The theory of the exam in physics. Physics

M.: 2016 - 320 p.

The new reference book contains all the theoretical material for the physics course required to pass the unified state exam. It includes all content elements tested by test materials, and helps to generalize and systematize the knowledge and skills of the school physics course. The theoretical material is presented in a concise and accessible form. Each topic is accompanied by examples of test tasks. Practical tasks correspond to the Unified State Exam format. Answers to the tests are provided at the end of the manual. The manual is addressed to schoolchildren, applicants and teachers.

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Size: 60.2 MB

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CONTENT
Preface 7
MECHANICS
Kinematics 9
Mechanical movement. Reference system. Material point. Trajectory. Path.
Move 9
Velocity and acceleration of a material point 15
Uniform linear motion 18
Uniformly accelerated linear motion 21
Examples of tasks 1 24
Free fall. Acceleration of gravity.
Motion of a body thrown at an angle to the horizontal 27
Movement of a material point in a circle 31
Examples of tasks 2 33
Dynamics 36
Newton's first law.
Inertial reference systems 36
Body mass. Substance density 38
Force. Newton's second law 42
Newton's third law for material points 45
Examples of tasks 3 46
The law of universal gravitation. Gravity 49
Elastic force. Hooke's Law 51
Friction force. Dry friction 55
Examples of tasks 4 57
Static 60
Equilibrium condition for a rigid body in ISO 60
Pascal's Law 61
Pressure in a fluid at rest relative to ISO 62
Archimedes' law. Sailing conditions for bodies 64
Examples of tasks 5 65
Conservation laws 68
Law of conservation of momentum 68
Work of force at small displacement 70
Examples of tasks 6 73
Law of conservation of mechanical energy 76
Examples of tasks 7 80
Mechanical vibrations and waves 82
Harmonic vibrations. Amplitude and phase of oscillations.
Kinematic description 82
Mechanical waves 87
Examples of tasks 8 91
MOLECULAR PHYSICS. THERMODYNAMICS
Fundamentals of molecular kinetic theory
structure of matter 94
Atoms and molecules, their characteristics 94
Movement of molecules 98
Interaction of molecules and atoms 103
Examples of tasks 9 107
Ideal gas pressure 109
Gas temperature and average
kinetic energy of molecules 111
Examples of tasks 10 115
Equation of state of an ideal gas 117
Examples of tasks 11 120
Isoprocesses in a rarefied gas with a constant number of particles N (with a constant amount of substance v) 122
Examples of tasks 12 127
Saturated and unsaturated pairs 129
Air humidity 132
Examples of tasks 13 135
Thermodynamics 138
Internal energy of a macroscopic system 138
Examples of tasks 14 147
Changes in the aggregate states of matter: evaporation and condensation, boiling 149
Examples of tasks 15 153
Changes in the aggregative states of matter: melting and crystallization 155
Examples of tasks 16 158
Working in Thermodynamics 161
First law of thermodynamics 163
Examples of tasks 17 166
Second Law of Thermodynamics 169
Operating principles of heat engines 171
Examples of tasks 18 176
ELECTRODYNAMICS
Electrostatics 178
The phenomenon of electrification.
Electric charge and its properties 178
Coulomb's Law 179
Electrostatic field 179
Capacitors 184
Examples of tasks 19 185
DC Laws 189
Direct electric current 189
DC Laws 191
Currents in various environments 193
Examples of tasks 20 196
Examples of tasks 21 199
Magnetic field 202
Magnetic interaction 202
Examples of tasks 22 204
Relationship between electrical and magnetic phenomena 208
Examples of tasks 23 210
Electromagnetic oscillations and waves 214
Free electromagnetic oscillations 214
Examples of tasks 24 222
OPTICS
Geometric optics 228
Lenses 233
Eye. Visual impairments 239
Optical instruments 241
Examples of tasks 25 244
Wave Optics 247
Interference of light 247
Jung's experience. Newton's rings 248
Applications of Light Interference 251
Examples of tasks 26 254
FUNDAMENTALS OF THE SPECIAL THEORY OF RELATIVITY
Fundamentals of the special theory of relativity (STR) 257
Examples of tasks 27 259
THE QUANTUM PHYSICS
Planck's hypothesis 260
Laws of external photoelectric effect 261
Wave-particle duality 262
Examples of tasks 28 264
ATOM PHYSICS
Planetary model of the atom 267
N. Bohr's postulates 268
Spectral analysis 271
Laser 271
Examples of tasks 29 273
Physics of the Atomic Nucleus 275
Proton-neutron model of the nucleus 275
Isotopes. Nuclear binding energy. Nuclear forces 276
Radioactivity. Law of Radioactive Decay 277
Nuclear reactions 279
Examples of tasks 30 281
Applications
1. Factors and prefixes for the formation of decimal multiples and submultiples and their names 284
2. Some non-system units 285
3. Fundamental physical constants 286
4. Some astrophysical characteristics 287
5. Physical quantities and their units in SI 288
6. Greek alphabet 295
7. Mechanical properties of solids 296
8. Pressure p and density p of saturated water vapor at different temperatures t 297
9. Thermal properties of solids 298
10. Electrical properties of metals 299
11. Electrical properties of dielectrics 300
12. Masses of atomic nuclei 301
13. Intense lines of the spectra of elements arranged by wavelength (MCM) 302
14. Reference data that may be needed when performing test tasks 303
Subject index 306
Replies 317

