Introduction. Law of conservation of mechanical energy. Addition of harmonic vibrations of the same direction
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, quantum physics, molecular physics and thermal phenomena.
School physics topics
In 7th grade There is a superficial introduction and introduction to the physics course. Basic physical concepts are examined, the structure of substances is studied, as well as the pressure force with which various substances act on 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. Constant is being studied electric current and basic laws of optics. 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 basics of electrical theory are studied magnetic field and electromagnetic waves. In addition, one gets acquainted with the elements of nuclear physics and studies the structure of the atom and atomic nucleus.
In 10th grade An in-depth study of mechanics (kinematics and dynamics) and conservation laws begins. The main types of mechanical forces are considered. 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.
11th grade dedicated to the study of the magnetic field and the phenomenon of electromagnetic induction. Are studied in detail various types 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 both students and their parents, and school teachers and tutors.
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.
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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 solid 14
Newton's first law. Weight. Strength. 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. Full energy. Law of conservation of energy. 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
Law universal gravity. 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 of the special theory of 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-kinetic theory of ideal gases 48
Sections of physics: 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 length 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 characteristics. 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-plate 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. Direct electric current 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. Basics of Maxwell's theory for 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. AC. Current through a resistor. Alternating current flowing through a coil of inductance L. Alternating current flowing through a capacitor of capacitance C. Circuit AC, 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. Chain reaction division. 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
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 for 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 product, 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 session.
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. Strength. 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 body (ATB). 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 energy conservation.
14. Absolutely elastic and absolutely inelastic collision of particles.
15. Simple mechanisms: inclined plane, block, lever. " Golden rule» mechanics. Efficiency of the mechanism.
Ministry of Education and Science of Ukraine
Odessa National Maritime Academy
V.I.Mikhailenko
SHORT COURSE IN PHYSICS
(textbook for university students)
Odessa – 2004
UDC 536.075
V.I. Mikhailenko. Short course in physics. Textbook for university students. Part 1. Odessa, ONMA, 2004.
The textbook on physics was developed by Doctor of Physical and Mathematical Sciences, Professor V.I. Mikhailenko in accordance with the order of the rector of OGMA No. 248 dated October 7, 1997 “about methodical care...” and is intended for university students.
The textbook on physics was discussed at a meeting of the Department of Physics and Chemistry of ONMA, protocol No. 2__ dated November 17, 2004, and the Academic Council of the Faculty of Automation of ONMA, protocol No. _______ dated ____________ 2004.
PREFACE
Purpose of the present teaching aid- assist students in studying the physics course.
The first part of the manual briefly outlines such sections as “Mechanics”, “Mechanical vibrations and waves”, “ Molecular physics", "Fundamentals of Thermodynamics", "Electrostatics" and "Direct Electric Current". When presenting the material special attention addressed the physical meaning of quantities, the interpretation of basic physical laws and the mechanism of occurrence of certain phenomena. The author tried to avoid complex mathematical transformations, choosing the most simple options derivation of basic formulas and laws of physics.
