The law of conservation of momentum for jet propulsion. Methodical development of a training lesson in the discipline "Physics" on the topic: "Impulse

Momentum conservation law

In subsection (5.8), the concept of the momentum of an arbitrary body was introduced and equation (5.19) was obtained, which describes the change in momentum under the action of external forces. Since the change in momentum is due only external forces,then equation (5.19) is conveniently used to describe the interactions of several bodies. In this case, interacting bodies are considered as one complex body (system of bodies). It can be shown that complex body impulse (system of bodies) is equal to the vector sum of the impulses of its parts:

p \u003d p 1 + p 2 +… (9.13)

For a system of bodies, an equation of the form (5.13) is written without any changes:

dp \u003d F dt.(9.14)

Change in momentumsystem of bodies is equal to the impulse of external forces acting on it.

Let's consider some examples to illustrate the operation of this law.

In fig. 9.10, and the athlete stands with her right foot resting on the skateboard, and with her left foot she pushes off the ground. The speed achieved during the push depends on the strength of the push and on the time during which this force acts.

In fig. 9.10, b shows a javelin thrower. The speed that a spear of a given mass will acquire depends on the force applied by the athlete's hand and on the time during which it is applied.

Figure: 9.10.a) Sportswoman on a skateboard; b) javelin thrower

Figure: 9.11.

Shot put

Therefore, before throwing the javelin, the athlete brings his hand far back. A similar process is analyzed in more detail in the example of an athlete pushing the core, Fig. 9.11.

Equality (9.14) implies one corollary important for practical application, called momentum conservation law.Consider a system of bodies that are not affected by external forces. This system is called closed.

A system of bodies that interact only with each other and do not interact with other bodies is called closed.

For such a system, there are no external forces (F \u003d0 and dp \u003d0). Therefore, there is momentum conservation law.

Vector sum of impulses of bodies,included in the closed system remains unchanged (saved).

In other words, for any two moments of time, the impulses of the closed-loop system are the same:

p 1 \u003d p 2(9.15)

The law of conservation of momentum is a fundamental law of nature that knows no exceptions. It is absolutely exactly observed both in the macrocosm and in the microcosm.

Of course, a closed system is an abstraction, since in almost all cases there are external forces. However, for some types of interactions with a very short duration, the presence of external forces can be neglected, since with a small interval of action, the force impulse can be considered equal to zero:

F dt 0 → dp 0.

The processes of short duration include

Collisions of moving bodies

The disintegration of the body into parts (explosion, shot, throw).

Examples of

In action films, there are often scenes in which, after being hit by a bullet, a person is thrown back in the course of a shot. It looks pretty impressive on the screen. Let's check if this is possible? Let the mass of people M\u003d 70 kg and he is at rest at the moment the bullet hits. We take the mass of a bullet equal t \u003d9 g, and its speed v \u003d750 m / s. If we assume that after being hit by a bullet, a person starts to move (in fact, this can be hindered by the friction force between the soles and the floor), then for the human-bullet system, the law of conservation of momentum can be written: p 1 = p 2.Before being hit by a bullet, a person does not move and, in accordance with (9.9), the impulse of the system p 1 \u003d m ∙ v+0. Let's assume that the bullet gets stuck in the body. Then the final momentum of the system r 2 = (M + t) ∙ u,where and- the speed that a person received when hit by a bullet. Substituting these expressions into the law of conservation of momentum, we get:

The obtained result shows that there can be no question of any human flying away by several meters (by the way, a body thrown up at a speed of 0.1 m / s will rise to a height of only 0.5 mm!).

2) Clash of hockey players.

Two hockey players weighing M 1and M 2move towards each other at speeds, respectively, v 1, v 2(fig.9.12). Determine the overall speed of their movement, counting the collision absolutely inelastic(in case of absolutely inelastic impact, the bodies “interlock” and move further as a whole).

Figure: 9.12.The absolutely inelastic clash of hockey players

Let's apply the law of conservation of momentum to a system consisting of two hockey players. System impulse before collision p 1 \u003d M 1 ∙ v 1- M 2 v 2.This formula contains a "-" sign because the speeds v 1and v 2directed towards each other. Direction of speed v 1is considered positive, and the direction of speed v 2- negative. After an inelastic collision, the bodies move with a general speed vand the impulse of the system p 2 \u003d (M l + M 2) ∙ v.Let's write down the law of conservation of momentum and find the speed v:

Direction of speed vis determined by its sign.