The new reference book contains all the theoretical material for the physics course in grades 10-11 and is intended to prepare students for the Unified State Exam (USE).
The contents of the main sections of the reference book are “Mechanics”, “Molecular Physics. Thermodynamics”, “Electrodynamics”, “Optics”, “Fundamentals of the special theory of relativity”, “Quantum physics” corresponds to the codifier of content elements and requirements for the level of training of graduates of general education organizations for the unified state exam in physics, on the basis of which test and measurement materials are compiled Unified State Exam.

• Problem 25, which was previously presented in Part 2 as a short-answer task, is now offered as an extended solution and is worth a maximum of 2 points. Thus, the number of tasks with a detailed answer increased from 5 to 6.
• For task 24, which tests mastery of the elements of astrophysics, instead of choosing two required correct answers, you are offered a choice of all correct answers, the number of which can be either 2 or 3.

Structure of Unified State Examination tasks in physics 2020

The examination paper consists of two parts, including 32 tasks.

Part 1 contains 26 tasks.

• In problems 1–4, 8–10, 14, 15, 20, 25–26, the answer is a whole number or a finite decimal fraction.
• The answer to tasks 5–7, 11, 12, 16–18, 21, 23 and 24 is a sequence of two numbers.
• The answer to task 13 is a word.
• The answer to tasks 19 and 22 are two numbers.

Part 2 contains 6 tasks. The answer to tasks 27–32 includes a detailed description of the entire progress of the task. The second part of the tasks (with a detailed answer) is assessed by an expert commission on the basis of.

Unified State Exam topics in physics that will be included in the exam paper

1. Mechanics(kinematics, dynamics, statics, conservation laws in mechanics, mechanical vibrations and waves).
2. Molecular physics(molecular kinetic theory, thermodynamics).
3. Electrodynamics and fundamentals of SRT(electric field, direct current, magnetic field, electromagnetic induction, electromagnetic oscillations and waves, optics, fundamentals of SRT).
4. Quantum physics and elements of astrophysics(wave-corpuscular dualism, atomic physics, physics of the atomic nucleus, elements of astrophysics).

Duration of the Unified State Exam in Physics

The entire examination work will be completed 235 minutes.

The approximate time to complete tasks of various parts of the work is:

1. for each task with a short answer – 3–5 minutes;
2. for each task with a detailed answer – 15–20 minutes.

What you can take for the exam:

• A non-programmable calculator is used (for each student) with the ability to calculate trigonometric functions (cos, sin, tg) and a ruler.
• The list of additional devices and devices, the use of which is permitted for the Unified State Examination, is approved by Rosobrnadzor.

Important!!! You should not rely on cheat sheets, tips or the use of technical means (phones, tablets) during the exam. Video surveillance at the Unified State Exam 2020 will be strengthened with additional cameras.

Unified State Exam scores in physics

• 1 point - for 1-4, 8, 9, 10, 13, 14, 15, 19, 20, 22, 23, 25, 26 tasks.
• 2 points - 5, 6, 7, 11, 12, 16, 17, 18, 21, 24, 28.
• 3 points - 27, 29, 30, 31, 32.

Total: 53 points(maximum primary score).

What you need to know when preparing tasks for the Unified State Exam:

• Know/understand the meaning of physical concepts, quantities, laws, principles, postulates.
• Be able to describe and explain physical phenomena and properties of bodies (including space objects), the results of experiments... give examples of the practical use of physical knowledge
• Distinguish hypotheses from scientific theory, draw conclusions based on experiment, etc.
• Be able to apply acquired knowledge when solving physical problems.
• Use acquired knowledge and skills in practical activities and everyday life.

