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“Newtonian mechanics is the basis of the classical description of nature. The main task of mechanics and the limits of its applicability.

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1. Introduction.__________________________________________________ 3

2. Newtonian mechanics.____________________________________________ 5

2.1. Newton's laws of motion.______________________________________________ 5

2.1.1. Newton's first law.________________________________________________ 6

2.1.2. Newton's second law.________________________________________________ 7

2.1.3. Newton's third law._________________________________________________ 8

2.2. Law gravity.___________________________________________ 11

2.3. The main task of mechanics._____________________________________________ 13

2.4. Limits of applicability._______________________________________________ 15

3. Conclusion.______________________________________________ 18

4. List of references.______________________________________ 20

Newton (1643-1727)

This world was shrouded in deep darkness.

Let there be light! And here comes Newton.

1. Introduction.

The concept of "physics" has its roots in the deep past, in Greek it means "nature". The main task of this science is to establish the "laws" of the surrounding world. One of the main works of Plato, a student of Aristotle, was called "Physics".

The science of those years had a natural-philosophical character, i.e. proceeded from the fact that the directly observed movements of celestial bodies are their actual movements. From this, a conclusion was drawn about the central position of the Earth in the Universe. This system correctly reflected some of the features of the Earth as a celestial body: the fact that the Earth is a ball, that everything gravitates towards its center. Thus, this doctrine was actually about the Earth. At the level of its time, it met the basic requirements that were imposed on scientific knowledge. Firstly, it explained the observed movements of celestial bodies from a unified point of view and, secondly, made it possible to calculate their future positions. At the same time, the theoretical constructions of the ancient Greeks were purely speculative in nature - they were completely divorced from experiment.

Such a system existed until the 16th century, until the appearance of the teachings of Copernicus, which received its further substantiation in the experimental physics of Galileo, culminating in the creation Newtonian mechanics, which united the movement of celestial bodies and terrestrial objects by unified laws of motion. It was the greatest revolution in natural science, which marked the beginning of the development of science in its modern sense.

Galileo Galilei believed that the world is infinite and matter is eternal. In all processes, nothing is destroyed or generated - there is only a change in the relative position of bodies or their parts. Matter consists of absolutely indivisible atoms, its movement is the only universal mechanical movement. The heavenly bodies are similar to the Earth and obey the same laws of mechanics.

For Newton, it was important to unambiguously find out, with the help of experiments and observations, the properties of the object under study and to build a theory based on induction without using hypotheses. He proceeded from the fact that in physics as an experimental science there is no place for hypotheses. Recognizing the imperfection of the inductive method, he considered it the most preferable among others.

Both in the era of antiquity and in the 17th century, the importance of studying the movement of heavenly bodies was recognized. But if for the ancient Greeks this problem had more philosophical significance, then for the 17th century, the practical aspect was predominant. The development of navigation necessitated the development of more accurate astronomical tables for navigation purposes than those required for astrological purposes. The main task was to determine the longitude, so necessary for astronomers and navigators. To solve this important practical problem, the first state observatories were created (in 1672, Paris, in 1675, Greenwich). In essence, this was the task of determining the absolute time, which, when compared with local time time interval, which could be converted into longitude. It was possible to determine this time by observing the movements of the Moon among the stars, as well as with the help of an accurate clock set in absolute time and held by the observer. For the first case, very accurate tables were needed to predict the position of celestial bodies, and for the second, absolutely accurate and reliable watch mechanisms. Work in these directions was not successful. Only Newton succeeded in finding a solution, who, thanks to the discovery of the law of universal gravitation and the three basic laws of mechanics, as well as differential and integral calculus, gave mechanics the character of an integral scientific theory.

2. Newtonian mechanics.

pinnacle scientific creativity I. Newton is his immortal work "Mathematical Principles of Natural Philosophy", first published in 1687. In it, he summarized the results obtained by his predecessors and his own research and created for the first time a unified harmonious system of terrestrial and celestial mechanics, which formed the basis of all classical physics. Here Newton gave definitions of the initial concepts - the amount of matter, equivalent to mass, density; amount of motion equivalent to momentum, and various kinds strength. Formulating the concept of quantity of matter, he proceeded from the idea that atoms consist of some single primary matter; Density was understood as the degree to which a unit volume of a body is filled with primary matter. This work outlines Newton's doctrine of universal gravitation, on the basis of which he developed the theory of the motion of planets, satellites and comets that form the solar system. Based on this law, he explained the phenomenon of tides and the compression of Jupiter.

Newton's concept was the basis for many technical advances During a long time. Many methods were formed on its foundation scientific research V various fields natural sciences.

2.1. Newton's laws of motion.

If kinematics studies the movement of a geometric body, which does not have any properties of a material body, except for the ability to occupy a certain place in space and change this position over time, then dynamics studies the movement of real bodies under the action of forces applied to them. The three laws of mechanics established by Newton underlie dynamics and form the main section of classical mechanics.

They can be directly applied to the simplest case of motion, when the moving body is considered as a material point, i.e. when the size and shape of the body is not taken into account and when the movement of the body is considered as the movement of a point with mass. In boiling water, to describe the movement of a point, you can choose any coordinate system, relative to which the quantities characterizing this movement are determined. Any body moving relative to other bodies can be taken as a reference body. In dynamics, one deals with inertial coordinate systems, characterized by the fact that relative to them a free material point moves at a constant speed.

2.1.1. Newton's first law.

The law of inertia was first established by Galileo for the case of horizontal motion: when a body moves along a horizontal plane, then its motion is uniform and would continue constantly if the plane extended in space without end. Newton gave a more general formulation of the law of inertia as the first law of motion: every body is in a state of rest or uniform rectilinear motion until the forces acting on it change this state.

In life, this law describes the case when, if you stop pulling or pushing a moving body, then it stops, and does not continue to move at a constant speed. So the car with the engine off stops. According to Newton's law, a braking force must act on a car rolling by inertia, which in practice is air resistance and friction car tires on the surface of the highway. They tell the car a negative acceleration until it stops.

The disadvantage of this formulation of the law is that it did not contain an indication of the need to refer motion to an inertial coordinate system. The fact is that Newton did not use the concept of an inertial coordinate system - instead, he introduced the concept of absolute space - homogeneous and immobile - with which he connected a certain absolute coordinate system, relative to which the speed of the body was determined. When the emptyness of absolute space as an absolute reference system was revealed, the law of inertia began to be formulated differently: with respect to the inertial coordinate system, a free body maintains a state of rest or uniform rectilinear motion.

2.1.2. Newton's second law.

In the formulation of the second law, Newton introduced the concepts:

Acceleration is a vector quantity (Newton called it momentum and took it into account when formulating the parallelogram rule of velocities), which determines the rate of change in the speed of a body.

Force is a vector quantity, understood as a measure of mechanical action on the body by other bodies or fields, as a result of which the body acquires acceleration or changes its shape and size.

The mass of a body is a physical quantity, one of the main characteristics of matter, which determines its inertial and gravitational properties.

The second law of mechanics says: the force acting on a body is equal to the product of the mass of the body and the acceleration imparted by this force. This is its modern formulation. Newton formulated it differently: the change in momentum is proportional to the applied acting force and occurs in the direction of the straight line along which this force acts, and is inversely proportional to the mass of the body or mathematically:

It is easy to confirm this law by experience, if a trolley is attached to the end of the spring and the spring is released, then in time t the cart will pass the way s 1(Fig. 1), then attach two carts to the same spring, i.e. double the body weight, and release the spring, then in the same time t they will go the way s2, two times smaller than s 1 .

This law is also valid only in inertial frames of reference. From a mathematical point of view, the first law is a special case of the second law, because if the resultant forces are zero, then the acceleration is also zero. However, Newton's first law is considered as an independent law, because it is he who asserts the existence of inertial systems.

2.1.3. Newton's third law.

Newton's third law says: there is always an equal and opposite reaction to an action, otherwise the bodies act on each other with forces directed along one straight line, equal in magnitude and opposite in direction or mathematically:

Newton extended the operation of this law to the case of collisions of bodies, and to the case of their mutual attraction. The simplest demonstration of this law is a body located on a horizontal plane, on which the force of gravity acts F t and support reaction force F about, lying on one straight line, equal in value and oppositely directed, the equality of these forces allows the body to be at rest (Fig. 2).

