Ministry of Transport of the Russian Federation

Federal Agency for Railway Transport

Omsk State Transport University

__________________

S. N. Krokhin

Short course in mechanics

Approved by the University's Editorial and Publishing Council

as a program and guidelines for studying the “Physics” course

for students correspondence form training

UDC 530.1(075.8)

Short course in mechanics: Program and guidelines on studying the course “Physics” / S. N. Krokhin; Omsk State University of Communications. Omsk, 2006. 25 p.

The guidelines contain the work program of the “Mechanics” section of the “Physics” discipline and a brief theoretical presentation of the main issues of this section.

Definitions of physical quantities, their units of measurement in the SI system, and the laws of classical mechanics are given.

intended for independent work part-time students.

Bibliography: 4 titles. Rice. 7.

Reviewers: Dr. Tech. Sciences, Professor V. A. Nekhaev;

Ph.D. physics and mathematics Sciences, Associate Professor V. I. Strunin.

________________________

© Omsk State. university

Railways, 2006

ABOUT THE CHAPTER

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1. Work program of the discipline “Physics”. Mechanics. . . . . . . . . . . . . . . . 6

2. Kinematics and dynamics of a material point. . . . . . . . . . . . . . . . . . . . . . . . 7

3. Kinematics and dynamics of rotation of a rigid body around

fixed axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

4. Conservation laws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Bibliographic list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Introduction

Mechanics is a branch of physics that studies the patterns of mechanical movement and the reasons that cause or change this movement. Mechanical motion exists in all higher and more complex forms of motion of matter (chemical, biological, etc.). These forms of movement are studied by other sciences (chemistry, biology, etc.).

In the main textbooks questions on the study of mechanical motion are presented in detail, often with cumbersome mathematical calculations, which significantly complicates the independent work of students.

The methodological instructions provide the working program of the “Mechanics” section, definitions of physical concepts, briefly outline the basic physical laws and regularities of classical mechanics, and record these laws in mathematical form.

The “Mechanics” section examines the kinematics and dynamics of a material point, the kinematics and dynamics of rotation of a rigid body around a fixed axis, and conservation laws.

To study the “Mechanics” section, you need knowledge of mathematics: elements of vector algebra (projection of a vector onto an axis, scalar and vector products, etc.), differential and integral calculus (calculation of the simplest derivatives and finding antiderivatives).

Due to limitations in the volume of the publication, the guidelines do not reflect experimental material.

These guidelines will help students in independently studying the mechanics course during the examination period.

1. Work program of the discipline “physics”

MECHANICS

1. Relativity of mechanical motion. Reference system. Material point (particle). Radius vector. Trajectory. Path and movement. Speed ​​and acceleration.

2. Rectilinear and curvilinear motion of a particle. Tangent (tangential) and normal acceleration.

3. Inertia. Inertial reference systems. Newton's first law. Addition of velocities and the principle of relativity in classical mechanics.

4. Interaction of bodies. Force. Inertia. Mass, density. Newton's second and third laws.

5. Forces in mechanics: gravitational, gravity, elasticity, weight, buoyancy, friction (rest, sliding, rolling, viscous).

6. Body movement in a gravity field. Free fall. The movement of a body under the influence of several forces. Resultant.

7. Absolutely solid(ATT). The center of inertia (center of mass) of the ATT and the law of its motion. Translational and rotational movement of ATT. Center of inertia system.

8. Angular displacement, angular velocity and angular acceleration. Relationship between the kinematic characteristics of translational and rotational motion.

9. Moment of force. Moment of inertia. Steiner's theorem. Basic equation for the dynamics of rotational motion.

10. Isolated system. Impulse (amount of movement) of the body. Law of conservation of momentum.

11. Angular momentum (angular momentum). Own angular momentum. Law of conservation of angular momentum.

12. Mechanical work, power. Work of constant and variable force. Work of moment of forces during rotational motion.

13. Kinetic energy. Conservative forces. Potential energy. Total mechanical energy. Law of conservation of energy in mechanics. Energy dissipation. General physical law of conservation of energy.

14. Absolutely elastic and absolutely inelastic collision of particles.

15. Simple mechanisms: inclined plane, block, lever. " Golden Rule» mechanics. Efficiency of the mechanism.

5th ed., erased. - M.: 2006.- 352 p.

The book presents in a concise and accessible form material on all sections of the Physics course program - from mechanics to the physics of the atomic nucleus and elementary particles. For university students. Useful for reviewing the material covered and in preparing for exams in universities, technical schools, colleges, schools, preparatory departments and courses.

