Introduction
The subject of physics and its relationship with other sciences
“Matter is a philosophical category for designating objective reality, which ... is displayed by our sensations, existing independently of them” (Lenin V.I. Poli. sobr. soch. T. 18. P. 131).
Motion is an integral property of matter and the form of its existence. Movement in the broad sense of the word is all kinds of changes in matter - from simple displacement to the most complex processes of thinking. “Movement, considered in the most general sense of the word, that is, understood as a way of existence of matter, as an attribute inherent in matter, embraces all changes and processes occurring in the Universe, ranging from simple movement to thinking” (Engels F. Dialectics of nature - K¦ Marx, F. Engels, Op. 2nd ed., vol. 20, p. 391).
Various forms of motion of matter are studied by various sciences, including physics. The subject of physics, as, indeed, of any science, can be revealed only as it is presented in detail. It is rather difficult to give a strict definition of the subject of physics, because the boundaries between physics and a number of related disciplines are arbitrary. At this stage of development, it is impossible to keep the definition of physics only as a science of nature.
Academician A.F. Ioffe (1880 - 1960; Soviet physicist) defined physics as a science that studies general properties and the laws of motion of matter and field. It is now generally accepted that all interactions are carried out by means of fields, such as gravitational, electromagnetic, nuclear force fields. The field, along with matter, is one of the forms of existence of matter. The inextricable connection between the field and matter, as well as the difference in their properties, will be considered as the course progresses.
Physics is the science of the simplest and at the same time the most general forms of the motion of matter and their mutual transformations. The forms of matter motion studied by physics (mechanical, thermal, etc.) are present in all higher and more complex forms of matter motion (chemical, biological, etc.). Therefore they, being the simplest, are at the same time the most general forms of motion of matter. Higher and more complex forms of the motion of matter are the subject of study of other sciences (chemistry, biology, etc.).
Physics is closely related to the natural sciences. As Academician S.I. Vavilov (1891-1955; Soviet physicist and public figure) said, this close connection between physics and other branches of natural science has led to the fact that physics has grown into astronomy, geology, chemistry, biology and other natural sciences with the deepest roots. As a result, a number of new related disciplines were formed, such as astrophysics, geophysics, physical chemistry, biophysics, etc.
Physics is closely connected with technology, and this connection is two-way. Physics grew out of the needs of technology (the development of mechanics among the ancient Greeks, for example, was caused by the demands of construction and military equipment of that time), and technology, in turn, determines the direction of physical research (for example, at one time the task of creating the most economical heat engines caused a stormy development of thermodynamics). On the other hand, the technical level of production depends on the development of physics. Physics is the basis for the creation of new branches of technology (electronic technology, nuclear technology, etc.).
Physics is closely related to philosophy. Such major discoveries in the field of physics as the law of conservation and transformation of energy, the uncertainty relation in atomic physics, etc., have been and are the scene of a sharp struggle between materialism and idealism. Correct philosophical conclusions from scientific discoveries in the field of physics have always confirmed the basic provisions of dialectical materialism, so the study of these discoveries and their philosophical generalization play an important role in shaping the scientific worldview.
The rapid pace of development of physics, its growing ties with technology indicate the dual role of the course of physics in the higher educational institution, "on the one hand, this is a fundamental basis for the theoretical training of an engineer, without which his successful activity is impossible, on the other hand, this is the formation of a dialectical-materialistic and scientific- atheistic outlook.
Units of physical quantities
The main method of research in physics is experience - sensory-empirical knowledge of objective reality based on practice, i.e., observation of the phenomena under study under precisely taken into account conditions that make it possible to monitor the course of phenomena and repeatedly reproduce it when these conditions are repeated.
Hypotheses are put forward to explain the experimental facts. A hypothesis is a scientific assumption put forward to explain a phenomenon and requires experimental verification and theoretical justification in order to become a reliable scientific theory.
As a result of the generalization of experimental facts, as well as the results of people's activities, physical
cal laws - stable repeating objective patterns that exist in nature. The most important laws establish a relationship between physical quantities, for which it is necessary to measure these quantities. The measurement of a physical quantity is an action performed with the help of measuring instruments to find the value of a physical quantity in accepted units. Units of physical quantities can be chosen arbitrarily, but then there will be difficulties in comparing them. Therefore, it is advisable to introduce a system of units that covers the units of all physical quantities and allows you to operate with them.
To build a system of units, units are arbitrarily chosen for several independent physical quantities. These units are called basic. The remaining quantities and their units are derived from the laws connecting these quantities with the main ones. They are called derivatives.
In the USSR, according to the State Standard (GOST 8.417 - 81), the International System (SI) is mandatory for use, which is based on seven basic units - meter, kilogram, second, ampere, kelvin, mole, candela - and two additional ones - radians and steradians .
A meter (m) is the length of the path traveled by light in a vacuum in 1/299,792,458 s.
The kilogram (kg) is a mass equal to the mass of the international prototype of the kilogram (a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in Sevres, near Paris).
A second (s) is a time equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
Ampere (A) - the strength of an unchanging current, which, when passing through two parallel straight conductors of infinite length and negligible cross-section, located in vacuum at a distance of 1 m from one another, creates a force between these conductors equal to 2 10-7 N for each meter length.
Kelvin (K) - 1/273.16 of the thermodynamic temperature of the triple point of water.
Mole (mol) - the amount of substance of a system containing as many structural elements as there are atoms in the nuclide | 2C with a mass of 0.012 kg.
Candela (cd) - luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540-1012 Hz, the luminous energy intensity of which in this direction is 1/683 W / sr.
Radian (rad) - the angle between two radii of a circle, the length of the arc between which is equal to the radius.
Steradian (sr) - a solid angle with a vertex in the center of the sphere, cutting out on the surface of the sphere an area equal to the area of a square with a side equal to the radius of the sphere.
To establish derived units, physical laws are used that connect them with basic units. For example, from the formula for uniform rectilinear motion v \u003d s / t (s is the distance traveled, i is time), the derived unit of speed is 1 m / s.
The dimension of a physical quantity is its expression in basic units. Proceeding, for example, from Newton's second law, we obtain that the dimension of the force
where M is the dimension of the mass; L is the dimension of length; T is the dimension of time.
The dimensions of both parts of physical equalities must be the same, since physical laws cannot depend on the choice of units of physical quantities.
Proceeding from this, it is possible to check the correctness of the obtained physical formulas (for example, when solving problems), as well as to establish the dimensions of physical quantities.
Physical foundations of mechanics
Mechanics is a part of physics that studies the patterns of mechanical movement and the causes that cause or change this movement. Mechanical movement is change over time relative position bodies or their parts.
The development of mechanics as a science begins in the 3rd century. BC e., when the ancient Greek scientist Archimedes (287 - 212 BC) formulated the law of equilibrium of the lever and the laws of equilibrium of floating bodies. The basic laws of mechanics were established by the Italian physicist and astronomer G. Galileo (1564 - 1642) and finally formulated by the English scientist I. Newton (1643 - 1727).