Where to start preparing for the Unified State Exam in Physics:

1. Study the theory required for each task.
2. Practice test tasks in physics, developed based on

Physics is a rather complex subject, so preparing for the Unified State Exam in Physics 2020 will take a sufficient amount of time. In addition to theoretical knowledge, the commission will test the ability to read diagrams and solve problems.

Let's look at the structure of the exam paper

It consists of 32 tasks distributed over two blocks. For understanding, it is more convenient to arrange all the information in a table.

The entire theory of the Unified State Examination in Physics by sections

• Mechanics. This is a very large, but relatively simple section that studies the movement of bodies and the interactions that occur between them, including dynamics and kinematics, conservation laws in mechanics, statics, vibrations and waves of a mechanical nature.
• Molecular physics. This topic places particular emphasis on thermodynamics and molecular kinetic theory.
• Quantum physics and components of astrophysics. These are the most difficult sections that cause difficulties both during study and during testing. But also, perhaps, one of the most interesting sections. Here, knowledge is tested on such topics as the physics of the atom and the atomic nucleus, wave-particle duality, and astrophysics.
• Electrodynamics and special theory of relativity. Here you can’t do without studying optics, the fundamentals of SRT; you need to know how the electric and magnetic fields operate, what direct current is, what are the principles of electromagnetic induction, how electromagnetic oscillations and waves arise.

Yes, there is a lot of information, the volume is very decent. In order to successfully pass the Unified State Exam in physics, you need to have a very good command of the entire school course in the subject, and it is studied for five whole years. Therefore, it will not be possible to prepare for this exam in a few weeks or even a month. You need to start now so that you can feel calm during the tests.

Unfortunately, the subject of physics causes difficulties for many graduates, especially for those who chose it as their major for admission to university. Effective learning of this discipline has nothing to do with memorizing rules, formulas and algorithms. In addition, mastering physics ideas and reading as much theory as possible is not enough; you need to be proficient in mathematical techniques. Often, poor mathematical preparation prevents a student from doing well in physics.

How to prepare?

Everything is very simple: choose a theoretical section, read it carefully, study it, trying to understand all physical concepts, principles, postulates. After this, reinforce your preparation by solving practical problems on the chosen topic. Use online tests to test your knowledge; this will allow you to immediately understand where you are making mistakes and get used to the fact that a certain amount of time is given to solve a problem. We wish you good luck!

The proposed manual is addressed to students in grades 10-11 who plan to take the Unified State Exam in physics, teachers and methodologists. The book is intended for the initial stage of active preparation for the exam, for practicing all topics and types of tasks of basic and advanced levels of complexity. The material presented in the book complies with the Unified State Exam-2016 specification in physics and the Federal State Educational Standard for secondary general education.
The publication contains the following materials:
- theoretical material on the topics “Mechanics”, “Molecular Physics”, “Electrodynamics”, “Oscillations and Waves”, “Optics”, “Quantum Physics”;
- tasks of basic and advanced levels of complexity for the above sections, distributed by topic and level;
- answers to all tasks.
The book will be useful for reviewing the material, for practicing the skills and competencies necessary to pass the Unified State Exam, for organizing preparation for the exam in the classroom and at home, as well as for use in the educational process not only for the purpose of exam preparation. The manual is also suitable for applicants planning to take the Unified State Exam after a break in their studies.
The publication is included in the educational and methodological complex “Physics. Preparation for the Unified State Exam."

Examples.
Two cars left points A and B towards each other. The speed of the first car is 80 km/h, the second is 10 km/h less than the first. What is the distance between points A and B if the cars meet in 2 hours?

Bodies 1 and 2 move along the x axis at constant speed. Figure 11 shows graphs of the dependence of the coordinates of moving bodies 1 and 2 on time t. Determine at what time t the first body will catch up with the second.

Two cars are driving along a straight section of highway in the same direction. The speed of the first car is 90 km/h, the second is 60 km/h. What is the speed of the first car relative to the second?

