# Сила

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Шаблон:Infobox Physical quantity

Во физиката, a force is any interaction that, when unopposed, will change the motion of an object.[1] In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object

Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque, which produces changes in rotational speed of an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-called mechanical stress. Pressure is a simple type of stress. Stress usually causes deformation of solid materials, or flow in fluids.

## Development of the concept

Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion.[2] A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years.[3] By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia.

With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational.[4]:2–10[5]:79 High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.[6]

## Pre-Newtonian concepts

Поврзано: Aristotelian physics и Theory of impetus
Aristotle famously described a force as anything that causes an object to undergo "unnatural motion"

Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids.[2]

Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground and that they will stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force.[7] This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. The place where the archer moves the projectile was at the start of the flight, and while the projectile sailed through the air, no discernible efficient cause acts on it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation demands a continuum like air for change of place in general.[8]

Aristotelian physics began facing criticism in Medieval science, first by John Philoponus in the 6th century.

The shortcomings of Aristotelian physics would not be fully corrected until the 17th century work of Galileo Galilei, who was influenced by the late Medieval idea that objects in forced motion carried an innate force of impetus. 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 that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction.[9]

## Newtonian mechanics

Главна статија: „Newton's laws of motion.

Sir Isaac Newton sought to describe the motion of all objects using the concepts of inertia and force, and in doing so he found that they obey certain conservation laws. In 1687, Newton went on to publish his thesis Philosophiæ Naturalis Principia Mathematica.[3][10] In this work Newton set out three laws of motion that to this day are the way forces are described in physics.[10]

### First law

Главна статија: „Newton's first law.

Newton's First Law of Motion states that objects continue to move in a state of constant velocity unless acted upon by an external net force or resultant force.[10] This law is an extension of Galileo's insight that constant velocity was associated with a lack of net force (see a more detailed description of this below). Newton proposed that every object with mass has an innate inertia that functions as the fundamental equilibrium "natural state" in place of the Aristotelian idea of the "natural state of rest". That is, the first law contradicts the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity. By making rest physically indistinguishable from non-zero constant velocity, Newton's First Law directly connects inertia with the concept of relative velocities. Specifically, in systems where objects are moving with different velocities, it is impossible to determine which object is "in motion" and which object is "at rest". In other words, to phrase matters more technically, the laws of physics are the same in every inertial frame of reference, that is, in all frames related by a Galilean transformation.

For instance, while traveling in a moving vehicle at a constant velocity, the laws of physics do not change from being at rest. A person can throw a ball straight up in the air and catch it as it falls down without worrying about applying a force in the direction the vehicle is moving. This is true even though another person who is observing the moving vehicle pass by also observes the ball follow a curving parabolic path in the same direction as the motion of the vehicle. It is the inertia of the ball associated with its constant velocity in the direction of the vehicle's motion that ensures the ball continues to move forward even as it is thrown up and falls back down. From the perspective of the person in the car, the vehicle and everything inside of it is at rest: It is the outside world that is moving with a constant speed in the opposite direction. Since there is no experiment that can distinguish whether it is the vehicle that is at rest or the outside world that is at rest, the two situations are considered to be physically indistinguishable. Inertia therefore applies equally well to constant velocity motion as it does to rest.

The concept of inertia can be further generalized to explain the tendency of objects to continue in many different forms of constant motion, even those that are not strictly constant velocity. The rotational inertia of planet Earth is what fixes the constancy of the length of a day and the length of a year. Albert Einstein extended the principle of inertia further when he explained that reference frames subject to constant acceleration, such as those free-falling toward a gravitating object, were physically equivalent to inertial reference frames. This is why, for example, astronauts experience weightlessness when in free-fall orbit around the Earth, and why Newton's Laws of Motion are more easily discernible in such environments. If an astronaut places an object with mass in mid-air next to himself, it will remain stationary with respect to the astronaut due to its inertia. This is the same thing that would occur if the astronaut and the object were in intergalactic space with no net force of gravity acting on their shared reference frame. This principle of equivalence was one of the foundational underpinnings for the development of the general theory of relativity.[11]

Though Sir Isaac Newton's most famous equation is
${\displaystyle \scriptstyle {{\vec {F}}=m{\vec {a}}}}$, he actually wrote down a different form for his second law of motion that did not use differential calculus.

### Second law

Главна статија: „Newton's second law.

A modern statement of Newton's Second Law is a vector equation:[Note 1]

${\displaystyle {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}},}$

where ${\displaystyle \scriptstyle {\vec {p}}}$ is the momentum of the system, and ${\displaystyle \scriptstyle {\vec {F}}}$ is the net (vector sum) force. In equilibrium, there is zero net force by definition, but (balanced) forces may be present nevertheless. In contrast, the second law states an unbalanced force acting on an object will result in the object's momentum changing over time.[10]

By the definition of momentum,

${\displaystyle {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}={\frac {\mathrm {d} \left(m{\vec {v}}\right)}{\mathrm {d} t}},}$

where m is the mass and ${\displaystyle \scriptstyle {\vec {v}}}$ is the velocity.[4]:9-1,9-2

Newton's second law applies only to a system of constant mass,[Note 2] and hence m may be moved outside the derivative operator. The equation then becomes

${\displaystyle {\vec {F}}=m{\frac {\mathrm {d} {\vec {v}}}{\mathrm {d} t}}.}$

By substituting the definition of acceleration, the algebraic version of Newton's Second Law is derived:

${\displaystyle {\vec {F}}=m{\vec {a}}.}$

Newton never explicitly stated the formula in the reduced form above.[12]

Newton's Second Law asserts the direct proportionality of acceleration to force and the inverse proportionality of acceleration to mass. Accelerations can be defined through kinematic measurements. However, while kinematics are well-described through reference frame analysis in advanced physics, there are still deep questions that remain as to what is the proper definition of mass. General relativity offers an equivalence between space-time and mass, but lacking a coherent theory of quantum gravity, it is unclear as to how or whether this connection is relevant on microscales. With some justification, Newton's second law can be taken as a quantitative definition of mass by writing the law as an equality; the relative units of force and mass then are fixed.