Consequences follow from Newton's three fundamental laws of motion, one of which is the addition of momentum according to the parallelogram rule. The acceleration of a body depends on the quantities that characterize the action of other bodies on a given body, as well as on the quantities that determine the features of this body. The mechanical action on the body from other bodies, which changes the speed of movement of this body, is called force. She may have different nature(gravity, elastic force, etc.). The change in the speed of a body does not depend on the nature of the forces, but on their magnitude. Since speed and force are vectors, the action of several forces is added according to the parallelogram rule. The property of a body, on which the acceleration acquired by it depends, is inertia, measured by mass. In classical mechanics, dealing with speeds much less than the speed of light, mass is a characteristic of the body itself, regardless of whether it is moving or not. The mass of a body in classical mechanics does not depend on the interaction of the body with other bodies either. This property of mass prompted Newton to accept mass as a measure of matter and to believe that its magnitude determines the amount of matter in the body. Thus, mass began to be understood as the amount of matter.

The amount of matter is measurable, being proportional to the weight of the body. Weight is the force with which a body acts on a support that prevents it from falling freely. Numerically, the weight is equal to the product of the mass of the body and the acceleration of gravity. Due to the compression of the Earth and its daily rotation, body weight changes with latitude and is 0.5% less at the equator than at the poles. Since mass and weight are strictly proportional, it turned out to be possible to practically measure the mass or quantity of matter. The understanding that weight is a variable effect on the body prompted Newton to establish the internal characteristic of the body - inertia, which he considered as the body's inherent ability to maintain uniform rectilinear motion proportional to the mass. Mass as a measure of inertia can be measured with a balance, as did Newton.

In a state of weightlessness, mass can be measured by inertia. Inertia measurement is a common way to measure mass. But inertia and weight are different physical concepts. Their proportionality to each other is very convenient in practical terms - for measuring mass with the help of scales. Thus, the establishment of the concepts of force and mass, as well as the method of their measurement, allowed Newton to formulate the second law of mechanics.

The first and second laws of mechanics refer respectively to the motion of a material point or one body. In this case, only the action of other bodies on this body is taken into account. However, every action is an interaction. Since in mechanics action is characterized by force, if one body acts on another with a certain force, then the second acts on the first with the same force, which fixes the third law of mechanics. In Newton's formulation, the third law of mechanics is valid only for the case of direct interaction of forces or for the instantaneous transfer of the action of one body to another. In the case of transferring an action over a finite period of time, this law applies when the time of transferring the action can be neglected.

2.2. The law of universal gravitation.

It is believed that the core of Newton's dynamics is the concept of force, and the main task of dynamics is to establish a law from a given movement and, conversely, to determine the law of motion of bodies according to a given force. From Kepler's laws, Newton deduced the existence of a force directed towards the Sun, which was inversely proportional to the square of the distance of the planets from the Sun. Generalizing the ideas expressed by Kepler, Huygens, Descartes, Borelli, Hooke, Newton gave them the exact form of a mathematical law, according to which the existence of a force of universal gravitation in nature, which determines the attraction of bodies, was affirmed. The force of gravity is directly proportional to the product of the masses of gravitating bodies and inversely proportional to the square of the distance between them, or mathematically:

Where G is the gravitational constant.

This law describes the interaction of any bodies - it is only important that the distance between the bodies be large enough compared to their sizes, this allows us to take bodies for material points. In the Newtonian theory of gravitation, it is assumed that the gravitational force is transferred from one gravitating body to another instantly, and without the mediation of any medium. The law of universal gravitation has caused long and furious discussions. This was not accidental, since this law had an important philosophical significance. The bottom line was that before Newton, the goal of creating physical theories was the identification and presentation of the mechanism of physical phenomena in all its details. In cases where this could not be done, the argument was put forward about the so-called "hidden qualities", which are not amenable to detailed interpretation. Bacon and Descartes declared references to "hidden qualities" to be unscientific. Descartes believed that it is possible to understand the essence of a natural phenomenon only if it is visually imagined. Thus, he represented the phenomena of gravity with the help of ethereal vortices. In the context of the widespread dissemination of such ideas, Newton's law of universal gravitation, despite the fact that it demonstrated the correspondence of astronomical observations made on its basis with unprecedented accuracy, was questioned on the grounds that mutual attraction bodies was very reminiscent of the peripatetic doctrine of "hidden qualities." And although Newton established the fact of its existence on the basis of mathematical analysis and experimental data, mathematical analysis has not yet become firmly established in the minds of researchers as a sufficiently reliable method. But the desire to limit physical research to facts that do not claim to be absolute truth allowed Newton to complete the formation of physics as an independent science and separate it from natural philosophy with its claims to absolute knowledge.

In the law of universal gravitation, science received an example of the law of nature as an absolutely precise rule applicable everywhere, without exception, with precisely defined consequences. This law was included by Kant in his philosophy, where nature was represented as the realm of necessity as opposed to morality - the realm of freedom.

Newton's physical concept was a kind of crowning achievement of 17th century physics. The static approach to the universe has been replaced by a dynamic one. The experimental-mathematical method of research, having made it possible to solve many problems of physics of the 17th century, turned out to be suitable for solving physical problems for another two centuries.

2.3. The main task of mechanics.

The result of the development of classical mechanics was the creation of a unified mechanical picture of the world, within which the entire qualitative diversity of the world was explained by differences in the movement of bodies, subject to the laws of Newtonian mechanics. According to the mechanical picture of the world, if the physical phenomenon of the world could be explained on the basis of the laws of mechanics, then such an explanation was recognized as scientific. Newtonian mechanics thus became the basis of the mechanical picture of the world that dominated until the scientific revolution at the turn of the 19th and 20th centuries.

Newton's mechanics, in contrast to previous mechanical concepts, made it possible to solve the problem of any stage of motion, both preceding and subsequent, and at any point in space when known facts, causing this movement, as well as the inverse problem of determining the magnitude and direction of these factors at any point with known basic elements of the movement. Thanks to this, Newtonian mechanics could be used as a method of quantitative analysis. mechanical movement. Any physical phenomena could be studied as, regardless of the factors causing them. For example, you can calculate the speed of an Earth satellite: For simplicity, let's find the speed of a satellite with an orbit equal to the radius of the Earth (Fig. 3). With sufficient accuracy, we can equate the acceleration of the satellite to the acceleration of free fall on the surface of the Earth:

On the other hand, the centripetal acceleration of the satellite.

where . - This speed is called the first space speed. A body of any mass, to which such a speed will be communicated, will become a satellite of the Earth.

The laws of Newtonian mechanics associated force not with motion, but with a change in motion. This made it possible to abandon the traditional notion that force is needed to maintain movement, and to divert friction, which made force necessary in operating mechanisms to maintain movement, to a secondary role. Having established a dynamic view of the world instead of the traditional static one, Newton made his dynamics the basis of theoretical physics. Although Newton was cautious in his mechanical interpretations natural phenomena, still considered it desirable to deduce other natural phenomena from the principles of mechanics. The further development of physics began to be carried out in the direction of the further development of the apparatus of mechanics in relation to the solution of specific problems, as they were solved, the mechanical picture of the world was strengthened.

2.4. Limits of applicability.

As a result of the development of physics at the beginning of the 20th century, the scope of classical mechanics was determined: its laws are valid for motions whose speed is much less than the speed of light. It was found that with increasing speed, body weight increases. In general, Newton's laws of classical mechanics are valid for the case of inertial frames of reference. In the case of non-inertial frames of reference, the situation is different. With the accelerated movement of a non-inertial coordinate system relative to the inertial system, Newton's first law (the law of inertia) does not take place in this system - free bodies in it will change their speed of movement over time.

The first inconsistency in classical mechanics was revealed when the microworld was discovered. In classical mechanics, displacements in space and the determination of velocity were studied regardless of how these displacements were realized. With regard to the phenomena of the microworld, such a situation, as it turned out, is impossible in principle. Here the spatio-temporal localization underlying the kinematics is possible only for some particular cases, which depend on the specific dynamic conditions of motion. On a macro scale, the use of kinematics is quite acceptable. For micro scales, where the main role belongs to quanta, kinematics, which studies motion regardless of dynamic conditions, loses its meaning.

