Theory of relativity. Special theory of relativity. Communication energy. mass defect. Energy yield of a nuclear reaction

Theory of relativity was proposed Albert Einstein in 1905, it is based on the premise that motion parameters one body can only be defined regarding movement parameters another body.

Appearance theory of relativity led to the concept four-dimensional space-time continuum, in which three spatial measurements And time are considered on the same basis, i.e. they are inextricably linked.

IN special theory relativity put forward by A. Einstein is taken as axioms, i.e. does not require proof due to obviousness, the fundamental connection between space And time. material universe, before the advent of the theory of relativity was considered in three spatial dimensions: up - down, right - left and forward - back. With the advent special relativity another dimension is introduced - time. Taken together, these four dimensions are collectively space-time continuum.

special theory, proposed by A. Einstein, is limited to the description of the course of an event, in the case when it occurs in the state uniform relative motion from the observer's point of view. She considers only one special case, when movement is straight and uniform.

Einstein in his theory gave an explanation of the motion of two objects with a constant speed, while they should be considered relative to each other, and not taken one as an absolute reference systems.

If you are moving at a different speed than other objects, then your observations about space and time will differ from those of other people moving at a different speed. speed .

Einstein's theory of relativity is based on the basic principles described below:

1. The principle of relativity: the action of physical laws is preserved even for bodies that are inertial reference systems, i.e. moving at a constant speed relative to each other.

2. The principle of the speed of light: the speed of light is permanent from the point of view of all observers, regardless of their speed with respect to light source.

Consider the most commonly used consequences from A. Einstein's theory of relativity:

1. speed of light is constant value for all observation points;

2. Body mass increases with increasing body movement speed, this consequence is noticeably observed only at speeds close to or tending to speed of light;

3. Mass and energy are equivalent or equivalent, i.e. mass is converted into energy, which means that in order to accelerate a body with mass to the speed of light, it will be necessary to spend energy:

where c is the speed of light;

m - body weight;

E is energy.

4. Phenomenon Lorentz-Fitzgerald compression shows that bodies shrink with an increase in speed, it is most pronounced when the speed of movement of bodies approaches the speed of light;

5. The phenomenon of "expansion of time" can be observed from a stationary point of view when time moves more slowly for a moving object.

The special theory of relativity (SRT) is based on two postulates:

1. The principle of relativity: in any inertial frame of reference, all physical phenomena under the same initial conditions, they proceed in the same way, i.e. no experiments carried out in a closed system of bodies can reveal whether the body is at rest or moves uniformly and rectilinearly.
2. The principle of constancy of the speed of light: in all inertial frames of reference the speed of light in vacuum is the same and does not depend on the speed of the moving light source.

Equal to the postulates of SRT, the position of SRT on the limiting nature of the speed of light in vacuum matters: the speed of any signal in nature cannot exceed the speed of light in vacuum: c= 3∙10 8 m/s. When objects move at a speed comparable to the speed of light, various effects are observed, described below.

1. Relativistic length contraction.

The length of a body in the reference frame where it is at rest is called its own length. L 0 . Then the length of the body moving with speed V in the inertial reference frame decreases in the direction of motion to a length:

Where: c is the speed of light in vacuum, L 0 is the length of the body in a fixed frame of reference (the length of a body at rest), L is the length of the body in the frame of reference moving with the speed V(length of a body moving at a speed V). Thus, body length is relative. The reduction of bodies is noticeable only at speeds comparable to the speed of light.

2. Relativistic lengthening of the event time.

The duration of a phenomenon occurring at a certain point in space will be the smallest in that inertial frame of reference, relative to which this point is stationary. This means that clocks moving relative to an inertial frame of reference run slower than stationary clocks and show a longer time interval between events. Relativistic time dilation becomes noticeable only at speeds comparable to the speed of light, and is expressed by the formula:

Time τ 0 , measured by a clock resting relative to the body, is called the proper time of the event.

