What do the following statements mean: speed is relative to trajectory. Relativity of motion

Good afternoon Speed ​​is relative because it depends on the chosen frame of reference. Example: a car is driving at a certain speed along the street. There is a house next to it and a cyclist is riding along the sidewalk. So, relative to the house the car moves at the same speed, but if we consider the speed of the car relative to the moving cyclist, then it will be different (because the cyclist is also moving).

Inna

In the simulator, I didn’t understand how to solve the problem: “A long cord moves along a smooth horizontal surface to the left at a speed of 2 m/s. Point A begins to move to the right at a speed of 1 m/s. How long will the part of the cord move to the right after 3 s?” Help with a solution :(

Teacher's answer: Postny Alexey Vitalievich

Consider the movement of one end relative to the other. It turns out that they are approaching at a speed of 3 m/s. Next, calculate how much the distance between the ends of the cord will decrease in 3 seconds. Then make a drawing: at the beginning of the movement and after 3 seconds. This will help you find the correct answer.

User 372914

When you explained the topic, 2 points were missed (1. You did not graphically show why v-banks are taken with a minus sign 2. An experiment with the chalk-ruler-board trajectory (it was not clearly explained why the chalk moves in a straight line relative to the ruler. Because our school is aimed at middle schoolers student, I would like students who are below average to be able to fully understand what you are saying. In general, the resource is very good, and you, as a physics teacher, are the best on this resource. I am not talking about knowledge, but about the methodology of teaching the subject. With great respect!

Teacher's answer: Postny Alexey Vitalievich

Thank you very much for your feedback! As for the comments, indeed, the moment with speed relative to the shore is not graphically highlighted, but it is explained verbally. Therefore, if you look carefully, you can understand why the “-” sign is taken. As for the chalk and ruler, no explanation is provided due to its intuitive understanding: ruler straight, which means the chalk moves along it directly linear.

User 362168

I would like to ask for a solution to the problem: While going up the river, a fisherman dropped a wooden hook from his boat as he passed under a bridge. Half an hour later, he discovered the loss and, turning back, caught up with the gaff at a distance of 2.7 km from the bridge. Find the speed of the river current, assuming the boat's speed relative to the water remains constant.

Teacher's answer: Postny Alexey Vitalievich

To solve the problem, first consider the motion relative to the river. The hook was at rest relative to the water, and the fisherman swam in one direction for half an hour, then returned (accordingly, another half hour passed, because the hook was at rest). That is, just an hour. Next consider the motion relative to the bridge. In the indicated hour, the hook floated 2.7 km.

Lukichev Mikhail

“What is the speed of the ball relative to the Earth after an absolutely elastic impact on the wall? (wall speed U = 2 m/s, ball speed before impact v = 3 m/s).” Tell me why the correct answer is 7 m/s and not 5 m/s, because... Is the impact elastic and the velocities are adding up?..

Teacher's answer: Postny Alexey Vitalievich

When solving the problem, you need to consider the speed of the ball relative to the wall. Then take into account that with an absolutely elastic impact, the modulus of the ball’s velocity will not change, but the direction will change to the opposite. Then again go to the reference system associated with the Earth. How to switch to a reference system associated with a moving body is described in detail in the lesson. Do all the above and you will get the correct answer. And the statement that during an absolutely elastic impact the velocities of the bodies add up is incorrect.

Islamia

Hello! One point is not entirely clear. The summary contains the following words: “So, movement in two reference systems. Look at Fig. 2. It can be noted that the chalk moves along the ruler in a straight line, therefore, the trajectory will be straight. And when we consider the movement - the chalk in the plane of the board, then the trajectory will be a curved line. In this case, it is easiest to talk about the distance traveled, since the distance traveled is the length of the trajectory, therefore, in the reference system associated with the ruler, the distance traveled will be less than the path traveled in the plane of the board. As can be seen from the experiment, both the trajectory of the body’s movement and the distance traveled depend on the choice of reference system.” I can’t understand why the chalk moves along the ruler not curvilinearly, but rectilinearly?

What is Landau's theory of relativity Lev Davidovich

Speed ​​has a limit

Speed ​​has a limit

Before World War II, airplanes flew at speeds slower than the speed of sound, and now “supersonic” airplanes have been built. Radio waves travel at the speed of light. But is it not possible to set ourselves the task of creating “superluminal” telegraphy in order to transmit signals at a speed even greater than the speed of light? This turns out to be impossible.