INTRODUCTION.. 4
I. MECHANICS.. 4
1. Kinematics of a material point. 4
1.1. Basic concepts of kinematics. 4
1.2. Normal and tangential acceleration. 4
1.3. Motion of a point in a circle. Angular velocity and acceleration. 4
2. Dynamics of forward motion. 4
2.1. Newton's laws. 4
2.2. Law of conservation of momentum. 4
3. Work and energy. 4
3.1. Job. 4
3.2. Relationship between work and change in kinetic energy. 4
3.3. Relationship between work and change in potential energy. 4
3.4. Law of conservation of mechanical energy. 4
3.5. Collisions. 4
4. Rotational motion of a rigid body. 4
4.1. Kinetic energy of rotational motion. Moment of inertia. 4
4.2. The basic law of the dynamics of rotational motion. 4
4.3. Law of conservation of angular momentum. 4
4.4. Gyroscope. 4
II. MECHANICAL VIBRATIONS AND WAVES... 4
5. General characteristics oscillatory processes. Harmonic vibrations. 4
6. Oscillations of a spring pendulum. 4
7. Energy of harmonic vibration. 4
8. Addition of harmonic vibrations of the same direction. 4
9. Damped oscillations. 4
10. Forced vibrations. 4
11. Elastic (mechanical) waves.. 4
12. Interference of waves. 4
13. Standing waves.. 4
14. Doppler effect in acoustics. 4
III. MOLECULAR PHYSICS.. 4
15. Basic equation of the molecular kinetic theory of gases. 4
16. Distribution of molecules by speed.. 4
17. Barometric formula. 4
18. Boltzmann distribution. 4
IV. FUNDAMENTALS OF THERMODYNAMICS.. 4
19. Basic concepts of thermodynamics. 4
20. The first law of thermodynamics and its application to isoprocesses.. 4
21. Number of degrees of freedom. Internal energy of an ideal gas. 4
22. Classical theory of heat capacity of gases. 4
23. Adiabatic process. 4
24. Reversible and irreversible processes. Circular processes (cycles). Operating principle of a heat engine.. 4
25. Ideal Carnot heat engine. 4
26. Second law of thermodynamics. 4
27. Entropy. 4
V. ELECTROSTATICS.. 4
28. Discreteness of electric charge. Law of conservation of electric charge. 4
29. Coulomb's law. Electrostatic field strength.
Electric displacement vector. 4
30. Lines of force. Vector flow. Ostrogradsky-Gauss theorem. 4
31. Applications of the Ostrogradsky-Gauss theorem to calculate fields. 4
32. Work on moving a charge in an electrostatic field.
Vector circulation .... 4
33. Relationship between field strength and potential.. 4
34. Electrical capacity of conductors. Capacitors.. 4
35. Electrostatic field energy. 4
VI. DC ELECTRIC CURRENT.. 4
36. Basic characteristics of current. 4
37. Ohm's law for a homogeneous section of a chain. 4
38. Joule-Lenz law. 4
39. Kirchhoff's rules. 4
40. Contact potential difference. 4
41. Seebeck effect. 4
42. Peltier effect. 4
INTRODUCTION
Physics is a science that studies the simplest and at the same time the most general patterns of natural phenomena, the properties and structure of matter and the laws of its motion. The concepts of physics and its laws underlie all natural science. Physics belongs to the exact sciences and studies the quantitative laws of phenomena.
In accordance with the variety of objects studied and forms of motion of matter, physics is divided into a number of disciplines (sections), to one degree or another connected with each other. Based on the objects studied, physics is divided into elementary particle physics, nuclear physics, physics of atoms and molecules, physics of gases and liquids, solid state physics, and plasma physics.
According to various forms the motion of matter in physics is distinguished: mechanics of a material point and a solid body, mechanics of continuous media, thermodynamics and statistical physics, electrodynamics (including optics), theory of gravity, quantum mechanics and quantum theory fields. These branches of physics partially overlap due to the deep internal connection between the objects of the material world and the processes in which they participate.
Physics is the foundation for all general engineering and special disciplines. Knowledge in the field of physics is necessary for engineers both when operating existing machines and mechanisms, and when designing new ones.
Basic SI units
Meter (m) is a unit of length. Until 1960, the international standard for the meter was a line measure of length - a bar made of platinum-iridium alloy. In I960 there was... In 1983, a new definition of the meter was adopted, based on the value of speed... The kilogram (kg) is a unit of mass. The mass of the international prototype stored in the International...I. MECHANICS
Under mechanical movement understand the change over time in the relative position of bodies or their parts in space. Considered in mechanics... Let's start studying the physics course with classical mechanics. At the heart of classical... Classical mechanics is usually divided into three sections:Kinematics of a material point
Basic concepts of kinematics
A material point is a body that has mass, but its size and shape can be neglected in the conditions of this problem.
Space and time are categories that determine the basic forms of existence of matter. Space determines the order of existence of individual objects, and time determines the order of change of phenomena.
 Rice. 1.1 |
A reference system is a set of systems of mutually motionless bodies and clocks associated with them, in relation to which the movement of some other material bodies is studied. The choice of reference system is arbitrary and depends on the purposes of the study. Usually a body (or system of bodies) is associated with a Cartesian coordinate system, in which the position of a material point in at the moment time is given by three coordinates x, y, z(Fig. 1.1).