3. Relativistic law of addition of velocities.

The law of addition of velocities in Newtonian mechanics contradicts the postulates of SRT and is replaced by a new relativistic law of addition of velocities. If two bodies move towards each other, then their speed of approach is expressed by the formula:

Where: V 1 and V 2 - speeds of movement of bodies relative to a fixed frame of reference. If the bodies move in the same direction, then their relative speed:

4. Relativistic increase in mass.

Mass of the moving body m greater than the rest mass of the body m 0:

5. Relationship between energy and body mass.

From the point of view of the theory of relativity, the mass of a body and the energy of a body are practically the same thing. Thus, only the fact of the existence of a body means that the body has energy. Least Energy E 0 the body has in the inertial reference frame relative to which it is at rest and is called the body's own energy (rest energy of the body):

Any change in body energy means a change in body mass and vice versa:

where: ∆ E is the change in body energy, ∆ m is the corresponding change in mass. Total body energy:

Where: m- body mass. Total body energy E proportional relativistic mass and depends on the speed of the moving body, in this sense the following relations are important:

By the way, the kinetic energy of a body moving at a relativistic speed can only be calculated using the formula:

From the point of view of the theory of relativity, the law of conservation of rest masses is unfair. For example, rest mass atomic nucleus less than the sum of the rest masses of the particles entering the nucleus. However, the rest mass of a particle capable of spontaneous decay more than the amount own masses of its constituents.

This does not mean a violation of the law of conservation of mass. In the theory of relativity, the law of conservation of relativistic mass is valid, since in an isolated system of bodies the total energy is preserved, and hence the relativistic mass, which follows from the Einstein formula, so we can talk about a single law of conservation of mass and energy. This does not mean that mass can be converted into energy and vice versa.

There is a relationship between the total energy of the body, rest energy and momentum:

Photon and its properties

Light is the flux of quanta electromagnetic radiation called photons. Photon is a particle that carries the energy of light. It cannot be at rest, but always moves at a speed equal to the speed of light. A photon has the following characteristics:

1. The photon energy is:

Where: h= 6.63∙10 –34 J∙s = 4.14∙10 –15 eV∙s – Planck’s constant, ν is the frequency of the light, λ is the wavelength of the light, c is the speed of light in vacuum. The energy of a photon in Joules is very small, therefore, for mathematical convenience, it is often measured in an off-system unit - electron volts:

1 eV = 1.6∙10 -19 J.

2. A photon travels in a vacuum at the speed of light. c.

3. A photon has momentum:

4. A photon does not have mass in the usual sense for us (the mass that can be measured on scales, calculated according to Newton's second law, and so on), but in accordance with Einstein's theory of relativity, it has mass as a measure of energy ( E = mc 2). Indeed, any body that has some energy also has mass. If we consider that a photon has energy, then it also has a mass, which can be found as:

5. A photon has no electric charge.

Light has a dual nature. When light propagates, its wave properties appear (interference, diffraction, polarization), and when interacting with matter, corpuscular (photoelectric effect). This dual nature of light is called wave-particle duality.

external photoelectric effect

photoelectric effect- a phenomenon consisting in the appearance of a photocurrent in a vacuum bottle when the cathode is illuminated with monochromatic light of a certain wavelength λ .

When the voltage across the anode is negative, the electric field between the cathode and anode slows down the electrons. Measuring the given retarding voltage at which the photocurrent disappears, it is possible to determine the maximum kinetic energy of photoelectrons escaping from the cathode:

Numerous experimenters have established the following basic laws of the photoelectric effect:

1. The photoelectric effect is inertialess. This means that electrons begin to fly out of the metal immediately after the start of irradiation with light.
2. The maximum kinetic energy of photoelectrons increases linearly with increasing light frequency ν and does not depend on its intensity.
3. For every substance there is a so-called red border photo effect, that is, the lowest frequency ν min (or maximum length waves λ max) at which the external photoelectric effect is still possible.
4. The number of photoelectrons pulled out by light from the cathode in 1 s is directly proportional to the light intensity.