Table of contents
From authors 7
Chapter I. Mechanics 11
Theoretical material 11
Kinematics 11
Dynamics of a material point 14
Conservation laws in mechanics 16
Statics 18
Basic difficulty level 19 tasks
§ 1. Kinematics 19
1.1. Speed ​​of uniform linear motion 19
1.2. Equation of uniform rectilinear motion 21
1.3. Speed ​​addition 24
1.4. Motion with constant acceleration 26
1.5. Free Fall 34
1.6. Circular movement 38
§ 2. Dynamics 39
2.1. Newton's laws 39
2.2. Force of universal gravitationlaw of universal gravitation 42
2.3. Gravity, body weight 44
2.4. Elastic force, Hooke's law 46
2.5. Friction force 47
§ 3. Conservation laws in mechanics 49
3.1. Pulse. Law of conservation of momentum 49
3.2. Work of force.^Power 54
3.3. Kinetic energy and its change 55
§ 4. Statics 56
4.1. Balance of bodies 56
4.2. Archimedes' law. Swimming condition of bodies 58
Advanced tasks 61
§ 5. Kinematics 61
§ 6. Dynamics of a material point 67
§ 7. Conservation laws in mechanics 76
§ 8. Statics 85
Chapter II. Molecular Physics 89
Theoretical material 89
Molecular Physics 89
Thermodynamics 92
Basic difficulty level 95 tasks
§ 1. Molecular physics 95
1.1. Models of the structure of gases, liquids and solids. Thermal movement of atoms and molecules. Interaction of particles of matter. Diffusion, Brownian motion, ideal gas model. Changes in the aggregate states of matter (explanation of phenomena) 95
1.2. Amount of substance 102
1.3. Basic equation MKT 103
1.4. Temperature is a measure of the average kinetic energy of molecules 105
1.5. Equation of state of an ideal gas 107
1.6. Gas laws 112
1.7. Saturated steam. Humidity 125
1.8. Internal energy, amount of heat, work in thermodynamics 128
1.9. First law of thermodynamics 143
1.10. Efficiency of heat engines 147
Advanced level tasks 150
§ 2. Molecular physics 150
§ 3. Thermodynamics 159
Chapter III. Electrodynamics 176
Theoretical material 176
Basic concepts and laws of electrostatics 176
Electrical capacity. Capacitors. Electric field energy 178
Basic concepts and laws of direct current 179
Basic concepts and laws of magnetostatics 180
Basic concepts and laws of electromagnetic induction 182
Basic difficulty level tasks 183
§ 1. Fundamentals of electrodynamics 183
1.1. Electrification of bodies. Law of conservation of electric charge (explanation of phenomena) 183
1.2. Coulomb's Law 186
1.3. Electric field strength 187
1.4. Electrostatic field potential 191
1.5. Electrical capacity, capacitors 192
1.6. Ohm's law for circuit section 193
1.7. Series and parallel connection of conductors 196
1.8. DC operation and power 199
1.9. Ohm's Law for a Complete Circuit 202
§ 2. Magnetic field 204
2.1. Interaction of currents 204
2.2. Ampere power. Lorentz force 206
§ 3. Electromagnetic induction 212
3.1. Induction current. Lenz's Rule 212
3.2. Law of electromagnetic induction 216
3.3. Self-induction. Inductance 219
3.4. Magnetic field energy 221
Tasks of increased difficulty level 222
§ 4. Fundamentals of electrodynamics 222
§ 5. Magnetic field 239
§ 6. Electromagnetic induction 243
Chapter IV. Oscillations and waves 247
Theoretical material 247
Mechanical vibrations and waves 247
Electromagnetic oscillations and waves 248
Basic difficulty level 250 tasks
§ 1. Mechanical vibrations 250
1.1. Math pendulum 250
1.2. Dynamics of oscillatory motion 253
1.3. Energy conversion during harmonic vibrations 257
1.4. Forced vibrations. Resonance 258
§ 2. Electromagnetic oscillations 260
2.1. Processes in an oscillatory circuit 260
2.2. Period of free oscillations 262
2.3. Alternating electric current 266
§ 3. Mechanical waves 267
§ 4. Electromagnetic waves 270
Advanced tasks 272
§ 5. Mechanical vibrations 272
§ 6. Electromagnetic oscillations 282
Chapter V. Optics 293
Theoretical material 293
Basic concepts and laws of geometric optics 293
Basic concepts and laws of wave optics 295
Fundamentals of the special theory of relativity (STR) 296
Basic difficulty level tasks 296
§ 1. Light waves 296
1.1. Law of Light Reflection 296
1.2. Law of light refraction 298
1.3. Constructing an image in lenses 301
1.4. Thin lens formula. Lens magnification 304
1.5. Dispersion, interference and diffraction of light 306
§ 2. Elements of the theory of relativity 309
2.1. Postulates of the theory of relativity 309
2.2. Main consequences of postulates 311
§ 3. Radiations and spectra 312
Tasks of increased difficulty level 314
§ 4. Optics 314
Chapter VI. Quantum Physics 326
Theoretical material 326
Basic concepts and laws of quantum physics 326
Basic concepts and laws of nuclear physics 327
Basic difficulty level tasks 328
§ 1. Quantum physics 328
1.1. Photo effect 328
1.2. Photons 333
§ 2. Atomic physics 335
2.1. The structure of the atom. Rutherford's experiments 335
2.2. Bohr model of the hydrogen atom 336
§ 3. Physics of the atomic nucleus 339
3.1. Alpha, beta and gamma radiation 339
3.2. Radioactive transformations 340
3.3. Law of Radioactive Decay 341
3.4. Structure of the atomic nucleus 346
3.5. Binding energy of atomic nuclei 347
3.6. Nuclear reactions 348
3.7. Fission of uranium 350 nuclei
3.8. Nuclear chain reactions 351
§ 4. Elementary particles 351
Tasks of increased difficulty level 352
§ 5. Quantum physics 352
§ 6. Atomic physics 356
Answers to the collection of tasks 359.