The mechanics of Galileo - Newton is called classical mechanics. It studies the laws of motion of macroscopic bodies whose velocities are small compared to the speed of light in a vacuum. The laws of motion of macroscopic bodies with velocities comparable to c are studied by relativistic mechanics based on the special theory of relativity formulated by A. Einstein (1879 - 1955). To describe the motion of microscopic bodies (individual atoms and elementary particles), the laws of classical mechanics are inapplicable - they are replaced by the laws of quantum mechanics.
In the first part of our course, we will deal with the mechanics of Galileo - Newton, i.e., we will consider the motion of macroscopic bodies with velocities that are much less than the speed c. AT classical mechanics the generally accepted concept of space and time, developed by I. Newton and dominating in natural science during the 17th - 19th centuries. The mechanics of Galileo - Newton considers space and time as objective forms of the existence of matter, but in isolation from each other and from the movement of material bodies, which corresponded to the level of knowledge of that time.
Since the mechanical description is visual and familiar, and with its help it is possible to explain many physical phenomena, in the 19th century. some physicists began to reduce all phenomena to mechanical ones. This view was in line with philosophical mechanistic materialism. Further development physics has shown, however, that many physical phenomena cannot be reduced to the simplest form of motion - mechanical. Mechanistic materialism had to give way to dialectical materialism, which considers more general types of motion of matter and takes into account all the diversity of the real world.
Mechanics is divided into three sections: 1) kinematics; 2) dynamics; 3) static.
Kinematics studies the motion of bodies without considering the causes that determine this motion.
Dynamics studies the laws of motion of bodies and the causes that cause or change this motion.
Statics studies the laws of equilibrium of a system of bodies. If the laws of motion of bodies are known, then the laws of equilibrium can also be established from them. Therefore, physics does not consider the laws of statics separately from the laws of dynamics.
11th ed., ster. - M.: 2006.- 560 p.
The textbook (9th edition, revised and expanded, 2004) consists of seven parts, which set out the physical foundations of mechanics, molecular physics and thermodynamics, electricity and magnetism, optics, quantum physics of atoms, molecules and solids, physics of the atomic nucleus and elementary particles. The question of combining mechanical and electromagnetic oscillations has been rationally resolved. The logical continuity and connection between classical and modern physics is established. Control questions and tasks for independent solution are given.
For students of engineering and technical specialties of higher educational institutions.
Format: pdf/zip (11- e ed., 2006, 560s.)
The size: 6 MB
Download:
RGhost
1. Physical foundations of mechanics.
Chapter 1. Elements of kinematics
§ 1. Models in mechanics. Reference system. Trajectory, path length, displacement vector
§ 2. Speed
§ 3. Acceleration and its components
§ 4. Angular velocity and angular acceleration
Tasks
Chapter 2. Dynamics of a material point and translational motion of a rigid body Force
§ 6. Newton's second law
§ 7. Newton's third law
§ 8. Forces of friction
§ 9. Law of conservation of momentum. Center of mass
§ 10. Equation of motion of a body of variable mass
Tasks
Chapter 3. Work and Energy
§ 11. Energy, work, power
§ 12. Kinetic and potential energies
§ 13. The law of conservation of energy
§ 14. Graphical representation of energy
§ 15. Impact of absolutely elastic and inelastic bodies
Tasks
Chapter 4
§ 16. Moment of inertia
§ 17. Kinetic energy rotation
§ 18. Moment of force. Equation of dynamics of rotational motion of a rigid body.
§ 19. Angular momentum and the law of its conservation
§ 20. Free axles. Gyroscope
§ 21. Deformations of a rigid body
Tasks
Chapter 5 Elements of field theory
§ 22. Kepler's laws. Law of gravity
§ 23. Gravity and weight. Weightlessness.. 48 y 24. The gravitational field and its strength
§ 25. Work in the gravitational field. Gravitational field potential
§ 26. Cosmic speeds
§ 27. Non-inertial frames of reference. Forces of inertia
Tasks
Chapter 6
§ 28. Pressure in liquid and gas
§ 29. Continuity equation
§ 30. Bernoull's equation and consequences from it
§ 31. Viscosity (internal friction). Laminar and turbulent regimes of fluid flow
§ 32. Methods for determining viscosity
§ 33. Movement of bodies in liquids and gases
Tasks
Chapter 7
§ 35. Postulates of the special (private) theory of relativity
§ 36. Lorentz transformations
§ 37. Consequences of the Lorentz transformations
§ 38. Interval between events
§ 39. Basic law of relativistic dynamics of a material point
§ 40. The law of the relationship of mass and energy
Tasks
2. Fundamentals of molecular physics and thermodynamics
Chapter 8
§ 41. Research methods. Experienced ideal gas laws
§ 42. Equation of Clapeyron - Mendeleev
§ 43. Basic equation of the molecular-kinetic theory of ideal gases
§ 44. Maxwell's law on the distribution of molecules of an ideal gas according to the velocities and energies of thermal motion
§ 45. Barometric formula. Boltzmann distribution
§ 46. Average number of collisions and average length free path of molecules
§ 47. Experimental substantiation of the molecular-kinetic theory
§ 48. Transport phenomena in thermodynamically nonequilibrium systems
§ 49. Vacuum and methods of obtaining it. Properties of ultra rarefied gases
Tasks
Chapter 9. Fundamentals of thermodynamics.