The use of Newton's Second Law as a definition of force has been disparaged in some of the more rigorous textbooks,[4]:12-1[5]:59[13] because it is essentially a mathematical truism. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach, Clifford Truesdell and Walter Noll.[14][15]

Newton's Second Law can be used to measure the strength of forces. For instance, knowledge of the masses of planets along with the accelerations of their orbits allows scientists to calculate the gravitational forces on planets.

### Third law

Главна статија: „Newton's third law.

Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies,[16][Note 3] and thus that there is no such thing as a unidirectional force or a force that acts on only one body. Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with F called the "action" and −F the "reaction". The action and the reaction are simultaneous:

${\displaystyle {\vec {F}}_{1,2}=-{\vec {F}}_{2,1}.}$

If object 1 and object 2 are considered to be in the same system, then the net force on the system due to the interactions between objects 1 and 2 is zero since

${\displaystyle {\vec {F}}_{1,2}+{\vec {F}}_{\mathrm {2,1} }=0}$
${\displaystyle \sum {\vec {F}}=0.}$

This means that in a closed system of particles, there are no internal forces that are unbalanced. That is, the action-reaction force shared between any two objects in a closed system will not cause the center of mass of the system to accelerate. The constituent objects only accelerate with respect to each other, the system itself remains unaccelerated. Alternatively, if an external force acts on the system, then the center of mass will experience an acceleration proportional to the magnitude of the external force divided by the mass of the system.[4]:19-1[5]

Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved. Using

${\displaystyle {\vec {F}}_{1,2}={\frac {\mathrm {d} {\vec {p}}_{1,2}}{\mathrm {d} t}}=-{\vec {F}}_{2,1}=-{\frac {\mathrm {d} {\vec {p}}_{2,1}}{\mathrm {d} t}}}$

and integrating with respect to time, the equation:

${\displaystyle \Delta {{\vec {p}}_{1,2}}=-\Delta {{\vec {p}}_{2,1}}}$

is obtained. For a system that includes objects 1 and 2,

${\displaystyle \sum {\Delta {\vec {p}}}=\Delta {{\vec {p}}_{1,2}}+\Delta {{\vec {p}}_{2,1}}=0}$,

which is the conservation of linear momentum.[17] Using the similar arguments, it is possible to generalize this to a system of an arbitrary number of particles. This shows that exchanging momentum between constituent objects will not affect the net momentum of a system. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained.[4][5]

1. Nave, C. R. (2014). „Force“. Dept. of Physics and Astronomy, Georgia State University. конс. 15 август 2014 г.
2. Heath, T.L.. The Works of Archimedes (1897). The unabridged work in PDF form (19 MB)“. Internet Archive. конс. 14 октомври 2007 г.
3. Грешка во наводот: Погрешна ознака <ref>; нема зададено текст за наводите по име uniphysics_ch2.
4. Feynman volume 1
5. Грешка во наводот: Погрешна ознака <ref>; нема зададено текст за наводите по име Kleppner.
6. Грешка во наводот: Погрешна ознака <ref>; нема зададено текст за наводите по име final_theory.
7. Lang, Helen S. (1998). The order of nature in Aristotle's physics : place and the elements (1. publ. издание). Cambridge: Cambridge Univ. Press. ISBN 9780521624534.
8. Hetherington, Norriss S. (1993). Cosmology: Historical, Literary, Philosophical, Religious, and Scientific Perspectives. Garland Reference Library of the Humanities. стр. 100. ISBN 0-8153-1085-4.
9. Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5
10. Newton, Isaac (1999). The Principia Mathematical Principles of Natural Philosophy. Berkeley: University of California Press. ISBN 0-520-08817-4.  This is a recent translation into English by I. Bernard Cohen and Anne Whitman, with help from Julia Budenz.
11. DiSalle, Robert (30 март 2002). „Space and Time: Inertial Frames“. Stanford Encyclopedia of Philosophy. конс. 24 март 2008 г.
12. Howland, R. A. (2006). Intermediate dynamics a linear algebraic approach (Online-Ausg. издание). New York: Springer. стр. 255–256. ISBN 9780387280592.
13. One exception to this rule is: Landau, L. D.; Akhiezer, A. I.; Lifshitz, A. M. (196). General Physics; mechanics and molecular physics (First English издание). Oxford: Pergamon Press. ISBN 0-08-003304-0.  Translated by: J. B. Sykes, A. D. Petford, and C. L. Petford. Library of Congress Catalog Number 67-30260. In section 7, pages 12–14, this book defines force as dp/dt.
14. Jammer, Max (1999). Concepts of force : a study in the foundations of dynamics (Facsim. издание). Mineola, N.Y.: Dover Publications. стр. 220–222. ISBN 9780486406893.
15. Noll, Walter (април 2007). „On the Concept of Force“ (pdf). Carnegie Mellon University. конс. 28 октомври 2013 г.
16. C. Hellingman. Newton's third law revisited. „Phys. Educ.“ том  27 (2): 112–115. doi:10.1088/0031-9120/27/2/011. Bibcode1992PhyEd..27..112H. „Quoting Newton in the Principia: It is not one action by which the Sun attracts Jupiter, and another by which Jupiter attracts the Sun; but it is one action by which the Sun and Jupiter mutually endeavour to come nearer together.“.
17. Dr. Nikitin (2007). „Dynamics of translational motion“. конс. 4 јануари 2008 г.

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