In fact, if it were possible to transmit signals at an infinite speed, then we would be able to unambiguously establish the simultaneity of two events. We would say that these events occurred simultaneously if the infinitely fast signal about the first event arrived simultaneously with the signal about the second event. Thus, simultaneity would acquire an absolute character, independent of the movement of the laboratory to which this statement refers.

But since the absoluteness of time is refuted by experience, we conclude that the transmission of signals cannot be instantaneous. The speed of transfer of action from one point in space to another cannot be infinite, in other words, it cannot exceed a certain finite value called the maximum speed.

This maximum speed coincides with the speed of light.

In fact, according to the principle of relativity of motion, in all laboratories moving relative to each other (rectilinearly and uniformly) the laws of nature must be the same. The statement that no speed can exceed a given limit is also a law of nature, and therefore the value of the limit speed must be exactly the same in different laboratories. As we know, the speed of light differs in these same properties.

Thus, the speed of light is not just the speed of propagation of some natural phenomenon. It plays the most important role of top speed.

The discovery of the existence of a world of extreme speed is one of the greatest triumphs of human thought and the experimental capabilities of mankind.

A physicist of the last century could not figure out that there is a limiting speed in the world, that the fact of its existence can be proven. Moreover, even if in his experiments he had stumbled upon the presence of a limiting speed in nature, he could not be sure that this was a law of nature, and not a consequence of limited experimental capabilities that could be eliminated in the process of further development of technology.

The principle of relativity shows that the existence of maximum speed lies in the very nature of things. Expecting that the progress of technology will make it possible to achieve speeds exceeding the speed of light is as ridiculous as believing that the absence of points on the earth’s surface separated by a distance of more than 20 thousand kilometers is not a geographical law, but the limitations of our knowledge, and hoping that according to As geography develops, it will be possible to find points on Earth that are even more distant from each other.

The speed of light plays such an exceptional role in nature because it is the maximum speed for the propagation of anything. Light either precedes any other phenomenon, or, in extreme cases, arrives simultaneously with it.

If the Sun were to split into two parts and form a double star, then, of course, the Earth's motion would change.

A physicist of the last century, who did not know about the existence of a limiting speed in nature, would certainly have assumed that the change in the Earth's motion would have occurred instantly following the splitting of the Sun. Meanwhile, it would have taken eight minutes for light to travel from the broken Sun to the Earth.

In reality, however, the change in the Earth's motion will also begin only eight minutes after the Sun breaks apart, and until that moment the Earth will move as if the Sun had not broken apart. And in general, not a single event that happened with the Sun or on the Sun will have any effect on either the Earth or its movement before the expiration of these eight minutes.

The finite speed of signal propagation, of course, does not deprive us of the opportunity to establish the simultaneity of two events. To do this, you just need to take into account the signal delay time, as is usually done.

However, this method of establishing simultaneity is already completely compatible with the relativity of this concept. In fact, to subtract the delay time, we will have to divide the distance between the places where the events occurred by the speed of propagation of the signal. On the other hand, while still discussing the issue of sending letters from the Moscow-Vladivostok express, we saw that the very place in space is also a very relative concept!

From the book The Newest Book of Facts. Volume 3 [Physics, chemistry and technology. History and archaeology. Miscellaneous] author Kondrashov Anatoly Pavlovich

From the book What is the theory of relativity author Landau Lev Davidovich

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From the book Physics at every step author Perelman Yakov Isidorovich

From the book Movement. Heat author Kitaygorodsky Alexander Isaakovich

From the book Tweets about the Universe by Chaun Marcus

From the book The Prevalence of Life and the Uniqueness of Mind? author Mosevitsky Mark Isaakovich

Does every statement have meaning? Obviously not. Even if you take completely meaningful words and combine them in full accordance with the rules of grammar, even then the result can be complete nonsense. For example, the statement “this water is triangular” is difficult to assign any

From the book Hyperspace by Kaku Michio

And speed is relative! From the principle of relativity of motion it follows that talking about the rectilinear and uniform motion of a body with a certain speed, without indicating which of the resting laboratories the speed is measured against, makes as little sense as saying

From the book The King's New Mind [On computers, thinking and the laws of physics] by Penrose Roger

Speed ​​of light In Galileo's "Conversations on the Two New Sciences" we find a conversation between a teacher and his students about the speed of light: Sagredo: But what kind and degree of speed should this movement of light be? Should we consider it instantaneous or taking place in time, as

From the book Who the Apple Fell On author Kesselman Vladimir Samuilovich

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Speed ​​of sound There is no need to be afraid of thunder after lightning has flashed. You've probably heard about this. Why? The fact is that light travels incomparably faster than sound—almost instantly. Thunder and lightning occur at the same moment, but we see lightning in

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35. Does the Sun have a surface? The Sun is a giant glowing ball of gas, so it does not have a solid surface like the Earth. But, of course, it seems so at first glance. Why? The solar “surface”, or photosphere, to which the sun’s rays have great difficulty penetrating

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Warp speed 5 Does this mean that black holes can be used to travel throughout the galaxy, like in Star Trek and other science fiction films? As we saw earlier, the curvature of a particular space is determined by the amount of matter-energy,

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“Interest has no conscience” Voltaire in his “English Letters” reports that in 1726, when he was in England, he happened to be present at a scientific dispute, the participants of which discussed the question: who was the greatest of people - Caesar, Alexander, Timur or Cromwell ?

Ticket No. 1

1.Mechanical movement is a change in the position of a body in space over time relative to other bodies.

Of all the diverse forms of motion of matter, this type of motion is the simplest.

For example: moving the clock hand around the dial, people walking, tree branches swaying, butterflies fluttering, an airplane flying, etc.

Determining the position of the body at any given time is the main task of mechanics.

The movement of a body in which all points move equally is called translational.

 A material point is a physical body, the dimensions of which under given conditions of motion can be neglected, assuming that all its mass is concentrated at one point.

 A trajectory is a line that a material point describes during its movement.

 Path is the length of the trajectory of a material point.

 Displacement is a directed straight line segment (vector) connecting the initial position of the body with its subsequent position.

 A reference system is: a reference body, a coordinate system associated with it, as well as a device for counting time.

An important feature of fur. movement is its relativity.

Relativity of motion– this is the movement and speed of a body relative to different reference systems are different (for example, a person and a train). The speed of a body relative to a fixed coordinate system is equal to the geometric sum of the speed of the body relative to a moving system and the speed of a moving coordinate system relative to a fixed one. (V 1 is the speed of a person on the train, V 0 is the speed of the train, then V = V 1 + V 0).

The classical law of addition of velocities is formulated as follows: the speed of movement of a material point in relation to the reference system, taken as a stationary one, is equal to the vector sum of the speeds of movement of the point in the moving system and the speed of movement of the moving system relative to the stationary one.

The characteristics of mechanical motion are interconnected by basic kinematic equations.

s =v 0 t + at 2 / 2;

v = v 0 + at .

Let us assume that a body is moving without acceleration (an airplane on a route), its speed does not change for a long time, A= 0, then the kinematic equations will look like: v = const, s =vt .

Movement in which the speed of a body does not change, i.e., the body moves by the same amount over any equal periods of time, is called uniform linear movement.

During launch, the speed of the rocket increases rapidly, i.e. acceleration A>Oh, a == const.

In this case, the kinematic equations look like this: v = V 0 + at , s = V 0 t + at 2 / 2.

With such movement, speed and acceleration have the same directions, and the speed changes equally over any equal intervals of time. This type of movement is called uniformly accelerated.

When braking a car, the speed decreases equally over any equal periods of time, the acceleration is less than zero; since the speed decreases, the equations take the form : v = v 0 + at , s = v 0 t - at 2 / 2 . This type of motion is called uniformly slow.

2.Everyone can easily divide bodies into solid and liquid. However, this division will only be based on external signs. In order to find out what properties solids have, we will heat them. Some bodies will begin to burn (wood, coal) - these are organic substances. Others will soften (resin) even at low temperatures - these are amorphous. Still others will change their state when heated as shown in the graph (Fig. 12). These are crystalline bodies. This behavior of crystalline bodies when heated is explained by their internal structure. Crystal bodies- these are bodies whose atoms and molecules are arranged in a certain order, and this order is preserved over a fairly large distance. The spatial periodic arrangement of atoms or ions in a crystal is called crystal lattice. The points of the crystal lattice at which atoms or ions are located are called nodes crystal lattice. Crystalline bodies are either single crystals or polycrystals. Monocrystal has a single crystal lattice throughout its entire volume. Anisotropy single crystals lies in the dependence of their physical properties on direction. Polycrystal It is a combination of small, differently oriented single crystals (grains) and does not have anisotropy of properties.

