Is it possible to be stationary and still move faster than a Formula 1 car? It turns out you can. Any movement depends on the choice of reference system, that is, any movement is relative. The topic of today's lesson: “Relativity of motion. The law of addition of displacements and velocities. We will learn how to choose a frame of reference in a particular case, how to find the displacement and speed of the body.

Mechanical motion is a change in the position of a body in space relative to other bodies over time. In this definition, the key phrase is "relative to other bodies." Each of us is motionless relative to any surface, but relative to the Sun, together with the entire Earth, we make orbital motion at a speed of 30 km / s, that is, the motion depends on the frame of reference.

Reference system - a set of coordinate systems and clocks associated with the body, relative to which the movement is being studied. For example, when describing the movements of passengers in a car, the frame of reference can be associated with a roadside cafe, or with a car interior or with a moving oncoming car if we estimate the overtaking time (Fig. 1).

Rice. 1. Choice of reference system

What physical quantities and concepts depend on the choice of reference system?

1. Position or coordinates of the body

Consider an arbitrary point . In different systems, it has different coordinates (Fig. 2).

Rice. 2. Point coordinates in different coordinate systems

2. Trajectory

Consider the trajectory of a point located on the propeller of an aircraft in two reference systems: the reference system associated with the pilot, and the reference system associated with the observer on Earth. For the pilot given point will make a circular rotation (Fig. 3).

Rice. 3. Circular rotation

While for an observer on Earth, the trajectory of this point will be a helix (Fig. 4). It is obvious that the trajectory depends on the choice of the frame of reference.

Rice. 4. Helical trajectory

Relativity of the trajectory. Body motion trajectories in different frames of reference

Let us consider how the trajectory of motion changes depending on the choice of the reference system using the problem as an example.

Task

What will be the trajectory of the point at the end of the propeller in different COs?

1. In the CO associated with the pilot of the aircraft.

2. In CO associated with an observer on Earth.

Decision:

1. Neither the pilot nor the propeller move relative to the aircraft. For the pilot, the trajectory of the point will appear as a circle (Fig. 5).

Rice. 5. Trajectory of the point relative to the pilot

2. For an observer on Earth, a point moves in two ways: rotating and moving forward. The trajectory will be helical (Fig. 6).

Rice. 6. Trajectory of a point relative to an observer on Earth

Answer : 1) circle; 2) helix.

Using the example of this problem, we have seen that the trajectory is a relative concept.

As an independent check, we suggest that you solve the following problem:

What will be the trajectory of the point at the end of the wheel relative to the center of the wheel if this wheel makes forward movement forward, and relative to points on the ground (stationary observer)?

3. Movement and path

Consider a situation where a raft is floating and at some point a swimmer jumps off it and seeks to cross to the opposite shore. The movement of the swimmer relative to the fisherman sitting on the shore and relative to the raft will be different (Fig. 7).

Movement relative to the earth is called absolute, and relative to a moving body - relative. The movement of a moving body (raft) relative to a fixed body (fisherman) is called portable.

Rice. 7. Move the swimmer

It follows from the example that displacement and path are relative values.

4. Speed

Using the previous example, you can easily show that speed is also a relative value. After all, speed is the ratio of displacement to time. We have the same time, but the movement is different. Therefore, the speed will be different.

The dependence of motion characteristics on the choice of reference system is called relativity of motion.

There have been dramatic cases in the history of mankind, connected precisely with the choice of a reference system. Execution of Giordano Bruno, abdication Galileo Galilei- all these are the consequences of the struggle between the supporters of the geocentric frame of reference and the heliocentric frame of reference. It was very difficult for mankind to get used to the idea that the Earth is not at all the center of the universe, but a completely ordinary planet. And the movement can be considered not only relative to the Earth, this movement will be absolute and relative to the Sun, stars or any other bodies. Describe movement celestial bodies in the frame of reference associated with the Sun, it is much more convenient and simpler, this was convincingly shown first by Kepler, and then by Newton, who, based on the consideration of the motion of the Moon around the Earth, derived his famous law of universal gravitation.

