This is a movement in which the speed of a body changes equally over any equal periods of time, i.e. acceleration is constant.

Examples of such motion are the free fall of bodies near the surface of the Earth and motion under the influence of a constant force.

With uniformly accelerated linear motion, the coordinate of the body changes over time in accordance with the law of motion:

Where x 0 – initial coordinate of the material point, 0 x– projection of initial speed and a x– projection of point acceleration onto axis 0 X.

Projection of the velocity of a material point onto axis 0 X in this case it changes according to the following law:

In this case, the projections of velocity and acceleration can take on different values, including negative ones.

Dependency graphs x (t) And x(t) represent a straight line and a parabola, respectively, and, as in algebra, the coefficients in the equations of a straight line and a parabola can be used to judge the location of the graph of a function relative to the coordinate axes.

Figure 6 shows graphs for x(t),x (t),s(t) when x 0 > 0, 0 x > 0,a x < 0. Соответственно прямая(t) has a negative slope (tg  =a x < 0).

3. Rotational motion and its kinematic parameters. Relationship between angular and linear speeds.

Uniform movement around a circle occurs at a constant absolute speed, i.e. = const (Fig. 7). However, the direction of velocity during such motion continuously changes, therefore the uniform motion of a body in a circle is motion with acceleration.

To describe the uniform motion of a body in a circle, the following physical quantities are introduced: period,circulation frequency,linear speed,angular velocity And centripetal acceleration.

Circulation periodT– the time it takes to complete one full revolution.

Frequency is the number of revolutions made by the body in 1 s. The SI unit of frequency of circulation is c –1.

Frequency and period of revolution are related by the relation.

When a point moves around a circle, the velocity vector constantly changes its direction (Fig. 8).

With uniform motion of a body in a circle, the path segment  s, traveled during a period of time t, is the length of the arc of a circle. The relationship is constant over time and is called linear speed module. For a time equal to the circulation period T, the point travels a distance equal to the circumference of the circle 2 R, That's why

The speed of rotation of solid bodies is usually characterized by a physical quantity called angular velocity , the module of which is equal to the ratio of the angle of rotation of the body  to the period of time during which this rotation is completed (Fig. 8):

The SI unit of angular velocity is c –1.

Since the orientation of a rigid body is the same in all reference systems moving translationally relative to each other, the angular velocity of rotation of the rigid body will be the same in all reference systems moving translationally relative to each other.

With uniform rotation of a rigid body about a certain axis, any point of this body moves around the same axis in a circle of radius R with linear speed, which is equal to

If the initial coordinates of the point are equal ( R; 0), then its coordinates change according to the law x(t) =R cos t And y(t) =R sin t.

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Question. Types of mechanical movement. Velocity and acceleration of a body during uniformly accelerated linear motion.

Mechanical movement – change in the position of a body in space relative to other bodies over time. The movement of the train relative to the ground, the movement of the passenger relative to the train, etc.

Speed– vector physical a quantity that characterizes the speed of movement and its direction of a material point in space.

Trajectory- This is the line along which the body moves.

Moving is the shortest distance between the start and end points.

Material point is a body whose dimensions can be neglected.

Path– this is the length of the territory covered by the body in a period of time.

There are several types of mechanical movement:

1) Uniform linear movement- this is a movement in which a body makes equal movements at any equal intervals of time.

Example: If a driver is driving in a straight line while maintaining a constant speed.

2) Uneven linear movement - This is a movement with variable speed.

Uniformly accelerated motion - This is a movement in which the speed of a body changes equally over any equal intervals of time. (velocity and acceleration are directed in the same direction)

Example: A flower pot falling from a balcony.

Equally slow motion - This is the movement of a body with negative acceleration, i.e. with such movement the body uniformly slows down. (speed and acceleration are in opposite directions)

Example: Movement of a stone thrown vertically upward.

3) Curvilinear movement – This is a movement whose trajectory is a curved line.

Example: the movement of the planets, the end of the clock hand on the dial.

With uniformly accelerated linear motion, the speed of a body increases over time.

The acceleration of a body during uniformly accelerated motion is a vector physical quantity equal to the ratio of the change in the speed of the body to the period of time during which this change occurred.

The velocity and acceleration vectors are directed in the same direction.

Question. Electromagnetic radiation of various ranges. Properties and applications of these radiations.

Electromagnetic radiation are interconnected and cannot exist without each other alternating electric and magnetic fields propagating in space at a finite speed. They have wave and quantum properties.

Radio waves.

Frequency: 3 kHz to 300 GHz.

Obtained using an oscillatory circuit and macroscopic vibrators.

Properties: Radio waves of different frequencies and with different wavelengths are absorbed and reflected differently by media, and exhibit diffraction and interference properties.

Application: Radio communications, television, radar.

Infrared radiation (thermal).

Frequency: 1.5 THz - 405 THz.

Wavelength:

· short: 0.74-2.5 microns;

medium: 2.5-50 microns;

· long: 50-2000 microns.

Emitted by atoms and molecules of matter. Infrared radiation is emitted by all bodies at any temperature. A person emits electromagnetic waves with a wavelength λ= l.9*10-6 m.

Properties:

1. Passes through some opaque bodies, also through rain, haze, snow.

2. Produces a chemical effect on photographic plates.

3. Absorbed by a substance, it heats it.

4. Causes an internal photoelectric effect in germanium.

5. Invisible.

6. Capable of interference and diffraction phenomena.

Recorded by thermal, photoelectric and photographic methods.