Let us pay attention to one important circumstance: the law of conservation of momentum can be applied only to free bodies.If the motion of one of the bodies is limited by external connections, then the total momentum will not be conserved.

Jet propulsion

Reactive motion is based on the use of the law of conservation of momentum. This is the name for the movement of a body that occurs when some part of it separates from the body at some speed. Consider the jet propulsion of a rocket. Let the rocket and its mass together with the fuel M is at rest.The initial impulse of the rocket with fuel is zero.When burning a portion of fuel mass tgases are formed, which are ejected through the nozzle at a speed and. According to the law of conservation of momentum, the total impulse of the rocket and fuel is conserved: p 2 \u003d p 1→ t ∙ u + (M - m) ∙ v \u003d0, where vis the speed received by the rocket. From this equation we find: v \u003d ─t ∙ and / (M ─ t).We see that the rocket acquires a speed directed in the direction opposite to the direction of gas emission. As the fuel burns, the rocket speed increases continuously.

An example of jet propulsion is recoil when fired from a rifle. Let the rifle, the mass of which m 1 \u003d4.5 kg, shoots a bullet mass t 2 \u003d11 g flying out at speed v 1 \u003d800 m / s. From the law of conservation of momentum, you can calculate the recoil rate:

This significant recoil velocity will occur if the rifle is not pinned to the shoulder. In this case, the shooter will receive a strong blow from the butt. With the correct shooting technique, the shooter presses the rifle to the shoulder and the recoil is perceived by the shooter's entire body. With a shooter weighing 70 kg, the recoil speed in this case will be 11.8 cm / s, which is quite acceptable.

In this lesson we will talk about conservation laws. Conservation laws are a powerful tool for solving mechanical problems. They are a consequence of the internal symmetry of space. The first conserved quantity we will study is momentum. In this lesson, we will give a definition of the momentum of the body, and we will connect the change in this quantity with the force that acts on the body.

Conservation laws are a very powerful tool for solving problems in mechanics. They are used when the equations of dynamics are difficult or impossible to solve. Conservation laws are a direct consequence of the laws of nature. It turns out that every conservation law corresponds to some kind of symmetry in nature. For example, the law of conservation of energy arises due to the fact that time is uniform, and the law of conservation of momentum is due to the homogeneity of space. Moreover, in nuclear physics, as a result of complex symmetries of the system, certain quantities arise that cannot be measured, but which are known to be conserved, for example, quantities such as strangeness and beauty.

Consider Newton's second law in vector form:

remember that acceleration is the rate of change in speed:

Now, if we substitute this expression into Newton's second law and multiply the left and right sides by, we get

Let us now introduce a certain quantity, which we will further call momentum, and obtain Newton's second law in momentum form:

The value to the left of the equal sign is called the impulse of force. In this way,

The change in the momentum of the body is equal to the momentum of the force.

Newton wrote down his famous second law in exactly this form. Note that Newton's second law in this form is more general, since the force acts on the body for some time not only when the speed of the body changes, but also when the body mass changes. Using such an equation, it is easy, for example, to find out the force acting on a rocket taking off, since the rocket changes its mass during takeoff. Such an equation is called the Meshchersky equation, or the Tsiolkovsky equation.

Let's consider in more detail the value introduced by us. This value is usually called the momentum of the body. So,

The momentum of a body is a physical quantity equal to the product of the mass of the body by its speed.

Impulse is measured in SI units in kilograms per meter divided by a second:

The impulse conservation law follows from Newton's second law in impulse form. Indeed, if the sum of the forces acting on the body is zero, then the change in the momentum of the body is zero, or, in other words, the momentum of the body is constant.

Let us consider the application of the law of conservation of momentum by examples. So, the ball with impulse hits the wall (Fig. 1). The momentum of the ball changes and the ball bounces in a different direction with momentum. If before the impact, the angle to the normal was equal, then after the impact, this angle, generally speaking, may be different. However, if only the normal pressure force acts on the ball from the side of the wall, directed perpendicular to the wall, then the component of the impulse changes in the direction perpendicular to the wall. If it was equal before the impact, then after the impact it will be equal, and the impulse component along the wall will not change. We come to the conclusion that the impulse after the impact is equal to the impulse before the impact and is directed at an angle to the normal.