If we say that the trajectory, path, displacement and speed are relative, that is, they depend on the choice of a reference frame, then we do not say this about time. Within the framework of classical, or Newtonian, mechanics, time is an absolute value, that is, it flows the same in all frames of reference.

Let's consider how to find displacement and speed in one frame of reference, if they are known to us in another frame of reference.

Consider the previous situation, when a raft is floating and at some point a swimmer jumps off it and tries to cross to the opposite shore.

How is the movement of the swimmer relative to the fixed CO (associated with the fisherman) related to the movement of the relatively mobile CO (associated with the raft) (Fig. 8)?

Rice. 8. Illustration for the problem

We called the movement in a fixed frame of reference . From the triangle of vectors it follows that . Now let's move on to finding the relationship between the speeds. Recall that, in Newtonian mechanics, time is absolute value(time flows in the same way in all frames of reference). This means that each term from the previous equality can be divided by time. We get:

This is the speed at which the swimmer is moving for the fisherman;

This is the swimmer's own speed;

This is the speed of the raft (the speed of the river).

Problem on the law of addition of velocities

Consider the law of addition of velocities using the problem as an example.

Task

Two cars are moving towards each other: the first car at speed , the second - at speed . How fast are the cars approaching (Fig. 9)?

Rice. 9. Illustration for the problem

Decision

Let's apply the law of addition of speeds. To do this, let's move from the usual CO associated with the Earth to the CO associated with the first car. Thus, the first car becomes stationary, and the second moves towards it at a speed (relative speed). With what speed, if the first car is stationary, does the Earth rotate around the first car? It rotates at speed and the speed is in the direction of the speed of the second vehicle (carrying speed). Two vectors that are directed along the same straight line are summed. .

Answer: .

Limits of applicability of the law of addition of velocities. The law of addition of velocities in the theory of relativity

For a long time it was believed that the classical law of velocity addition is always valid and applicable to all frames of reference. However, about a year ago it turned out that in some situations this law does not work. Let's consider such a case on the example of a problem.

Imagine that you are on a space rocket that is moving at a speed of . And the captain space rocket turns on the flashlight in the direction of the rocket movement (Fig. 10). The speed of light propagation in vacuum is . What will be the speed of light for a stationary observer on Earth? Will it be equal to the sum of the speeds of light and rocket?

Rice. 10. Illustration for the problem

The fact is that here physics is faced with two contradictory concepts. On the one hand, according to Maxwell's electrodynamics, maximum speed is the speed of light, and it is equal to . On the other hand, according to Newtonian mechanics, time is an absolute quantity. The problem was solved when Einstein proposed the special theory of relativity, or rather its postulates. He was the first to suggest that time is not absolute. That is, somewhere it flows faster, and somewhere slower. Of course, in our world of low speeds, we do not notice this effect. In order to feel this difference, we need to move at speeds close to the speed of light. Based on Einstein's conclusions, the law of addition of velocities in special theory relativity. It looks like this:

This is the speed relative to the stationary CO;

This is the speed relative to the mobile CO;

This is the speed of the moving CO relative to the stationary CO.

If we substitute the values ​​from our problem, we get that the speed of light for a stationary observer on Earth will be .

The controversy has been resolved. You can also see that if the velocities are very small compared to the speed of light, then the formula for the theory of relativity turns into the classical formula for adding velocities.

In most cases, we will use the classical law.