Application: Obtain images of objects in the dark, night vision devices (night binoculars), and fog. Used in forensics, physiotherapy, and in industry for drying painted products, building walls, wood, and fruit.

Visible radiation.

This is part of the solar radiation spectrum (from red to violet).

Frequency: 4*1014-8*1014Hz

Properties: Reflects, refracts, affects the eye, is capable of the phenomena of dispersion, interference, diffraction.

Ultraviolet radiation.

Frequency: 10 13 -10 16 Hz.

Sources: gas-discharge lamps with quartz tubes (quartz lamps).

Emitted by all solids with t>1000ºС, as well as luminous mercury vapor.

Properties: High chemical activity (decomposition of silver chloride, glow of zinc sulfide crystals), invisible, high penetrating ability, kills microorganisms, in small doses has a beneficial effect on the human body (tanning), but in large doses has a negative biological effect: changes in cell development and metabolism, effects on the eyes.

Application: In medicine, in industry.

X-rays.

Emitted during high acceleration of electrons, for example their deceleration in metals. Obtained using an X-ray tube: electrons in a vacuum tube (p = 10-3-10-5 Pa) are accelerated by an electric field at high voltage, reaching the anode, and are sharply decelerated upon impact. When braking, electrons move with acceleration and emit electromagnetic waves with a short length (from 100 to 0.01 nm).

Properties: Interference, X-ray diffraction on a crystal lattice, high penetrating power. Irradiation in large doses causes radiation sickness.

Application: In medicine (diagnosis of diseases of internal organs), in industry (control of the internal structure of various products, welds).

Gamma radiation (gamma rays).

A type of electromagnetic radiation with an extremely short wavelength - less than 2·10−10 m - and, as a result, pronounced corpuscular and weakly expressed wave properties

Gamma radiation has great penetrating power, i.e. it can pass through large thicknesses of matter.

Gamma radiation is used in technology (for example, flaw detection), radiation chemistry (for initiating chemical transformations, for example, during polymerization), agriculture and the food industry (mutations for the generation of economically useful forms, sterilization of products), in medicine (sterilization premises, objects, radiation therapy), etc.

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Question. Newton's laws. Their manifestation, accounting and use.

Newton's laws.

1) There are inertial reference systems relative to which a body, in the absence of external forces acting on it (or with their mutual compensation), maintains a state of rest or uniform linear motion.

2) The acceleration of a body is directly proportional to the resultant of all forces applied to the body.

3) Material points interact with each other by forces of the same nature, directed along the straight line connecting these points, equal in magnitude and opposite in direction

All classical mechanics is based on these laws.
Newton's laws are the basic laws of mechanics. From these the equations of motion of mechanical systems can be derived. However, not all laws of mechanics can be derived from Newton's laws. For example, the law of universal gravitation or Hooke's law are not consequences of Newton's three laws.

Newton's laws make it possible to explain the patterns of motion of planets and their natural and artificial satellites. Otherwise, they make it possible to predict the trajectories of planets, calculate the trajectories of spacecraft and their coordinates at any given time. Under terrestrial conditions, they make it possible to explain the flow of water, the movement of numerous and varied vehicles (the movement of cars, ships, airplanes, rockets). For all these movements, bodies and forces, Newton's laws are valid.

Question. Experimental methods for recording ionizing radiation.

Wilson chamber.

Along the path of charged particles, tracks of condensed supersaturated vapor are formed on the ions. Using a cloud chamber, energy, speed, and charge are determined. Consists of a glass plate, piston and valve.

Operating principle: The working volume of the chamber is filled with gas, which contains saturated steam. When the piston moves down quickly, the gas in the volume expands and cools, becoming supersaturated. When a particle flies through this space, creating ions along its path, then droplets of condensed vapor are formed on these ions. A particle track appears in the chamber in the form of a strip of fog.

Geiger counter. It consists of a cathode, a thin thread stretched along the axis, and an anode.

Operating principle: A gas mixture is pumped into a sealed cylinder with two electrodes. A high voltage is applied to the electrodes. The appearance of particles arriving from outside leads to the fact that primary electrons, accelerated in the corresponding field, begin to ionize other molecules of the gaseous medium. As a result, under the influence of an electric field, an avalanche-like creation of new electrons and ions occurs, which sharply increase the conductivity of the electron-ion cloud. A discharge occurs in the gas environment of the Geiger counter.

Using a Geiger counter, the fact that electrons and photons enter the tube is recorded.

Bubble chamber. Consists of a sealed chamber filled with liquefied gas.

Operating principle: The working volume is filled with liquid hydrogen heated almost to boiling and under high pressure. The liquid is transferred to a superheated state by sharply reducing the pressure. A charged particle forms a chain of ions along its path, which leads to a sudden boiling of the liquid. Vapor bubbles appear along the particle trajectory. Based on the photograph of the track, alpha, beta, and gamma particles are distinguished.

Scintillation counter.

The main elements are: a substance that luminesces under the influence of charged particles (scintillator) and a photomultiplier tube (PMT)

Operating principle: The particle causes a flash of light in the phosphor, which is detected by a photomultiplier. Heavy particles are detected.

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Ideal gas.

The main differences between an ideal gas and a real gas:

1) Particles of an ideal gas are spherical bodies of very small sizes, practically material points.

2) There is no intermolecular interaction force between particles.

3) The collision of particles is absolutely elastic.