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To successfully pass the Unified State Exam in physics, the ability to solve problems from all sections of physics included in the high school curriculum is required. On our website you can independently test your knowledge and practice solving Unified State Exam tests in physics on various topics. The tests include tasks of basic and advanced difficulty levels. After completing them, you will determine the need for a more detailed repetition of this or that section of physics and improving problem-solving skills on individual topics in order to successfully pass the Unified State Exam in physics.

One of the most important stages preparation for the Unified State Exam in physics 2020 is an introduction to demo version of the Unified State Exam in Physics 2020 . The 2020 demo version has already been approved by the Federal Institute of Pedagogical Measurements (FIPI). The demo version has been developed taking into account all the amendments and features of the upcoming exam in the subject next year. What is the demo version of the Unified State Exam in Physics 2020? The demo version contains standard tasks that, in their structure, quality, topics, level of complexity and volume, fully correspond to the tasks of future real versions of CMM in physics in 2020. You can view the demo version of the Unified State Exam in Physics 2020 on the FIPI website: www.fipi.ru

In 2020, there were minor changes in the structure of the Unified State Exam in Physics: task 28 became a task with a detailed answer for 2 primary points, and task 27 was a qualitative task, similar to task 28 in the Unified State Exam 2019. Thus, instead of 5, there were 6 tasks with a detailed answer. Astrophysics Assignment 24 has also changed slightly: instead of choosing two correct answers, you now need to choose all correct answers, of which there can be either 2 or 3.

When participating in the main stream of the Unified State Exam, it is advisable to familiarize yourself with the examination materials of the early period of the Unified State Exam in Physics, published on the FIPI website after the early exam.

Fundamental theoretical knowledge in physics is essential for successfully passing the Unified State Exam in physics. It is important that this knowledge is systematized. A sufficient and necessary condition for mastering the theory is mastery of the material presented in school textbooks on physics. This requires systematic classes aimed at studying all sections of the physics course. Particular attention should be paid to solving computational and qualitative problems included in the Unified State Exam in Physics in terms of problems of increased complexity.

Only a deep, thoughtful study of the material with conscious assimilation, knowledge and interpretation of physical laws, processes and phenomena, combined with problem-solving skills, will ensure successful passing of the Unified State Exam in physics.

If you need preparation for the Unified State Exam in physics , will be happy to help you - Victoria Vitalievna.

Unified State Exam formulas in Physics 2020

Mechanics- one of the most significant and most widely represented sections of physics in Unified State Examination tasks. Preparation for this section takes up a significant part of the preparation time for the Unified State Exam in Physics. The first section of mechanics is kinematics, the second is dynamics.

Kinematics

Uniform movement:

x = x 0 + S x x = x 0 + v x t

Uniformly accelerated motion:

S x = v 0x t + a x t 2 /2 S x =(v x 2 - v 0x 2)/2a x

x = x 0 + S x x = x 0 + v 0x t + a x t 2 /2

Free fall:

y = y 0 + v 0y t + g y t 2 /2 v y = v 0y + g y t S y = v 0y t + g y t 2 /2

The path traveled by the body is numerically equal to the area of ​​the figure under the velocity graph.

Average speed:

v av = S/t S = S 1 + S 2 +.....+ S n t = t 1 + t 2 + .... + t n

Law of addition of speeds:

The velocity vector of a body relative to a fixed frame of reference is equal to the geometric sum of the speed of the body relative to a moving frame of reference and the speed of the most mobile reference frame relative to a stationary frame.

Movement of a body thrown at an angle to the horizontal

Speed ​​equations:

v x = v 0x = v 0 cosa

v y = v 0y + g y t = v 0 sina - gt

Coordinate equations:

x = x 0 + v 0x t = x 0 + v 0 cosa t

y = y 0 + v 0y t + g y t 2 /2 = y 0 + v 0 sina t + g y t 2 /2

Gravity acceleration: g x = 0 g y = - g

Circular movement

a c = v 2 /R = ω 2 R v = ω R T = 2 πR/v

Statics

Moment of power M = Fl, where l is the arm of the force F is the shortest distance from the fulcrum to the line of action of the force

Lever balance rule: The sum of the moments of forces rotating the lever clockwise is equal to the sum of the moments of forces rotating counterclockwise

M 1 + M 2 + M n ..... = Mn+1 + M n+2 + .....