Format: djvu/zip

Size: 7.45 MB

Download:

RGhost

TABLE OF CONTENTS
Preface 3
Introduction 4
Physics subject 4
Connection of physics with other sciences 5
1. PHYSICAL FOUNDATIONS OF MECHANICS 6
Mechanics and its structure 6
Chapter 1. Elements of kinematics 7
Models in mechanics. Kinematic equations of motion of a material point. Trajectory, path length, displacement vector. Speed. Acceleration and its components. Angular velocity. Angular acceleration.
Chapter 2 Dynamics of a material point and translational motion of a rigid body 14
Newton's first law. Weight. Force. Newton's second and third laws. Law of conservation of momentum. Law of motion of the center of mass. Friction forces.
Chapter 3. Work and energy 19
Work, energy, power. Kinetic and potential energy. Relationship between conservative force and potential energy. Total Energy. Law of energy conservation. Graphical representation of energy. Absolutely elastic impact. Absolutely inelastic impact
Chapter 4. Solid mechanics 26
Moment of inertia. Steiner's theorem. Moment of power. Kinetic energy of rotation. Equation of dynamics of rotational motion of a rigid body. Angular momentum and the law of its conservation. Deformations of a solid body. Hooke's law. Relationship between strain and stress.
Chapter 5. Gravity. Elements of field theory 32
The law of universal gravitation. Characteristics of the gravitational field. Work in a gravitational field. Relationship between the gravitational field potential and its intensity. Cosmic speeds. Inertia forces.
Chapter 6. Elements of fluid mechanics 36
Pressure in liquid and gas. Continuity equation. Bernoulli's equation. Some applications of Bernoulli's equation. Viscosity (internal friction). Fluid flow regimes.
Chapter 7. Elements special theory relativity 41
Mechanical principle of relativity. Galileo's transformations. Postulates of SRT. Lorentz transformations. Corollaries from Lorentz transformations (1). Corollaries from Lorentz transformations (2). Interval between events. Basic law of relativistic dynamics. Energy in relativistic dynamics.
2. FUNDAMENTALS OF MOLECULAR PHYSICS AND THERMODYNAMICS 48
Chapter 8. Molecular genetic theory ideal gases 48
Physics sections: Molecular physics and thermodynamics. Thermodynamics research method. Temperature scales. Ideal gas. Laws of Boyle-Marie-Otga, Avogadro, Dalton. Gay-Lussac's law. Clapeyron-Mendeleev equation. Basic equation of molecular kinetic theory. Maxwell's law on the velocity distribution of ideal gas molecules. Barometric formula. Boltzmann distribution. Average free path of molecules. Some experiments confirming MCT. Transfer phenomena (1). Transfer phenomena (2).
Chapter 9. Fundamentals of Thermodynamics 60
Internal energy. Number of degrees of freedom. The law on the uniform distribution of energy across the degrees of freedom of molecules. The first law of thermodynamics. The work of a gas when its volume changes. Heat capacity (1). Heat capacity (2). Application of the first law of thermodynamics to isoprocesses (1). Application of the first law of thermodynamics to isoprocesses (2). Adiabatic process. Circular process (cycle). Reversible and irreversible processes. Entropy (1). Entropy (2). Second law of thermodynamics. Thermal engine. Carnot's theorem. Refrigeration machine. Carnot cycle.
Chapter 10. Real gases, liquids and solids 76
Forces and potential energy of intermolecular interaction. Van der Waals equation (equation of state of real gases). Van der Waals isotherms and their analysis (1). Van der Waals isotherms and their analysis (2). Internal energy of real gas. Liquids and their description. Surface tension of liquids. Wetting. Capillary phenomena. Solids: crystalline and amorphous. Mono- and polycrystals. Crystallographic feature of crystals. Types of crystals according to physical sign. Defects in crystals. Evaporation, sublimation, melting and crystallization. Phase transitions. Status diagram. Triple point. Analysis of the experimental phase diagram.
3. ELECTRICITY AND ELECTROMAGNETISM 94
Chapter 11. Electrostatics 94
Electric charge and its properties. Law of conservation of charge. Coulomb's law. Electrostatic field strength. Electrostatic field strength lines. Tension vector flow. Superposition principle. Dipole field. Gauss's theorem for the electrostatic field in vacuum. Application of Gauss's theorem to the calculation of fields in vacuum (1). Application of Gauss's theorem to the calculation of fields in vacuum (2). Circulation of the electrostatic field strength vector. Electrostatic field potential. Potential difference. Superposition principle. The relationship between tension and potential. Equipotential surfaces. Calculation of potential difference from field strength. Types of dielectrics. Polarization of dielectrics. Polarization. Field strength in a dielectric. Electrical displacement. Gauss's theorem for a field in a dielectric. Conditions at the interface between two dielectric media. Conductors in an electrostatic field. Electrical capacity. Flat capacitor. Connecting capacitors into batteries. Energy of a system of charges and a solitary conductor. Energy of a charged capacitor. Electrostatic field energy.
