successor and founder of the Scottish school. He derived the concept of force from the consciousness we have of the operations of our own mind, and especially from the consciousness of our voluntary exertions in producing effects. Reid concluded that if we were not conscious of such exertions, we would not have formed any conception of force and consequently would not have projected this notion into nature and the changes in it that we observe. Immanuel Kant's younger contemporary, Maine de Biran, whose personalistic philosophy has many points in common with Reid's empirical intuitionalism, considered our own will as the source of the notion of force; in his view, the resistance to muscular effort felt in the case of voluntary activity makes us aware that certain actions are not involuntary acts, but the results of our ego as a source of force. From the twofold nature of the ego as an individual source of action and as inseparably united to a resisting organism, we acquire the universal and necessary notion of force. While the Berkeley-Hume criticism led almost to the exclusion of the concept of force from science and natural philosophy, at the same time it supplied to the more psychologically and physiologically oriented philosophy important arguments to oppose such elimination. For it was claimed that the concept of force stands in the same relation to the sensation of muscular effort as the concept of motion to visual perception, and science without the concept of motion is inconceivable. Moreover, if one kind of sensation is to be preferred to the others, it should certainly be muscular sensation, the nearest to the psychological experience of volition. Even William James, who, in "The Feeling of Effort," in Collected Essays and Reviews (1920), rejected the so-called feeling of innervation and opposed the view that the resistance to our muscular effort is the only sense that brings us into close contact with reality, contended that reality reveals itself in the form of a force like the force of effort we exert ourselves. The concept of force, according to James, thus remains "one of those universal ideas which belong of necessity to the intellectual furniture of every human mind."
See also al-Kindī, Abū-Yūsuf Yaʿqūb ibn Isḥāq; Anaximander; Anaximenes; Aristotle; Bacon, Roger; Berkeley, George; Bradwardine, Thomas; Buridan, John; Descartes, René; Empedocles; Energy; Galileo Galilei; Heraclitus of Ephesus; Hertz, Heinrich Rudolf; Hobbes, Thomas; Hume, David; Ibn Bājja; James, William; Kant, Immanuel; Kepler, Johannes; Kirchhoff, Gustav Robert; Laplace, Pierre Simon de; Laws, Scientific; Leibniz, Gottfried Wilhelm; Mach, Ernst; Maine de Biran; Mass; Matter; Medieval Philosophy; Neoplatonism; Newtonian Mechanics and Mechanical Explanation; Newton, Isaac; Panpsychism; Philoponus, John; Plato; Power; Reid, Thomas; Stoicism; Thales of Miletus.
Ellis, Brian D. "Newton's Concept of Motive Force." Journal of the History of Ideas 23 (1962): 273–278.
Hesse, Mary B. Forces and Fields. London: Nelson, 1961.
James, William. "The Feeling of Effort." In Collected Essays and Reviews. New York: Longman, 1920.
Mach, Ernst. Die Mechanik in Ihrer Entwicklung, historisch-kritisch dargestellt. Leipzig, 1883. Translated by T. J. McCormack as Science of Mechanics. La Salle, IL: Open Court, 1960. With introduction by Karl Menger.
Margenau, Henry. The Nature of Physical Reality. New York: McGraw-Hill, 1950. Ch. 12.
Röhr, Julius. Der Okkulte Kraftbegriff im Altertum. Leipzig, 1923.
Weyl, Hermann. Philosophy of Mathematics and Natural Science. Princeton, NJ: Princeton University Press, 1949. Pp. 148ff.
M. Jammer (1967)
force / fôrs/ • n. 1. strength or energy as an attribute of physical action or movement: he was thrown backward by the force of the explosion. ∎ Physics an influence tending to change the motion of a body or produce motion or stress in a stationary body. The magnitude of such an influence is often calculated by multiplying the mass of the body by its acceleration. ∎ a person or thing regarded as exerting power or influence: he might still be a force for peace and unity. ∎ [in comb.] used with a number as a measure of wind strength on the Beaufort scale: a force-nine gale. 2. coercion or compulsion, esp. with the use or threat of violence: they ruled by law and not by force. 3. mental or moral strength or power: the force of popular opinion. ∎ the state of being in effect or valid: the law came into force in January. ∎ the powerful effect of something: the force of her writing is undiminished. 4. an organized body of military personnel or police: a soldier in a UN peacekeeping force. ∎ (forces) troops and weaponry: concealment from enemy forces | fig. a battle between the forces of good and evil. ∎ a group of people brought together and organized for a particular activity: a sales force. ∎ (the force) inf. a police department. 5. Baseball a force out. ∎ a situation in which a force out is possible. • v. [tr.] 1. make a way through or into by physical strength; break open by force: they broke into Fred's house and forced every cupboard door with ax or crowbar. ∎ [tr.] drive or push into a specified position or state using physical strength or against resistance: she forced her feet into flat leather sandals| fig. Fields was forced out as director. ∎ achieve or bring about (something) by coercion or effort: Sabine forced a smile she forced her way up the ladder. ∎ push or strain (something) to the utmost: she knew if she forced it she would rip it. ∎ artificially hasten the development or maturity of (a plant). 2. (often be forced) make (someone) do something against their will: she was forced into early retirement | [tr.] the universities were forced to cut staff. ∎ rape (a woman). ∎ Baseball put out (a runner) , or cause (a runner) to be put out, at the base to which they are advancing when they are forced to run on a batted ball: I was forced at second base as the first half of a double play. ∎ (in cards) make a play or bid that compels another player to make (a particular response); make a play or bid that compels (another player) to make such a response: East could force declarer to ruff another spade PHRASES: by force of by means of: exercising authority by force of arms. force the bidding (at an auction) make bids to raise the price rapidly. force someone's hand make someone do something: the exchange markets may force the Fed's hand. force the issue compel the making of an immediate decision. force the pace adopt a fast pace in a race in order to tire out one's opponents quickly. in force 1. in great strength or numbers: birdwatchers were out in force. 2. in effect; valid: the U.S. has over $8 trillion worth of life insurance in force. PHRASAL VERBS: force something down 1. manage to swallow food or drink when one does not want to: I forced down a slice of toast. 2. compel an aircraft to land: the plane might have been forced down by fighters. force oneself on/upon rape (a woman). force something on/upon impose or press something on (a person or organization): economic cutbacks were forced on the government.DERIVATIVES: force·a·ble adj. forc·er n. ORIGIN: Middle English: from Old French force (noun), forcer (verb), based on Latin fortis ‘strong.’