Pascal's law: The pressure exerted on a liquid or gas is transmitted to any point equally in all directions

Fluid pressure at depth h: p =ρgh, taking into account atmospheric pressure: p = p 0+ρgh

Archimedes' law: F Arch = P displaced - Archimedes' force is equal to the weight of the liquid in the volume of the immersed body

Archimedes' force F Arch =ρg Vimmersed- buoyant force

Lifting force F under = F Arch - mg

Sailing conditions for bodies:

F Arch > mg - the body floats up

F Arch = mg - body floats

F Arch< mg - тело тонет

Dynamics

Newton's first law:

There are inertial frames of reference relative to which free bodies maintain their speed.

Newton's second law: F = ma

Newton's second law in impulse form: FΔt = Δp The impulse of the force is equal to the change in the momentum of the body

Newton's third law: The action force is equal to the reaction force. WITH silts are equal in magnitude and opposite in direction F 1 = F 2

Gravity F heavy = mg

Body weight P = N(N - ground reaction force)

Elastic force Hooke's law F control = kΙΔxΙ

Friction force F tr =µ N

Pressure p = F d / S[1 Pa]

Body density ρ = m/V[1 kg/m3]

Law of Gravity I F = G m 1m2/R2

F strand = GM z m/R z 2 = mg g = GM z /R z 2

According to Newton's Second Law: ma c = GmMz/(R z + h) 2

mv 2 /(R z + h) = GmM z /(R z + h) 2

ʋ 1 2 = GM s / R s- square of first escape velocity

ʋ 2 2 = GM s / R s - square of second escape velocity

Work done by force A = FScosα

Power P = A/t = Fvcosα

Kinetic energy Ek = mʋ 2 /2 = P 2 /2m

Kinetic energy theorem: A= ΔE k

Potential energy E p = mgh - body energy above the Earth at height h

E p = kx 2 /2 - energy of an elastically deformed body

A = - Δ E p - work of potential forces

Law of conservation of mechanical energy

ΔE = 0 (E k1 + E p1 = E k2 + E p2)

Law of change of mechanical energy

ΔE = Asopr (A resist - work of all non-potential forces)

Oscillations and waves

Mechanical vibrations

T-oscillation period - time of one complete oscillation [1s]

ν - oscillation frequency- number of oscillations per unit time [1Hz]

T = 1/ ν

ω - cyclic frequency

ω = 2π ν = 2π/T T = 2π/ω

Period of oscillation of a mathematical pendulum:T = 2π(l/g) 1/2

Oscillation period of a spring pendulum:T = 2π(m/k) 1/2

Harmonic vibration equation: x = xm sin( ωt +φ 0 )

Speed ​​reduction: ʋ = x , = x mω cos(ωt + φ 0) = ʋ m cos(ωt +φ 0) ʋ m = x m ω

Acceleration equation: a =ʋ , = - x m ω 2 sin(ωt + φ 0 ) a m = x mω 2

Energy of harmonic vibrations mʋ m 2 /2 = kx m 2 /2 = mʋ 2 /2 + kx 2 /2 = const

Wave - propagation of vibrations in space

wave speedʋ = λ /T

Traveling wave damage

x = xm sinωt - vibration equation

x- displacement at any time , x m - vibration amplitude

ʋ - speed of propagation of vibrations

Ϯ - time after which the oscillations will arrive at point x: Ϯ = x/ʋ

Uranation of the traveling wave: x = x m sin(ω(t - Ϯ)) = x m sin(ω(t - x/ʋ))

x- displacement at any time

Ϯ - delay time of oscillations at a given point

Molecular physics and thermodynamics

Quantity of substance v = N/N A

Molar mass M = m 0 N A

Number of moles v = m/M

Number of molecules N = vN A = N A m/M

Basic MKT equation p = m 0 nv avg 2 /3

Relationship between pressure and average kinetic energy of molecules p = 2nE avg /3

Temperature is a measure of the average kinetic energy of molecules E av = 3kT/2

Dependence of gas pressure on concentration and temperature p = nkT

Temperature relationship T = t + 273

Equation of state of an ideal gas pV = mRT/M =vRT = NkT - Mendeleev's equation

p = ρRT/M

p 1 V 1/ /T 1 = p 2 V 2 /T 2 = const for constant gas mass - Clapeyron equation

Gas laws

Boyle-Marriott Law: pV = const if T = const m = const

Gay-Lussac's Law: V/T = const if p = const m = const

Charles's Law: p/T = const if V = const m = const

Relative humidity

φ = ρ/ρ 0 · 100%

Internal energy U = 3mRT/2M

Change in internal energy ΔU = 3mRΔT/2M

We judge the change in internal energy by the change in absolute temperature!!!