For the scales of the microworld, Newton's second law turned out to be untenable - it is valid only for large-scale phenomena. It turned out that attempts to measure any quantity characterizing the system under study entails an uncontrolled change in other quantities characterizing this system: if an attempt is made to establish a position in space and time, then this leads to an uncontrolled change in the corresponding conjugate value, which determines the dynamic state of the system. Thus, it is impossible to accurately measure two mutually conjugate quantities at the same time. The more precisely the value of one quantity characterizing the system is determined, the more uncertain is the value of its conjugate quantity. This circumstance entailed a significant change in views on the understanding of the nature of things.

The discrepancy in classical mechanics proceeded from the fact that the future in in a certain sense is completely contained in the present - this determines the possibility of accurately predicting the behavior of the system at any future moment in time. This possibility offers the simultaneous determination of mutually conjugate quantities. In the field of the microcosm, this turned out to be impossible, which introduces significant changes in the understanding of the possibilities of foresight and the relationship of natural phenomena: since the value of the quantities characterizing the state of the system at a certain point in time can only be established with a certain degree of uncertainty, then the possibility of accurately predicting the values ​​of these quantities in subsequent periods is excluded. points in time, i.e. one can only predict the probability of obtaining certain values.

Another discovery that shook the foundations of classical mechanics was the creation of field theory. Classical mechanics tried to reduce all natural phenomena to the forces acting between the particles of matter - the concept of electric fluids was based on this. Within the framework of this concept, only the substance and its changes were real - here the description of the action of two electric charges with the help of concepts related to them was recognized as the most important. The description of the field between these charges, and not of the charges themselves, was very essential for understanding the action of the charges. Here is a simple example of violation of Newton's third law under such conditions: if a charged particle moves away from a conductor through which current flows, and accordingly a magnetic field is created around it, then the resulting force acting from the charged particle on the conductor with current is exactly zero.

Created new reality there was no place in the mechanical picture of the world. As a result, physics began to deal with two realities - matter and field. If classical physics was based on the concept of matter, then with the revelation of a new reality, the physical picture of the world had to be revised. Attempts to explain electromagnetic phenomena with the help of the ether turned out to be untenable. The ether has not been found experimentally. This led to the creation of the theory of relativity, which forced us to reconsider the ideas about space and time that are characteristic of classical physics. Thus, two concepts - the theory of quanta and the theory of relativity - became the foundation for new physical concepts.

3. Conclusion.

The contribution made by Newton to the development of natural science was that he gave a mathematical method of converting physical laws into quantitatively measurable results that could be confirmed by observations, and, conversely, deduce physical laws based on such observations. As he himself wrote in the preface to the "Principles", "... we propose this work as the mathematical foundations of physics. The whole difficulty of physics ... lies in recognizing the forces of nature by the phenomena of motion, and then using these forces to explain the rest of the phenomena ... It would be desirable to derive from the principles of mechanics the rest of the phenomena of nature, arguing in a similar way, for many things make me suppose that all these phenomena are determined by certain forces with which the particles of bodies, due to reasons still unknown, or tend to each other and cleave into regular figures, or mutually repulse and move away from each other. Since these forces are unknown, until now the attempts of philosophers to explain the phenomena of nature have remained fruitless. I hope, however, that either this way of reasoning, or another, more correct, the grounds set forth here will provide some illumination."

The Newtonian method has become the main tool for understanding nature. The laws of classical mechanics and methods of mathematical analysis demonstrated their effectiveness. The physical experiment, relying on measuring technique, ensured unprecedented accuracy. Physical knowledge increasingly became the basis of industrial technology and technology, stimulated the development of other natural sciences. In physics, previously isolated light, electricity, magnetism and heat were united in the electromagnetic theory. And although the nature of gravity remained unexplained, its effects could be calculated. The concept of Laplace's mechanistic determinism was established, based on the possibility to uniquely determine the behavior of the system at any time, given the known initial conditions. The structure of mechanics as a science seemed solid, reliable and almost completely complete - i.e. the phenomena that did not fit into the existing classical canons, which one had to deal with, seemed quite explicable in the future by more sophisticated minds from the standpoint of classical mechanics. One got the impression that the knowledge of physics was close to its full completion - such a powerful force was demonstrated by the foundation of classical physics.

4. List of references.

1. Karpenkov S.Kh. Basic concepts of natural science. M.: UNITI, 1998.

2. Newton and philosophical problems of physics of the XX century. A team of authors, ed. M.D. Akhundova, S.V. Illarionov. M.: Nauka, 1991.

3. Gursky I.P. Elementary physics. Moscow: Nauka, 1984.

4. Great Soviet Encyclopedia in 30 volumes. Ed. Prokhorova A.M., 3rd edition, M., Soviet Encyclopedia, 1970.

5. Dorfman Ya.G. World history of physics with early XIX until the middle of the 20th century. M., 1979.

S. Marshak, Op. in 4 volumes, Moscow, Goslitizdat, 1959, v. 3, p. 601

Cit. Quoted from: Bernal J. Science in the history of society. M., 1956.S.265

From Wikipedia, the free encyclopedia

classical mechanics- a kind of mechanics (a section of physics that studies the laws of change in the positions of bodies in space over time and the causes that cause it), based on Newton's laws and Galileo's principle of relativity. Therefore, it is often called Newtonian mechanics».

Classical mechanics is subdivided into:

statics (which considers the equilibrium of bodies)

kinematics (which studies geometric property movement without considering its causes)

dynamics (which considers the movement of bodies).

Classical mechanics gives very accurate results if its application is limited to bodies whose speeds are much less than the speed of light, and whose dimensions are much larger than the dimensions of atoms and molecules. Relativistic mechanics is a generalization of classical mechanics for bodies moving at an arbitrary speed, and quantum mechanics for bodies whose dimensions are comparable to atomic ones. Quantum field theory considers quantum relativistic effects.

Nevertheless, classical mechanics retains its value because:

it is much easier to understand and use than other theories

in a wide range, it describes reality quite well.

Classical mechanics can be used to describe the motion of objects such as tops and baseballs, many astronomical objects (such as planets and galaxies), and sometimes even many microscopic objects such as molecules.

Classical mechanics is a self-consistent theory, that is, within its framework there are no statements that contradict each other. However, its combination with other classical theories, such as classical electrodynamics and thermodynamics, leads to the appearance of insoluble contradictions. In particular, classical electrodynamics predicts that the speed of light is constant for all observers, which is inconsistent with classical mechanics. At the beginning of the 20th century, this led to the need to create a special theory of relativity. When considered together with thermodynamics, classical mechanics leads to the Gibbs paradox, in which it is impossible to accurately determine the value of entropy, and to the ultraviolet catastrophe, in which absolutely black body must radiate an infinite amount of energy. Attempts to solve these problems led to the emergence and development of quantum mechanics.

10 ticket MECHANICAL PICTURE OF THE WORLD. THERMODYNAMICS

Thermodynamics(Greek θέρμη - “heat”, δύναμις - “force”) - a branch of physics that studies the relationships and transformations of heat and other forms of energy. Chemical thermodynamics, which studies physical and chemical transformations associated with the release or absorption of heat, as well as heat engineering, have separated into separate disciplines.

In thermodynamics, one does not deal with individual molecules, but with macroscopic bodies consisting of a huge number of particles. These bodies are called thermodynamic systems. In thermodynamics, thermal phenomena are described by macroscopic quantities - pressure, temperature, volume, ..., which are not applicable to individual molecules and atoms.

In theoretical physics, along with phenomenological thermodynamics, which studies the phenomenology of thermal processes, statistical thermodynamics is singled out, which was created for the mechanical justification of thermodynamics and was one of the first sections of statistical physics.

Thermodynamics can be applied to a wide range of topics in science and technology, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. Thermodynamics is important to other areas of physics and chemistry, chemical engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and is useful in other areas such as economics [

11 ticket ELECTRODYNAMICS

Electrodynamics- a branch of physics that studies the electromagnetic field in the most general case (that is, time-dependent variable fields are considered) and its interaction with bodies that have an electric charge (electromagnetic interaction). The subject of electrodynamics includes the relationship of electrical and magnetic phenomena, electromagnetic radiation (in different conditions, both free and in various cases of interaction with matter), electric current (generally speaking, alternating) and its interaction with an electromagnetic field (electric current can be considered in this case as a set of moving charged particles). Any electrical and magnetic interaction between charged bodies is considered in modern physics as carried out through the electromagnetic field, and, therefore, is also the subject of electrodynamics.

Most often under the term electrodynamics the default is classical electrodynamics, which describes only the continuous properties of an electromagnetic field through a system of Maxwell's equations; to denote the modern quantum theory of electro magnetic field and its interactions with charged particles, the stable term is commonly used quantum electrodynamics.