§ 50. Number of degrees of freedom of a molecule. The law of uniform distribution of energy over the degrees of freedom of molecules
§ 51. The first law of thermodynamics
§ 52. The work of a gas with a change in its volume
§ 53. Heat capacity
§ 54. Application of the first law of thermodynamics to isoprocesses
§ 55. Adiabatic process. Polytropic process
§ 57. Entropy, its statistical interpretation and connection with thermodynamic probability
§ 58. The second law of thermodynamics
§ 59. Heat engines and refrigerators Carnot cycle and its efficiency for an ideal gas
Tasks
Chapter 10
§ 61. Van der Waals equation
§ 62. Van der Waals isotherms and their analysis
§ 63. Internal energy of a real gas
§ 64. Joule-Thomson effect
§ 65. Liquefaction of gases
§ 66. Properties of liquids. Surface tension
§ 67. Wetting
§ 68. Pressure under the curved surface of a liquid
§ 69. Capillary phenomena
§ 70. Solid bodies. Mono- and polycrystals
§ 71. Types of crystalline solids
§ 72. Defects in crystals
§ 75. Phase transitions of the first and second kind
§ 76. State diagram. triple point
Tasks
3. Electricity and magnetism
Chapter 11
§ 77. The law of conservation of electric charge
§ 78. Coulomb's law
§ 79. Electrostatic field. Electrostatic field strength
§ 80. The principle of superposition of electrostatic fields. dipole field
§ 81. Gauss's theorem for an electrostatic field in vacuum
§ 82. Application of the Gauss theorem to the calculation of some electrostatic fields in vacuum
§ 83. Circulation of the electrostatic field intensity vector
§ 84. Potential of an electrostatic field
§ 85. Tension as a potential gradient. Equipotential surfaces
§ 86. Calculation of the potential difference from the field strength
§ 87. Types of dielectrics. Polarization of dielectrics
§ 88. Polarization. Field strength in a dielectric
§ 89. Electrical mixing. Gauss' theorem for an electrostatic field in a dielectric
§ 90. Conditions at the interface between two dielectric media
§ 91. Ferroelectrics
§ 92. Conductors in an electrostatic field
§ 93. Electric capacitance of a solitary conductor
§ 94. Capacitors
§ 95. Energy of a system of charges, a solitary conductor and a capacitor. Electrostatic field energy
Tasks
Chapter 12 electricity
§ 96. Electric current, strength and current density
§ 97. External forces. Electromotive force and tension
§ 98. Ohm's law. Conductor resistance
§ 99. Work and power. Joule-Lenz law
§ 100. Ohm's law for an inhomogeneous section of a chain
§ 101. Kirchhoff's rules for branched circuits
Tasks
Chapter 13
§ 104. Work function of electrons from metal
§ 105. Emission phenomena and their application
§ 106. Ionization of gases. Non-self-sustained gas discharge
§ 107. Independent gas discharge and its types
§ 108. Plasma and its properties
Tasks
Chapter 14
§ 109. Magnetic field and its characteristics
§ 110. Law Biot - Savart - Laplace and its application to the calculation of the magnetic field
§ 111. Ampère's law. Interaction of parallel currents
§ 112. Magnetic constant. Units of magnetic induction and magnetic field strength
§ 113. Magnetic field of a moving charge
§ 114. The action of a magnetic field on a moving charge
§ 115. Movement of charged particles in a magnetic field
§ 117. Hall effect
§ 118. Circulation of the vector B of a magnetic field in a vacuum
§ 119. Magnetic fields solenoid and toroid
§ 121. Work on moving a conductor and a current-carrying circuit in a magnetic field
Tasks
Chapter 15
§ 122. The phenomenon of electromagnetic induction (experiments of Faraday
§ 123. Faraday's law and its derivation from the law of conservation of energy
§ 125. Eddy currents (Foucault currents
§ 126. Inductance of the circuit. self induction
§ 127. Currents when opening and closing the circuit
§ 128. Mutual induction
§ 129. Transformers
§130. Magnetic field energy
dachas
Chapter 16
§ 131. Magnetic moments of electrons and atoms
§ 132. Dna- and paramagnetism
§ 133. Magnetization. Magnetic field in matter
§ 134. Conditions at the interface between two magnets
§ 135. Ferromagnets and their properties
§ 136. The nature of ferromagnetism
Tasks
Chapter 17
§ 137. Vortex electric field
§ 138. Displacement current
§ 139. Maxwell's equations for the electromagnetic field
4. Oscillations and waves.
Chapter 18
§ 140. Harmonic oscillations and their characteristics
§ 141. Mechanical harmonic vibrations
§ 142. Harmonic oscillator. Spring, physical and mathematical pendulums
§ 144. Addition of harmonic oscillations of the same direction and the same frequency. beats
§ 145. Addition of mutually perpendicular vibrations
§ 146. Differential equation free damped oscillations (mechanical and electromagnetic) and its solution. Self-oscillations
§ 147. Differential equation of forced oscillations (mechanical and electromagnetic) and its solution
§ 148. Amplitude and phase of forced oscillations (mechanical and electromagnetic). Resonance
§ 149. Alternating current
§ 150. Stress resonance
§ 151. Resonance of currents
§ 152. Power released in the alternating current circuit
Tasks
Chapter 19 elastic waves.
§ 153. Wave processes. Longitudinal and transverse waves
§ 154. The equation of a traveling wave. phase speed. wave equation
§ 155. The principle of superposition. group speed
§ 156. Interference of waves
§ 157. standing waves
§ 158. Sound waves
§ 159. Doppler effect in acoustics
§ 160. Ultrasound and its application
Tasks
Chapter 20
§ 161. Experimental production of electromagnetic waves
§ 162. Differential equation of an electromagnetic wave
§ 163. Energy of electromagnetic waves. Electromagnetic field impulse
§ 164. Radiation of a dipole. Application of electromagnetic waves
Tasks
5. Optics. Quantum nature of radiation.
Chapter 21. Elements of geometric and electronic optics.
§ 165. Basic laws of optics. total reflection
§ 166. Thin lenses. Image of objects using lenses
§ 167. Aberrations (errors) of optical systems
§ 168. Basic photometric quantities and their units
Tasks
Chapter 22
§ 170. Development of ideas about the nature of light
§ 171. Coherence and monochromaticity of light waves
§ 172. Interference of light
§ 173. Methods for observing the interference of light
§ 174. Interference of light in thin films
§ 175. Application of light interference
Chapter 23
§ 177. Method of Fresnel zones. Rectilinear propagation of light
§ 178. Fresnel diffraction by a round hole and a disk
§ 179. Fraunhofer diffraction by one slit
§ 180. Fraunhofer diffraction on a diffraction grating
§ 181. Spatial lattice. light scattering
§ 182. Diffraction on a spatial lattice. Wolfe-Braggs formula
§ 183. Resolution of optical instruments
§ 184. The concept of holography
Tasks
Chapter 24. Interaction of electromagnetic waves with matter.
§ 185. Dispersion of light
§ 186. Electronic theory of light dispersion
§ 188. Doppler effect
§ 189. Vavilov-Cherenkov radiation
Tasks
Chapter 25
§ 190. Natural and polarized light
§ 191. Polarization of light during reflection and refraction at the boundary of two dielectrics
§ 192. Double refraction
§ 193. Polarizing prisms and polaroids
§ 194. Analysis of polarized light
§ 195. Artificial optical anisotropy
§ 196. Rotation of the plane of polarization
Tasks
Chapter 26. Quantum nature of radiation.
§ 197. Thermal radiation and its characteristics.
§ 198. Kirchhoff's law
§ 199. Stefan-Boltzmann laws and Wien displacements
§ 200. Formulas of Rayleigh-Jeans and Planck.
§ 201. Optical pyrometry. Thermal light sources
§ 203. Einstein's equation for the external photoelectric effect. Experimental confirmation of the quantum properties of light
§ 204. Application of the photoelectric effect
§ 205. Mass and momentum of a photon. light pressure
§ 206. The Compton effect and its elementary theory
§ 207. Unity of corpuscular and wave properties of electromagnetic radiation
Tasks
6. Elements of quantum physics
Chapter 27. Bohr's theory of the hydrogen atom.