Gas work in thermodynamics A" = pΔV

Work of external forces on gas A = - A"

Calculation of heat amount

The amount of heat required to heat a substance (released when it cools) Q = cm(t 2 - t 1)

c - specific heat capacity of the substance

The amount of heat required to melt a crystalline substance at its melting point Q = λm

λ - specific heat of fusion

The amount of heat required to convert a liquid into steam Q = Lm

L- specific heat of vaporization

The amount of heat released during fuel combustion Q = qm

q-specific heat of combustion of fuel

First law of thermodynamics ΔU = Q + A

Q = ΔU + A"

Q- the amount of heat received by the gas

The first law of thermodynamics for isoprocesses:

Isothermal process: T = const

Isochoric process: V = const

Isobaric process: p = const

ΔU = Q + A

Adiabatic process: Q = 0 (in a thermally insulated system)

Heat engine efficiency

η = (Q 1 - Q 2) /Q 1 = A"/Q 1

Q 1- amount of heat received from the heater

Q 2- the amount of heat transferred to the refrigerator

Maximum efficiency value of a heat engine (Carnot cycle:) η =(T 1 - T 2)/T 1

T 1- heater temperature

T 2- refrigerator temperature

Heat balance equation: Q 1 + Q 2 + Q 3 + ... = 0 (Q received = Q dept)

Electrodynamics

Along with mechanics, electrodynamics occupies a significant part of the Unified State Examination tasks and requires intensive preparation to successfully pass the physics exam.

Electrostatics

Law of conservation of electric charge:

In a closed system, the algebraic sum of the electric charges of all particles is conserved

Coulomb's law F = kq 1 q 2 /R 2 = q 1 q 2 /4π ε 0 R 2- the force of interaction between two point charges in a vacuum

Like charges repel, and unlike charges attract

Tension- power characteristic of the electric field of a point charge

E = kq 0 /R 2 - modulus of the field strength of a point charge q 0 in vacuum

The direction of vector E coincides with the direction of the force acting on the positive charge at a given point in the field

Principle of field superpositions: The intensity at a given field point is equal to the vector sum of the field strengths acting at this point:

φ = φ 1 + φ 2 + ...

The work of the electric field when moving a charge A = qE(d 1 - d 2) = - qE(d 2 - d 1) =q(φ 1 - φ 2) = qU

A = - (W p2 - W p1)

Wp = qEd = qφ - potential energy of the charge at a given point in the field

Potential φ = W p /q =Ed

Potential difference - voltage: U = A/q

Relationship between tension and potential differenceE = U/d

Electrical capacity

C=εε 0 S/d - electrical capacity of a flat capacitor

Energy of a parallel plate capacitor: W p = qU/2 = q 2 /2C = CU 2/2

Parallel connection of capacitors: q = q 1 +q 2 + ... ,U 1 = U 2 = ... ,C = C 1 + C 2 + ...

Series connection connection of capacitors: q 1 = q 2 = ...,U = U 1 + U 2 + ...,1/С =1/С 1 +1/С 2 + ...

DC laws

Determination of current: I = Δq/Δt

Ohm's law for a circuit section: I = U/R

Conductor resistance calculation: R =ρl/S

Laws for serial connection of conductors:

I = I 1 = I 2 U = U 1 + U 2 R = R 1 + R 2

U 1 / U 2 = R 1 / R 2

Laws for parallel connection of conductors:

I = I 1 + I 2 U = U 1 = U 2 1/R = 1/R 1 +1/R 2 + ... R = R 1 R 2 /(R 1 + R 2) - for 2 conductors

I 1 /I 2 = R 2 /R 1

Electric field work A = IUΔt
Electric current power P = A/Δt = IU I 2 R = U 2 /R

Joule-Lenz law Q = I 2 RΔt - amount of heat generated by a current-carrying conductor

EMF of the current source ε = A stor /q

Ohm's law for a complete circuit

Electromagnetism

Magnetic field is a special form of matter that arises around moving charges and acts on moving charges

Magnetic induction - strength characteristic of a magnetic field

B = F m /IΔl

F m = BIΔl

Ampere force is the force acting on a current-carrying conductor in a magnetic field