An ideal gas does not exist in nature.

A qualitative explanation of gas pressure is that ideal gas molecules, when colliding with the walls of a container, interact with them according to the laws of mechanics as elastic bodies.

Based on the use of the basic principles of molecular kinetic theory, an equation was obtained that made it possible to calculate gas pressure if the density of the substance and speed were known.

Molecular kinetic theory - a theory that arose in the 19th century and considers the structure of matter, mainly gases, from the point of view of three main approximately correct provisions:

· all bodies consist of particles: atoms and molecules;

· particles are in continuous chaotic motion (thermal);

· particles interact with each other through absolutely elastic collisions.

The beginning of the formation of MCT was the theory of M.V. Lomonosov.

On the basis of MCT, a number of branches of modern physics have been developed, in particular, physical kinetics and statistical mechanics.

The basic MKT equation connects macroscopic parameters (pressure, volume, temperature) of a thermodynamic system with microscopic ones (mass of molecules, average speed of their movement).

Temperature - it is a measure of the average kinetic energy of molecules.

The limiting temperature at which the pressure of an ideal gas vanishes at a fixed volume is called absolute zero temperature. Absolute zero temperature: -273̊ C. It is convenient to count the temperature from absolute zero. This is how the absolute temperature scale is constructed.

Absolute temperature– temperature measured from absolute zero.

The average kinetic energy of translational motion of gas molecules is proportional to temperature. The higher the temperature, the faster the molecules move.

Avogadro's Law: Equal volumes of gases at the same temperatures and pressures contain the same number of molecules.

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Bohr's postulates.

1 postulate. There are special, stationary states of the atom, in which the atom does not emit energy, while the electrons in the atom move with acceleration. Each stationary state corresponds to a certain energy.

2nd postulate. Light emission occurs when an atom transitions from a stationary state with higher energy to a stationary state with lower energy. The energy of the emitted photon is equal to the energy difference between the stationary states.

In 1914, Frank and Hertz conducted an experiment confirming Bohr's theory: atoms of a rarefied gas were bombarded with slow electrons, followed by a study of the distribution of electrons in absolute velocity values ​​before and after the collision. During an elastic impact, the distribution should not change, since only the direction of the velocity vector changes. The results showed that when electron speeds are less than a certain critical value, the collisions are elastic, and at a critical speed the collisions become inelastic, the electrons lose energy, and the gas atoms go into an excited state. With a further increase in speed, the impacts again became elastic until a new critical speed was reached. The observed phenomenon allowed us to conclude that the atom may either not absorb energy at all, or absorb in quantities equal to the energy difference of stationary states.

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Spectral analysis.

The main property of spectra is that the wavelengths of the line spectrum of a substance depend only on the properties of the atoms of this substance, but are completely independent of the method of excitation of the luminescence of atoms. Atoms of any chemical elements give a spectrum that is not similar to the spectra of all other elements. This is what it is based on spectral analysis– method for determining chemical composition of a substance according to its spectrum. Currently, the spectra of all atoms have been determined and tables of the spectra have been compiled. With the help of spectral analysis, many new elements were discovered: rubidium, cesium, etc. It was with the help of spectral analysis that the chemical composition of the Sun and stars was learned. Helium was first discovered in the Sun and only then in the Earth's atmosphere. Spectral analysis is also used to determine the chemical composition of ores and minerals.

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Law of conservation of momentum.

The forces arising as a result of the interaction of a body belonging to the system with a body not belonging to it are called external forces.

The forces arising as a result of the interaction of bodies belonging to the system are called internal forces.

The momentum of a system of bodies can only be changed by external forces.

The law of conservation of momentum is formulated as follows: if the sum of external forces is zero, then the momentum of the system is conserved.

Momentum is also conserved in an isolated system, because in this system the bodies are not acted upon by external forces at all.

Jet propulsion.

Under jet propulsion understand the movement of a body that occurs when a certain part is separated with a certain speed relative to it. In this case, there arises Reactive force.

For example, you can inflate a child's rubber ball and release it. The ball will fly quickly. The reaction force will act as long as the outflow of air continues.

Jet engines are now widely used. Not only missiles, but also most modern aircraft are equipped with them.

Any jet engine must have at least two components:

· Combustion chamber - it is where the chemical energy of the fuel is released and converted into thermal energy of gases.

· Jet nozzle - in which the thermal energy of gases is converted into their kinetic energy when gases flow outward from the nozzle at high speed, thereby creating jet thrust.

The main technical parameter characterizing a jet engine is traction- the force that the engine develops in the direction of movement of the device.

K. E. Tsiolkovsky - founder of the theory of space flight. Scientific proof of the possibility of using a rocket for flights into outer space, beyond the Earth's atmosphere and to other planets of the solar system was first given by the Russian scientist and inventor Konstantin Eduardovich Tsiolkovsky (1857-1935). In his work “Exploration of World Spaces by Jet Instruments,” published in 1903, a formula was derived that established the relationship between the speed of the rocket, the speed of gas flow, the mass of the rocket and the mass of the fuel. Tsiolkovsky theoretically substantiated the possibility of creating a rocket capable of accelerating to a speed of 8 km/s and flying into outer space. He proposed using liquid hydrogen as fuel for such a rocket, and liquid oxygen as an oxidizer. The design of a liquid rocket, according to K. E. Tsiolkovsky, is presented in Figure 62. In 1929, K. E. Tsiolkovsky developed the idea of ​​​​creating “space rocket trains”. The theoretical works of K. E. Tsiolkovsky were more than half a century ahead of the level of technological development. These works served as the basis for the creation of modern theoretical and practical astronautics.

Successes of the USSR in space exploration. The ideas of K. E. Tsiolkovsky about the creation of “space rocket trains” - multi-stage rockets - were implemented by Soviet scientists and technicians under the leadership of the outstanding Soviet scientist, Academician Sergei Pavlovich Korolev (1907-1966).

The world's first artificial Earth satellite was launched by rocket in the Soviet Union on October 4, 1957.

On April 12, 1961, citizen of the Soviet Union Yuri Alekseevich Gagarin (1934-1968) made the world's first flight in outer space on the Vostok spacecraft.

Soviet space rockets delivered soil samples from the surface of the Moon to Earth, soft-landed automatic interplanetary stations on the surface of Venus and Mars, and launched long-term orbital stations into low-Earth orbit.

Flights of spacecraft with astronauts on board, automatic interplanetary stations and artificial Earth satellites are used both for scientific research in near-Earth and interplanetary space, and for solving practical problems of the national economy.

Using satellites and automatic interplanetary stations, the composition and structure of the Earth's atmosphere at high altitudes, the chemical composition and physical properties of the atmosphere of Venus and Mars were studied, and images of the surface of the Moon, Venus and Mars were obtained.

Molniya communication satellites, through Orbit ground stations, broadcast television programs and telephone communications at any distance within our country.

Meteorological satellites are used to study processes occurring in the earth's atmosphere and make weather forecasts.

Special satellites help ships and aircraft determine their coordinates. Studies of the surface of continents and oceans, carried out by astronauts during flights at orbital stations, make it possible to assess and clarify natural resources in various regions of the globe.

Question 2. Electric current in a vacuum. Thermionic emission. Application of vacuum devices.

Vacuum- a medium that contains gas at a pressure significantly lower than atmospheric pressure.

To create a current in a vacuum, a special source of charged particles is required. The action of such a source is usually based on thermionic emission.

Thermionic emission- the phenomenon of electrons being ejected from a metal at high temperatures.

The phenomenon of thermionic emission leads to the fact that a heated metal electrode, unlike a cold one, continuously emits electrons. The electrons form an electron cloud around the electrode. The electrode becomes positively charged, and under the influence of the electric field of the charged cloud, electrons from the cloud are partially returned to the electrode.

When the electrodes are connected to a current source, an electric field arises between them.

One-way conductivity was previously widely used in electronic devices with two electrodes - vacuum diodes, which, like semiconductor diodes, served to rectify electric current. However, at present, vacuum diodes are practically not used.

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Development of communications.

Until relatively recently, intercity telephone communications was carried out exclusively by wire.

Currently, cable and radio relay lines are being increasingly used, and the level of communication automation is increasing.

Ultrashort (decimeter and centimeter) waves are used in radio relay communication lines. These waves travel within line of sight.

Fiber optic communication lines are becoming increasingly popular, allowing the transfer of large amounts of information. The transmission process is based on multiple reflections of a laser beam propagating through a thin tube (fiber).

Advances in the field of space radio communications made it possible to create a new communication system called Orbita. This system uses relay communication satellites.

Powerful and reliable systems have been created to provide television broadcasting to the regions of Siberia and the Far East. They allow telephone and telegraph communication with remote areas of our country.

Such relatively old means of communication as the telegraph and phototelegraph are also being improved and found new applications.

A Unified Automated Communication System is being created in our country. In this regard, various technical means of communication are developing, improving and finding new areas of application.

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A value equal to the ratio of the work done by external forces when moving a point positive charge along the entire circuit, including the current source, to the charge is called the electromotive force of the current source.

Ohm's law is a formula that shows the dependence of the main characteristics of an electrical circuit, namely voltage (electromotive force), electric current (flow of charged particles) and resistance (opposition to the flow of electrons in a solid conductor).

Ohm's law for a complete circuit sounds like this: the current strength in an electrical circuit will be directly proportional to the voltage applied to this circuit, and inversely proportional to the sum of the internal resistance of the power source and the total resistance of the entire circuit.

Using Ohm's Law for a complete circuit, you can calculate the total voltage across the power supply terminals, the total current (consumed by the circuit), and the total resistance of the entire circuit.

I = U ⁄ r + R

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1 question. Photoelectric effect and its laws. Explanation of the photoelectric effect and its application .

Photo effect- This is the phenomenon of the emission of electrons by a substance under the influence of light.

Stoletov's laws for the photoelectric effect:

Formulation of the 1st law of the photoelectric effect: The strength of the photocurrent is directly proportional to the density of the light flux.

According to the 2nd law of the photoelectric effect, the maximum kinetic energy of electrons ejected by light increases linearly with the frequency of light and does not depend on its intensity.

3rd law of the photoelectric effect: for each substance there is a red limit of the photoelectric effect, that is, the minimum frequency of light (or maximum wavelength λ0) at which the photoelectric effect is still possible, and if , then the photoelectric effect no longer occurs.

The theoretical explanation of these laws was given in 1905 by Einstein. According to him, electromagnetic radiation is a stream of individual quanta (photons) with energy hν each, where h- Planck's constant. With the photoelectric effect, part of the incident electromagnetic radiation is reflected from the metal surface, and part penetrates into the surface layer of the metal and is absorbed there. Having absorbed a photon, the electron receives energy from it and, performing work function φ, leaves the metal: where is the maximum kinetic energy that the electron has when leaving the metal.

Application.

Devices based on the photoelectric effect are called photocells. The simplest such device is a vacuum photocell. The disadvantages of such a photocell are: low current, low sensitivity to long-wave radiation, difficulty in manufacturing, impossibility of use in alternating current circuits. It is used in photometry to measure luminous intensity, brightness, illumination, in cinema for sound reproduction, in phototelegraphs and photophones, in the management of production processes.

There are semiconductor photocells in which the concentration of current carriers changes under the influence of light. They are used in the automatic control of electrical circuits (for example, in subway turnstiles), in alternating current circuits, as non-renewable current sources in watches, microcalculators, the first solar cars are being tested, and are used in solar batteries on artificial Earth satellites, interplanetary and orbital automatic stations .

The phenomenon of the photoelectric effect is associated with photochemical processes occurring under the influence of light in photographic materials.

Question 2 . Deformations of solids and their types. Hooke's law. Accounting and application of deformation in technology.

Hooke's law

The deformation that occurs in an elastic body (spring, rod, console, beam, etc.) is proportional to the force applied to this body.

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Composition of the atomic nucleus.

The nucleus of an atom consists of nucleons, which are divided into protons and neutrons.

A is the number of nucleons, i.e. protons + neutrons (or atomic mass)

Z- number of protons (equal to the number of electrons)

N is the number of neutrons (or atomic number)

Isotopes

Isotopes- varieties of atoms (and nuclei) of a chemical element that have the same atomic (ordinal) number, but at the same time different mass numbers. All chemical isotopes elements are radioactive.

Examples of hydrogen isotopes (H): Deuterium, Tritium, Quadium, etc.

Binding energy of atomic nuclei.

Atomic nuclei are strongly bound systems of a large number of nucleons.
To completely split the nucleus into its component parts and remove them at large distances from each other, it is necessary to expend a certain amount of work A.

Energy of communication they call energy equal to the work that must be done to split a nucleus into free nucleons.

E connection = - A
According to the law of conservation, the binding energy is simultaneously equal to the energy that is released during the formation of a nucleus from individual free nucleons.

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INDUCTANCE

Electric current creates its own magnetic field. The magnetic flux through the circuit is proportional to the magnetic field induction (Ф ~ B), the induction is proportional to the current strength in the conductor
(B ~ I), therefore the magnetic flux is proportional to the current strength (Ф ~ I).
The self-induction emf depends on the rate of change of current in the electrical circuit and on the properties of the conductor
(size and shape) and on the relative magnetic permeability of the medium in which the conductor is located.
A physical quantity showing the dependence of the self-induction emf on the size and shape of the conductor and on the environment in which the conductor is located is called the self-induction coefficient or inductance.

Inductance- physical a value numerically equal to the self-inductive emf that occurs in the circuit when the current changes by 1 Ampere in 1 second.
Inductance can also be calculated using the formula:

where Ф is the magnetic flux through the circuit, I is the current strength in the circuit.

SI units of inductance:

The inductance of the coil depends on:
the number of turns, the size and shape of the coil and the relative magnetic permeability of the medium
(core possible).
SELF-INDUCTION EMF

The self-inductive emf prevents the current from increasing when the circuit is turned on and the current from decreasing when the circuit is opened.
ENERGY OF THE MAGNETIC FIELD OF CURRENT

Around a current-carrying conductor there is a magnetic field that has energy.
Where does it come from? The current source included in the electrical circuit has a reserve of energy.
At the moment of closing the electrical circuit, the current source spends part of its energy to overcome the effect of the self-inductive emf that arises. This part of the energy, called the current’s own energy, goes to the formation of a magnetic field.

The energy of the magnetic field is equal to the intrinsic energy of the current.
The self-energy of the current is numerically equal to the work that the current source must do to overcome the self-induction emf in order to create a current in the circuit.

The energy of the magnetic field created by the current is directly proportional to the square of the current.
Where does the magnetic field energy go after the current stops? - stands out (when a circuit with a sufficiently large current is opened, a spark or arc may occur)

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SERIAL CONNECTION

with series connection of resistances:

1. the current strength in all series-connected sections of the circuit is the same

2. voltage in a circuit consisting of several sections connected in series,
equal to the sum of stresses in each section

3. resistance of a circuit consisting of several sections connected in series,
equal to the sum of the resistances of each section

4. the work of electric current in a circuit consisting of sections connected in series,
equal to the sum of work in individual areas

5. the power of electric current in a circuit consisting of sections connected in series,
equal to the sum of the capacities in individual sections

PARALLEL CONNECTION

Calculation of electrical circuit parameters
with parallel connection of resistances:

1. the current strength in the unbranched section of the circuit is equal to the sum of the current strengths
in all parallel connected sections

3. When connecting resistances in parallel, the reciprocal values ​​of the resistance are added:

(R - conductor resistance,
1/R - electrical conductivity of the conductor)

If only two resistances are connected in parallel in a circuit, then O:

(with a parallel connection, the total resistance of the circuit is less than the smaller of the included resistances)

4. the work of electric current in a circuit consisting of parallel connected sections,
equal to the sum of work in individual areas:

5. the power of electric current in a circuit consisting of parallel connected sections,
equal to the sum of capacities in individual sections:

For two resistances:

those. The greater the resistance, the less current it contains.