§ 208. Models of the atom by Thomson and Rutherford
§ 209. Line spectrum of the hydrogen atom
§ 210. Bohr's postulates
§ 211. Frank's experiments in Hertz
§ 212. The spectrum of the hydrogen atom according to Bohr
Tasks
Chapter 28
§ 213. Corpuscular-wave dualism of the properties of matter
§ 214. Some properties of de Broglie waves
§ 215. Uncertainty relation
§ 216. Wave function and its statistical meaning
§ 217. The general Schrödinger equation. Schrödinger equation for stationary states
§ 218. The principle of causality in quantum mechanics
§ 219. Motion of a free particle
§ 222. Linear harmonic oscillator in quantum mechanics
Tasks
Chapter 29
§ 223. Hydrogen atom in quantum mechanics
§ 224. L-state of an electron in a hydrogen atom
§ 225. Electron spin. Spin quantum number
§ 226. The principle of indistinguishability of identical particles. Fermions and bosons
Mendeleev
§ 229. X-ray spectra
§ 231. Molecular spectra. Raman scattering of light
§ 232. Absorption, spontaneous and stimulated emission
(lasers
Tasks
Chapter 30
§ 234. Quantum statistics. phase space. distribution function
§ 235. The concept of Bose-Einstein and Fermi-Dirac quantum statistics
§ 236. Degenerate electron gas in metals
§ 237. The concept of the quantum theory of heat capacity. Phonols
§ 238. Conclusions of the quantum theory of electrical conductivity of metals
! Joseph effect
Tasks
Chapter 31
§ 240. The concept of the zone theory of solids
§ 241. Metals, dielectrics and semiconductors according to zone theory
§ 242. Intrinsic conductivity of semiconductors
§ 243. Impurity conductivity of semiconductors
§ 244. Photoconductivity of semiconductors
§ 245. Luminescence of solids
§ 246. Contact of two metals according to the band theory
§ 247. Thermoelectric phenomena and their application
§ 248. Rectification at a metal-semiconductor contact
§ 250. Semiconductor diodes and triodes (transistors
Tasks
7. Elements of the physics of the atomic nucleus and elementary particles.
Chapter 32
§ 252. Mass defect and binding energy, nuclei
§ 253. Spin of the nucleus and its magnetic moment
§ 254. Nuclear forces. Kernel Models
§ 255. Radioactive radiation and its types Displacement rules
§ 257. Regularities of a-decay
§ 259. Gamma radiation and its properties.
§ 260. Resonant absorption of y-radiation (Mössbauer effect
§ 261. Methods of observation and registration of radioactive radiation and particles
§ 262. Nuclear reactions and their main types
§ 263. Positron. /> -Decomposition. Electronic capture
§ 265. Nuclear fission reaction
Section 266 Chain reaction division
§ 267. The concept of nuclear energy
§ 268. The reaction of the fusion of atomic nuclei. The problem of controlled thermonuclear reactions
Tasks
Chapter 33
§ 269. Cosmic radiation
§ 270. Muons and their properties
§ 271. Mesons and their properties
§ 272. Types of interactions of elementary particles
§ 273. Particles and antiparticles
§ 274. Hyperons. Strangeness and parity of elementary particles
§ 275. Classification of elementary particles. Quarks
Tasks
Basic laws and formulas
1. Physical foundations of mechanics
2. Fundamentals of molecular physics and thermodynamics
4. Oscillations and waves
5. Optics. The quantum nature of radiation
6. Elements of quantum physics of atoms, molecules and solids
7. Elements of the physics of the atomic nucleus and elementary particles
Subject index
11th ed., ster. - M.: 2006.- 560 p.
The textbook (9th edition, revised and expanded, 2004) consists of seven parts, which outline the physical foundations of mechanics, molecular physics and thermodynamics, electricity and magnetism, optics, quantum physics of atoms, molecules and solids, atomic physics nucleus and elementary particles. The question of combining mechanical and electromagnetic oscillations has been rationally resolved. The logical continuity and connection between classical and modern physics is established. Control questions and tasks for independent solution are given.
For students of engineering and technical specialties of higher educational institutions.
Format: pdf/zip (11- e ed., 2006, 560s.)
The size: 6 MB
Download:
RGhost
1. Physical foundations of mechanics.
Chapter 1. Elements of kinematics
§ 1. Models in mechanics. Reference system. Trajectory, path length, displacement vector
§ 2. Speed
§ 3. Acceleration and its components
§ 4. Angular velocity and angular acceleration
Tasks
Chapter 2. Dynamics of a material point and translational motion of a rigid body Force
§ 6. Newton's second law
§ 7. Newton's third law
§ 8. Forces of friction
§ 9. Law of conservation of momentum. Center of mass
§ 10. Equation of motion of a body of variable mass
Tasks
Chapter 3. Work and Energy
§ 11. Energy, work, power
§ 12. Kinetic and potential energies
§ 13. The law of conservation of energy
§ 14. Graphical representation of energy
§ 15. Impact of absolutely elastic and inelastic bodies
Tasks
Chapter 4
§ 16. Moment of inertia
§ 17. Kinetic energy of rotation
§ 18. Moment of force. Equation of dynamics of rotational motion of a rigid body.
§ 19. Angular momentum and the law of its conservation
§ 20. Free axles. Gyroscope
§ 21. Deformations of a rigid body
Tasks
Chapter 5 Elements of field theory
§ 22. Kepler's laws. Law of gravity
§ 23. Gravity and weight. Weightlessness.. 48 y 24. The gravitational field and its strength
§ 25. Work in the gravitational field. Gravitational field potential
§ 26. Cosmic speeds
§ 27. Non-inertial frames of reference. Forces of inertia
Tasks
Chapter 6
§ 28. Pressure in liquid and gas
§ 29. Continuity equation
§ 30. Bernoull's equation and consequences from it
§ 31. Viscosity (internal friction). Laminar and turbulent regimes of fluid flow
§ 32. Methods for determining viscosity
§ 33. Movement of bodies in liquids and gases
Tasks
Chapter 7
§ 35. Postulates of the special (private) theory of relativity
§ 36. Lorentz transformations
§ 37. Consequences of the Lorentz transformations
§ 38. Interval between events
§ 39. Basic law of relativistic dynamics of a material point
§ 40. The law of the relationship of mass and energy
Tasks
2. Fundamentals of molecular physics and thermodynamics
Chapter 8
§ 41. Research methods. Experienced ideal gas laws
§ 42. Equation of Clapeyron - Mendeleev
§ 43. Basic equation of the molecular-kinetic theory of ideal gases
§ 44. Maxwell's law on the distribution of molecules of an ideal gas according to the velocities and energies of thermal motion
§ 45. Barometric formula. Boltzmann distribution
§ 46. Average number of collisions and mean free path of molecules
§ 47. Experimental substantiation of the molecular-kinetic theory
§ 48. Transport phenomena in thermodynamically nonequilibrium systems
§ 49. Vacuum and methods of obtaining it. Properties of ultra rarefied gases
Tasks
Chapter 9. Fundamentals of thermodynamics.
§ 50. Number of degrees of freedom of a molecule. The law of uniform distribution of energy over the degrees of freedom of molecules
§ 51. The first law of thermodynamics
§ 52. The work of a gas with a change in its volume
§ 53. Heat capacity
§ 54. Application of the first law of thermodynamics to isoprocesses
§ 55. Adiabatic process. Polytropic process
§ 57. Entropy, its statistical interpretation and connection with thermodynamic probability
§ 58. The second law of thermodynamics
§ 59. Heat engines and refrigerators Carnot cycle and its efficiency for an ideal gas
Tasks
Chapter 10
§ 61. Van der Waals equation
§ 62. Van der Waals isotherms and their analysis
§ 63. Internal energy of a real gas
§ 64. Joule-Thomson effect
§ 65. Liquefaction of gases
§ 66. Properties of liquids. Surface tension
§ 67. Wetting
§ 68. Pressure under the curved surface of a liquid
§ 69. Capillary phenomena
§ 70. Solid bodies. Mono- and polycrystals
§ 71. Types of crystalline solids
§ 72. Defects in crystals
§ 75. Phase transitions of the first and second kind
§ 76. State diagram. triple point
Tasks
3. Electricity and magnetism
Chapter 11
§ 77. The law of conservation of electric charge
§ 78. Coulomb's law
§ 79. Electrostatic field. Electrostatic field strength
§ 80. The principle of superposition of electrostatic fields. dipole field
§ 81. Gauss's theorem for an electrostatic field in vacuum
§ 82. Application of the Gauss theorem to the calculation of some electrostatic fields in vacuum
§ 83. Circulation of the electrostatic field intensity vector
§ 84. Potential of an electrostatic field
§ 85. Tension as a potential gradient. Equipotential surfaces
§ 86. Calculation of the potential difference from the field strength
§ 87. Types of dielectrics. Polarization of dielectrics
§ 88. Polarization. Field strength in a dielectric
§ 89. Electrical mixing. Gauss' theorem for an electrostatic field in a dielectric
§ 90. Conditions at the interface between two dielectric media
§ 91. Ferroelectrics
§ 92. Conductors in an electrostatic field
§ 93. Electric capacitance of a solitary conductor
§ 94. Capacitors
§ 95. Energy of a system of charges, a solitary conductor and a capacitor. Electrostatic field energy
Tasks
Chapter 12
§ 96. Electric current, strength and current density
§ 97. External forces. Electromotive force and voltage
§ 98. Ohm's law. Conductor resistance
§ 99. Work and power. Joule-Lenz law
§ 100. Ohm's law for an inhomogeneous section of a chain
§ 101. Kirchhoff's rules for branched circuits
Tasks
Chapter 13
§ 104. Work function of electrons from metal
§ 105. Emission phenomena and their application
§ 106. Ionization of gases. Non-self-sustained gas discharge
§ 107. Independent gas discharge and its types
§ 108. Plasma and its properties
Tasks
Chapter 14
§ 109. Magnetic field and its characteristics
§ 110. Law Biot - Savart - Laplace and its application to the calculation of the magnetic field
§ 111. Ampère's law. Interaction of parallel currents
§ 112. Magnetic constant. Units of magnetic induction and magnetic field strength
§ 113. Magnetic field of a moving charge
§ 114. The action of a magnetic field on a moving charge
§ 115. Movement of charged particles in a magnetic field
§ 117. Hall effect
§ 118. Circulation of the vector B of a magnetic field in a vacuum
§ 119. Magnetic fields of the solenoid and toroid
§ 121. Work on moving a conductor and a current-carrying circuit in a magnetic field
Tasks
Chapter 15
§ 122. The phenomenon of electromagnetic induction (experiments of Faraday
§ 123. Faraday's law and its derivation from the law of conservation of energy
§ 125. Eddy currents (Foucault currents
§ 126. Inductance of the circuit. self induction
§ 127. Currents when opening and closing the circuit
§ 128. Mutual induction
§ 129. Transformers
§130. Magnetic field energy
dachas
Chapter 16
§ 131. Magnetic moments of electrons and atoms
§ 132. Dna- and paramagnetism
§ 133. Magnetization. Magnetic field in matter
§ 134. Conditions at the interface between two magnets
§ 135. Ferromagnets and their properties
§ 136. The nature of ferromagnetism
Tasks
Chapter 17
§ 137. Vortex electric field
§ 138. Displacement current
§ 139. Maxwell's equations for the electromagnetic field
4. Oscillations and waves.
Chapter 18
§ 140. Harmonic oscillations and their characteristics
§ 141. Mechanical harmonic vibrations
§ 142. Harmonic oscillator. Spring, physical and mathematical pendulums
§ 144. Addition of harmonic oscillations of the same direction and the same frequency. beats
§ 145. Addition of mutually perpendicular vibrations
§ 146. Differential equation of free damped oscillations (mechanical and electromagnetic) and its solution. Self-oscillations
§ 147. Differential equation of forced oscillations (mechanical and electromagnetic) and its solution
§ 148. Amplitude and phase of forced oscillations (mechanical and electromagnetic). Resonance
§ 149. Alternating current
§ 150. Stress resonance
§ 151. Resonance of currents
§ 152. Power released in the alternating current circuit
Tasks
Chapter 19
§ 153. Wave processes. Longitudinal and transverse waves
§ 154. The equation of a traveling wave. phase speed. wave equation
§ 155. The principle of superposition. group speed
§ 156. Interference of waves
§ 157. Standing waves
§ 158. Sound waves
§ 159. Doppler effect in acoustics
§ 160. Ultrasound and its application
Tasks
Chapter 20
§ 161. Experimental production of electromagnetic waves
§ 162. Differential equation of an electromagnetic wave
§ 163. Energy of electromagnetic waves. Electromagnetic field impulse
§ 164. Radiation of a dipole. Application of electromagnetic waves
Tasks
5. Optics. Quantum nature of radiation.
Chapter 21. Elements of geometric and electronic optics.
§ 165. Basic laws of optics. total reflection
§ 166. Thin lenses. Image of objects using lenses
§ 167. Aberrations (errors) of optical systems
§ 168. Basic photometric quantities and their units
Tasks
Chapter 22
§ 170. Development of ideas about the nature of light
§ 171. Coherence and monochromaticity of light waves
§ 172. Interference of light
§ 173. Methods for observing the interference of light
§ 174. Interference of light in thin films
§ 175. Application of light interference
Chapter 23
§ 177. Method of Fresnel zones. Rectilinear propagation of light
§ 178. Fresnel diffraction by a round hole and a disk
§ 179. Fraunhofer diffraction by one slit
§ 180. Fraunhofer diffraction on a diffraction grating
§ 181. Spatial lattice. light scattering
§ 182. Diffraction on a spatial lattice. Wolfe-Braggs formula
§ 183. Resolution of optical instruments
§ 184. The concept of holography
Tasks
Chapter 24. Interaction of electromagnetic waves with matter.
§ 185. Dispersion of light
§ 186. Electronic theory of light dispersion
§ 188. Doppler effect
§ 189. Vavilov-Cherenkov radiation
Tasks
Chapter 25
§ 190. Natural and polarized light
§ 191. Polarization of light during reflection and refraction at the boundary of two dielectrics
§ 192. Double refraction
§ 193. Polarizing prisms and polaroids
§ 194. Analysis of polarized light
§ 195. Artificial optical anisotropy
§ 196. Rotation of the plane of polarization
Tasks
Chapter 26. Quantum nature of radiation.
§ 197. Thermal radiation and its characteristics.
§ 198. Kirchhoff's law
§ 199. Stefan-Boltzmann laws and Wien displacements
§ 200. Formulas of Rayleigh-Jeans and Planck.
§ 201. Optical pyrometry. Thermal light sources
§ 203. Einstein's equation for the external photoelectric effect. Experimental confirmation of the quantum properties of light
§ 204. Application of the photoelectric effect
§ 205. Mass and momentum of a photon. light pressure
§ 206. The Compton effect and its elementary theory
§ 207. Unity of corpuscular and wave properties of electromagnetic radiation
Tasks
6. Elements of quantum physics
Chapter 27. Bohr's theory of the hydrogen atom.
§ 208. Models of the atom by Thomson and Rutherford
§ 209. Line spectrum of the hydrogen atom
§ 210. Bohr's postulates
§ 211. Frank's experiments in Hertz
§ 212. The spectrum of the hydrogen atom according to Bohr
Tasks
Chapter 28
§ 213. Corpuscular-wave dualism of the properties of matter
§ 214. Some properties of de Broglie waves
§ 215. Uncertainty relation
§ 216. Wave function and its statistical meaning
§ 217. The general Schrödinger equation. Schrödinger equation for stationary states
§ 218. The principle of causality in quantum mechanics
§ 219. Motion of a free particle
§ 222. Linear harmonic oscillator in quantum mechanics
Tasks
Chapter 29
§ 223. Hydrogen atom in quantum mechanics
§ 224. L-state of an electron in a hydrogen atom
§ 225. Electron spin. Spin quantum number
§ 226. The principle of indistinguishability of identical particles. Fermions and bosons
Mendeleev
§ 229. X-ray spectra
§ 231. Molecular spectra. Raman scattering of light
§ 232. Absorption, spontaneous and stimulated emission
(lasers
Tasks
Chapter 30
§ 234. Quantum statistics. phase space. distribution function
§ 235. The concept of Bose-Einstein and Fermi-Dirac quantum statistics
§ 236. Degenerate electron gas in metals
§ 237. The concept of the quantum theory of heat capacity. Phonols
§ 238. Conclusions of the quantum theory of electrical conductivity of metals
! Joseph effect
Tasks
Chapter 31
§ 240. The concept of the zone theory of solids
§ 241. Metals, dielectrics and semiconductors according to zone theory
§ 242. Intrinsic conductivity of semiconductors
§ 243. Impurity conductivity of semiconductors
§ 244. Photoconductivity of semiconductors
§ 245. Luminescence of solids
§ 246. Contact of two metals according to the band theory
§ 247. Thermoelectric phenomena and their application
§ 248. Rectification at a metal-semiconductor contact
§ 250. Semiconductor diodes and triodes (transistors
Tasks
7. Elements of the physics of the atomic nucleus and elementary particles.
Chapter 32
§ 252. Mass defect and binding energy, nuclei
§ 253. Spin of the nucleus and its magnetic moment
§ 254. Nuclear forces. Kernel Models
§ 255. Radioactive radiation and its types Displacement rules
§ 257. Regularities of a-decay
§ 259. Gamma radiation and its properties.
§ 260. Resonant absorption of y-radiation (Mössbauer effect
§ 261. Methods of observation and registration of radioactive radiation and particles
§ 262. Nuclear reactions and their main types
§ 263. Positron. /> -Decomposition. Electronic capture
§ 265. Nuclear fission reaction
§ 266. Chain reaction of fission
§ 267. The concept of nuclear energy
§ 268. The reaction of the fusion of atomic nuclei. The problem of controlled thermonuclear reactions
Tasks
Chapter 33
§ 269. Cosmic radiation
§ 270. Muons and their properties
§ 271. Mesons and their properties
§ 272. Types of interactions of elementary particles
§ 273. Particles and antiparticles
§ 274. Hyperons. Strangeness and parity of elementary particles
§ 275. Classification of elementary particles. Quarks
Tasks
Basic laws and formulas
1. Physical foundations of mechanics
2. Fundamentals of molecular physics and thermodynamics
4. Oscillations and waves
5. Optics. The quantum nature of radiation
6. Elements of quantum physics of atoms, molecules and solids
7. Elements of the physics of the atomic nucleus and elementary particles
Subject index
Reviewer: Professor of the Department of Physics named after A. M. Fabrikant of the Moscow Power Engineering Institute (Technical University) V. A. Kasyanov
ISBN 5-06-003634-0 State Unitary Enterprise "Publishing House" graduate School", 2001
The original layout of this publication is the property of the Vysshaya Shkola publishing house, and its reproduction (reproduction) in any way without the consent of the publisher is prohibited.
Foreword
The textbook is written in accordance with the current program of the physics course for engineering and technical specialties of higher educational institutions and is intended for students of higher technical educational institutions of full-time education with a limited number of hours in physics, with the possibility of its use in the evening and correspondence forms of education.
The small volume of the textbook is achieved through careful selection and concise presentation of the material.
The book consists of seven parts. The first part provides a systematic presentation physical foundations classical mechanics, as well as elements of the special (private) theory of relativity. The second part is devoted to the basics of molecular physics and thermodynamics. The third part deals with electrostatics, direct electric current and electromagnetism. In the fourth part, devoted to the exposition of the theory of oscillations and will, mechanical and electromagnetic oscillations are considered in parallel, their similarities and differences are indicated, and the physical processes occurring during the corresponding oscillations are compared. The fifth part deals with the elements of geometric and electronic optics, wave optics and the quantum nature of radiation. The sixth part is devoted to the elements of quantum physics of atoms, molecules and solids. The seventh part outlines the elements of the physics of the atomic nucleus and elementary particles.
The presentation of the material is carried out without cumbersome mathematical calculations, due attention is paid to the physical essence of phenomena and the concepts and laws that describe them, as well as to the continuity of modern and classical physics. All biographical data are given according to the book by Yu. A. Khramov "Physics" (M .: Nauka, 1983).
For the designation of vector quantities in all figures and in the text, bold type is used, except for the quantities indicated by Greek letters, which, for technical reasons, are typed in the text in light type with an arrow.
The author expresses his deep gratitude to colleagues and readers, whose kind remarks and suggestions contributed to the improvement of the book. I am especially grateful to Professor V. A. Kasyanov for reviewing the textbook and for his comments.
Introduction
The subject of physics and its relationship with other sciences
The world around you, everything that exists around you and that we discover through sensations, is matter.
Motion is an integral property of matter and the form of its existence. Movement in the broad sense of the word is all kinds of changes in matter - from simple displacement to the most complex processes of thinking.
Various forms of motion of matter are studied by various sciences, including physics. The subject of physics, as, indeed, of any science, can be revealed only as it is presented in detail. It is rather difficult to give a strict definition of the subject of physics, because the boundaries between physics and a number of related disciplines are arbitrary. At this stage of development, it is impossible to keep the definition of physics only as a science of nature.
Academician A.F. Ioffe (1880-1960; Russian physicist)* defined physics as a science that studies the general properties and laws of motion of matter and field. It is now generally accepted that all interactions are carried out by means of fields, such as gravitational, electromagnetic, nuclear force fields. The field, along with matter, is one of the forms of existence of matter. The inextricable connection between the field and matter, as well as the difference in their properties, will be considered as the course progresses.
*All data are given according to Yu. A. Khramov's biographical guide "Physics" (M.: Nauka, 1983).
Physics is the science of the simplest and at the same time the most general forms of the motion of matter and their mutual transformations. The forms of matter motion studied by physics (mechanical, thermal, etc.) are present in all higher and more complex forms of matter motion (chemical, biological, etc.). Therefore they, being the simplest, are at the same time the most general forms of motion of matter. Higher and more complex forms of the motion of matter are the subject of study of other sciences (chemistry, biology, etc.).
Physics is closely related to the natural sciences. This close connection of physics with other branches of natural science, as academician S. I. Vavilov (1891-1955; Russian physicist and public figure) noted, led to the fact that physics has grown into astronomy, geology, chemistry, biology and other natural sciences with the deepest roots. . As a result, a number of new related disciplines were formed, such as astrophysics, biophysics, etc.
Physics is also closely connected with technology, and this connection has a two-way character. Physics grew out of the needs of technology (the development of mechanics among the ancient Greeks, for example, was caused by the demands of construction and military equipment of that time), and technology, in turn, determines the direction of physical research (for example, at one time the task of creating the most economical heat engines caused a stormy development of thermodynamics). On the other hand, the technical level of production depends on the development of physics. Physics is the basis for the creation of new branches of technology (electronic technology, nuclear technology, etc.).
The rapid pace of development of physics, its growing ties with technology indicate the significant role of the physics course in the technical college: this is the fundamental basis for the theoretical training of an engineer, without which his successful activity is impossible.
Units of physical quantities
The main method of research in physics is experience - based on practice, sensory-empirical knowledge of objective reality, i.e., observation of the studied phenomena under precisely taken into account conditions that make it possible to monitor the course of phenomena and repeatedly reproduce it when these conditions are repeated.
Hypotheses are put forward to explain the experimental facts. Hypothesis- this is a scientific assumption put forward to explain a phenomenon and requiring experimental verification and theoretical justification in order to become a reliable scientific theory.
As a result of the generalization of experimental facts, as well as the results of people's activities, physical laws- stable repeating objective patterns that exist in nature. The most important laws establish a relationship between physical quantities, for which it is necessary to measure these quantities. The measurement of a physical quantity is an action performed with the help of measuring instruments to find the value of a physical quantity in accepted units. Units of physical quantities can be chosen arbitrarily, but then there will be difficulties in comparing them. Therefore, it is advisable to introduce a system of units covering the units of all physical quantities.
To build a system of units, units are arbitrarily chosen for several independent physical quantities. These units are called basic. The remaining quantities and their units are derived from the laws connecting these quantities and their units with the main ones. They're called derivatives.
At present, the International System (SI) is mandatory for use in scientific and educational literature, which is based on seven basic units - meter, kilogram, second, ampere, kelvin, mole, candela - and two additional ones - radians and steradians.
Meter(m) is the length of the path traveled by light in vacuum in 1/299792458 s.
Kilogram(kg) - a mass equal to the mass of the international prototype of the kilogram (a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in Sevres, near Paris).
Second(s) - time equal to 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
Ampere(A) - the strength of an unchanging current, which, when passing through two parallel rectilinear conductors of infinite length and negligible cross section, located in vacuum at a distance of 1 m from one another, will create a force between these conductors equal to 210 - 7 N for each meter length.
Kelvin(K) - 1/273.16 part of the thermodynamic temperature of the triple point of water.
mole(mol) - the amount of substance of a system containing as many structural elements as there are atoms in the 12 C nuclide with a mass of 0.012 kg.
Candela(cd) - luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 54010 12 Hz, the luminous energy intensity of which in this direction is 1/683 W/sr.
Radian(rad) - the angle between two radii of a circle, the length of the arc between which is equal to the radius.
Steradian(cp) - a solid angle with a vertex in the center of the sphere, cutting out on the surface of the sphere an area equal to the area of a square with a side equal to the radius of the sphere.
To establish derived units, physical laws are used that connect them with basic units. For example, from the formula for uniform rectilinear motion v= s/ t (s – distance traveled, t - time) the derived unit of velocity is 1 m/s.
1 PHYSICAL FOUNDATIONS OF MECHANICS
Chapter 1 Elements of kinematics
§ 1. Models in mechanics. Reference system. Trajectory, path length, displacement vector
Mechanics- a part of physics that studies the laws of mechanical movement and the causes that cause or change this movement. mechanical movement- this is a change over time in the relative position of bodies or their parts.
The development of mechanics as a science begins in the 3rd century. BC e., when the ancient Greek scientist Archimedes (287-212 BC) formulated the law of equilibrium of the lever and the laws of equilibrium of floating bodies. The basic laws of mechanics were established by the Italian physicist and astronomer G. Galileo (1564-1642) and finally formulated by the English scientist I. Newton (1643-1727).
Galileo-Newtonian mechanics is called classical mechanics. It studies the laws of motion of macroscopic bodies whose velocities are small compared to the speed of light c in vacuum. The laws of motion of macroscopic bodies with velocities comparable to the speed c are studied relativistic mechanics, based on special theory of relativity, formulated by A. Einstein (1879-1955). To describe the motion of microscopic bodies (individual atoms and elementary particles), the laws of classical mechanics are inapplicable - they are replaced by the laws whale mechanics.
In the first part of our course, we will study Galileo-Newton mechanics, i.e. consider the motion of macroscopic bodies with velocities much lower than the speed c. In classical mechanics, the concept of space and time, developed by I. Newton and dominating natural science during the 17th-19th centuries, is generally accepted. The mechanics of Galileo-Newton considers space and time as objective forms of the existence of matter, but in isolation from each other and from the movement of material bodies, which corresponded to the level of knowledge of that time.
Mechanics is divided into three sections: I) kinematics; 2) dynamics; 3) static.
Kinematics studies the motion of bodies without considering the causes that determine this motion.
Dynamics studies the laws of motion of bodies and the causes that cause or change this motion.
Statics studies the laws of equilibrium of a system of bodies. If the laws of motion of bodies are known, then the laws of equilibrium can also be established from them. Therefore, physics does not consider the laws of statics separately from the laws of dynamics.
Mechanics to describe the movement of bodies, depending on the conditions of specific tasks, uses different physical models. The simplest model is material point- a body with a mass, the dimensions of which in this problem can be neglected. The concept of a material point is abstract, but its introduction facilitates the solution of practical problems. For example, when studying the movement of planets in orbits around the Sun, one can take them for material points.
An arbitrary macroscopic body or system of bodies can be mentally divided into small interacting parts, each of which is considered as a material point. Then the study of the motion of an arbitrary system of bodies is reduced to the study of a system of material points. In mechanics, one first studies the motion of one material point, and then proceeds to study the motion of a system of material points.
Under the influence of bodies on each other, bodies can be deformed, i.e., change their shape and size. Therefore, another model is introduced in mechanics - an absolutely rigid body. An absolutely rigid body is a body that under no circumstances can be deformed and under all conditions the distance between two points (or more precisely between two particles) of this body remains constant.
Any motion of a rigid body can be represented as a combination of translational and rotational motions. Translational motion is a motion in which any straight line rigidly connected to the moving body remains parallel to its original position. Rotational motion is a motion in which all points of the body move along circles whose centers lie on the same straight line, called the axis of rotation.
The movement of bodies occurs in space and time. Therefore, in order to describe the motion of a material point, it is necessary to know in what places in space this point was and at what moments in time it passed one or another position.
The position of a material point is determined in relation to some other, arbitrarily chosen body, called the reference body. A reference system is associated with it - a set of coordinate systems and clocks associated with the reference body. In the most commonly used Cartesian coordinate system, the position of a point BUT at a given time with respect to this system is characterized by three coordinates x, y and z or radius vector r drawn from the origin of the coordinate system to given point(Fig. 1).
When a material point moves, its coordinates change over time. In the general case, its motion is determined by the scalar equations
x = x(t), y = y(t), z = z(t), (1.1)
equivalent to the vector equation
r = r(t). (1.2)
Equations (1.1) and, accordingly, (1.2) are called kinematic equations movements material point.
The number of independent coordinates that completely determine the position of a point in space is called number of degrees of freedom. If a material point moves freely in space, then, as already mentioned, it has three degrees of freedom (coordinates x, y and z), if it moves along some surface, then by two degrees of freedom, if along some line, then by one degree of freedom.
Excluding t in equations (1.1) and (1.2), we obtain the equation for the trajectory of the material point. Trajectory motion of a material point - a line described by this point in space. Depending on the shape of the trajectory, the movement can be rectilinear or curvilinear.
Consider the motion of a material point along an arbitrary trajectory (Fig. 2). Let's start counting the time from the moment when the point was in the position BUT. Trajectory section length AB, passed by a material point from the moment the time began, is called path length s and is scalar function time: s = s(t) .Vector r = r -r 0 , drawn from the initial position of the moving point to its position at a given time (increment of the radius-vector of the point over the considered time interval), is called moving.
With rectilinear motion, the displacement vector coincides with the corresponding section of the trajectory and the displacement modulus | r| equal to the distance traveled s.
§ 2. Speed
To characterize the movement of a material point, a vector quantity is introduced - the speed, which is defined as rapidity movement, as well as direction at this point in time.
Let the material point move along some curvilinear trajectory so that at the moment of time t it corresponds to the radius vector r 0 (Fig. 3). For a short period of time t point will pass the path s and will receive an elementary (infinitely small) displacement r.
Average speed vector is the ratio of the increment r of the radius-vector of the point to the time interval t:
(2.1)
The direction of the average velocity vector coincides with the direction of r. With an unlimited decrease in t average speed tends to a limiting value, which is called instantaneous speed v:
The instantaneous velocity v, therefore, is a vector quantity equal to the first derivative of the radius-vector of the moving point with respect to time. Since the secant coincides with the tangent in the limit, the velocity vector v is directed tangentially to the trajectory in the direction of motion (Fig. 3). As decreases t path s will increasingly approach |r|, so the module of instantaneous velocity
Thus, the module of instantaneous speed is equal to the first derivative of the path with respect to time:
(2.2)
At uneven movement - the instantaneous velocity modulus changes over time. In this case, use the scalar value v - average speed uneven movement:
From fig. 3 it follows that v> |v|, because s> |r|, and only in the case of rectilinear motion
If the expression d s = v d t (see formula (2.2)) integrate over time within the range of t before t + t, then we find the length of the path traveled by the point in time t:
(2.3)
When uniform motion the numerical value of the instantaneous speed is constant; then expression (2.3) takes the form
The length of the path traveled by a point in the time interval from t 1 to t 2 is given by the integral
§ 3. Acceleration and its components
In the case of uneven motion, it is important to know how quickly the speed changes over time. The physical quantity characterizing the rate of change of speed in absolute value and direction is acceleration.
Consider flat Movement, those. movement in which all parts of the trajectory of a point lie in the same plane. Let the vector v define the speed of the point BUT at the time t. During the time t moving point moved to position AT and acquired a speed different from v both in modulus and direction and equal to v 1 = v + v. Move the vector v 1 to the point BUT and find v (Fig. 4).
Average acceleration uneven movement in the interval from t before t + t called a vector quantity equal to the ratio of the change in speed v to the time interval t
Instant acceleration a (acceleration) of a material point at time t there will be a limit of average acceleration:
Thus, the acceleration a is a vector quantity equal to the first derivative of the velocity with respect to time.
We decompose the vector v into two components. For this, from the point BUT(Fig. 4) in the direction of the velocity v, we plot the vector 
, modulo equal to v 1 . It is obvious that the vector 
,
equal 
, determines the change in speed over time t
modulo:
. The second component 
vector v characterizes the change in speed over time t
towards.
Tangential component of acceleration
i.e., equal to the first time derivative of the modulus of speed, thereby determining the rate of change of speed modulo.
Let's find the second component of acceleration. Let's say the point AT close enough to the point BUT, so s can be considered an arc of a circle of some radius r, not much different from a chord AB. Then from the similarity of triangles AOB and EAD follows v n /AB = v 1 /r, but since AB = vt, then
In the limit at 
we get 
.
Since , the angle EAD tends to zero, and since the triangle EAD isosceles, then the angle ADE between v and v n tends to be straight. Therefore, for the vectors v n and v are mutually perpendicular. Tax as the velocity vector is directed tangentially to the trajectory, then the vector v n, perpendicular to the velocity vector, is directed to the center of its curvature. The second component of acceleration, equal to
called normal component of acceleration and is directed along the normal to the trajectory to the center of its curvature (which is why it is also called centripetal acceleration).
Full acceleration body is the geometric sum of the tangential and normal components (Fig. 5):
So, tangential acceleration component characterizes rate of change of speed modulo(directed tangentially to the trajectory), and normal acceleration component - rate of change of speed in direction(directed towards the center of curvature of the trajectory).
Depending on the tangential and normal components of acceleration, motion can be classified as follows:
1)
,
a n
=
0 -
rectilinear uniform motion;
2)
,
a n
=
0 -
rectilinear uniform motion. With this type of movement
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