Today we found out that the movement depends on the frame of reference, that speed, path, displacement and trajectory are relative concepts. And time within the framework of classical mechanics is an absolute concept. We learned how to apply the acquired knowledge by analyzing some typical examples.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) - M.: Mnemozina, 2012.
2. Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

1. Internet portal Class-fizika.narod.ru ().
2. Internet portal Nado5.ru ().
3. Internet portal Fizika.ayp.ru ().

Homework

1. Define the relativity of motion.
2. What physical quantities depend on the choice of reference system?

Imagine an electric train. She rides quietly along the rails, carrying passengers to their dachas. And suddenly, the hooligan and parasite Sidorov, sitting in the last car, notices that controllers are entering the car at the Sady station. Of course, Sidorov did not buy a ticket, and he wants to pay a fine even less.

Relativity of a free rider in a train

And so, in order not to be caught, he quickly commits to another car. Controllers, having checked the tickets of all passengers, move in the same direction. Sidorov again moves to the next car, and so on.

And now, when he reaches the first car and there is nowhere to go further, it turns out that the train has just reached the Ogorody station he needs, and the happy Sidorov gets out, rejoicing that he rode like a hare and didn’t get caught.

What can we learn from this action-packed story? We can, no doubt, rejoice for Sidorov, and we can, in addition, discover one more interesting fact.

While the train traveled five kilometers from the Sady station to the Ogorody station in five minutes, Sidorov the hare covered the same distance plus the distance in the same time, equal to the length train in which he rode, that is, about five thousand two hundred meters in the same five minutes.

It turns out that Sidorov was moving faster than the train. However, the controllers following on his heels developed the same speed. Considering that the speed of the train was about 60 km / h, it was just right to give them all several Olympic medals.

However, of course, no one will engage in such stupidity, because everyone understands that Sidorov’s incredible speed was developed by him only relative to stationary stations, rails and gardens, and this speed was due to the movement of the train, and not at all incredible abilities Sidorov.

Regarding the train, Sidorov did not move at all quickly and did not reach not only the Olympic medal, but even the ribbon from it. This is where we come across such a concept as the relativity of motion.

The concept of relativity of motion: examples

The relativity of motion has no definition, since it is not physical quantity. The relativity of mechanical motion is manifested in the fact that some characteristics of motion, such as speed, path, trajectory, and so on, are relative, that is, they depend on the observer. In different reference systems, these characteristics will be different.

In addition to the above example with citizen Sidorov on the train, you can take almost any movement of any body and show how relative it is. When you go to work, you are moving forward relative to your home, and at the same time you are moving backward relative to the bus you missed.

You are standing still in relation to the player in your pocket, and are rushing at great speed relative to a star called the Sun. Each step you take will be a gigantic distance for the asphalt molecule and insignificant for the planet Earth. Any movement, like all its characteristics, always makes sense only in relation to something else.

Questions.

1. What do the following statements mean: speed is relative, trajectory is relative, path is relative?

This means that these quantities (velocity, trajectory and path) for motion differ depending on which reference frame the observation is made from.

2. Show with examples that speed, trajectory and distance traveled are relative values.

For example, a person stands motionless on the surface of the Earth (there is no speed, no trajectory, no path), but at this time the Earth rotates around its axis, and therefore a person, relative to, for example, the center of the Earth, moves along a certain trajectory (in a circle), moves and has a certain speed.

3. Formulate briefly what the relativity of motion is.

The movement of the body (speed, path, trajectory) is different in different frames of reference.

4. What is the main difference between the heliocentric and geocentric systems?

In the heliocentric system, the reference body is the Sun, and in the geocentric system, the Earth.

5. Explain the change of day and night on Earth in the heliocentric system (see Fig. 18).

In the heliocentric system, the change of day and night is explained by the rotation of the Earth.

Exercises.

1. Water in a river moves at a speed of 2 m/s relative to the bank. A raft floats on the river. What is the speed of the raft relative to the shore? about the water in the river?

The speed of the raft relative to the shore is 2 m/s, relative to the water in the river - 0 m/s.

2. In some cases, the speed of a body can be the same in different frames of reference. For example, a train moves at the same speed in the frame of reference associated with the station building and in the frame of reference associated with a tree growing near the road. Doesn't this contradict the statement that speed is relative? Explain the answer.

If both bodies, with which the frames of reference of these bodies are connected, remain motionless relative to each other, then they are connected with the third frame of reference - the Earth, relative to which the measurements take place.

3. Under what condition will the speed of a moving body be the same with respect to two frames of reference?

If these frames of reference are fixed relative to each other.

4. Due to the daily rotation of the Earth, a person sitting on a chair in his house in Moscow moves relative to earth's axis at a speed of approximately 900 km/h. Compare this speed with the muzzle velocity of the bullet relative to the gun, which is 250 m/s.

5. A torpedo boat is moving along the sixtieth parallel of south latitude at a speed of 90 km/h relative to land. Speed daily rotation Earth at this latitude is 223 m/s. What is equal to in (SI) and where is the speed of the boat relative to the earth's axis directed if it moves to the east? to the west?

Relativity of mechanical motion

Motion in physics is the movement of a body in space, which has its own specific features.

Mechanical movement can be represented as a change in the position of a particular material body in space. All changes must occur relative to each other over time.

Types of mechanical movement

There are three main types of mechanical movement:

• rectilinear movement;
• uniform movement;
• curvilinear movement.

To solve problems in physics, it is customary to use assumptions in the form of a representation of an object by a material point. This makes sense in cases where the shape, size and body can be ignored in its true parameters and the object under study can be selected as a specific point.

There are several basic conditions when the implementation method is used in solving a problem. material point:

• in cases where the dimensions of the body are extremely small in relation to the distance it travels;
• when the body is moving forward.

Translational motion occurs at the moment when all points of the material body move in the same way. Also, the body will move in a translational manner when a straight line is drawn through two points of this object, and it should move parallel to the original location.

At the beginning of the study of the relativity of mechanical motion, the concept of a frame of reference is introduced. It is formed together with the body of reference and the coordinate system, including the clock for counting the time of movement. All elements form a single frame of reference.

Reference system

Remark 2

A reference body is such a body, relative to which the position of other bodies in motion is determined.

If you do not specify additional data in the solution of the problem of calculating mechanical movement, then it will not be possible to notice it, since all body movements are calculated relative to interaction with other physical bodies.

Scientists have introduced additional concepts to understand the phenomenon, including:

• rectilinear uniform motion;
• body movement speed.

With their help, the researchers tried to figure out how the body moved in space. In particular, it was possible to determine the type of body movement relative to observers who had different speeds. It turned out that the result of the observation depends on the ratio of the velocities of the body and the observers relative to each other. All calculations used the formulas of classical mechanics.

There are several basic reference systems that are used in solving problems:

• mobile;
• motionless;
• inertial.

When considering motion relative to a moving frame of reference, the classical law of addition of velocities is used. The speed of the body relative to the fixed frame of reference will be equal to the vector sum of the speed of the body relative to the moving frame of reference, as well as the speed of the moving frame of reference relative to the fixed one.

$\overline(v) = \overline(v_(0)) + \overline(v_(s))$ where:

• $\overline(v)$ - speed of the body in a fixed frame of reference,
• $\overline(v_(0))$ is the speed of the body in the moving reference frame,
• $\overline(v_(s))$ is the speed of an additional factor that affects the definition of speed.

The relativity of mechanical motion lies in the relativity of the speeds with which bodies move. The velocities of bodies relative to different reference systems will also differ. For example, the speed of a person on a train or plane will differ depending on which reference frame these speeds are determined in.

Velocities vary in direction and magnitude. The definition of a specific object of study during mechanical movement plays a crucial role in calculating the parameters of the movement of a material point. Velocities can be determined in a frame of reference that is associated with a moving vehicle, or it can be relative to a stationary Earth or its rotation in orbit in space.