12 ticket CONCEPT OF SYMMETRY IN NATURAL SCIENCE

Emmy Noether's theorem asserts that each continuous symmetry of a physical system corresponds to a certain conservation law. Thus, the law of conservation of energy corresponds to the homogeneity of time, the law of conservation of momentum to the homogeneity of space, the law of conservation of momentum to the isotropy of space, the law of conservation of electric charge to gauge symmetry, etc.

The theorem is usually formulated for systems with an action functional and expresses the invariance of the Lagrangian with respect to some continuous group of transformations.

The theorem was established in the works of the scientists of the Göttingen school D. Gilbert, F. KleinaiE. Noether. The most common formulation was proved by Emmy Noether in 1918.

Symmetry types found in mathematics and natural sciences:

bilateral symmetry - symmetry with respect to mirror reflection. (Bilateral symmetry)

symmetry of the nth order - symmetry with respect to rotations through an angle of 360 ° / n around any axis. Described by the group Z n .

axial symmetry (radial symmetry, ray symmetry) - symmetry with respect to rotations through an arbitrary angle around an axis. Described by the SO(2) group.

spherical symmetry - symmetry with respect to rotations in three-dimensional space through arbitrary angles. Described by the SO(3) group. Local spherical symmetry of space or medium is also called isotropy.

rotational symmetry is a generalization of the previous two symmetries.

translational symmetry - symmetry with respect to shifts of space in any direction by a certain distance.

Lorentz invariance - symmetry with respect to arbitrary rotations in Minkowski's space-time.

gauge invariance is the independence of the type of equations of gauge theories in quantum field theory (in particular, Yang-Mills theories) under gauge transformations.

supersymmetry - the symmetry of the theory with respect to the replacement of bosons by fermions.

higher symmetry - symmetry in group analysis.

Kainosymmetry is a phenomenon of electronic configuration (the term was introduced by S. A. Shchukarev, who discovered it), which determines the secondary periodicity (discovered by E. V. Biron).

13 ticket service station

Special theory of relativity(ONE HUNDRED; Also private theory of relativity) is a theory that describes movement, laws of mechanics, space-time relations at arbitrary speeds of movement that are less than the speed of light in vacuum, including those close to the speed of light. Within the framework of special relativity, Newton's classical mechanics is an approximation of low velocities. The generalization of SRT for gravitational fields is called the general theory of relativity.

The deviations in the course of physical processes from the predictions of classical mechanics described by the special theory of relativity are called relativistic effects, and the rates at which such effects become significant are relativistic speeds.

14 OTO ticket

General theory of relativity(general relativity; it. allgemeine Relativitätstheorie) is a geometric theory of gravity that develops the special theory of relativity (SRT), published by Albert Einstein in 1915-1916. Within the framework of the general theory of relativity, as in other metric theories, it is postulated that gravitational effects are due to non-force interaction of bodies and fields located in space-time, but to the deformation of space-time itself, which is associated, in particular, with the presence of mass-energy. General relativity differs from other metric theories of gravity by using Einstein's equations to relate the curvature of space-time to the matter present in it.

General relativity is currently the most successful theory of gravity, well supported by observations. The first success of general relativity was to explain the anomalous precession of Mercury's perihelion. Then, in 1919, Arthur Eddington reported observing the deflection of light near the Sun at the time of a total eclipse, which qualitatively and quantitatively confirmed the predictions of general relativity. Since then, many other observations and experiments have confirmed a significant number of the theory's predictions, including gravitational time dilation, gravitational redshift, signal delay in a gravitational field, and, so far only indirectly, gravitational radiation. In addition, numerous observations are interpreted as confirmation of one of the most mysterious and exotic predictions of the general theory of relativity - the existence of black holes.

Despite the stunning success of the general theory of relativity, there is discomfort in the scientific community, connected, firstly, with the fact that it cannot be reformulated as the classical limit of quantum theory, and secondly, with the fact that the theory itself indicates the limits of its applicability, since it predicts the appearance of irremovable physical divergences when considering black holes and, in general, space-time singularities. To solve these problems, a number of alternative theories have been proposed, some of which are also quantum. Current experimental evidence, however, indicates that any type of deviation from general relativity should be very small, if it exists at all.

15 ticket EXPANSION OF THE UNIVERSE.HUBBLE LAW

Universe expansion- a phenomenon consisting in an almost uniform and isotropic expansion of outer space on the scale of the entire Universe. Experimentally, the expansion of the Universe is observed in the form of the implementation of the Hubble law. Science considers the so-called Big Bang to be the beginning of the expansion of the Universe. Theoretically, the phenomenon was predicted and substantiated by A. Friedman at an early stage of development of the general theory of relativity from general philosophical considerations about the homogeneity and isotropy of the Universe.

Hubble law(the law of the general recession of galaxies) is an empirical law that relates the redshift of the galaxy to the distance to them in a linear way:

Where z- redshift of the galaxy D- distance to it H 0 is a proportionality factor, called the Hubble constant. With a small value z the approximate equality holds cz=V r, Where V r is the speed of the galaxy along the observer's line of sight, c- the speed of light. In this case, the law takes the classical form:

This age is the characteristic time for the expansion of the Universe this moment and, up to a factor of 2, corresponds to the age of the Universe calculated according to the standard Friedman cosmological model.

16 ticket FRIEDMAN MODEL. SINGULARITY

Friedman's universe(Friedman-Lemaitre-Robertson-Walker metric) is one of the cosmological models that satisfy the field equations of the general theory of relativity, the first of the non-stationary models of the Universe. Received by Alexander Fridman in 1922. The Friedman model describes a homogeneous isotropic non-stationary A universe with matter that has a positive, zero, or negative constant curvature. This work of the scientist became the main theoretical development General relativity after the work of Einstein 1915-1917.

gravitational singularity- the region of space-time through which it is impossible to continue the geodetic line. Often in it the curvature of the space-time continuum turns to infinity, or the metric has other pathological properties that do not allow physical interpretation (for example, cosmological singularity- the state of the Universe at the initial moment of the Big Bang, characterized by an infinite density and temperature of matter);

17 ticket BIG BANG THEORY. RELICT RADIATION

Relic radiation(or cosmic microwave background radiation from English cosmic microwave background radiation) - cosmic electromagnetic radiation with a high degree of isotropy and with a spectrum characteristic of an absolutely black body with a temperature of 2.725 K.

The existence of the CMB was predicted theoretically within the framework of the Big Bang theory. Although many aspects of the original Big Bang theory have now been revised, the fundamentals that made it possible to predict the temperature of the CMB have not changed. It is believed that the relict radiation has been preserved from the initial stages of the existence of the Universe and evenly fills it. Its existence was experimentally confirmed in 1965. Along with the cosmological redshift, the cosmic microwave background radiation is considered as one of the main confirmations of the Big Bang theory.

Big Bang(English) big bang) is a cosmological model describing the early development of the Universe, namely, the beginning of the expansion of the Universe, before which the Universe was in a singular state.

Usually now automatically combine the theory of the Big Bang and the model of the hot Universe, but these concepts are independent and historically there was also a concept of a cold initial Universe near the Big Bang. It is the combination of the Big Bang theory with the theory of the hot Universe, supported by the existence of cosmic microwave background radiation, that is considered further.

18 ticket SPACE VACUUM

Vacuum(rel. vacuum- void) - space free from matter. In engineering and applied physics, vacuum is understood as a medium containing gas at pressures well below atmospheric pressure. Vacuum is characterized by the ratio between the mean free path of gas molecules λ and the characteristic size of the medium d. Under d the distance between the walls of the vacuum chamber, the diameter of the vacuum pipeline, etc. can be taken. Depending on the value of the ratio λ / d distinguish between low (), medium () and high () vacuum.

It is necessary to distinguish between concepts physical vacuum And technical vacuum.

19 ticket QUANTUM MECHANICS

Quantum mechanics- a section of theoretical physics that describes physical phenomena in which the action is comparable in magnitude to Planck's constant. The predictions of quantum mechanics can differ significantly from the predictions of classical mechanics. Since Planck's constant is an extremely small quantity compared to the action of everyday objects, quantum effects mostly appear only on a microscopic scale. If the physical action of the system is much greater than Planck's constant, quantum mechanics goes organically into classical mechanics. In turn, quantum mechanics is a non-relativistic approximation (that is, an approximation of small energies compared to the rest energy of the massive particles of the system) of quantum field theory.