When interacting with matter, a photon transfers all of its energy E = hν one electron. Part of this energy can be dissipated by an electron in collisions with atoms of matter. In addition, part of the electron energy is spent on overcoming the potential barrier at the metal–vacuum interface. To do this, the electron must make work function A out, depending on the properties of the cathode material. The highest kinetic energy that a photoelectron emitted from the cathode can have, in this case, is determined by the law of conservation of energy:

This formula is called Einstein's equation for the external photoelectric effect. Using the Einstein equation, one can explain all the regularities of the external photoelectric effect. For red border photo effect, according to Einstein's formula, we can get the expression:

Bohr's postulates

Bohr's first postulate (stationary state postulate): an atomic system can only be in special stationary or quantum states, each of which corresponds to a certain number n and energy E n. In stationary states, an atom does not emit or absorb energy.

The state with the lowest energy is assigned the number "1". It's called main. All other states are assigned sequential numbers "2", "3", and so on. They're called excited. An atom can remain in its ground state indefinitely. In the excited state, the atom lives for some time (about 10 ns) and passes into the ground state.

According to Bohr's first postulate, an atom is characterized by a system of energy levels, each of which corresponds to a certain stationary state. The mechanical energy of an electron moving along a closed path around a positively charged nucleus is negative. Therefore, all stationary states correspond to the energy values E n < 0. При E n≥ 0 the electron moves away from the nucleus (ionization occurs). Value | E 1 | called ionization energy. State with energy E 1 is called the ground state of the atom.

Bohr's second postulate (frequency rule): during the transition of an atom from one stationary state with energy E n to another stationary state with energy E m a quantum is emitted or absorbed, the energy of which is equal to the difference between the energies of the stationary states:

hydrogen atom

The simplest of the atoms is the hydrogen atom. It contains a single electron. The nucleus of an atom is a proton - a positively charged particle, the charge of which is equal in absolute value to the charge of an electron. Usually, an electron is at the first (main, unexcited) energy level (an electron, like any other system, tends to a state with a minimum of energy). In this state, its energy is E 1 = -13.6 eV. In the hydrogen atom, the following relations are satisfied that relate the radius of the trajectory of an electron rotating around the nucleus, its speed and energy in the first orbit with similar characteristics in other orbits:

On any orbit in a hydrogen atom, the kinetic ( TO) and potential ( P) the electron energies are related to the total energy ( E) the following formulas:

atomic nucleus

At present, it is firmly established that the atomic nuclei of various elements consist of two particles - protons and neutrons, which are usually called nucleons. A number of notations are introduced to characterize atomic nuclei. The number of protons that make up the atomic nucleus is denoted by the symbol Z and is called the charge number or atomic number (this is the serial number in periodic table Mendeleev). The number of neutrons is denoted by the symbol N. The total number of nucleons (that is, protons and neutrons) is called the mass number A, for which the following formula can be written:

Communication energy. mass defect

The most important role in nuclear physics is played by the concept nuclear binding energy. The binding energy of the nucleus is equal to the minimum energy that must be expended for the complete splitting of the nucleus into individual particles. It follows from the law of conservation of energy that the binding energy is equal to the energy that is released during the formation of a nucleus from individual particles.

The binding energy of any nucleus can be determined using accurate measurement its masses. Such measurements show that the mass of any nucleus M i is always less than the sum of the masses of its constituent protons and neutrons: M I< Zm p + N m n. The difference between these masses is called mass defect, and is calculated by the formula:

The mass defect can be determined using the Einstein formula E = mc 2 the energy released during the formation of a given nucleus, that is, the binding energy of the nucleus E St:

But it is more convenient to calculate the binding energy using a different formula (here, the masses are taken in atomic units, and the binding energy is obtained in MeV):

Radioactivity. Law of radioactive decay

Almost 90% of known atomic nuclei are unstable. An unstable nucleus spontaneously transforms into other nuclei with the emission of particles. This property of nuclei is called radioactivity.