F= BIΔlsinα

The direction of the Ampere force is determined by the left-hand rule:

If the 4 fingers of the left hand are directed in the direction of the current in the conductor so that the lines of magnetic induction enter the palm, then the thumb bent 90 degrees will indicate the direction of action of the Ampere force

Lorentz force is a force acting on an electric charge moving in a magnetic field

F l = qBʋ sinα

The direction of the Lorentz force is determined by the left-hand rule:

If the 4 fingers of the left hand are directed in the direction of movement of the positive charge (against the movement of the negative charge), so that the magnetic lines enter the palm, then the thumb bent 90 degrees will indicate the direction of the Lorentz force

Magnetic flux Ф = BScosα [F] = 1 Wb

Lenz's rule:

The induced current arising in a closed circuit with its magnetic field prevents the change in the magnetic flux that causes it

Law of electromagnetic induction:

The induced emf in a closed loop is equal in magnitude to the rate of change of magnetic flux through the surface bounded by the loop

Induction emf in moving conductors:

Inductance L = Ф/I[L] = 1 H

Self-induced emf:

Current magnetic field energy: W m = LI 2 /2

Electric field energy: Wel = qU/2 = CU 2 /2 = q 2 /2C

Electromagnetic oscillations - harmonic oscillations of charge and current in an oscillatory circuit

q = q m sinω 0 t - charge fluctuations on the capacitor

u = Um sinω 0 t - voltage fluctuations across the capacitor

U m = q m /C

i = q" = q mω 0 cosω 0 t- fluctuations in current strength in the catalytic convertershke

I max = q mω 0 - current amplitude

Thomson's formula

Law of conservation of energy in an oscillatory circuit

CU 2 /2 = LI 2 /2 = CU 2 max /2 = LI 2 max /2 = Const

Alternating current:

Ф = BScosωt

e = - Ф’ = BSω sinω t = E m sinω t

u = Um sinω t

i = I m sin(ω t+π​/2)

Properties of electromagnetic waves

Optics

Law of Reflection: The angle of reflection is equal to the angle of incidence

Law of refraction: sinα/sinβ = ʋ 1/ ʋ 2 = n

n is the relative refractive index of the second medium to the first

n 1 - absolute refractive index of the first medium n 1 = c/ʋ 1

n 2 - absolute refractive index of the second medium n 2 = c/ʋ 2

When light passes from one medium to another, its wavelength changes, but the frequency remains unchanged v 1 = v 2 n 1 λ 1 = n 1 λ 2

Total reflection

The phenomenon of total internal reflection is observed when light passes from a denser medium to a less dense one, when the angle of refraction reaches 90°

Limit angle of total reflection: sinα 0 = 1/n = n 2 /n 1

Thin lens formula 1/F = 1/d + 1/f

d - distance from object to lens

f - distance from lens to image

F - focal length

Optical power of the lens D = 1/F

Lens magnification Г = H/h = f/d

h - object height

H - image height

Dispersion- decomposition of white color into spectrum

Interference - addition of waves in space

Maximum conditions:Δd = kλ -integer number of wavelengths

Minimum conditions: Δd = (2k + 1) λ/2 -odd number of half-wavelengths

Δd- difference between two waves

Diffraction- wave bending around an obstacle

Diffraction grating

dsinα = k λ - diffraction grating formula

d - lattice constant

dx/L = k λ

x - distance from the central maximum to the image

L - distance from the grille to the screen

The quantum physics

Photon energy E = hv

Einstein's equation for the photoelectric effect hv = A out +mʋ 2 /2

mʋ 2 /2 = eU z U z - blocking voltage

Photoelectric effect red border: hv = A out v min = A out /h λmax = c/ v min

The energy of photoelectrons is determined by the frequency of light and does not depend on the intensity of light. The intensity is proportional to the number of quanta in the light beam and determines the number of photoelectrons

Photon momentum

E = hv = mc 2

m = hv/c 2 p = mc = hv/c = h/ λ - photon momentum

Bohr's quantum postulates:

An atom can only be in certain quantum states in which it does not emit

The energy of an emitted photon during the transition of an atom from a stationary state with energy E k to a stationary state with energy En:

h v = E k - E n

Energy levels of the hydrogen atom E n = - 13.55/ n 2 eV, n =1, 2, 3,...

Nuclear physics

Law of radioactive decay. Half-life T

N = N 0 2 -t/T

Binding energy of atomic nuclei E b = ΔMc 2 = (Zm P + Nm n - M i)c 2

Radioactivity

Alpha Decay: