Presentation
on the topic of:
Newton's laws
Newton's laws
three laws that underlie classical mechanics and make it possible to write down the equations of motion for any mechanical system if the force interactions for its constituent bodies are known.
Newton's laws- depending on the angle from which you look at them - represent either the end of the beginning or the beginning of the end of classical mechanics.
In any case, this is a turning point in the history of physical science - a brilliant compilation of all the knowledge accumulated up to that historical moment about the movement of physical bodies within the framework of physical theory, which is now commonly called classical mechanics.
We can say that Newton's laws of motion began the history of modern physics and the natural sciences in general.
For centuries, thinkers and mathematicians have tried to derive formulas to describe the laws of motion of material bodies.
It never even occurred to the ancient philosophers that celestial bodies could move in orbits other than circular ones; at best, the idea arose that planets and stars revolve around the Earth in concentric (that is, nested within each other) spherical orbits.
Why? Yes, because since the times of the ancient thinkers of Ancient Greece, it never occurred to anyone that the planets could deviate from perfection, the embodiment of which is a strict geometric circle.
It would have taken the genius of Johannes Kepler to honestly look at this problem from a different angle, analyze real observational data and deduce from them that in reality the planets revolve around the Sun along elliptical trajectories.
Imagine something like an athletics hammer - a cannonball on the end of a string that you spin around your head.
In this case, the nucleus does not move in a straight line, but in a circle - which means, according to Newton’s first law, something is holding it back; this “something” is the centripetal force that you apply to the nucleus, spinning it. In reality, you can feel it yourself - the handle of the athletics hammer is noticeably pressing on your palms.
If you open your hand and release the hammer, it - in the absence of external forces - will immediately set off in a straight line.
It would be more accurate to say that this is how the hammer will behave in ideal conditions (for example, in outer space), since under the influence of the gravitational attraction of the Earth it will fly strictly in a straight line only at the moment when you let go of it, and in the future the flight path will be deviate more towards the earth's surface.
If you try to actually release the hammer, it turns out that the hammer released from a circular orbit will travel strictly along a straight line, which is tangent (perpendicular to the radius of the circle along which it was spun) with a linear speed equal to the speed of its revolution in the “orbit”.
Now let's replace the core of the athletics hammer with the planet, the hammer with the Sun, and the string with the force of gravitational attraction:
Here is Newton's model of the solar system.
Such an analysis of what happens when one body revolves around another in a circular orbit at first glance seems to be something self-evident, but we should not forget that it incorporated a whole series of conclusions of the best representatives of scientific thought of the previous generation (just remember Galileo Galilei). The problem here is that when moving in a stationary circular orbit, the celestial (and any other) body looks very serene and appears to be in a state of stable dynamic and kinematic equilibrium. However, if you look at it, only the modulus (absolute value) of the linear velocity of such a body is conserved, while its direction is constantly changing under the influence of the force of gravitational attraction. This means that the celestial body moves with uniform acceleration. By the way, Newton himself called acceleration a “change in motion.”
Newton's first law also plays another important role from the point of view of our natural scientist's attitude to the nature of the material world.
He tells us that any change in the nature of the movement of a body indicates the presence of external forces acting on it.
Relatively speaking, if we observe how iron filings, for example, jump up and stick to a magnet, or, taking clothes out of the dryer of a washing machine, we find out that things have stuck together and dried to one another, we can feel calm and confident: these effects have become a consequence of the action of natural forces (in the examples given these are the forces of magnetic and electrostatic attraction, respectively).
If Newton's first law helps us determine whether a body is under the influence of external forces, then the second law describes what happens to a physical body under their influence.
The greater the sum of external forces applied to the body, this law states, the greater the acceleration the body acquires. This time. At the same time, the more massive the body to which an equal amount of external forces is applied, the less acceleration it acquires. That's two. Intuitively, these two facts seem self-evident, and in mathematical form they are written as follows: F = ma
Where F - force, m - weight, A - acceleration.
This is probably the most useful and most widely used of all physics equations.
It is enough to know the magnitude and direction of all the forces acting in a mechanical system, and the mass of the material bodies of which it consists, and one can calculate its behavior in time with complete accuracy.
It is Newton's second law that gives all of classical mechanics its special charm - it begins to seem as if the entire physical world is structured like the most precise chronometer, and nothing in it escapes the gaze of an inquisitive observer.
Tell me the spatial coordinates and velocities of all material points in the Universe, as if Newton is telling us, tell me the direction and intensity of all the forces acting in it, and I will predict to you any of its future states. And this view of the nature of things in the Universe existed until the advent of quantum mechanics.
It is for this law that Newton most likely gained honor and respect from not only natural scientists, but also humanities scientists and simply the general public.
They love to quote him (both on business and without business), drawing the broadest parallels with what we are forced to observe in our everyday life, and they pull him almost by the ears to substantiate the most controversial provisions during discussions on any issues, from interpersonal and ending with international relations and global politics.
Newton, however, put a very specific physical meaning into his subsequently named third law and hardly intended it in any other capacity than as an accurate means of describing the nature of force interactions.
Here it is important to understand and remember that Newton is talking about two forces of completely different natures, and each force acts on “its own” object.
When an apple falls from a tree, it is the Earth that acts on the apple with the force of its gravitational attraction (as a result of which the apple rushes uniformly towards the surface of the Earth), but at the same time the apple also attracts the Earth to itself with equal force.
And the fact that it seems to us that it is the apple that falls to the Earth, and not vice versa, is already a consequence of Newton’s second law. The mass of an apple compared to the mass of the Earth is incomparably low, therefore it is its acceleration that is noticeable to the eye of the observer. The mass of the Earth, compared to the mass of an apple, is enormous, so its acceleration is almost imperceptible. (If an apple falls, the center of the Earth moves upward by a distance less than the radius of the atomic nucleus.)
Taken together, Newton’s three laws gave physicists the tools necessary to begin a comprehensive observation of all phenomena occurring in our Universe.
And, despite all the enormous advances in science that have occurred since Newton's time, to design a new car or send a spaceship to Jupiter, you will use the same three laws of Newton.
What did we study in previous lessons? Deriving formulas:
- I escape velocity
- Acceleration of gravity Working with cards C-level No. 4 No. 5 Repetition of formulas of grades 7-10
Physics teacher
MBOU secondary school No. 2
Makashutina L.V.
Today in class: Let's repeat:
- Addition of forces Let's find out what it is
- inertia
- weight
- inertia
- Let's learn Newton's 1st law and its application in life and technology
- What types of movement are there?
- All forces Competition: Who can write the most names of known forces?
- Mass is a property of a body that characterizes its inertia. Under the same influence from surrounding bodies, one body can quickly change its speed, while another, under the same conditions, can change much more slowly. It is customary to say that the second of these two bodies has greater inertia, or, in other words, the second body has greater mass.
Inertia
Manifestation of inertia The usefulness of inertia:
- without inertia, all planets would leave their orbits;
- Helps in shot put;
- When attaching the hammer to the handle;
- Shaking carpets.
- A tripped pedestrian;
- Impossibility of sudden stopping of cars;
- Passengers fall during sudden braking.
- 5.) Why do they take a run-up when doing long jumps? 1 To jump higher. 2 To increase the length of the body's trajectory. 3 To gain speed for the push.
0 → =0 → =const → door uniform, straight
Examples of Newton's first law 1. 2. 3. 4. 5. 6.
1. Earth - support body at rest
2. Earth – thread v = 0
3. Earth - air
4. Earth - water
5. Earth is the engine
6. No action
uniform rectilinear v = const
Newton's laws in nature and technology
According to Newton's first law, if no other bodies act on a body or the actions of other bodies are compensated, then the body maintains its speed constant (is at rest or moves uniformly and rectilinearly)
A puck lying on ice is at rest relative to the reference frame associated with the Earth: the influence of the Earth on it is compensated by the action of ice.
When the skis press on the snow, a thin ice film is formed which reduces the friction force and the skier continues to slide by inertia.
The force of inertia can be observed when a car brakes sharply. The car stops, but the driver continues to move. Therefore, it is necessary to use a seat belt.
Having overcome the force of gravity, the spacecraft continues to move at a constant speed even with the engines turned off, since there is no friction force. The ship moves despite the fact that there is also no moving force. Thanks to the force of inertia, interplanetary probes are able to overcome cosmic distances.
In space, where there is no frictional force, a body can move at a constant speed indefinitely. In outer space, the astronaut regulates his movements using a miniature jet engine mounted in the chair. The jet engine allows the astronaut to suppress inertia and he can move in any direction.
Solving quality problems.
1. Why is there a special sign on the rear window when a car is equipped with studded tires that prevent it from slipping on ice? ?? Or maybe this sign can be installed on the front glass? 2. A.P. Gaidar. "Chuk and Gek." “Squealing joyfully, Chuk and Huck jumped up, but the sleigh was pulled, and they plopped down into the hay.” ?? Why did the boys “flop into the hay”? 3. M.M. Prishvin. "Pantry of the sun." An episode in which the dog Travka chases a hare. “The grass behind the juniper bush crouched down and strained its hind legs for a mighty throw, and when it saw the ears, it rushed. Just at this time the hare, a big, old, seasoned hare, decided to suddenly stop and even, standing up on his hind legs, listen to how far away the fox was yapping. So it all came together at the same time - the grass rushed, and the hare stopped. And the Grass was carried by the hare.” ?? Explain what happened.
4. Wise Kid (Mongolian fairy tale) An official, a man without conscience and honor, wanted to force the poor man who gave him lodging for the night to pay for the fact that the goats chewed the horse’s girth. “The wise kid stood up for his father: - Honorable guest! The goats chewed up your horse's girth. So make them pay. The official remained silent, jumped on his horse and set it off at a gallop. But then the horse fell with his foot into a mole hole, and the rider flew to the ground" ?? Why did the rider fly to the ground? 5. The Seven Adventures of Hatem (Persian fairy tale) In search of a talking head, the beautiful young man Hatem walked for a long time through the desert. Tired and thirsty, he sat down to rest. “After some time, an eagle flew in and landed on the ground not far from Hatem. The eagle walked and walked and disappeared into some hole, but soon it appeared again, and when it shook its wings, water spray flew from its feathers. Hatem immediately went to the hole and saw that it was full of clean and clear water.” ?? Why does water splash when a bird shakes its wings?
Solving quality problems.
6. Baron Munchausen told how he once ran and jumped through a swamp. During the jump, he noticed that he would not make it to the shore. Then he turned back in the air and returned to the bank from which he jumped. ?? Is it possible? 7. Why, when a carpet is beaten with a stick, does the dust not “beat” into the carpet, but flies out of it? ?? what is the correct way to say: “motes of dust fly out of the carpet or the carpet “flies out” from under the motes of dust” 8. How can you put a shovel on the handle? ?? Explain. 9. What is the cause of destruction during an earthquake? 10. Explain what the action of “shaking” a medical thermometer is based on?
Solving quality problems.
Let's sum it up
Thank you for attention!
2. Resultant force Find the resultant force by plotting
- What is the main task of mechanics?
Main task mechanics- determine the position (coordinates) of a moving body at any time.
- Why was the concept of a material point introduced?
In order not to describe the movement of every point of a moving body.
A body whose own dimensions can be neglected under given conditions is called material point.
- When can a body be considered a material point? Give an example.
What is a frame of reference?
The body of reference, the coordinate system associated with it and the clock for counting the time of movement form reference system .
z
at
X
at
X
X
KINEMATICS
Kinematics (Greek “kinematos” – movement) – this is a branch of physics that examines various types of motion of bodies without taking into account the influence of forces acting on these bodies.
Kinematics answers the question:
"How to describe the movement of a body?"
The main question is why?
Dynamics – a branch of mechanics in which various types of mechanical movements are studied, taking into account the interaction of bodies with each other.
Structure of dynamics.
A change in the speed of a body is always caused by the influence of some other bodies on this body. If the body is not acted upon by other bodies, then the speed of the body never changes.
Aristotle:
To maintain a constant speed of a body, it is necessary for something (or someone) to act on it.
Rest relative to the Earth is a natural state of the body, not requiring a special reason.
Aristotle
Seem logical statements:
Who's pushing?
Let's take a proper look at the processes
It is force that changes the speed of a body
If the force is less, then the speed changes...
If you don’t have the strength, then...
Power is not bound with speed , and with changing speed
Based on experimental studies of the movement of balls on an inclined plane
The speed of any body changes only as a result of its interactions with other bodies.
Galileo Galilei
G. Galileo:
free body, i.e. a body that does not interact with other bodies can maintain its speed constant for as long as desired or be at rest.
Phenomenon conservation of the speed of a body in the absence of the action of other bodies on it is called inertia .
Isaac Newton
Newton:
gave a strict formulation of the law of inertia and included it among the fundamental laws of physics as Newton's First Law.
(1687 "Mathematical principles of natural philosophy")
- Based on the book: I. Newton. Mathematical principles of natural philosophy. lane from lat. A. N. Krylova. M.: Nauka, 1989.
- Every body continues to be maintained in a state of rest or uniform and rectilinear motion until and unless it is forced by applied forces to change this state.
Newton in his work relied on the existence absolute fixed frame of reference, that is, absolute space and time, and this is the representation modern physics rejects .
Failure to comply with the law of inertia
There are such reference systems in which the law of inertia is satisfied will not
Newton's first law:
There are such reference systems relative to which bodies retain their speed unchanged if other bodies do not act on them or the action of other bodies is compensated .
Such reference systems are called inertial.
The resultant is equal to zero
The resultant is equal to zero
Inertial reference frame(ISO) is a reference system in which the law of inertia is valid.
Newton's first law is valid only for ISO
Non-inertial reference frame- an arbitrary reference system that is not inertial.
Examples of non-inertial reference systems: a system moving in a straight line with constant acceleration, as well as a rotating system.
Questions to consolidate:
- What is the phenomenon of inertia?
2. What is Newton's First Law?
3. Under what conditions can a body move rectilinearly and uniformly?
4. What reference systems are used in mechanics?
1. Rowers trying to force the boat to move against the current cannot cope with this, and the boat remains at rest relative to the shore. The action of which bodies is compensated in this case?
2. An apple lying on the table of a uniformly moving train rolls off when the train brakes sharply. Indicate the reference systems in which Newton's first law: a) is satisfied; b) is violated.
3. By what experiment can you establish inside a closed ship cabin whether the ship is moving uniformly and in a straight line or is standing still?
Homework
Everyone: §10, exercise 10.
For those interested:
Prepare messages on the following topics:
- "Ancient mechanics"
- "Mechanics of the Renaissance"
- "I. Newton."
Basic concepts:
Weight; force; ISO.
DYNAMICS
Dynamics. What is he studying?
Means of description
LAWS OF DYNAMICS:
- Newton's first law is a postulate about the existence of ISO;
- Newton's second law -
- Newton's third law -
Reason changes in speed (cause of acceleration)
INTERACTION
LAWS FOR FORCES:
gravity –
elasticity -
MAIN (inverse) task of mechanics: establishing laws for forces
MAIN (direct) task of mechanics: determination of the mechanical state at any time.
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Slide captions:
Basic concepts and laws of dynamics.
a c b v v v Sandpaper Ordinary table Glass Friction resistance
Galileo Galilei (1564-1642 Based on experimental studies of the movement of balls on an inclined plane Based on experimental studies of the movement of balls on an inclined plane The speed of any body changes only as a result of its interaction with other bodies. Inertia is the phenomenon of maintaining the speed of a body in the absence of external influences.
Newton's first law. Law of inertia (Newton's first law, first law of mechanics): every body is at rest or moves uniformly and rectilinearly if other bodies do not act on it. Inertia of bodies is the property of bodies to maintain their state of rest or motion at a constant speed. The inertia of different bodies may be different. (1643-1727)
A reference system is called inertial if it is at rest or moves uniformly and rectilinearly. A reference system moving with acceleration is non-inertial m F F y t The action of one body on another is called a force. F - action of the earth - gravity t y F - action of the thread - elastic force
F t F y Let's eliminate the action of the thread Mentally eliminate the action of the Earth
Now let’s imagine that both actions on the ball are eliminated; logic dictates that it should remain at rest
m F y F t Let us now imagine that this ball is at rest in the carriage, moving uniformly and rectilinearly. At the same time, the same bodies Earth and the thread act on it, and both of these actions are balanced. However, relative to the Earth, the ball is not at rest; it moves uniformly and in a straight line.
Summarizing both of these examples, we can conclude: The body is at rest or moves uniformly and rectilinearly if other bodies do not act on it or their actions are balanced (compensated). From the point of view of modern concepts, Newton's first law is formulated as follows: There are such reference systems relative to which bodies retain their speed unchanged unless other bodies act on them.
On the topic: methodological developments, presentations and notes
Open lesson Newton's first law
Reasons for movement. Reasons for speed changes. Newton's first law. The principle of inertia. Experimental confirmation of the law of inertia. Relativity of motion and rest. Convert...
Lesson No.
Topic: “Inertial reference systems. Newton's First Law"
Lesson objectives:
Expand the content of Newton's 1st law.
Form the concept of an inertial reference system.
Show the importance of such a section of physics as “Dynamics”.
Lesson objectives:
1. Find out what the dynamics physics section studies,
2. Find out the difference between inertial and non-inertial frames of reference,
Understand the application of Newton's first law in nature and its physical meaning
During the lesson, a presentation is shown.
During the classes
Contents of the lesson stage
Student activities
Slide number
Icebreaker "Mirror"
Distribute cards, let the children fill in their names themselves, seat an appraiser
Repetition
What is the main task of mechanics?
Why was the concept of a material point introduced?
What is a frame of reference? Why is it introduced?
What types of coordinate systems do you know?
Why does a body change its speed?
Uplifting, motivation
1-5
II. New material
Kinematics (Greek “kinematos” – movement) – this is a branch of physics that examines various types of motion of bodies without taking into account the influence of forces acting on these bodies.
Kinematics answers the question:
"How to describe the movement of a body?"
In another section of mechanics - dynamics - the mutual action of bodies on each other is considered, which is the reason for the change in the movement of bodies, i.e. their speeds.
If kinematics answers the question: “how does the body move?”, then the dynamics reveal why exactly?.
Dynamics is based on Newton's three laws.
If a body lying motionless on the ground begins to move, then you can always detect an object that pushes this body, pulls it, or acts on it at a distance (for example, if we bring a magnet to an iron ball).
Students study the diagram
Experiment 1
Let's take any body (a metal ball, a piece of chalk or an eraser) in our hands and unclench our fingers: the ball will fall to the floor.
What body acted on the chalk? (Earth.)
These examples suggest that a change in the speed of a body is always caused by the influence of some other bodies on this body. If the body is not acted upon by other bodies, then the speed of the body never changes, i.e. the body will be at rest or moving at a constant speed.
Students perform an experiment, then analyze the model, draw conclusions, and make notes in their notebooks
A mouse click starts the experiment model
This fact is by no means self-evident. It took the genius of Galileo and Newton to realize it.
Starting with the great ancient Greek philosopher Aristotle, for almost twenty centuries, everyone was convinced: in order to maintain a constant speed of a body, it is necessary for something (or someone) to act on it. Aristotle considered rest relative to the Earth to be a natural state of the body that does not require a special cause.
In reality, a free body, i.e. a body that does not interact with other bodies can maintain its speed constant for as long as desired or be at rest. Only the action of other bodies can change its speed. If there were no friction, then the car would maintain its speed constant with the engine turned off.
The first law of mechanics, or the law of inertia, as it is often called, was established by Galileo. But Newton gave a strict formulation of this law and included it among the fundamental laws of physics. The law of inertia applies to the simplest case of motion - the motion of a body that is not influenced by other bodies. Such bodies are called free bodies.
An example of reference systems in which the law of inertia is not satisfied is considered.
Students take notes in their notebooks
Newton's first law is formulated as follows:
There are such reference systems relative to which bodies retain their speed unchanged if they are not acted upon by other bodies.
Such reference systems are called inertial (IFR).
Cards are distributed into groups and
Consider the following examples:
Characters of the fable “Swan, Crayfish and Pike”
Body floating in liquid
Airplane flying at constant speed
Students draw a poster showing the forces acting on the body.Protection of the poster
In addition, it is impossible to carry out a single experiment that would show in its pure form how a body moves if other bodies do not act on it (Why?). But there is one way out: you need to put the body in conditions under which the influence of external influences can be made less and less, and observe what this leads to.
The phenomenon of maintaining the speed of a body in the absence of the action of other bodies on it is called inertia.
III. Consolidation of what has been learned
Questions to consolidate:
What is the phenomenon of inertia?
What is Newton's First Law?
Under what conditions can a body move rectilinearly and uniformly?
What reference systems are used in mechanics?
Students answer the questions asked
Rowers trying to force the boat to move against the current cannot cope with this, and the boat remains at rest relative to the shore. The action of which bodies is compensated in this case?
An apple lying on the table of a uniformly moving train rolls off when the train brakes sharply. Indicate the reference systems in which Newton's first law: a) is satisfied; b) is violated. (In the reference frame associated with the Earth, Newton's first law is satisfied. In the reference frame associated with the carriages, Newton's first law is not satisfied.)
By what experiment can you determine inside a closed cabin of a ship whether the ship is moving uniformly and in a straight line or is standing still? (None.)
Tasks and exercises for consolidation:
In order to consolidate the material, you can offer a number of high-quality tasks on the topic studied, for example:
1.Can a puck thrown by a hockey player move uniformly along
ice?
2. Name the bodies whose action is compensated in the following cases: a) an iceberg floats in the ocean; b) the stone lies at the bottom of the stream; c) the submarine drifts evenly and rectilinearly in the water column; d) the balloon is held near the ground by ropes.
3. Under what condition will a steamship sailing against the current have a constant speed?
We can also propose a number of slightly more complex problems on the concept of an inertial frame of reference:
1. The reference system is rigidly connected to the elevator. In which of the following cases can the reference system be considered inertial? The elevator: a) falls freely; b) moves uniformly upward; c) moves rapidly upward; d) moves slowly upward; e) moves uniformly downwards.
2. Can a body at the same time in one frame of reference maintain its speed, and change it in another? Give examples to support your answer.
3. Strictly speaking, the reference frame associated with the Earth is not inertial. Is this due to: a) the gravity of the Earth; b) the rotation of the Earth around its axis; c) the movement of the Earth around the Sun?
Now let’s test your knowledge that you gained in today’s lesson.
Peer check, answers on screen
Students answer the questions asked
Students taking a test
Test in Excel format
(TEST. xls)
Homework
Learn §10, answer the questions in writing at the end of the paragraph;
Do exercise 10;
Those who wish: prepare reports on the topics “Ancient mechanics”, “Mechanics of the Renaissance”, “I. Newton”.
Students make notes in their notebooks.
List of used literature
Butikov E.I., Bykov A.A., Kondratiev A.S. Physics for applicants to universities: Textbook. – 2nd ed., rev. – M.: Nauka, 1982.
Golin G.M., Filonovich S.R. Classics of physical science (from ancient times to the beginning of the 20th century): Reference book. allowance. – M.: Higher School, 1989.
Gromov S.V. Physics 10th grade: Textbook for 10th grade of general education institutions. – 3rd ed., stereotype. – M.: Education 2002
Gursky I.P. Elementary physics with examples of problem solving: Study guide / Ed. Savelyeva I.V. – 3rd ed., revised. – M.: Nauka, 1984.
Feathers A.V. Gutnik E.M. Physics. 9th grade: Textbook for general education institutions. – 9th ed., stereotype. – M.: Bustard, 2005.
Ivanova L.A. Activation of students' cognitive activity when studying physics: A manual for teachers. – M.: Education, 1983.
Kasyanov V.A. Physics. 10th grade: Textbook for general education institutions. – 5th ed., stereotype. – M.: Bustard, 2003.
Kabardi O. F. Orlov V. A. Zilberman A. R. Physics. Problem book 9-11 grades
Kuperstein Yu. S. Physics Basic notes and differentiated problems 10th grade St. Petersburg, BHV 2007
Methods of teaching physics in secondary school: Mechanics; teacher's manual. Ed. E.E. Evenchik. Second edition, revised. – M.: Education, 1986.
Peryshkin A.V. Physics. 7th grade: Textbook for general education institutions. – 4th ed., revised. – M.: Bustard, 2001
Proyanenkova L. A. Stefanova G. P. Krutova I. A. Lesson planning for the textbook Gromova S. V., Rodina N. A. “Physics 7th grade” M.: “Exam”, 2006
Modern physics lesson in high school / V.G. Razumovsky, L.S. Khizhnyakova, A.I. Arkhipova and others; Ed. V.G. Razumovsky, L.S. Khizhnyakova. – M.: Education, 1983.
Fadeeva A.A. Physics. Workbook for grade 7 M. Genzher 1997
Internet resources:
educational electronic publication PHYSICS 7-11 grade practice
Physics 10-11 Preparation for the Unified State Exam 1C education
Library of electronic visual aids - Kosmet
Physics library of visual aids grades 7-11 1C education
And also pictures upon request from http://images.yandex.ru
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