A trajectory is a continuous line that a material point describes during its movement. If the trajectory is a straight line, then the movement is called rectilinear, otherwise it is called curvilinear. The type of trajectory depends on the choice of reference system.
where is the change in radius vector over time dt(Fig. 1.3).
From (1.2) it is clear that speed is numerically equal to the path traveled by a material point per unit of time. The velocity vector is directed in the direction of motion tangential to the trajectory.
Acceleration - vector quantity, characterizing the rate of change in speed, both in magnitude and direction.
| . | (1.3) |
At dt=1, || = ||, i.e. acceleration is numerically equal to the change in speed per unit time.
Normal and tangential acceleration
In the general case, acceleration during curvilinear motion can be represented as a vector sum of tangential (or tangential) acceleration t and... Tangential acceleration characterizes the rate of change in speed modulo....Dynamics of translational motion
Newton's laws
Newton's first law. If no forces act on a body, then it is in a state of rest or uniform rectilinear motion relative to... The property of bodies to maintain a state of rest or uniform rectilinear... Newton's second law. The acceleration with which a body moves is proportional to the applied force and inversely proportional...Law of conservation of momentum
Let there be a system of three interacting material points (Fig. 2.2). Each material point of this system is acted upon as internal...Work and Energy
Job
Work is a measure of the action of a force, depending on the value and direction of the force, as well as on the amount of movement of its point of application.
If the force is in value and direction, then with rectilinear movement the work
If the force is variable, then first calculate the elementary work dA=Fdlcosa, where a - the angle between the tangent to the trajectory at a given point and the direction of the force (Fig. 3.2).
The total work on the final section of the trajectory can be found as an integral along the curve WITH, coinciding with the trajectory:
.
Relationship between work and change in kinetic energy
Such a movement will be accelerated: the initial (at time t1) value of the speed will change and by time t2 it will become equal (Fig. 3.3). In this case, there is a double manifestation of force: on the one hand, there is... Work A=Fl=mal. Since when uniformly accelerated motion, ThatRelationship between work and change in potential energy
.Law of conservation of mechanical energy
The total mechanical energy of a system is the sum of the kinetic and potential energy of all bodies included in this system: W=Wk+Wp. Let the system transition from state 1, characterized by the values... W2 – W1=(Wk2+Wp2) - (Wk1+ Wp1)=(Wk2 - Wk1) + (Wp2 - Wp1).Collisions
Elastic impact. An absolutely elastic impact is one in which the mechanical energy of the colliding bodies is not converted into other types. ... Let us consider, as a simple example, a direct central blow, in which... Let. Then at some point in time the first body will overtake the second and a collision will occur. At the moment of impact...Basic law of the dynamics of rotational motion
A tangential force will cause a tangential acceleration to appear. According to Newton's second law, Ft=mat or F cos a=mat. Let's express the tangential acceleration in terms of the angular acceleration: at=re. Then F cos a=mre. Let's multiply...Law of conservation of angular momentum
. (4.6) Expression (4.6) represents the law of conservation of angular momentum: in... When an absolutely rigid body rotates around a fixed axis, its moment of inertia remains constant. From the law...Gyroscope
If a uniformly rotating gyroscope is not acted upon by external moments of force, then, according to the law of conservation of angular momentum, the direction of its axis... Let us now consider what will happen if the free gyroscope is... Axis own rotation the gyroscope is vertical (coincides with the z axis); the angular momentum vector is oriented along this...II. MECHANICAL VIBRATIONS AND WAVES
General characteristics of oscillatory processes. Harmonic vibrations
In technology, devices using oscillatory processes can perform certain functional responsibilities(pendulum, oscillatory circuit,... Oscillations are called periodic if the system through certain equal...Oscillations of a spring pendulum
When a body is displaced by an amount x from the equilibrium position, an elastic force F=-kx arises, (6.1)Energy of harmonic vibration
It is obvious that the total energy of the spring pendulum is W=Wk+Wp, where the kinetic Wk and potential Wp energies are determined by the expressionsAddition of harmonic vibrations of the same direction