Chapter 12. Constant electricity 116
Electric current, strength and current density. Outside forces. Electromotive force (EMF). Voltage. Conductor resistance. Ohm's law for a homogeneous section in a closed circuit. Work and current power. Ohm's law for a non-uniform section of a circuit (generalized Ohm's law (GLO)). Kirchhoff's rules for branched chains.
Chapter 13. Electric currents in metals, vacuum and gases 124
The nature of current carriers in metals. Classical theory of electrical conductivity of metals (1). Classical theory of electrical conductivity of metals (2). The work function of electrons leaving metals. Emission phenomena. Ionization of gases. Non-self-sustaining gas discharge. Self-contained gas discharge.
Chapter 14. Magnetic field 130
Description of the magnetic field. Basic characteristics of the magnetic field. Magnetic induction lines. Superposition principle. Biot-Savart-Laplace law and its application. Ampere's law. Interaction of parallel currents. Magnetic constant. Units B and N. Magnetic field of a moving charge. The effect of a magnetic field on a moving charge. Movement of charged particles in
magnetic field. Theorem on the circulation of vector B. Magnetic fields of the solenoid and toroid. Magnetic induction vector flux. Gauss's theorem for field B. Work on moving a conductor and a circuit with current in a magnetic field.
Chapter 15. Electromagnetic induction 142
Faraday's experiments and consequences from them. Faraday's law (law of electromagnetic induction). Lenz's rule. Induction emf in stationary conductors. Rotation of the frame in a magnetic field. Eddy currents. Loop inductance. Self-induction. Currents when opening and closing a circuit. Mutual induction. Transformers. Magnetic field energy.
Chapter 16. Magnetic properties of matter 150
Magnetic moment of electrons. Dia- and paramagnets. Magnetization. Magnetic field in matter. The law of total current for the magnetic field in matter (the theorem on the circulation of vector B). Theorem on the circulation of the vector H. Conditions at the interface between two magnets. Ferromagnets and their properties.
Chapter 17. Fundamentals of Maxwell's theory for the electromagnetic field 156
Vortex electric field. Bias current (1). Bias current (2). Maxwell's equations for the electromagnetic field.
4. OSCILLATIONS AND WAVES 160
Chapter 18. Mechanical and electromagnetic vibrations 160
Vibrations: free and harmonic. Period and frequency of oscillations. Rotating amplitude vector method. Mechanical harmonic vibrations. Harmonic oscillator. Pendulums: spring and mathematical. Physical pendulum. Free oscillations in an idealized oscillatory circuit. Equation of electromagnetic oscillations for an idealized circuit. Addition of harmonic vibrations of the same direction and the same frequency. Beating. Addition of mutually perpendicular vibrations. Free damped oscillations and their analysis. Free damped oscillations of a spring pendulum. Decrement of attenuation. Free damped oscillations in an electrical oscillatory circuit. Quality factor of the oscillatory system. Forced mechanical vibrations. Forced electromagnetic oscillations. Alternating current. Current through a resistor. Alternating current flowing through a coil of inductance L. Alternating current flowing through a capacitor of capacitance C. Circuit alternating current, containing a resistor, inductor and capacitor connected in series. Voltage resonance (series resonance). Resonance of currents (parallel resonance). Power released in an alternating current circuit.
Chapter 19. Elastic waves 181
Wave process. Longitudinal and transverse waves. Harmonic wave and its description. Traveling wave equation. Phase speed. Wave equation. Superposition principle. Group speed. Wave interference. Standing waves. Sound waves. Doppler effect in acoustics. Receiving electromagnetic waves. Electromagnetic wave scale. Differential equation
electromagnetic waves. Consequences of Maxwell's theory. Electromagnetic energy flux density vector (Umov-Poinging vector). Electromagnetic field pulse.
5. OPTICS. QUANTUM NATURE OF RADIATION 194
Chapter 20. Elements of geometric optics 194
Basic laws of optics. Total reflection. Lenses, thin lenses, their characteristics. Thin lens formula. Optical power of the lens. Construction of images in lenses. Aberrations (errors) of optical systems. Energy quantities in photometry. Light quantities in photometry.
Chapter 21. Interference of Light 202
Derivation of the laws of reflection and refraction of light based on wave theory. Coherence and monochromaticity of light waves. Interference of light. Some methods for observing light interference. Calculation of the interference pattern from two sources. Stripes of equal inclination (interference from a plane-parallel plate). Stripes of equal thickness (interference from a plate of variable thickness). Newton's rings. Some applications of interference (1). Some applications of interference (2).
Chapter 22. Diffraction of light 212