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Electromagnetic field

1. An alternating magnetic field creates a vortex electric field.

Electromagnetic field

This is a special form of matter - a combination of electric and magnetic fields.

Alternating electric and magnetic fields exist simultaneously and form a single electromagnetic field.

Electromagnetic wave

AND
an electromagnetic field varying in time and propagating in space (vacuum) at a speed of 3∙10 8 m/s forms electromagnetic wave.

The finite speed of propagation of the electromagnetic field leads to the fact that electromagnetic oscillations in space propagate in the form of waves.

Electromagnetic wave is transverse.

N The direction of the speed of the electromagnetic wave coincides with the direction of movement of the right screw when turning the handle of the vector gimlet to vector .

Vector values And coincide in phase (far from the antenna).

Wave properties

1. Reflection, refraction, interference, diffraction, polarization.

2. Pressure on a substance.

3. Absorption by the environment.

4. The final speed of propagation in a vacuum.

5. Causes the phenomenon of photoelectric effect.

6. The speed in the medium decreases.

Uniform straight motion. Speed

Uniform linear movement call such a movement occurring along a rectilinear trajectory in which a body (material point) makes identical movements in any equal intervals of time.

The displacement of a body in rectilinear motion is usually denoted by s. If a body moves in a straight line in only one direction, the modulus of its displacement is equal to the distance traveled, i.e. |s|=s. In order to find the movement of a body s over a period of time t, it is necessary to know its movement over a unit time. For this purpose, the concept of speed v of a given movement is introduced.

Speed ​​of uniform linear motion call a vector quantity equal to the ratio of the movement of a body to the period of time during which this movement was made:

The direction of speed in linear motion coincides with the direction of movement.

Since in uniform rectilinear motion for any equal periods of time the body makes equal movements, the speed of such movement is a constant value (v=const). Modulo

From formula (1.2) the unit of speed is determined.

Currently, the main system of units is International system of units(abbreviated SI - international system). This system is described below. The SI unit of speed is 1 m/s (meter per second); 1 m/s is the speed of such uniform rectilinear motion at which a material point moves 1 m in 1 s.

Let the Ox axis of the coordinate system associated with the reference body coincide with the straight line along which the body moves, and x 0 is the coordinate of the starting point of the body’s movement. Both the displacement s and the speed v of the moving body are directed along the Ox axis. From formula (1.1) it follows that s=vt. According to this formula, the vectors s and vt are equal, therefore their projections on the O x axis are also equal:

s x =v x ·t. (1.3)

Now it is possible to establish the kinematic law of uniform rectilinear motion, i.e., find an expression for the coordinates of a moving body at any time. Since x=x 0 +s x , taking into account (1.3) we have

x=x 0 + v x ·t. (1.4)

According to formula (1.4), knowing the coordinate x 0 of the initial point of movement of the body and the speed of the body v (its projection v x on the O x axis), at any moment in time it is possible to determine the position of the moving body. The right side of formula (1.4) is an algebraic sum, since both x 0 and v x can be both positive and negative (a graphical representation of uniform rectilinear motion is given below).

Average and instantaneous speeds
rectilinear uneven movement

A movement in which a body makes unequal movements at equal intervals of time is called uneven(or variables). With variable motion, the speed of a body changes over time, therefore, to characterize such motion, the concepts of average and instantaneous speeds were introduced.

Medium speed variable motion v cp is a vector quantity equal to the ratio of the movement of the body s to the time period t during which this movement was made:

v cp =s/t. (1.5)

Average speed characterizes variable motion during only the period of time for which this speed is determined. Knowing the average speed for a given period of time, it is possible to determine the movement of a body using the formula s=v av ·t only for a specified period of time. It is impossible to find the position of a moving body at any time using the average speed determined by formula (1.5).

As mentioned above, when a body moves along a straight path in one direction, the modulus of its displacement is equal to the path traveled by the body, i.e. |s|=s. In this case, the average speed is determined by the formula v=s/t, from which we have

s=v av ·t. (1.6)

Instant speed variable motion is the speed that a body has at a given moment in time (and therefore at a given point on the trajectory).

Let's find out how to determine the instantaneous speed of a body. Let the body (material point) perform rectilinear uneven motion. Let us determine the instantaneous speed v of this body at an arbitrary point C of its trajectory (Fig. 2).

Let us select a small section D s 1 of this trajectory, which includes point C. The body passes this section in a period of time D t 1 . Dividing D s 1 by D t 1, we find the value of the average speed v cp1 = D s 1 / D t 1 in the section D s 1. Then for the time interval D t 2

Obviously, the shorter the time interval D t, the shorter the length of the section D s traversed by the body, and the less the value of the average speed v cp = D s/D t differs from the value of the instantaneous speed at point C. If the time interval D t tends to zero, the length of the path section D s decreases infinitely, and the value of the average speed v cp in this section tends to the value of the instantaneous speed at point C. Consequently, the instantaneous speed v is the limit to which the average speed of the body v cp tends when the time interval of the body's movement tends to zero:

v=lim(D s/D t). (1.7)

It is known from a mathematics course that the limit of the ratio of the increment of a function to the increment of the argument, when the latter tends to zero (if this limit exists), is the first derivative of this function with respect to a given argument. Therefore, we write formula (1.7) in the form

v=(ds/dt)=s" (1.8)

where the symbols d/dt or the dash at the top right of a function indicate the derivative of this function. Consequently, the instantaneous speed is the first derivative of the path with respect to time.

If the analytical form of the dependence of the path on time is known, using the rules of differentiation it is possible to determine the instantaneous speed at any time. In vector form

Uniformly accelerated linear motion. Acceleration

Such rectilinear motion, in which the speed of a body changes equally over any equal periods of time, is called uniformly accelerated linear motion.

The rate of change in speed is characterized by a value denoted by a and called acceleration. Acceleration call a vector quantity equal to the ratio of the change in the speed of a body v-v 0 to the time interval t during which this change occurred:

a=(v-v 0)/t. (1.9)

Here V 0 is the initial speed of the body, i.e. its instantaneous speed at the moment the time begins to count; v is the instantaneous speed of the body at the considered moment of time.

From formula (1.9) and the definition of uniformly accelerated motion it follows that in such motion the acceleration does not change. Consequently, rectilinear uniformly accelerated motion is motion with constant acceleration (a=const). In rectilinear uniformly accelerated motion, the vectors v 0, v and a are directed along the same straight line. Therefore, the moduli of their projections onto this line are equal to the moduli of these vectors themselves, and formula (1.9) can be written in the form

a=(v-v 0)/t. (1.10)

From formula (1.10) the acceleration unit is determined.
The SI unit of acceleration is 1 m/s2 (meter per second squared); 1 m/s 2 is the acceleration of such uniformly accelerated motion, in which for every second the speed of the body increases by 1 m/s.

Formulas for instantaneous and average speeds
uniformly accelerated motion

From (1.9) it follows that v= v 0 +at.

Using this formula, the instantaneous speed v of a body in uniformly accelerated motion is determined if its initial speed v 0 and acceleration a are known. For rectilinear uniformly accelerated motion, this formula can be written in the form

v=v 0 +at. (1.11)

If v 0 =0, then

Let us obtain an expression for the average speed of rectilinear uniformly accelerated motion. From formula (1.11) it is clear that v=v 0 at t=0, v 1 =v 0 +a at t=1, v 2 =v 0 +2a=v 1 +a at t=2, etc. Consequently, in uniformly accelerated motion, the values ​​of the instantaneous speed that a body has at equal intervals of time form a series of numbers in which each of them (starting from the second) is obtained by adding a constant number a to the previous one. This means that the considered values ​​of instantaneous speed form an arithmetic progression. Consequently, the average speed of rectilinear uniformly accelerated motion can be determined by the formula

v av =(v 0 +v)/2, (1.13)

where v 0 is the initial speed of the body; v is the speed of the body at a given time.

Equation of uniformly accelerated rectilinear motion

Let us find the kinematic law of rectilinear uniformly accelerated motion. To do this, we use formulas (1.6), (1.11) and (1.13). It follows from them that s=v av ·t=(v 0 +v) ·t/2=(2v 0 +at) ·t/2,
hence,

s=v 0 t+at 2 /2. (1.14)

If the initial speed of the body is zero (v 0 =0), then

s=at 2 /2. (1.15)

Using formulas (1.14) and (1.15), the path traveled by a body in uniformly accelerated rectilinear motion is determined (the modulus of displacement of a body that does not change the direction of its movement). For the case when the body moves along the O x axis. from the point with coordinate x 0, from formula (1.14) we obtain an equation expressing the dependence of the coordinates of this body on time. Because the

x=x o +s x, and s x =v 0x t+a x t 2 /2,

x=x 0 +v 0x t+at 2 /2. (1.16)

Formula (1.16) is the equation of rectilinear uniformly accelerated motion (the kinematic law of this motion). It should be remembered that in formula (1.16) v 0x and a x can be both positive and negative, since these are projections of the vectors v 0 and a onto the O x axis.

Relationship between the movement of a body and its speed

Let us establish a connection between the modulus of displacement s of a body performing uniformly accelerated rectilinear motion and its speed. From formula (1.10) we find that t=(v-v 0)/a. Substituting this expression and formula (1.13) into formula (1.7), we obtain

s=[(v 0 +v)/2]·[(v-v 0)/a],

hence,

s=(v 2 -v 0 2)/(2a) or v 2 =v 0 2 +2as. (1.17)

If the initial velocity of the body is zero (v 0 =0), then v 2 =2as.

In general uniformly accelerated motion called such a movement in which the acceleration vector remains unchanged in magnitude and direction. An example of such movement is the movement of a stone thrown at a certain angle to the horizon (without taking into account air resistance). At any point in the trajectory, the acceleration of the stone is equal to the acceleration of gravity. For a kinematic description of the movement of a stone, it is convenient to choose a coordinate system so that one of the axes, for example the axis OY, was directed parallel to the acceleration vector. Then the curvilinear movement of the stone can be represented as the sum of two movements - rectilinear uniformly accelerated motion along the axis OY And uniform rectilinear motion in the perpendicular direction, i.e. along the axis OX(Fig. 1.4.1).

Thus, the study of uniformly accelerated motion is reduced to the study of rectilinear uniformly accelerated motion. In the case of rectilinear motion, the velocity and acceleration vectors are directed along the straight line of motion. Therefore, the speed υ and acceleration a in projections onto the direction of movement can be considered as algebraic quantities.

Figure 1.4.1. Projections of velocity and acceleration vectors onto coordinate axes. ax = 0, ay = –g

In uniformly accelerated rectilinear motion, the speed of a body is determined by the formula

(*)

In this formula, υ 0 is the speed of the body at t = 0 (starting speed ), a= const – acceleration. On the speed graph υ ( t) this dependence looks like a straight line (Fig. 1.4.2).