From the point O taken on the x-axis, we construct a vector that forms an angle j0 with the axis (Fig. 8.1). The projection of this vector onto the x-axis is equal toDamped oscillations
Let us consider the case when an oscillating body is in a viscous medium and its speed v is small - Fig. 9.1. Then the body is acted upon by a resistance force equal to (9.1)Forced vibrations
Let us assume that an external (forcing) force acts on the oscillating system, changing according to a harmonic law: Fin = F0 cos wt,Elastic (mechanical) waves
Elastic waves are the process of propagation of mechanical deformations in an elastic medium. The region of space covered by the wave process is called wave... The surface at all points of which the wave at a given time has the same phase is called the wave front....Wave interference
Waves that have the same frequency and a time-independent (constant) phase difference are called coherent. Let's find the conditions for the appearance of interference maxima and minima at... Each of the sources “sends” waves to point M, the equations of which have the form:Standing waves
The incident wave is described by the equation.Doppler effect in acoustics
Sound waves in liquid and gaseous media they are longitudinal. In solid bodies, both longitudinal and transverse sound can propagate... The Doppler effect consists of changing the frequency of sound vibrations during movement... Let us denote: c - the speed of sound in a given medium; u and v are the speeds of the source and receiver, respectively, relative to...III. MOLECULAR PHYSICS
Molecular physics is a branch of physical science that studies physical properties and aggregate states of physical bodies depending on their molecular structure, the nature of the thermal movement of molecules and the forces of interaction between them.
Basic equation of the molecular kinetic theory of gases
1) the sizes of molecules are so small that they can be considered as material points; 2) the potential energy of interaction between molecules is zero for any... The chaotic movement of gas molecules can be represented as the movement of 1/3 of their total number in the direction of the x-axis, 1/3 - along...Distribution of molecules by speed
Let's count the number of molecules dN whose velocities fall within the velocity range from v to (Fig. 16.1). Obviously, dN is proportional to the total number... From (16.1) it followsBarometric formula
Let's find the dependence of atmospheric pressure on altitude above sea level using the following simplified model: 1. The temperature of the gas and its molecular composition do not depend on altitude; 2. The acceleration of free fall at all altitudes where the atmosphere exists is constant. Rice. 17.1…Boltzmann distribution
P = nkT; (18.1) P0 = n0kT. (18.2)Basic concepts of thermodynamics
1. A thermodynamic system is a set of macroscopic bodies that exchange energy between themselves and the environment.
2. The state of a thermodynamic system is determined by the totality of the values of its thermodynamic parameters (state parameters) - all physical quantities that characterize the macroscopic properties of the system (pressure, volume, temperature, etc.). The relationship between thermodynamic parameters is determined by the equation of state. Thus, for an ideal gas, the equation of state is the Mendeleev-Clapeyron equation.
3. The state of thermodynamic equilibrium is a generalization of the concept of mechanical equilibrium and is formulated as follows. In a system in a state of thermodynamic equilibrium, the pressure in all its parts (condition of mechanical equilibrium) and temperature (condition of thermal equilibrium) must be equal.
4. Thermodynamic process is a change in the state of a thermodynamic system, characterized by a change in its state parameters.
5. Equilibrium process - an infinite sequence of equilibrium states.
6. Internal energy - the total kinetic and potential energy of interaction of all particles (atoms or molecules) of the body.
For an ideal gas, the potential energy of interaction between molecules can be neglected, therefore the internal energy of an ideal gas is completely determined by the kinetic energy of all its molecules located in a certain limited volume. The internal energy of an ideal gas can be found as the product of the average kinetic energy wav of the motion of the molecules of their number. Since wav depends only on temperature (see formula (15.11)), it can be argued that the internal energy of an ideal gas is completely determined by its temperature.
6. Work is a quantitative measure of the conversion of the energy of chaotic motion of molecules or directed motion of bodies into the energy of directed motion of macroscopic bodies. This energy conversion process is shown schematically in Fig. 19.1.