Huygens-Fresnel principle. Fresnel zone method (1). Fresnel zone method (2). Fresnel diffraction by round hole and disk. Fraunhofer diffraction by a slit (1). Fraunhofer diffraction by a slit (2). Fraunhofer diffraction by a diffraction grating. Diffraction by a spatial grating. Rayleigh criterion. Resolution of the spectral device.
Chapter 23. Interaction of electromagnetic waves with matter 221
Dispersion of light. Differences in diffraction and prismatic spectra. Normal and anomalous dispersion. Elementary electron theory of dispersion. Absorption (absorption) of light. Doppler effect.
Chapter 24. Polarization of Light 226
Natural and polarized light. Malus's law. Passage of light through two polarizers. Polarization of light during reflection and refraction at the boundary of two dielectrics. Birefringence. Positive and negative crystals. Polarizing prisms and polaroids. Quarter wave record. Analysis of polarized light. Artificial optical anisotropy. Rotation of the plane of polarization.
Chapter 25. Quantum nature of radiation 236
Thermal radiation and its characteristics. Kirchhoff's, Stefan-Boltzmann's, Wien's laws. Rayleigh-Jeans and Planck formulas. Deriving particular laws of thermal radiation from Planck's formula. Temperatures: radiation, color, brightness. Current-voltage characteristics of the photoelectric effect. Laws of the photoelectric effect. Einstein's equation. Photon momentum. Light pressure. Compton effect. Unity of corpuscular and wave properties of electromagnetic radiation.
6. ELEMENTS OF QUANTUM PHYSICS OF ATOMS, MOLECULES-SOLID BODIES 246
Chapter 26. Bohr's theory of the hydrogen atom 246
Thomson and Rutherford models of the atom. Linear spectrum of a hydrogen atom. Bohr's postulates. Experiments of Frank and Hertz. Bohr spectrum of the hydrogen atom.
Chapter 27. Elements of quantum mechanics 251
Particle-wave dualism of the properties of matter. Some properties of de Broglie waves. Uncertainty relationship. Probabilistic approach to the description of microparticles. Description of microparticles using the wave function. Superposition principle. General equation Schrödinger. Schrödinger equation for stationary states. Movement of a free particle. A particle in a one-dimensional rectangular "potential well" with infinitely high "walls". Potential barrier of rectangular shape. Passage of a particle through a potential barrier. Tunnel effect. Linear harmonic oscillator in quantum mechanics.
Chapter 28. Elements of modern physics of atoms and molecules 263
Hydrogen-like atom in quantum mechanics. Quantum numbers. Spectrum of a hydrogen atom. ls-state of an electron in a hydrogen atom. Electron spin. Spin quantum number. The principle of indistinguishability of identical particles. Fermions and bosons. Pauli's principle. Distribution of electrons in an atom according to states. Continuous (bremsstrahlung) X-ray spectrum. Characteristic X-ray spectrum. Moseley's Law. Molecules: chemical bonds, concept of energy levels. Molecular spectra. Absorption. Spontaneous and stimulated emission. Active media. Types of lasers. Operating principle of a solid-state laser. Gas laser. Properties of laser radiation.
Chapter 29. Elements of Solid State Physics 278
Band theory of solids. Metals, dielectrics and semiconductors according to band theory. Intrinsic conductivity of semiconductors. Electronic impurity conductivity (i-type conductivity). Donor impurity conductivity (p-type conductivity). Photoconductivity of semiconductors. Luminescence of solids. Contact between electron and hole semiconductors (pn junction). Conductivity of the p-i junction. Semiconductor diodes. Semiconductor triodes (transistors).
7. ELEMENTS OF PHYSICS OF THE ATOMIC NUCLEUS AND ELEMENTARY PARTICLES 289
Chapter 30. Elements of the physics of the atomic nucleus 289
Atomic nuclei and their description. Mass defect. Nuclear binding energy. Nuclear spin and its magnetic moment. Nuclear seeps. Kernel models. Radioactive radiation and its types. Law of radioactive decay. Offset rules. Radioactive families. a-Decomposition. p-decay. y-Radiation and its properties. Instruments for recording radioactive radiation and particles. Scintillation counter. Pulse ionization chamber. Gas discharge meter. Semiconductor counter. Wilson chamber. Diffusion and bubble chambers. Nuclear photographic emulsions. Nuclear reactions and their classification. Positron. P+-Decomposition. Electron-positron pairs, their annihilation. Electronic capture. Nuclear reactions under the influence of neutrons. Nuclear fission reaction. Fission chain reaction. Nuclear reactors. The reaction of fusion of atomic nuclei.
Chapter 31. Elements of particle physics 311
Cosmic radiation. Muons and their properties. Mesons and their properties. Types of interactions of elementary particles. Description of three groups of elementary particles. Particles and antiparticles. Neutrinos and antineutrinos, their types. Hyperons. Strangeness and parity of elementary particles. Characteristics of leptons and hadrons. Classification of elementary particles. Quarks.
Periodic table of elements by D. I. Mendeleev 322
Basic laws and formulas 324
Subject index 336