This situation can be modeled for simple example. moving along railway the train will make mechanical movements relative to another train that is moving on parallel tracks or relative to the earth. The solution of the problem depends directly on the chosen reference system. In different reference systems there will be different trajectories of motion. In mechanical motion, the trajectory is also relative. The path traveled by the body depends on the chosen frame of reference. In mechanical motion, the path is relative.

Development of the relativity of mechanical motion

Also, according to the law of inertia, began to form inertial systems reference.

The process of understanding the relativity of mechanical motion took a considerable historical period of time. If at first the model of the geocentric system of the world (the Earth is the center of the Universe) was considered acceptable for a long time, then the movement of bodies in different reference systems began to be considered at the time of the famous scientist Nicolaus Copernicus, who formed the heliocentric model of the world. According to her, the planets solar system rotate around the sun and rotate around their own axis.

The structure of the reference system changed, which later led to the construction of a progressive heliocentric system. This model today allows solving various scientific goals and tasks, including in the field of applied astronomy, when the trajectories of stars, planets, galaxies are calculated based on the relativity method.

At the beginning of the 20th century, the theory of relativity was formulated, which is also based on the fundamental principles of mechanical motion and the interaction of bodies.

All formulas that are used to calculate mechanical movements bodies and the definition of their speed, make sense at speeds less than the speed of light in a vacuum.

Also in school curriculum there is a provision that any movement of one body can be fixed only relative to another body. This position is called the term "relativity of motion". From the pictures in the textbooks, it was clear that for a boat standing on the river bank, a boat passing by is made up of its speed and the speed of the river. After such a detailed examination, it becomes clear that the relativity of motion surrounds us in all aspects of our lives. The speed of an object is a relative quantity, but its derivative, acceleration, also becomes important. The importance of this conclusion lies in the fact that it is acceleration that is included in the formula of Newton's second law (the basic law of mechanics). According to this law, any force acting on a body gives it an acceleration proportional to it. The relativity of motion forces us to ask an additional question: relative to what body is the acceleration given?

In this law there are no explanations on this matter, but by simple logical conclusions one can come to the conclusion that, since the force is a measure of the impact of one body (1) on another (2), then the same force tells the body (2) acceleration relative to the body (1) and not just some abstract acceleration.

The relativity of motion is the dependence of a certain body, a certain path, speed and displacement on the selected frames of reference. In the aspect of kinematics, any reference systems used are equal, but at the same time, all the kinematic characteristics of this movement (trajectory, speed, displacement) are different in them. All quantities that depend on the chosen reference system with which they will be measured are called relative.

The relativity of motion, the definition of which is rather difficult to give without a detailed consideration of other concepts, requires an accurate mathematical calculation. It is possible to talk about whether the body is moving or not when it is absolutely clear with respect to what (reference body) its position changes. The reference system is a combination of such elements as the reference body, as well as the associated coordinate systems and time reference systems. In relation to these elements, the movement of any bodies or is considered. Mathematically, the movement of an object (point) in relation to the chosen reference system is described by equations that establish how the coordinates change in time, which determine the position of the object in this system. Such equations that determine the relativity of motion are called the equations of motion.

In modern mechanics, any movement of an object is relative, so it should be considered only in relation to another object (reference body) or an entire system of bodies. For example, one cannot simply state that the Moon is moving at all. Correct statement it will be that the Moon moves in relation to the Sun, the Earth, the stars.

Often in mechanics, the frame of reference is linked not to a body, but to a whole continuum of basic bodies (real or imaginary) that determine the coordinate system.

Movies often show movement relative to various bodies. So, for example, in some frames they show a train that moves against the background of some kind of landscape (this is movement relative to the surface of the Earth), and in the next - a carriage compartment with trees flashing through the windows (movement relative to one carriage). Any movement or rest of the body, which is a special case of movement, is relative. Therefore, answering a simple question, whether a body moves or is at rest, and how it moves, it is necessary to specify in relation to which objects its movement is being considered. The choice of reference systems, as a rule, is made depending on the conditions of the problem.