Process 1 is accompanied by the execution mechanical work, which is numerically equal to the change in the kinetic energy of the body (3.4).
Where dV=Sdx - change in gas volume.
Formula (19.1) is a thermodynamic expression for elementary work. Total work done during gas expansion based on volume V1 to volume V2 is determined by the formula
| . | (19.2) |
 Rice. 19.3 |
Heat is a quantitative measure of the conversion of the energy of directed or chaotic motion into the energy of chaotic motion (Fig. 19.3).
Process 1 occurs when bodies decelerate under the influence of friction. This process is accompanied by the transformation of the energy of directed motion (kinetic energy) of a body into the energy of chaotic motion of particles of the environment, which is equivalent to the transfer of a certain amount of heat to it. The same energy conversion is observed in the process opposite to that shown in Fig. 19.2 (i.e. during gas compression).
The process of converting the energy of chaotic motion into the energy of chaotic motion (channel 2 in Fig. 19.3) is nothing more than the process of transferring heat from a hot body to a cold one.
The first law of thermodynamics and its application to isoprocesses
dQ=dA+dU. (20.1)Number of degrees of freedom. Internal energy of an ideal gas
A system of two material points, the distance between which remains constant, has five degrees of freedom: three of them are at... The average kinetic energy of the translational motion of a molecule is equal to 3/2 kT -.... (21.1)Adiabatic process
In an adiabatic process, dQ = 0, therefore the first law of thermodynamics in relation to this process takes the form dA + dU = 0; dA = -dU, (23.1)Reversible and irreversible processes. Circular processes (cycles). Operating principle of a heat engine
1. After passing through these processes and returning the thermodynamic system to its original state in environment there should not be any left... 2. The process can spontaneously proceed both in the direct and in the reverse... An example of reversible processes are all mechanical processes in which the laws of conservation of energy are satisfied,...Ideal Carnot heat engine
The Carnot cycle consists of two adiabats and two isotherms (Fig. 25.1). In this figure 1®2 is isothermal expansion at temperature T1; 2®3 -... In an ideal Carnot machine, such sources of losses as friction between the cylinders and the piston, heat leakage are neglected...Second law of thermodynamics
1. It is impossible to build a cyclically operating heat engine that would do work only by cooling some body. Such a car...A process is impossible, the only result of which would be the transfer of heat from a cold body to a hot one.
Entropy
Using formula (21.7), we write down the expression of the first law of thermodynamics...V. ELECTROSTATICS
Discreteness of electric charge. Law of conservation of electric charge
There are two types of electrical charges: positive and negative. Electric charge is discrete: the charge of any body is an integer multiple... One of the fundamental strict laws of nature is the law of conservation... 29. Coulomb’s law. Electrostatic field strength. Electrical displacement vectorElectrostatic field energy
We will sequentially transfer portions of charge dq from one plate to another - Fig. 35.1 When transferring a charge dq, work is performed dA=Udq. From (34.2) it follows that... Integrating this expression from Q to 0, we obtain:VI. DC ELECTRIC CURRENT
Main characteristics of current
The current strength is numerically equal to the charge passing through cross section conductor per unit of time: . (36.1) Current strength is measured in amperes (definition given in the Introduction). The current density vector is numerically equal to current strength,…Ohm's law for a homogeneous section of a chain
Ohm experimentally established that the current strength in a homogeneous section of the circuit is proportional to the voltage and inversely proportional to the resistance: ... Fig. 37.1 Let us represent Ohm’s law (37.1) in differential form. To do this, we select an elementary section inside the current-carrying conductor...Joule-Lenz law
Let us present the Joule-Lenz law (38.1) in differential form. Let's highlight how...Kirchhoff's rules
Kirchhoff's first rule. The algebraic sum of currents converging at a node is equal to zero, i.e. .Contact potential difference
electrons are able to move from one conductor to another and back. The equilibrium state of such a system will occur when... The magnitude of the contact potential difference is determined by the difference in work functions1...Seebeck effect
If contacts are maintained with different temperatures(by heating or cooling one of them), then an excellent emf from zero will arise in the circuit (Fig. 41.1): ... .Peltier effect
The Peltier heat released or absorbed at the contact during time t, in contrast to the Joule-Lenz heat, is proportional to the current strength to the first power: ..., where P is the Peltier coefficient, depending on the nature of the contacting conductors and the contact temperature. ...What will we do with the received material:
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The general course "Mechanics" is part of the course general physics. Students will become familiar with the basic mechanical phenomena and methods of their theoretical description. The lectures include video recordings of physical demonstrations of the mechanical phenomena being studied.