Force, within physics, is defined as the term used for an outside influence or action exerted by one body on another body, which produces a change in state of motion or state of configuration; specifically, it produces an acceleration. This limited meaning in science compared to everyday usage is most important because of the specific results of this outside influence.
A force that produces a change in the state of motion of a body gives that body acceleration. If forces acting on a body produces no acceleration, the body will experience some change in configuration: a change of size (longer or shorter), a change of shape (twisted or bent), or a positional change (relative to other masses, charges, or magnets). Changes of size or shape involve elastic properties of materials.
Force is a vector, which means it has both magnitude and direction. For example, a force upward with a magnitude of one unit of force is opposite in direction of a downward force that also has one unit of force. In this case, the magnitudes are equal. When several forces act on a body, the forces can be grouped together to produce a net force. English physicist and mathematician Sir Isaac Newton (1642–1727) created his second law of motion that states: A net force (Fnet) acting on a body is related to the mass (m)and acceleration (a) of the body as Fnet = ma. Two forces of equal magnitude, for example, but opposite directions will produce no acceleration. The two forces will cancel each other out for zero acceleration, or a net force of zero. If the body had a velocity before the two forces acted on it, then it will continue to have that same velocity afterwards.
The unit of force in the international system (SI) of units is called the newton, named after Isaac Newton. It is the force that is on an abject with a mass of one kilogram to produce an acceleration of one meter per second squared.
Forces are given various names to indicate some specific character. For example, a wagon can be made to go forward by pushing from behind or pulling from the front so push or pull is more descriptive. Electrical and magnetic forces can result in attraction (tendency to come together) or repulsion (tendency to move apart) but gravitational force results only in attraction of masses. The gravitational force exerted by the Earth, or any other massive body such as a planet, on a body is called weight. A body moving, or attempting to move, over another body experiences a force opposing the motion called friction. When wires, cables, or ropes are stretched, they then in turn exert a force that is called tension. Specific names give information about the nature of the force, what it does, and direction of action.
See also Laws of motion.
Force is the term used for an outside influence exerted by one body on another which produces a change in state of motion or state of configuration. This limited meaning in science compared to our everyday usage is most important because of the specific results of this out-side influence.
Force producing a change in state of motion gives a body acceleration . If forces acting on a body produces no acceleration, the body will experience some change in configuration: a change of size (longer or shorter), a change of shape (twisted or bent), or a positional change (relative to other masses, charges, or magnets). Changes of size or shape involve elastic properties of materials.
Forces are given various names to indicate some specific character. For example, a wagon can be made to go forward by pushing from behind or pulling from the front so push or pull is more descriptive. Electrical and magnetic forces can result in attraction (tendency to come together) or repulsion (tendency to move apart) but gravitational force results only in attraction of masses. The gravitational force exerted by Earth on a body is called weight. A body moving, or attempting to move, over another body experiences a force opposing the motion called friction . When wires, cables, or ropes are stretched, they then in turn exert a force which is called tension. Specific names give information about the nature of the force, what it does, and direction of action.
See also Laws of motion.
Power, violence, compulsion, or constraint exerted upon or against a person or thing. Power dynamically considered, that is, in motion or in action; constraining power, compulsion; strength directed to an end. Commonly the word occurs in such connections as to show that unlawful or wrongful action is meant, e.g., forcible entry.
Power statically considered, that is, at rest, or latent, but capable of being called into activity upon occasion for its exercise. Efficacy; legal validity. This is the meaning when we say that a statute or a contract is in force.
Reasonable force is that degree of force that is appropriate and not inordinate in defending one's person or property. A person who employs such force is justified in doing so and is neither criminally liable nor civilly liable in tort for the conduct.
deadly force is utilized when a person intends to cause death or serious bodily harm or when he or she recognizes personal involvement in the creation of a substantial risk that death or bodily harm will occur.
So vb. XIII. forcible done by force XV; †strong; producing a powerful effect XVI.