Alpha decay. Alpha decay is the spontaneous transformation of an atomic nucleus with the number of protons Z and neutrons N into another (daughter) nucleus containing the number of protons Z - 2 and neutrons N - 2. In this case, α -particle - the nucleus of a helium atom 4 2 He. General scheme alpha decay:

Beta decay. During beta decay, an electron (0 –1 e) flies out of the nucleus. Scheme of beta decay:

Gamma decay. Unlike α - And β -radioactivity γ -radioactivity of nuclei is not associated with a change in the internal structure of the nucleus and is not accompanied by a change in charge or mass numbers. As with α - as well as β -decay, the daughter nucleus may be in some excited state and have an excess of energy. The transition of the nucleus from the excited state to the ground state is accompanied by the emission of one or more γ -quanta, the energy of which can reach several MeV.

Law of radioactive decay. Any sample of radioactive material contains a huge number of radioactive atoms. Since radioactive decay is random and does not depend on external conditions, then the law of decreasing quantity N(t) undecayed to this point in time t nuclei can serve as an important statistical characteristic radioactive decay process. The law of radioactive decay has the form:

Value T called half-life, N 0 – initial number radioactive nuclei at t= 0. The half-life is the main quantity that characterizes the rate of radioactive decay. The shorter the half-life, the more intense the decay.

At α - And β In radioactive decay, the daughter nucleus may also be unstable. Therefore, a series of successive radioactive decays are possible, which end in the formation of stable nuclei.

Nuclear reactions

nuclear reaction- this is the process of interaction of an atomic nucleus with another nucleus or elementary particle, accompanied by a change in the composition and structure of the nucleus and the release of secondary particles or γ -quanta. As a result of nuclear reactions, new radioactive isotopes can be formed that are not found on Earth in natural conditions.

In nuclear reactions, several conservation laws are fulfilled: momentum, energy, angular momentum, charge. In addition to these classical conservation laws, nuclear reactions hold the law of conservation of the so-called baryon charge(that is, the number of nucleons - protons and neutrons). For example, in a general reaction:

Performed following conditions(the total number of nucleons before and after the reaction remains unchanged):

Energy yield of a nuclear reaction

Nuclear reactions are accompanied by energy transformations. The energy yield of a nuclear reaction is the value:

Where: M A and M B are the masses of initial products, M C and M D are the masses of the final reaction products. Value Δ M called mass defect. Nuclear reactions can proceed with the release ( Q> 0) or with energy absorption ( Q < 0). Во втором случае первоначальная кинетическая энергия исходных продуктов должна превышать величину |Q|, which is called reaction threshold.

In order for a nuclear reaction to have a positive energy yield, the specific binding energy of nucleons in the nuclei of the initial products must be less than the specific binding energy of nucleons in the nuclei of the final products. This means that the value Δ M

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result on the CT, the maximum of what you are capable of.

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 2 . The space rocket is moving at a high relative speed. The relativistic contraction of its length was 36 % . Determine the speed of the rocket. [solution ]

 3 . Rectangular block with sides 3,3 And 6.9 cm moves parallel to the large rib. At what speed will the rectangular block turn into a cube? How will the movement affect the volume of the body? [solution ]

 4 . From formation to collapse π - meson has flown a distance 1.35 km. Lifetime π -meson in a fixed coordinate system is equal to 5 µs. Determine lifetime π -meson by the clock in the coordinate system moving with it. [solution ]

 5 . At what speed of motion is the kinetic energy of an electron equal to 5 MeV? [solution ]

 6 . Determine the momentum of an electron with kinetic energy 5 MeV. [solution ]

 7 . The proton moves at a speed equal to 0.8 of the speed of light. An electron moves towards it with a speed 0,9 the speed of light. What are their speeds relative to each other? Determine the total and kinetic energy of the electron. [solution ]

 8 . The proper lifetime of the particle differs by 1,5 % from the time of life according to a fixed clock. Define v/c. [solution ]

 9 . Annihilation of a slowly moving electron and positron produces two gamma rays. At what angle to each other do they scatter? What is the frequency of the generated radiation? [solution ]

 10 . Flying with speed v = 0.8s the neutral particle decays into two photons, which then move in opposite directions (Fig.). What is the ratio of the frequencies of these quanta? [solution ]

 11 . During the decay of a neutral particle, two photons were formed, moving at angles α 1 = 30° And α 2 = 60° to the original direction of particle motion. What was her speed? [solution ]