Most solids have a polycrystalline structure (minerals, alloys, ceramics).

The main properties of crystalline bodies are: certainty of melting point, elasticity, strength, dependence of properties on the order of arrangement of atoms, i.e., on the type of crystal lattice.

Amorphous are substances that have no order in the arrangement of atoms and molecules throughout the entire volume of this substance. Unlike crystalline substances, amorphous substances isotropic. This means that the properties are the same in all directions. The transition from an amorphous state to a liquid occurs gradually; there is no specific melting point. Amorphous bodies do not have elasticity, they are plastic. Various substances are in an amorphous state: glass, resins, plastics, etc.

Elasticity- the property of bodies to restore their shape and volume after the cessation of external forces or other causes that caused the deformation of bodies. For elastic deformations, Hooke’s law is valid, according to which elastic deformations are directly proportional to the external influences causing them, where is mechanical stress,

 - relative elongation, E - Young's modulus (modulus of elasticity). Elasticity is due to the interaction and thermal movement of the particles that make up the substance.

Plastic- the property of solids under the influence of external forces to change their shape and size without collapsing and to retain residual deformations after the action of these forces ceases

Ticket#2

Mechanical movement. Relativity of motion. Reference system. Material point. Trajectory. Path and movement. Instant speed. Acceleration. Uniform and uniformly accelerated movement. Mechanical movement is a change in the position of a body (or its parts) relative to other bodies. For example, a person riding an escalator in the subway is at rest relative to the escalator itself and is moving relative to the walls of the tunnel; Mount Elbrus is at rest relative to the Earth and moves with the Earth relative to the Sun. From these examples it is clear that it is always necessary to indicate the body relative to which the movement is being considered; it is called the body of reference. The coordinate system, the reference body with which it is associated, and the chosen method of measuring time form a reference system. The position of the body is specified by the coordinate. Let's look at two examples. The dimensions of an orbital station located in orbit near the Earth can be ignored, and when calculating the trajectory of a spacecraft when docking with a station, one cannot do without taking its dimensions into account. Thus, sometimes the size of a body compared to the distance to it can be neglected; in these cases, the body is considered a material point. The line along which a material point moves is called a trajectory. The length of the trajectory is called path (l). The unit of path is meter. Mechanical motion is characterized by three physical quantities: displacement, speed and acceleration. A directed line segment drawn from the initial position of a moving point to its final position is called displacement (s). Displacement is a vector quantity. The unit of movement is meter. Speed ​​is a vector physical quantity that characterizes the speed of movement of a body, numerically equal to the ratio of movement over a short period of time to the value of this interval. A period of time is considered to be sufficiently small if the speed during uneven movement did not change during this period. The defining formula for speed is v = s/t. The unit of speed is m/s. In practice, the speed unit used is km/h (36 km/h = 10 m/s). Speed ​​is measured with a speedometer. Acceleration is a vector physical quantity that characterizes the rate of change in speed, numerically equal to the ratio of the change in speed to the period of time during which this change occurred. If the speed changes equally throughout the entire time of movement, then the acceleration can be calculated using the formula Acceleration unit - . The characteristics of mechanical motion are related to each other by basic kinematic equations: Suppose that a body moves without acceleration (an airplane on a route), its speed does not change for a long time, a = 0, then the kinematic equations will have the form: Movement in which the speed of the body does not changes, i.e. the body moves by the same amount over any equal periods of time, is called uniform rectilinear motion. During launch, the rocket speed increases rapidly, i.e. acceleration a > 0, a = const. In this case, the kinematic equations look like this: With such movement, speed and acceleration have the same directions, and the speed changes equally over any equal periods of time. This type of motion is called uniformly accelerated. When braking a car, the speed decreases equally over any equal periods of time, acceleration is directed in the direction opposite to the movement; since the speed decreases, the equations take the form: Such movement is called uniformly slow. All physical quantities characterizing the movement of a body (speed, acceleration, displacement), as well as the type of trajectory, can change when moving from one system to another, that is, the nature of the movement depends on the choice of the reference system, and this is where the relativity of movement is manifested. For example, an aircraft is refueled in the air. In the reference frame associated with the plane, the other plane is at rest, and in the reference frame associated with the Earth, both planes are in motion. When a cyclist moves, the wheel point in the reference system associated with the axis has a trajectory presented in Figure 1. In the reference system associated with the Earth, the type of trajectory turns out to be different (Figure 2).

Ticket No. 3

The position of a point in space can also be determined by a radius vector drawn from a certain origin to a given point (Fig. 2). In this case, to describe the movement you need to set:

a) origin of the radius vector r;

b) start of time t;

c) law of motion of a point r(t).

Since specifying one vector quantity r is equivalent to specifying its three projections x, y, z on the coordinate axes; it is easy to move from the vector method to the coordinate one. If we introduce unit vectors i, j, k (i= j = k= 1), directed respectively along the x, y and z axes (Fig. 2), then, obviously, the law of motion can be represented in the form *)

r(t) = x(t) i+y(t) j+z(t) k. (1)

The advantage of the vector form of recording over the coordinate form is compactness (instead of three quantities one operates with one) and often greater clarity.

To solve the first part of the problem, we will use the coordinate method, directing the x-axis of the Cartesian system along the rod and choosing its origin at point A. Since the inscribed AMS is a straight line (as based on the diameter),

x(t) = AM = 2Rcos = 2Rcost,

where R is the radius of the semicircle. The resulting law of motion is called a harmonic oscillation (this oscillation will obviously continue only until the moment the ring reaches point A).

We will solve the second part of the problem using the natural method. Let us choose the positive direction of counting the distance along the trajectory (semicircle AC) counterclockwise (Fig. 3), and zero coinciding with point C. Then the length of the arc CM as a function of time will give the law of motion of point M

S(t) = R2 = 2R t,

those. the ring will move uniformly around a circle of radius R with an angular velocity of 2. As is clear from the examination,

the zero of the time count in both cases corresponded to the moment when the ring was at point C.

Ticket No. 4

Coordinate method. We will set the position of the point using coordinates ( Fig.1.7). If a point moves, then its coordinates change over time. Since the coordinates of a point depend on time, we can say that they are functions time.

Mathematically, this is usually written in the form

Equations (1.1) are called kinematic equations of motion of a point, written in coordinate form. If they are known, then for each moment in time we will be able to calculate the coordinates of the point, and therefore its position relative to the selected reference body. The form of equations (1.1) for each specific movement will be quite specific. The line along which a point moves in space is called trajectory . Depending on the shape of the trajectory, all movements of a point are divided into rectilinear and curvilinear. If the trajectory is a straight line, the movement of the point is called straightforward, and if the curve is curvilinear.

To describe any physical processes

A. All reference systems are equal.

B. All inertial reference systems are equal.

Which of these statements is true according to the special theory of relativity?

1) only A

2) only B

4) neither A nor B

Solution.

The main postulate of Einstein's theory, the principle of relativity, states: “All inertial frames of reference are equal in describing any physical process.” Thus, statement B is true.

Correct answer: 2.

Answer: 2

Which of the following statements are postulates of the special theory of relativity?

A. All inertial frames of reference are equal when describing any physical process.

B. The speed of light in a vacuum does not depend on the speed of the source and receiver of light.

B. The rest energy of any body is equal to the product of its mass times the square of the speed of light in vacuum.

Solution.

The first postulate of the special theory of relativity: “All inertial frames of reference are equal in describing any physical process.” The second postulate: “The speed of light in a vacuum does not depend on the speed of the source and receiver of light.” Thus, the postulates are statements A and B.

Correct answer: 1.

Answer: 1

In the installation, a spark discharge creates a flash of light and a sound pulse, recorded by a sensor located at a distance of 1 m from the spark gap. Schematically the relative position of the arrester R and sensor D depicted by an arrow. The light propagation time from the spark gap to the sensor is T, and sound -

By conducting experiments with two installations 1 and 2 located in a spacecraft flying at a speed relative to the Earth, as shown in the figure, the astronauts discovered that

1) 2) 3) 4)

Solution.

Since the spacecraft flies at a constant speed, it represents an inertial frame of reference. According to the principle of relativity (the first postulate of the special theory of relativity), all inertial frames of reference are equal in describing any physical process. Consequently, the astronauts aboard the spacecraft could not detect any dependence of the speed of propagation of light and sound signals on the orientation of the installation.

Correct answer: 2.

Answer: 2

One scientist tests the patterns of oscillation of a spring pendulum in a laboratory on Earth, and another - in a laboratory on a spaceship flying far from the stars and planets with the engine turned off. If the pendulums are the same, then in both laboratories these patterns will be

1) the same at any speed of the ship

2) different, since time flows slower on a ship

3) the same if the ship’s speed is low

4) the same or different depending on the module and direction of the ship’s speed

Solution.

Since the spacecraft flies at a constant speed, it represents an inertial frame of reference. According to the principle of relativity (the first postulate of the special theory of relativity), all inertial frames of reference are equal in describing any physical process. Consequently, if the pendulums are the same, then in both laboratories the patterns of oscillation of the spring pendulum will be the same at any speed of the ship.

Correct answer: 1.

Ida Gorbacheva (Ukhta) 16.05.2012 20:01

Hello! But according to the theory of relativity, time flows slower in moving objects... Moreover, in terrestrial conditions there is weight, but in a ship there is none... Could you comment on these contradictions?

Alexey (St. Petersburg)

Good afternoon

Thank God there are no contradictions! Don't worry.

Regarding your questions. First, about time dilation. We must not forget that this is a relative effect. To a stationary observer on Earth, it seems that in an object moving relative to him (for example, a laboratory), time flows more slowly than on Earth; in addition, this object also seems to him to be flattened in the longitudinal direction. But for a scientist in this moving object, the Earth already seems to be rushing past him at the same speed, but in the opposite direction. This means that it will also seem to him that the observer on Earth is too slow and amazingly flattened :). Einstein's postulate guarantees that everything will look the same in all inertial frames of reference (which is great). That is, if you perform the same experiments, you will get the same results. For example, if each scientist has his own pendulum, then both the readings of his own pendulums and the readings of other people’s pendulums will coincide for both scientists :)

Now about the weight. Do not confuse that weight is the force with which the body presses on the support or stretches the suspension; this is not the force of gravity at all. On Earth, indeed, most often the source of weight is attraction to the Earth, but if you look at a freely falling elevator, then there will be no weight there. In the case of a spring pendulum, it turns out that gravity does not affect the nature of its oscillations; it only leads to a shift in the equilibrium position. Therefore, if you put the pendulum “on its side,” thereby removing gravity from the game, you will get absolutely the same thing as in a rocket, where there is no gravity at all :)

I hope that I have satisfied your curiosity!

Ida Gorbacheva (Ukhta) 18.05.2012 20:51

Thanks for the answer. There are two more nuances - 1. The Earth is only approximately an inertial frame of reference. 2. The special theory of relativity considers the concept of gravitational time dilation.

Alexey (St. Petersburg)

The reference frame associated with the Earth can indeed be considered inertial only with some accuracy. That's right.

Regarding your second remark (I’ll correct it a little): the influence of gravity on time is beyond the scope of the special theory of relativity (SRT). In service stations they work with flat space. The generalization to gravity was made by Einstein already within the framework of the general theory of relativity (GTR). But its consideration is far beyond the scope of the school curriculum :)

Yuri Shoitov (Kursk) 28.11.2012 21:27

Hello, Alexey!

I am surprised by both the formulation of the question and your (most likely not your) decision.

It is completely unclear what the words “processes proceed in the same way” mean.

This formulation throws us back to the time of Galileo, when there was no concept of a reference system. Yes, Galileo wrote exactly this way: “Flies in the cabin will fly the same way, regardless of whether the ship is standing still or moving straight and evenly.” Translated into modern language, this means: “If a material point is acted upon by some force, then the point will receive the same acceleration in all reference systems that move relative to each other in a rectilinear uniform and translational manner.” But even in classical mechanics it is impossible in this case to talk about “the same course of processes” in these systems. The speed of a point in different systems will be different, and accordingly, the kinetic energy will be different. So, if in a moving train a passenger walks relative to the car at a speed of 1 m/s and suddenly stops relative to the car, then nothing special will happen. If it stops in the same amount of time relative to the ground, then it is a train wreck. So much for the “identicality of processes”!

From the Lorentz transformations it follows that the time in the moving and stationary reference systems will be different, therefore, the periods of oscillation of the pendulum will also be different. Where did you see the “identicality of processes”?!

The equality of reference systems in SRT lies in the fact that in both systems the value of the relativistic interval in the four-dimensional Minkowski space will be the same (invariant). And nothing more.

Reasoning about what will “seem” to one observer and another is absurd. If something seems to one or two subjects, then this phenomenon is studied not by physics, but by psychiatry.

Reasoning about the inertiality of the reference system associated with the Earth is also erroneous. The Earth rotates around its axis, therefore a point fixed in this system has a portable acceleration omega square multiplied by the distance of this point from the axis of rotation. For points located on the surface of the Earth, this acceleration is many times less than the acceleration of gravity and can be neglected. But the condition says that the ship is located far from planets (including the Earth). Then the distance from the spacecraft is great, and the force of inertia becomes of great importance.

Both the condition and the solution represent a clumsy attempt to clearly explain to a student something that you yourself do not understand.

If your goal is to completely confuse a schoolchild and force him to cram some dogmas instead of studying nature, then by “solving” such problems, you will achieve this goal.

Alexey (St. Petersburg)

Good afternoon

Yuri, you are again making a mountain out of a molehill. The problem only asks whether observers in laboratories on the ground and in a rocket will see that the pendulums oscillate in the same way (with the same periods). Each observer monitors his own pendulum, both laboratories are naturally considered inertial, the observers are motionless relative to the laboratories.

Evgeniy Kirik (Otradnoye) 27.02.2013 17:05

Good afternoon “Since a spaceship flies at a constant speed” - where did this statement come from? does it mean that if a ship flies with the engine turned off, it is not accelerating? After all, if the friction force can be neglected, then according to Newton’s 2nd law F=ma. This means that initially the force was given and then the engine was turned off. Therefore, the ship is moving with acceleration. ??Explain this point in more detail please :)

Alexey

Good afternoon

There really is no friction force. The words that the rocket is “far from the stars” mean that it does not experience the gravitational attraction of celestial bodies; it can also be ignored.

Thus, at the moment, no forces are acting on the rocket, which means, according to Newton’s second law that you wrote down, the acceleration is zero. Yes, once the engines were working, they imparted acceleration to the rocket, but as soon as they were turned off, the rocket began to move evenly, and now there is nothing to accelerate it.

The laser beam in a stationary rocket hits the receiver located at point 0 (see figure). Which receiver can this beam hit in a rocket moving to the right at constant speed?

1) 1, regardless of the rocket speed

2) 0, regardless of the rocket speed

3) 2, regardless of the rocket speed

4) 0 or 1, depending on the speed of the rocket

Solution.

Since a rocket flies at a constant speed, it represents an inertial frame of reference. According to the principle of relativity (the first postulate of the special theory of relativity), all inertial frames of reference are equal in describing any physical process. Consequently, if the laser beam hit the receiver located at point 0, in a stationary rocket. It will hit it in a uniformly moving rocket, regardless of its speed.

Correct answer: 2.

Answer: 2

Light from a stationary source is incident perpendicular to the surface of a mirror, which is moving away from the light source at a speed of What is the speed of reflected light in the inertial frame associated with the mirror?

Solution.

According to the second postulate of the special theory of relativity, the speed of light in vacuum is the same for all inertial frames of reference. Thus, the speed of reflected light in the inertial frame associated with the mirror is equal to c.

Correct answer: 3.

Answer: 3

In an inertial reference frame, light from a stationary source propagates at speed With. Let the light source move in some inertial frame with speed and the mirror with speed u in the opposite direction. At what speed does light reflected from the mirror travel in this reference frame?

Solution.

According to the second postulate of the special theory of relativity, the speed of light in vacuum is the same for all inertial frames of reference. Thus, the speed of light reflected from the mirror in this inertial frame is equal to c.

Correct answer: 4.

Answer: 4

Which of the following statements are postulates of the special theory of relativity?

A. The principle of relativity is the equality of all inertial frames of reference.

B. Invariance of the speed of light in a vacuum - the invariance of its value upon transition from one inertial reference system to another.

1) only A

2) only B

4) neither A nor B

Solution.

The first postulate of the special theory of relativity: “All inertial frames of reference are equal in describing any physical process.” The second postulate: “The speed of light in a vacuum does not depend on the speed of movement of the light source or observer and is the same in all inertial frames of reference.” Thus, both statements A and B are postulates.



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