Physics is one of the basic sciences of natural science. The study of physics at school begins in the 7th grade and continues until the end of school. By this time, schoolchildren should already have developed the proper mathematical apparatus necessary for studying a physics course.

• The school curriculum in physics consists of several large sections: mechanics, electrodynamics, oscillations and waves, optics, the quantum physics, molecular physics and thermal phenomena.

School physics topics

In the 7th grade There is a superficial familiarization and introduction to the physics course. Basic physical concepts are considered, the structure of substances is studied, as well as the pressure force with which various substances affect others. In addition, the laws of Pascal and Archimedes are studied.

In 8th grade various physical phenomena are studied. Initial information is given about the magnetic field and the phenomena in which it occurs. Direct electric current and the basic laws of optics are studied. The various aggregate states of matter and the processes that occur during the transition of a substance from one state to another are analyzed separately.

9th grade is devoted to the basic laws of motion of bodies and their interaction with each other. The basic concepts of mechanical vibrations and waves are considered. The topic of sound and sound waves is discussed separately. The fundamentals of electromagnetic field theory and electromagnetic waves. In addition, there is an acquaintance with the elements nuclear physics and the structure of the atom and the atomic nucleus is studied.

In 10th grade An in-depth study of mechanics (kinematics and dynamics) and conservation laws begins. The main types are considered mechanical forces. There is an in-depth study of thermal phenomena, molecular kinetic theory and the basic laws of thermodynamics are studied. The basics of electrodynamics are repeated and systematized: electrostatics, the laws of constant electric current and electric current in various media.

Grade 11 devoted to the study of the magnetic field and the phenomenon of electromagnetic induction. Are studied in detail different kinds vibrations and waves: mechanical and electromagnetic. There is a deepening of knowledge from the optics section. Elements of the theory of relativity and quantum physics are considered.

• Below is a list of classes from 7 to 11. Each class contains physics topics that are written by our tutors. These materials can be used by students and their parents, as well as school teachers and tutors.

D.V.Sivukhin

GENERAL PHYSICS COURSE. T.I MECHANICS

The main content of the proposed course is an extended presentation of lectures on physics, which the author read for many years (since 1956) at the Moscow Institute of Physics and Technology. Overall plan The lecture course, as well as the basic approach to presenting fundamental issues in physics, changed little over the years. However, every year the course was updated to include new private questions and examples. Many previously considered issues were excluded. This was done not for reasons of principle, but due to lack of time.

This course includes almost all the issues presented in the lectures in different years. Questions that were not discussed in the lectures were also included. They occupy about 10-15% of the text. In addition, many problems are included with answers or detailed solutions. All this material can be of benefit to students when in-depth study physicists and teachers during seminar classes. It, the author hopes, will contribute to the development of students' physical thinking skills and the ability to independently pose and solve fundamental questions and specific physical problems, which is the main goal of the proposed manual. Of course, not all of this material is required. For the convenience of the reader, the main questions are printed in large font, all the rest are printed in small font.

NAME INDEX