Classical mechanics, which well describes systems of macroscopic scales, is not capable of describing phenomena at the level of atoms, molecules, electrons and photons. Quantum mechanics adequately describes the basic properties and behavior of atoms, ions, molecules, condensed matter, and other systems with an electron-nuclear structure. Quantum mechanics is also capable of describing the behavior of electrons, photons, and other elementary particles, but a more accurate relativistically invariant description of the transformations of elementary particles is built within the framework of quantum field theory. Experiments confirm the results obtained with the help of quantum mechanics.

The basic concepts of quantum kinematics are the concepts of an observable and a state.

The basic equations of quantum dynamics are the Schrödinger equation, the von Neumann equation, the Lindblad equation, the Heisenberg equation, and the Pauli equation.

The equations of quantum mechanics are closely related to many branches of mathematics, including: operator theory, probability theory, functional analysis, operator algebras, group theory.

Completely black body- physical idealization used in thermodynamics, a body that absorbs all electromagnetic radiation incident on it in all ranges and reflects nothing. Despite the name, a black body itself can emit electromagnetic radiation of any frequency and visually have a color. The radiation spectrum of a black body is determined only by its temperature.

The importance of a black body in the question of the spectrum thermal radiation of any (gray and colored) bodies in general, besides the fact that it is the simplest non-trivial case, it also consists in the fact that the question of the spectrum of equilibrium thermal radiation of bodies of any color and the reflection coefficient is reduced by the methods of classical thermodynamics to the question of radiation of absolutely black (and historically this has already been done to late XIX century, when the problem of black body radiation came to the fore).

The blackest real substances, for example, soot, absorb up to 99% of the incident radiation (that is, they have an albedo equal to 0.01) in the visible wavelength range, but they absorb infrared radiation much worse. Among the bodies of the Solar System, the Sun has the properties of an absolutely black body to the greatest extent.

The term was introduced by Gustav Kirchhoff in 1862.

20 ticket PRINCIPLES OF QUANTUM MECHANICS

All the problems of modern physics can be divided into two groups: the problems of classical physics and the problems of quantum physics. When studying the properties of ordinary macroscopic bodies, one almost never encounters quantum problems, because quantum properties become tangible only in the microcosm. Therefore, the physics of the 19th century, which studied only macroscopic bodies, was completely unaware of quantum processes. This is classical physics. It is typical for classical physics that it does not take into account the atomistic structure of matter. Now, however, the development of experimental technology has pushed the boundaries of our acquaintance with nature so widely that we now know, and, moreover, in great detail, the strictness of individual atoms and molecules. modern physics studies the atomic structure of matter and, therefore, the principles of the old classical physics of the XIX century. had to change in accordance with the new facts, and change radically. This change in principles is the transition to quantum physics.

21 tickets CORPUSCULAR-WAVE DUALISM

Corpuscular-wave dualism- the principle that any object can exhibit both wave and particle properties. It was introduced during the development of quantum mechanics to interpret the phenomena observed in the microcosm from the point of view of classical concepts. A further development of the principle of wave-particle duality was the concept of quantized fields in quantum field theory.

As a classic example, light can be interpreted as a stream of corpuscles (photons), which in many physical effects exhibit the properties of electromagnetic waves. Light exhibits the properties of a wave in the phenomena of diffraction and interference at scales comparable to the wavelength of light. For example, even single photons passing through the double slit create an interference pattern on the screen, determined by Maxwell's equations.

Nevertheless, the experiment shows that a photon is not a short pulse of electromagnetic radiation, for example, it cannot be divided into several beams by optical beam splitters, which was clearly shown by an experiment conducted by French physicists Grangier, Roger and Aspe in 1986. The corpuscular properties of light are manifested in the photoelectric effect and in the Compton effect. A photon also behaves like a particle that is emitted or absorbed entirely by objects whose dimensions are much smaller than its wavelength (for example, atomic nuclei), or can generally be considered pointlike (for example, an electron).

At present, the concept of wave-particle duality is only of historical interest, since it served only as an interpretation, a way to describe the behavior of quantum objects, choosing analogies from classical physics for it. In fact, quantum objects are neither classical waves nor classical particles, acquiring the properties of the former or the latter only in some approximation. Methodologically more correct is the formulation of quantum theory in terms of path integrals (propagator), free from the use of classical concepts.

22 ticket THE CONCEPT OF THE STRUCTURE OF THE ATOM. MODELS OF THE ATOM

Thomson model of the atom(model "Pudding with raisins", eng. plum pudding model).J. J. Thomson proposed to consider the atom as some positively charged body with electrons enclosed inside it. It was finally refuted by Rutherford after his famous experiment on the scattering of alpha particles.

Nagaoka's early planetary model of the atom. In 1904, the Japanese physicist Hantaro Nagaoka proposed a model of the atom, built by analogy with the planet Saturn. In this model, electrons, united in rings, revolved around a small positive nucleus in orbits. The model turned out to be wrong.

Bohr-Rutherford planetary model of the atom. In 1911, Ernest Rutherford, having done a series of experiments, came to the conclusion that the atom is a kind of planetary system in which electrons move in orbits around a heavy positively charged nucleus located in the center of the atom ("Rutherford's model of the atom"). However, such a description of the atom came into conflict with classical electrodynamics. The fact is that, according to classical electrodynamics, an electron, when moving with centripetal acceleration, must emit electromagnetic waves, and, consequently, lose energy. Calculations showed that the time it takes for an electron in such an atom to fall onto the nucleus is absolutely negligible. To explain the stability of atoms, Niels Bohr had to introduce postulates that boiled down to the fact that an electron in an atom, being in some special energy states, does not radiate energy (“the Bohr-Rutherford model of the atom”). Bohr's postulates showed that classical mechanics is not applicable to describe the atom. Further study of the radiation of the atom led to the creation of quantum mechanics, which made it possible to explain the overwhelming majority of the observed facts.

Atom(other Greek ἄτομος- indivisible) - the smallest chemically indivisible part of a chemical element, which is the carrier of its properties. An atom consists of an atomic nucleus and electrons. The nucleus of an atom is made up of positively charged protons and uncharged neutrons. If the number of protons in the nucleus coincides with the number of electrons, then the atom as a whole is electrically neutral. Otherwise, it has some positive or negative charge and is called an ion. Atoms are classified according to the number of protons and neutrons in the nucleus: the number of protons determines whether an atom belongs to some chemical element, and the number of neutrons is the isotope of this element.

Atoms of various kinds in different quantities, connected by interatomic bonds, form molecules.

23 ticket FUNDAMENTAL INTERACTIONS

Fundamental interactions- qualitatively different types of interaction of elementary particles of bodies composed of them.

Today, the existence of four fundamental interactions is reliably known:

gravitational

electromagnetic

strong

weak

At the same time, electromagnetic and weak interactions are manifestations of a single electroweak interaction.

Searches are underway for other types of fundamental interactions, both in the phenomena of the microworld and on a cosmic scale, but so far no other type of fundamental interaction has been discovered.

In physics, mechanical energy is divided into two types - potential and kinetic energy. The reason for the change in the movement of bodies (changes in kinetic energy) is the force (potential energy) (see Newton's second law). Exploring the world around us, we can notice a wide variety of forces: gravity, thread tension, spring compression force, collision force of bodies , friction force, air resistance force, explosion force, etc. However, when the atomic structure of matter was clarified, it became clear that all the variety of these forces is the result of the interaction of atoms with each other. Since the main type of interatomic interaction is electromagnetic, it turned out that most of these forces are just various manifestations of electromagnetic interaction. One of the exceptions is, for example, the force of gravity, which is caused by the gravitational interaction between bodies that have mass.

24 ticket ELEMENTARY PARTICLES AND THEIR PROPERTIES

Elementary particle- a collective term referring to micro-objects on a sub-nuclear scale that cannot be broken down into their component parts.

It should be borne in mind that some elementary particles (electron, photon, quarks, etc.) are currently considered structureless and are considered as primary fundamental particles. Other elementary particles (so-called constituent particles-proton, neutron, etc.) have a complex internal structure, but, nevertheless, according to modern concepts, it is impossible to separate them into parts (see Confinement).

The structure and behavior of elementary particles is studied by elementary particle physics.