Figure 1.4.2. Speed ​​graphs of uniformly accelerated motion

Acceleration can be determined from the slope of the velocity graph a bodies. The corresponding constructions are shown in Fig. 1.4.2 for graph I. Acceleration is numerically equal to the ratio of the sides of the triangle ABC:

The greater the angle β that the velocity graph forms with the time axis, i.e., the greater the slope of the graph ( steepness), the greater the acceleration of the body.

For graph I: υ 0 = –2 m/s, a= 1/2 m/s 2.

For schedule II: υ 0 = 3 m/s, a= –1/3 m/s 2

The velocity graph also allows you to determine the projection of movement s bodies for some time t. Let us select on the time axis a certain small period of time Δ t. If this period of time is small enough, then the change in speed over this period is small, i.e. the movement during this period of time can be considered uniform with a certain average speed, which is equal to the instantaneous speed υ of the body in the middle of the interval Δ t. Therefore, the displacement Δ s in time Δ t will be equal to Δ s = υΔ t. This movement is equal to the area of ​​the shaded strip (Fig. 1.4.2). Breaking down the time period from 0 to some point t for small intervals Δ t, we find that the movement s for a given time t with uniformly accelerated rectilinear motion is equal to the area of ​​the trapezoid ODEF. The corresponding constructions were made for graph II in Fig. 1.4.2. Time t taken equal to 5.5 s.

Since υ – υ 0 = at, the final formula for moving s body with uniformly accelerated motion over a time interval from 0 to t will be written in the form:

(**)

To find the coordinates y bodies at any time t needed to the starting coordinate y 0 add movement in time t:

(***)

This expression is called law of uniformly accelerated motion .

When analyzing uniformly accelerated motion, sometimes the problem arises of determining the movement of a body based on the given values ​​of the initial υ 0 and final υ velocities and acceleration a. This problem can be solved using the equations written above by eliminating time from them t. The result is written in the form

From this formula we can obtain an expression for determining the final speed υ of a body if the initial speed υ 0 and acceleration are known a and moving s:

If the initial speed υ 0 is zero, these formulas take the form

It should be noted once again that the quantities υ 0, υ, included in the formulas for uniformly accelerated rectilinear motion s, a, y 0 are algebraic quantities. Depending on the specific type of movement, each of these quantities can take on both positive and negative values.

Uniformly accelerated motion is motion with acceleration, the vector of which does not change in magnitude and direction. Examples of such movement: a bicycle rolling down a hill; a stone thrown at an angle to the horizontal.

Let's consider the last case in more detail. At any point of the trajectory, the stone is affected by the acceleration of gravity g →, which does not change in magnitude and is always directed in one direction.

The motion of a body thrown at an angle to the horizontal can be represented as the sum of motions relative to the vertical and horizontal axes.

Along the X axis the movement is uniform and rectilinear, and along the Y axis it is uniformly accelerated and rectilinear. We will consider the projections of the velocity and acceleration vectors on the axis.

Formula for speed during uniformly accelerated motion:

Here v 0 is the initial velocity of the body, a = c o n s t is the acceleration.

Let us show on the graph that with uniformly accelerated motion the dependence v (t) has the form of a straight line.

Acceleration can be determined by the slope of the velocity graph. In the figure above, the acceleration modulus is equal to the ratio of the sides of triangle ABC.

a = v - v 0 t = B C A C

The larger the angle β, the greater the slope (steepness) of the graph relative to the time axis. Accordingly, the greater the acceleration of the body.

For the first graph: v 0 = - 2 m s; a = 0.5 m s 2.

For the second graph: v 0 = 3 m s; a = - 1 3 m s 2 .

Using this graph, you can also calculate the displacement of the body during time t. How to do it?

Let us highlight a small period of time ∆ t on the graph. We will assume that it is so small that the movement during the time ∆t can be considered a uniform movement with a speed equal to the speed of the body in the middle of the interval ∆t. Then, the displacement ∆ s during the time ∆ t will be equal to ∆ s = v ∆ t.

Let us divide the entire time t into infinitesimal intervals ∆ t. The displacement s during time t is equal to the area of ​​the trapezoid O D E F .

s = O D + E F 2 O F = v 0 + v 2 t = 2 v 0 + (v - v 0) 2 t .

We know that v - v 0 = a t, so the final formula for moving the body will take the form:

s = v 0 t + a t 2 2

In order to find the coordinate of the body at a given time, you need to add displacement to the initial coordinate of the body. The change in coordinates during uniformly accelerated motion expresses the law of uniformly accelerated motion.

Law of uniformly accelerated motion

Law of uniformly accelerated motion

y = y 0 + v 0 t + a t 2 2 .

Another common problem that arises when analyzing uniformly accelerated motion is finding the displacement for given values ​​of the initial and final velocities and acceleration.

Eliminating t from the equations written above and solving them, we obtain:

s = v 2 - v 0 2 2 a.

Using the known initial velocity, acceleration and displacement, the final velocity of the body can be found:

v = v 0 2 + 2 a s .

For v 0 = 0 s = v 2 2 a and v = 2 a s

Important!

The quantities v, v 0, a, y 0, s included in the expressions are algebraic quantities. Depending on the nature of the movement and the direction of the coordinate axes under the conditions of a specific task, they can take on both positive and negative values.

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