 12 . A particle moving initially with a speed v = 0.8s, decays into two photons. Find the minimum angle of scattering of these photons. [solution ]

 13 . Can a free electron absorb a photon? [solution ]

 14 . In moving at speed v wagon having a width L(the vector is directed perpendicular to this width), a mirror is installed on the side wall 3 (rice.). At the opposite wall near the point A arrange a short flash of light, which is registered by a sensor mounted on the wall near the place of radiation (i.e. A). What is the ratio of the propagation time of light t o in the car reference system to the time of its propagation t relative to the road surface? [solution ]

 15 . Muons (unstable particles belonging to the class of leptons, a muon is a “heavy” analog of an electron) are formed during the interaction of cosmic rays with air molecules in upper layers atmosphere, but are recorded near the Earth's surface. Muon lifetime t o = 2.2 µs. Estimate the speed of the muon, assuming that it was formed at a height H = 20 km and disintegrated at the Earth's surface. [solution ]

 16 . Two electrons move towards the target one after the other with equal speeds v 1 \u003d v 2 \u003d (3/5) s. The second one hits the target t = 1 µs after the first. Determine what was the distance between the electrons in the LSO and in the frame of reference associated with one of the electrons. [solution ]

 17 . Two rulers, each having its own length equal to lo, moving towards each other parallel to the common axis x with relativistic speeds (Fig.). An observer associated with one of them recorded that time elapsed between the coincidences of the left and right ends of the rulers. t. What is the relative speed of the lines? Make a calculation for t = 30 µs, l o = 3 km. [solution ]

 18 . The spaceship is moving at a speed v = 0.6s from one space beacon to another. At the moment when it is in the middle between the beacons, each of them emits a light pulse in the direction of the ship. Find what time interval will pass on the ship between the moments of registration of these impulses. The distance between the beacons the light travels for 2 months. Assume that the beacons do not move relative to each other. [

To describe any physical processes

A. All frames of reference are equal.

B. All inertial frames of reference are equal.

Which of these statements is true according to special 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". So statement B is true.

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 in describing any physical process.

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

B. The rest energy of any body is equal to the product of its mass and 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, statements A and B are postulates.

Answer: 1.

Answer: 1

In the installation, a spark discharge creates a flash of light and a sound pulse, which are recorded by a sensor located at a distance of 1 m from the spark gap. Schematically mutual arrangement arrester R and sensor D shown with an arrow. The propagation time of light from the spark gap to the sensor is T, and the sound

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

Solution.

Because spaceship flies at a constant speed, it is 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 who were on board the spacecraft could not detect any dependence of the speed of propagation of light and sound signals from installation orientation.

Answer: 2.

Answer: 2

One scientist tests the oscillation patterns of a spring pendulum in a laboratory on Earth, and another in a laboratory on a spacecraft flying away from stars and planets with the engine 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 more slowly on the ship

3) the same if the speed of the ship is low

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

Solution.

Since the spacecraft is flying at a constant speed, it is 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.

Answer: 1.

Ida Gorbacheva (Ukhta) 16.05.2012 20:01

Hello! But according to the theory of relativity, in moving objects, time flows more slowly... Besides, there is weight in terrestrial conditions, but it is not in a ship... Could you comment on these contradictions?

Alexey (St. Petersburg)

Good afternoon

Thank God there are no contradictions! Do not worry.

About your questions. First, about time dilation. Do not forget that this is a relative effect. It seems to a stationary observer on Earth 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 the scientist in this moving object, the Earth already seems to be rushing past him at the same speed, but in the opposite direction. So, it will also seem to him that the observer on Earth is too slow and amazingly flattened :). Einstein's postulate guarantees that in all inertial reference frames everything will look the same (and this is wonderful). That is, if you set the same experiments, you will get the same results. For example, if each scientist has his own pendulum, then the readings of his own pendulums and the readings of other people's pendulums will be the same 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, it is not gravity at all. On Earth, indeed, most often the source of weight is gravity to the Earth, but if you look at a free-falling elevator, then there will be no more weight. In the case of a spring pendulum, it turns out that gravity does not affect the nature of its oscillations in any way, it only leads to a shift in the equilibrium position. Therefore, if you put the pendulum "on the side", thereby removing gravity from the game, you get exactly the same as in a rocket, where there is no gravity at all :)

I hope I 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 concept of gravitational time dilation is considered in the special theory of relativity.