The course structure is traditional. The course covers classic material in the course of general physics, section “Mechanics”, taught in the first year of the Faculty of Physics of Moscow State University in the first semester. The course will include sections “Kinematics and dynamics of a material point and the simplest systems”, “Conservation laws”, “Motion of a material point in non-inertial reference systems”, “Fundamentals of relativistic mechanics”, “Kinematics and dynamics of a rigid body”, “Fundamentals of the mechanics of deformable media” , “Fundamentals of hydromechanics and aeromechanics”, “Mechanical vibrations and waves”.
The course is aimed at bachelors specializing in natural sciences, as well as at secondary school physics teachers and university professors. It will also be useful for schoolchildren who study physics in depth.
Format
The form of study is correspondence (distance).
Weekly classes will include viewing thematic video lectures, including video recordings of lecture experiments and performing test tasks With automated check results. An important element studying the discipline is independent decision physical tasks. The solution will have to contain rigorous and logically correct reasoning leading to the correct answer.
Requirements
The course is designed for 1st year bachelors. Knowledge of physics and mathematics required high school(11 classes).
Course program
Introduction
B.1 Space and time in Newtonian mechanics
B.2 Reference system
Chapter 1. Kinematics and dynamics of simple systems
P.1.1. Kinematics of a material point and simplest systems
P.1.2. Newton's laws
P.1.3. Laws describing the individual properties of forces
Chapter 2. Conservation laws in the simplest systems
P.2.1. Law of conservation of momentum
P.2.2. Mechanical energy
P.2.3. Relationship between conservation laws and homogeneity of space and time
Chapter 3. Non-inertial frames of reference
P.3.1. Non-inertial reference systems. Inertia forces
P.3.2. Manifestation of inertial forces on Earth
P.3.3. Equivalence principle
Chapter 4. Fundamentals of relativistic mechanics
P.4.1. Space and time in the theory of relativity
P.4.2. Lorentz transformations
P.4.3. Consequences of Lorentz transformations
P.4.4. Interval
P.4.5. Speed addition
P.4.6. Equation of motion
P.4.7. Momentum, energy and mass in the theory of relativity
Chapter 5. Kinematics and rigid body dynamics
P.5.1. Rigid body kinematics
P.5.2. Rigid body dynamics
P.5.3. Kinetic energy of a solid
P.5.4. Gyroscopes, tops
Chapter 6. Fundamentals of mechanics of deformable bodies
P.6.1. Deformations and stresses in solids
P.6.2. Poisson's ratio
P.6.3. Relationship between Young's modulus and shear modulus
P.6.4. Energy of elastic deformations
Chapter 7. Oscillations
P.7.1. Free vibrations of systems with one degree of freedom
P.7.2. Forced vibrations
P.7.3. Addition of vibrations
P.7.4. Oscillations in coupled systems
P.7.5. Nonlinear oscillations
P.7.6. Parametric oscillations
P.7.7. Self-oscillations
Chapter 8. Waves
P.8.1. Propagation of impulse in a medium. Wave equation
P.8.2. Density and energy flow in a traveling wave. Vector Umov
P.8.3. Wave reflection, vibration modes
P.8.4. Acoustics elements
P.8.5. Shock waves
Chapter 9 Fundamentals of hydro and aeromechanics
Clause 9.1. Basics of hydro- and aerostatics
P.9.2. Steady flow of incompressible fluid
P.9.3. Laminar and turbulent flow. Flow of liquid or gas around bodies
Learning outcomes
As a result of mastering the discipline, the student must know the basic mechanical phenomena, methods of their theoretical description and methods of their use in physical devices; be able to solve problems from the “Mechanics” section of the general physics course.