Main article:Quarks

Quarks and antiquarks have never been found in a free state - this is explained by the phenomenon of confinement. Based on the symmetry between leptons and quarks, which is manifested in electromagnetic interaction, hypotheses are put forward that these particles consist of more fundamental particles - preons.

25 ticket CONCEPT OF BIFURCATION. BIFURCATION POINT

Bifurcation is the acquisition of a new quality in the movements of a dynamic system with a small change in its parameters.

The central concept of the bifurcation theory is the concept of a (non)rough system (see below). Any dynamical system is taken and such a (multi)parametric family of dynamical systems is considered that the original system is obtained as a special case - for any one value of the parameter (parameters). If the qualitative picture of the partition of the phase space into trajectories is preserved for the value of the parameters sufficiently close to the given one, then such a system is called rough. Otherwise, if such a neighborhood does not exist, then the system is called rough.

Thus, regions of rough systems appear in the parameter space, which are separated by surfaces consisting of non-rough systems. The theory of bifurcations studies the dependence of a qualitative picture when a parameter changes continuously along a certain curve. The scheme by which the qualitative picture changes is called bifurcation diagram.

The main methods of bifurcation theory are the methods of perturbation theory. In particular, it applies small parameter method(Pontryagin).

bifurcation point- change of the established operating mode of the system. A term from non-equilibrium thermodynamics and synergetics.

bifurcation point- the critical state of the system, in which the system becomes unstable relative to fluctuations and uncertainty arises: will the state of the system become chaotic or will it move to a new, more differentiated and high level of order. A term from the theory of self-organization.

26 ticket SYNERGETICS - THE SCIENCE OF OPEN SELF-ORGANIZING SYSTEMS

Synergetics(other Greek συν-- prefix with the meaning of compatibility and ἔργον- "activity") - an interdisciplinary direction of scientific research, the task of which is to study natural phenomena and processes based on the principles of self-organization of systems (consisting of subsystems). "... A science that studies the processes of self-organization and the emergence, maintenance, stability and decay of structures of the most diverse nature ...".

Synergetics was originally declared as an interdisciplinary approach, since the principles governing the processes of self-organization seem to be the same (regardless of the nature of the systems), and a common mathematical apparatus should be suitable for their description.

From an ideological point of view, synergetics is sometimes positioned as “global evolutionism” or “universal theory of evolution”, which provides a single basis for describing the mechanisms for the emergence of any innovations, just as cybernetics was once defined as “universal control theory”, equally suitable for describing any regulation and optimization operations. : in nature, in technology, in society, etc., etc. However, time has shown that the general cybernetic approach has far from justified all the hopes placed on it. Similarly, the broad interpretation of the applicability of synergetic methods is also criticized.

The basic concept of synergetics is the definition of structure as states, arising as a result of the multivariant and ambiguous behavior of such multi-element structures or multi-factor media that do not degrade to the thermodynamic averaging standard for closed systems, but develop due to openness, energy inflow from the outside, nonlinearity of internal processes, the appearance of special regimes with sharpening and the presence of more than one stable state. In the indicated systems, neither the second law of thermodynamics nor Prigogine's theorem on the minimum rate of entropy production is applicable, which can lead to the formation of new structures and systems, including those more complex than the original ones.

This phenomenon is interpreted by synergetics as a general mechanism of the direction of evolution observed everywhere in nature: from elementary and primitive to complex and more perfect.

In some cases, the formation of new structures has a regular, wave character, and then they are called autowave processes (by analogy with self-oscillations).

27 ticket THE CONCEPT OF LIFE. THE PROBLEM OF THE ORIGIN OF LIFE

Life- the active form of the existence of a substance, in a sense, the highest in comparison with its physical and chemical forms of existence; a set of physical and chemical processes occurring in the cell, allowing the exchange of matter and its division. The main attribute of living matter is the genetic information used for replication. More or less accurately define the concept of "life" can only enumerate the qualities that distinguish it from non-life. Life does not exist outside the cell, viruses exhibit the properties of living matter only after the transfer of genetic material into the cell [ source not specified 268 days] . Adapting to the environment, a living cell forms the whole variety of living organisms.

Also, the word "life" is understood as the period of existence of a single organism from the moment of occurrence to its death (ontogeny).

In 1860, the French chemist Louis Pasteur took up the problem of the origin of life. Through his experiments, he proved that bacteria are ubiquitous, and that non-living materials can easily be contaminated by living things if they are not properly sterilized. The scientist boiled various media in water in which microorganisms could form. Additional boiling killed the microorganisms and their spores. Pasteur attached a sealed flask with a free end to the S-shaped tube. Spores of microorganisms settled on a curved tube and could not penetrate into nutrient medium. A well-boiled nutrient medium remained sterile; no life was found in it, despite the fact that air access was provided.

As a result of a series of experiments, Pasteur proved the validity of the theory of biogenesis and finally refuted the theory of spontaneous generation.

28 ticket THE CONCEPT OF THE ORIGIN OF OPARIN'S LIFE

Mechanics- this is a part of physics that studies the laws of mechanical movement and the reasons that cause or change this movement.

Mechanics, in turn, is divided into kinematics, dynamics and statics.

mechanical movement- this is a change in the relative position of bodies or body parts over time.

Weight is a scalar physical quantity that quantitatively characterizes the inert and gravitational properties of matter.

inertia- this is the desire of the body to maintain a state of rest or uniform rectilinear motion.

inertial mass characterizes the ability of a body to resist a change in its state (rest or motion), for example, in Newton's second law

gravitational mass characterizes the body's ability to create a gravitational field, which is characterized by a vector quantity called tension. The intensity of the gravitational field of a point mass is equal to:

The gravitational mass characterizes the body's ability to interact with the gravitational field:

P equivalence principle gravitational and inertial masses: each mass is both inertial and gravitational at the same time.

The mass of the body depends on the density of the substance ρ and the size of the body (body volume V):

The concept of mass is not identical to the concepts of weight and gravity. It does not depend on the fields of gravity and accelerations.

Moment of inertia is a tensor physical quantity that quantitatively characterizes the inertia of a solid body, which manifests itself in rotational motion.

When describing the rotational motion, it is not enough to specify the mass. The inertia of a body in rotational motion depends not only on the mass, but also on its distribution relative to the axis of rotation.

1. Moment of inertia of a material point

where m is the mass of a material point; r is the distance from the point to the axis of rotation.

2. Moment of inertia of the system of material points

3. Moment of inertia of a perfectly rigid body

Force- this is a vector physical quantity, which is a measure of the mechanical impact on the body from other bodies or fields, as a result of which the body acquires acceleration or deforms (changes its shape or size).

Mechanics uses various models to describe mechanical motion.

Material point(m.t.) is a body with a mass, the dimensions of which can be neglected in this problem.

Absolutely rigid body(a.t.t.) is a body that does not deform in the process of movement, that is, the distance between any two points in the process of movement remains unchanged.
§ 2. Laws of motion.

• 
  First law n newton : any material point (body) retains a state of rest or uniform rectilinear motion until the impact from other bodies makes it change this state.

Those frames of reference, in relation to which Newton's first law is fulfilled, are called inertial frames of reference (ISR). Therefore, Newton's first law asserts the existence of IFR.

• 
  Newton's second law (basic law of dynamics forward movement): the rate of change of momentum of a material point (body) is equal to the sum of the forces acting on it

• 
  Newton's third law : any action of material points (bodies) on each other has the character of interaction; the forces with which the material points act on each other are always equal in absolute value, oppositely directed and act along the straight line connecting these points

,

here is the force acting on the first material point from the second; - the force acting on the second material point from the side of the first. These forces are applied to different material points (bodies), always act in pairs and are forces of the same nature.

,

here is the gravitational constant. .

Conservation laws in classical mechanics.

The laws of conservation are fulfilled in closed systems of interacting bodies.

A system is called closed if no external forces act on the system.

Pulse - vector physical quantity that quantitatively characterizes the stock of translational motion:

Law of conservation of momentum systems of material points(m.t.): in closed systems, m.t. total momentum is conserved

Where - i-th speed material point before interaction; is its speed after interaction.

angular momentum is a physical vector quantity that quantitatively characterizes the reserve of rotational motion.

is the momentum of the material point, is the radius vector of the material point.
Law of conservation of angular momentum : in a closed system, the total angular momentum is conserved:

The physical quantity that characterizes the ability of a body or system of bodies to do work is called energy.