Alexey (St. Petersburg)

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

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

Yuri Shoitov (Kursk) 28.11.2012 21:27

Hello Alexey!

It surprises me how the question is posed, and your (most likely not your) decision.

It is completely incomprehensible what the words "processes proceed in the same way" mean.

Such a formulation throws us back to the time of Galileo, when there was no concept of a frame of reference yet. Yes, Galileo wrote exactly like this: "Flies in a cabin will fly the same way, regardless of whether the ship is standing still or moving in a straight line 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 frames of reference, which move relative to each other in a straight line uniformly and translationally." But even in classical mechanics it is impossible in this case to speak of "the same course of processes" in these systems. Point speed in different systems will be different, respectively, 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 stops abruptly relative to the car, then nothing special will happen. If it stops in the same time relative to the ground, then this is a train wreck. Here you have the "sameness of the processes"!

It follows from the Lorentz transformations that the time in the moving and stationary frames of reference will be different, therefore, the periods of oscillation of the pendulum will also be different. Where did you see the "identity of processes" here ?!

The equality of reference systems in SRT is that in both systems the value of the relativistic interval in the four-dimensional Minkowski space will be the same (invariant). And no more.

Arguments about what will "appear" to one and the other observer are 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 frame associated with the Earth is also erroneous. The Earth rotates around its axis, therefore, a point that is stationary in this system has a portable acceleration omega square times 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 free fall, it can be neglected. But the condition says that the ship is far from the 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 decision are a clumsy attempt to explain clearly to the student something that you do not understand yourself.

If your goal is to completely confuse the student 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 again make an elephant out of a fly. The problem only asks whether the observers in the laboratories on the ground and in the rocket will see that the pendulums oscillate in the same way (with the same periods). Each observer follows his own pendulum, both laboratories are naturally considered to be inertial, the observers are stationary relative to the laboratories.

Evgeny Kirik (Otradnoye) 27.02.2013 17:05

Good afternoon "Since the spacecraft is flying at a constant speed" - where did this statement come from? unless if the ship is flying with the engine off, does this mean that it is not accelerating? After all, if you can neglect the force of friction, then according to Newton's 2nd law F=ma. it means that initially the force was given and then the engine was turned off. Therefore, the ship moves with acceleration. ??Please explain this point in more detail :)

Alexei

Good afternoon

There is no real friction force. The words about the fact that the rocket is "far from the stars" means that it does not experience the gravitational attraction of celestial bodies, it can also be neglected.

Thus in this moment no forces act on the rocket, which means that, according to Newton's second law you wrote out, the acceleration is zero. Yes, once the engines worked, they gave the rocket acceleration, but as soon as they were turned off, the rocket began to move evenly, there is nothing to accelerate it now.

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

1) 1, regardless of rocket speed

2) 0, regardless of rocket speed

3) 2, regardless of rocket speed

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

Solution.

Since the rocket flies at a constant speed, it is 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. Therefore, if the laser beam hit the receiver located at point 0, in a stationary rocket. It will hit him in a uniformly moving rocket, regardless of its speed.

Answer: 2.

Answer: 2

Light from a stationary source is incident perpendicular to the surface of a mirror that moves away from the light source at a speed What is the speed of the reflected light in the inertial reference 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 reference frame associated with the mirror is c.

Answer: 3.

Answer: 3

In an inertial frame of reference, light from a stationary source propagates at a speed With. Let the light source move in some inertial frame with the speed and the mirror - with the speed u in the opposite direction. With what speed does the light reflected from the mirror propagate 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 the light reflected from the mirror in this inertial frame of reference is equal to c.

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. The invariance of the speed of light in a vacuum is the invariance of its magnitude during the transition from one inertial frame of reference 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 vacuum does not depend on the speed of the light source or the observer and is the same in all inertial frames of reference." Thus, both A and B are postulates.