Energy is a scalar physical quantity, which is the most general characteristic of the state of the system.

The state of the system is determined by its movement and configuration, i.e., by the mutual arrangement of its parts. The motion of the system is characterized by the kinetic energy K, and the configuration (being in the potential field of forces) is characterized by the potential energy U.

total energy defined as the sum:

E = K + U + E int,

where E ext is the internal energy of the body.

The kinetic and potential energies add up to mechanical energy .

Einstein formula(relationship of energy and mass):

In the reference frame associated with the center of mass of the m.t. system, m \u003d m 0 is the rest mass, and E \u003d E 0 \u003d m 0. c 2 - rest energy.

Internal energy is determined in the frame of reference associated with the body itself, that is, the internal energy is at the same time the rest energy.

Kinetic energy is the energy of the mechanical movement of a body or system of bodies. The relativistic kinetic energy is determined by the formula

At low speeds v
.

Potential energy is a scalar physical quantity that characterizes the interaction of bodies with other bodies or with fields.

Examples:

potential energy of elastic interaction

;

• 
  potential energy of gravitational interaction of point masses

;

Law of energy conservation : the total energy of a closed system of material points is conserved

In the absence of dissipation (scattering) of energy, both total and mechanical energies are conserved. In dissipative systems, total energy is conserved, while mechanical energy is not conserved.

§ 2. Basic concepts of classical electrodynamics.

The source of the electromagnetic field is an electric charge.

Electric charge is the property of some elementary particles to enter into electromagnetic interaction.

Electric charge properties :

1. The electric charge can be positive and negative (it is generally accepted that the proton is positively charged, and the electron is negatively charged).

2. Electric charge is quantized. A quantum of electric charge is an elementary electric charge (е = 1.610 –19 C). In the free state, all charges are multiples of an integer number of elementary electric charges:

3. The law of conservation of charge: the total electric charge of a closed system is preserved in all processes involving charged particles:

q 1 + q 2 +...+ q N = q 1 * + q 2 * +...+ q N * .

4. relativistic invariance: the value of the total charge of the system does not depend on the motion of charge carriers (the charge of moving and resting particles is the same). In other words, in all ISOs, the charge of any particle or body is the same.

Description of the electromagnetic field.

The charges interact with each other (Fig. 1). The magnitude of the force with which charges of the same sign repel each other, and charges of opposite signs attract each other, is determined using the empirically established Coulomb's law:

Here, is the electric constant.

Fig.1

And what is the mechanism of interaction of charged bodies? One can put forward the following hypothesis: bodies with an electric charge generate an electromagnetic field. In turn, the electromagnetic field acts on other charged bodies that are in this field. A new material object emerged – an electromagnetic field.

Experience shows that in any electromagnetic field a force acts on a stationary charge, the magnitude of which depends only on the magnitude of the charge (the magnitude of the force is proportional to the magnitude of the charge) and its position in the field. It is possible to assign to each point of the field a certain vector , which is the coefficient of proportionality between the force acting on a fixed charge in the field and the charge . Then the force with which the field acts on a fixed charge can be determined by the formula:

The force acting from the side of the electromagnetic field on a fixed charge is called electric force. The vector quantity characterizing the state of the field that causes the action is called the electric strength of the electromagnetic field.

Further experiments with charges show that the vector does not completely characterize the electromagnetic field. If the charge begins to move, then some additional force appears, the magnitude and direction of which are in no way related to the magnitude and direction of the vector. The additional force that occurs when a charge moves in an electromagnetic field is called magnetic force. Experience shows that the magnetic force depends on the charge and on the magnitude and direction of the velocity vector. If we move a trial charge through any fixed point of the field with the same velocity, but in different directions, then the magnetic force will be different each time. However, always. Further analysis of the experimental facts made it possible to establish that for each point of the electromagnetic field there is a single direction MN (Fig. 2), which has the following properties:

Fig.2

If a certain vector is directed along the MN direction, which has the meaning of the coefficient of proportionality between the magnetic force and the product, then setting , and uniquely characterizes the state of the field that causes the appearance of . The vector was called the vector of electromagnetic induction. Since and , then

In an electromagnetic field, an electromagnetic Lorentz force acts on a charge moving at a speed q (Fig. 3):

.
The vectors and , that is, the six numbers , are equal components of a single electromagnetic field (components of the electromagnetic field tensor). In a particular case, it may turn out that all or all ; then the electromagnetic field is reduced to either electric or magnetic fields.

The experiment confirmed the correctness of the constructed two-vector model of the electromagnetic field. In this model, each point of the electromagnetic field is given a pair of vectors and . The model we have constructed is a model of a continuous field, since the functions and describing the field are continuous functions of the coordinates.

The theory of electromagnetic phenomena using the continuous field model is called classical.

In reality, the field, like matter, is discrete. But this begins to affect only at distances comparable to the sizes of elementary particles. The discreteness of the electromagnetic field is taken into account in quantum theory.

The principle of superposition.

Fields are usually depicted using lines of force.

force line is a line, the tangent to which at each point coincides with the field strength vector.

D
For point immobile charges, the pattern of force lines of the electrostatic field is shown in fig. 6.

The intensity vector of the electrostatic field created by a point charge is determined by the formula (Fig. 7 a and b) the magnetic field line is constructed so that at each point of the line of force the vector is directed tangentially to this line. The lines of force of the magnetic field are closed (Fig. 8). This suggests that the magnetic field is a vortex field.

Rice. 8

And if the field creates not one, but several point charges? Do the charges influence each other, or does each of the system's charges contribute to the resulting field independently of the others? Will there be an electromagnetic field created by i charge in the absence of other charges is the same as the field created i-th charge in the presence of other charges?

Superposition principle : the electromagnetic field of an arbitrary system of charges is the result of the addition of fields that would be created by each of the elementary charges of this system in the absence of the others:

And .
Laws of the electromagnetic field

The laws of the electromagnetic field are formulated as a system of Maxwell's equations.

First

It follows from Maxwell's first equation that electrostatic field - potential (converging or diverging) and its source are motionless electric charges.

Second Maxwell's equation for a magnetostatic field:

It follows from Maxwell's second equation that the magnetostatic field is vortex non-potential and has no point sources.

Third Maxwell's equation for an electrostatic field:

It follows from Maxwell's third equation that the electrostatic field is not vortex.

In electrodynamics (for a variable electromagnetic field), Maxwell's third equation is:

i.e. the electric field is not potential (not Coulomb), but vortex and is created by a variable flux of the magnetic field induction vector.

Fourth Maxwell's equation for a magnetostatic field

It follows from the fourth Maxwell equation in magnetostatics that the magnetic field is vortex and is created by constant electric currents or moving charges. The direction of twisting of the magnetic field lines is determined by the right screw rule (Fig. 9).

R
Fig.9

In electrodynamics, Maxwell's fourth equation is:

The first term in this equation is the conduction current I associated with the movement of charges and creating a magnetic field.

The second term in this equation is the "displacement current in vacuum", i.e., the variable flux of the intensity vector electric field.

The main provisions and conclusions of Maxwell's theory are as follows.

A change in time of the electric field leads to the appearance of a magnetic field and vice versa. Therefore, there are electromagnetic waves.

The transfer of electromagnetic energy occurs at a finite speed . The speed of transmission of electromagnetic waves is equal to the speed of light. From this followed the fundamental identity of electromagnetic and optical phenomena.

The pinnacle of I. Newton's scientific work is his immortal work "The Mathematical Principles of Natural Philosophy", first published in 1687. In it, he summarized the results obtained by his predecessors and his own research and created for the first time a unified harmonious system of terrestrial and celestial mechanics, which formed the basis of all classical physics.

Here Newton gave definitions of the initial concepts - the amount of matter, equivalent to mass, density; amount of motion equivalent to momentum, and various types of force. Formulating the concept of quantity of matter, he proceeded from the idea that atoms consist of some single primary matter; Density was understood as the degree to which a unit volume of a body is filled with primary matter.

This work outlines Newton's doctrine of universal gravitation, on the basis of which he developed the theory of the motion of planets, satellites and comets that form the solar system. Based on this law, he explained the phenomenon of tides and the compression of Jupiter. Newton's concept was the basis for many technical advances over a long period of time. Many methods of scientific research in various fields of natural sciences were formed on its foundation.

The result of the development of classical mechanics was the creation of a unified mechanical picture of the world, within which the entire qualitative diversity of the world was explained by differences in the movement of bodies, subject to the laws of Newtonian mechanics.

Newton's mechanics, in contrast to previous mechanical concepts, made it possible to solve the problem of any stage of movement, both preceding and subsequent, and at any point in space with known facts that determine this movement, as well as the inverse problem of determining the magnitude and direction of these factors. at any point with known basic elements of motion. Because of this, Newtonian mechanics could be used as a method for the quantitative analysis of mechanical motion.

The law of universal gravitation.

The law of universal gravitation was discovered by I. Newton in 1682. According to his hypothesis, attractive forces act between all bodies of the Universe, directed along the line connecting the centers of mass. For a body in the form of a homogeneous ball, the center of mass coincides with the center of the ball.

In subsequent years, Newton tried to find a physical explanation for the laws of planetary motion discovered by I. Kepler at the beginning of the 17th century, and to give a quantitative expression for gravitational forces. So, knowing how the planets move, Newton wanted to determine what forces act on them. This path is called the inverse problem of mechanics.

If the main task of mechanics is to determine the coordinates of a body of known mass and its speed at any moment of time from the known forces acting on the body, then when solving the inverse problem, it is necessary to determine the forces acting on the body if it is known how it moves.

The solution of this problem led Newton to the discovery of the law of universal gravitation: "All bodies are attracted to each other with a force directly proportional to their masses and inversely proportional to the square of the distance between them."

There are several important remarks to be made about this law.

1, its action explicitly extends to all physical material bodies in the Universe without exception.

2 the force of gravity of the Earth at its surface equally affects all material bodies located at any point the globe. Right now, the force of gravity is acting on us, and we really feel it as our own weight. If we drop something, it, under the influence of the same force, will rush to the ground with uniform acceleration.

Many phenomena are explained by the action of universal gravitational forces in nature: the movement of the planets in the solar system, artificial satellites of the Earth - all of them are explained on the basis of the law of universal gravitation and the laws of dynamics.

Newton was the first to suggest that gravitational forces determine not only the motion of planets solar system; they act between any bodies of the Universe. One of the manifestations of the force of universal gravitation is the force of gravity - this is how it is customary to call the force of attraction of bodies to the Earth near its surface.

The force of gravity is directed towards the center of the earth. In the absence of other forces, the body falls freely to the Earth with free fall acceleration.

Three principles of mechanics.

Newton's laws of mechanics, the three laws underlying the so-called. classical mechanics. Formulated by I. Newton (1687).

First law: "Every body continues to be held in its state of rest or uniform and rectilinear motion, until and insofar as it is forced by applied forces to change this state."

The second law: "The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts."

The third law: "There is always an equal and opposite reaction to an action, otherwise, the interactions of two bodies against each other are equal and directed in opposite directions." N. h. m. appeared as a result of the generalization of numerous observations, experiments and theoretical studies of G. Galileo, H. Huygens, Newton himself, and others.

According to modern ideas and terminology, in the first and second laws, a body should be understood as a material point, and under movement - movement relative to an inertial frame of reference. The mathematical expression of the second law in classical mechanics has the form or mw = F, where m is the mass of the point, u is its speed, a w is the acceleration, F is the acting force.

N. h. m cease to be valid for the movement of objects of very small sizes (elementary particles) and for movements with speeds close to the speed of light

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Definition 1

Mechanics is an extensive branch of physics that studies the laws of change in positions physical bodies in space and time, as well as postulates based on Newton's laws.

Figure 1. Basic law of dynamics. Author24 - online exchange of student papers

Often this scientific direction of physics is called "Newtonian mechanics". Classical mechanics today is divided into the following sections:

• statics - considers and describes the balance of bodies;
• kinematics - studies the geometric features of motion without considering its causes;
• dynamics - deals with the study of the movement of material substances.

Mechanical motion is one of the simplest and at the same time the most common form of existence of living matter. Therefore, classical mechanics occupies an exceptionally significant place in natural science and is considered the main subsection of physics.

Basic laws of classical mechanics

Classical mechanics in its postulates studies the movement of working bodies, with speeds that are much less than the speed of light. According to the special hypothesis of relativity, there is no absolute space and time for elements moving at great speed. As a result, the nature of the interaction of substances becomes more complicated, in particular, their mass begins to depend on the speed of movement. All this has become an object of consideration for the formulas of relativistic mechanics, for which the light velocity constant plays a fundamental role.

Classical mechanics is based on the following fundamental laws.

1. Galileo's principle of relativity. According to this principle, there are many frames of reference in which any free body is at rest or moves with a constant speed in direction. These concepts in science are called inertial, and I move relative to each other in a straight line and uniformly.
2. Newton's three laws. The first establishes the obligatory presence of the property of inertness in physical bodies and postulates the presence of such reference concepts in which the movement of free matter occurs at a constant speed. The second postulate introduces the concept of force as the main measure of the interaction of active elements and, on the basis of theoretical facts, postulates the relationship between the acceleration of a body, its magnitude and inertia. Newton's third law - for every force acting on the first body, there is a counteracting factor equal in magnitude and opposite in direction.
3. The law of conservation of internal energy is a consequence of Newton's laws for stable, closed systems in which only conservative forces act. The total mechanical force of a closed system of material bodies, between which only thermal energy, remains constant.

Parallelogram rules in mechanics

Certain consequences follow from the three fundamental theories of Newton's body motion, one of which is addition total elements according to the parallelogram rule. According to this idea, the acceleration of any physical substance depends on the quantities that mainly characterize the action of other bodies, which determine the features of the process itself. Mechanical action on the object under study from the side external environment, which radically changes the speed of movement of several elements at once, is called force. It can be multifaceted.

In classical mechanics, which deals with speeds much less than the speed of light, mass is considered one of the main characteristics of the body itself, regardless of whether it is moving or at rest. The mass of a physical body is independent of the interaction of matter with other parts of the system.

Remark 1

Thus, mass gradually came to be understood as the amount of living matter.

The establishment of the concepts of mass and force, as well as the method for measuring them, allowed Newton to describe and formulate the second law of classical mechanics. So, mass is one of the key characteristics of matter, which determines its gravitational and inertial properties.

The first and second laws of mechanics refer, respectively, to the systematic motion of a single body or material point. In this case, only the action of other elements in a certain concept is taken into account. However, any physical action is an interaction.

The third law of mechanics already fixes this statement and says: an action always corresponds to an oppositely directed and equal reaction. In Newton's formulation, this postulate of mechanics is valid only for the case of a direct relationship of forces or in the case of a sudden transfer of the action of one material body to another. In the case of movement over a long period of time, the third law applies when the time of transfer of the action can be neglected.

In general, all the laws of classical mechanics are valid for the functioning of inertial frames of reference. In the case of non-inertial concepts, the situation is completely different. With accelerated movement of coordinates relative to the inertial frame itself, Newton's first law cannot be used - free bodies in it will change their speed of movement over time and depend on the speed of movement and energy of other substances.

Limits of applicability of the laws of classical mechanics

Figure 3. Limits of applicability of the laws of classical mechanics. Author24 - online exchange of student papers

As a result of the rather rapid development of physics at the beginning of the 20th century, a certain scope of application of classical mechanics was formed: its laws and postulates are valid for the motions of physical bodies, the speed of which is much less than the speed of light. It was determined that with increasing speed, the mass of any substance will automatically increase.

The discrepancy between the principles in classical mechanics mainly proceeded from the fact that the future, in a certain sense, is completely in the present - this determines the probability of accurately predicting the behavior of the system in any period of time.

Remark 2

The Newtonian method immediately became the main tool for understanding the essence of nature and all life on the planet. The laws of mechanics and methods of mathematical analysis soon showed their effectiveness and significance. The physical experiment, which was based on measuring technology, provided scientists with unprecedented accuracy.

Physical knowledge increasingly became the central industrial technology, which stimulated general development other important natural sciences.

In physics, all previously isolated electricity, light, magnetism and heat became whole and united in the electromagnetic hypothesis. And although the nature of gravity itself remained uncertain, its effects could be calculated. The concept of Laplace's mechanistic determinism was approved and implemented, which proceeds from the possibility of accurately determining the behavior of bodies at any time, if the initial conditions are initially determined.

The structure of mechanics as a science seemed quite reliable and solid, and also practically complete. As a result, the impression was that the knowledge of physics and its laws is close to its finale - such a powerful force was shown by the foundation of classical physics.