Figure: 1. The ball bounces off the wall

Note that the force of gravity acting on the ball will not affect the result in any way, since it is directed along the wall. Such an impact, in which the modulus of the body's momentum is preserved, and the angle of incidence is equal to the angle of reflection, is called absolutely elastic. Note that in a real situation, when the impact is inelastic, the angle of reflection may be different (Fig. 2)

Figure: 2. The ball does not bounce elastic

The impact will be inelastic if the ball is subjected to so-called dissipative forces, such as friction or resistance.

Thus, in this lesson, you got acquainted with the concept of momentum, with the law of conservation of momentum, and with Newton's second law, written in pulse form. In addition, you have considered the problem of a ball bouncing absolutely elastically off a wall.

List of references

1. G. Ya. Myakishev, B. B. Bukhovtsev, N. N. Sotsky. Physics 10. - M .: Education, 2008.
2. A.P. Rymkevich. Physics. Problem book 10-11. - M .: Bustard, 2006.
3. O. Ya. Savchenko. Physics tasks. - M .: Nauka, 1988.
4. A. V. Peryshkin, V. V. Krauklis. Physics course. T. 1. - M .: State. uch.-ped. ed. min. education of the RSFSR, 1957.

Question: We found out that with an absolutely elastic impact of the ball against the wall, the angle of incidence is equal to the angle of reflection. The same law is also true for the reflection of a ray in a mirror. How can this be explained?

Answer: This is explained very simply: light can be considered a stream of particles - photons, which elastically hit the mirror. Accordingly, the angle of incidence when the photon is incident is equal to the angle of reflection.

Question: Airplanes, when flying, are repelled by the propeller from the air. What does the rocket push off from when flying?

Answer: The rocket is not repelled, the rocket moves under the influence of the jet thrust force. This is achieved due to the fact that fuel particles fly out of the rocket nozzle at high speed.

His movements, i.e. magnitude.

Pulse - vector value, coinciding in direction with the velocity vector.

Pulse unit in SI: kg m / s .

The momentum of the system of bodies is equal to the vector sum of the impulses of all bodies included in the system:

Momentum conservation law

If additional external forces act on the system of interacting bodies, for example, then in this case the relation is valid, which is sometimes called the law of momentum change:

For a closed system (in the absence of external forces), the momentum conservation law is valid:

The action of the law of conservation of momentum can explain the phenomenon of recoil when shooting from a rifle or when firing artillery. Also, the action of the law of conservation of momentum underlies the principle of operation of all jet engines.

When solving physical problems, the law of conservation of momentum is used when knowledge of all the details of motion is not required, but the result of the interaction of bodies is important. Such problems, for example, are the problems of collision or collision of bodies. The law of conservation of momentum is used when considering the motion of bodies of variable mass, such as launch vehicles. Most of the mass of such a rocket is fuel. In the active phase of the flight, this fuel burns out, and the mass of the rocket in this segment of the trajectory rapidly decreases. Also, the law of conservation of momentum is necessary in cases where the concept is inapplicable. It is difficult to imagine a situation when a stationary body acquires a certain speed instantly. In normal practice, bodies always accelerate and pick up speed gradually. However, when electrons and other subatomic particles move, their state changes abruptly without being in intermediate states. In such cases, the classical concept of "acceleration" cannot be applied.

Examples of problem solving

EXAMPLE 1

The task	A projectile weighing 100 kg, flying horizontally along the railway track at a speed of 500 m / s, hits a car with sand weighing 10 tons and gets stuck in it. What speed will the car get if it moved at a speed of 36 km / h in the direction opposite to the movement of the projectile?
Decision	The system car + projectile is closed; therefore, in this case, the law of conservation of momentum can be applied. Let's complete the drawing, indicating the state of the bodies before and after the interaction. When the projectile and the car interact, an inelastic impact occurs. In this case, the law of conservation of momentum will be written as: Choosing the direction of the axis coinciding with the direction of movement of the car, we write down the projection of this equation on the coordinate axis: whence the speed of the car after being hit by a shell: We translate the units into the SI system: t kg. Let's calculate:
Answer	After being hit by a shell, the car will move at a speed of 5 m / s.

EXAMPLE 2

The task	A projectile with a mass of m \u003d 10 kg had a speed of v \u003d 200 m / s at the top point. At this point, it split in two. A smaller part with a mass of m 1 \u003d 3 kg received a speed of v 1 \u003d 400 m / s in the same direction at an angle to the horizon. At what speed and in what direction will most of the projectile fly?
Decision	The trajectory of the projectile is a parabola. The body's speed is always tangential to the path. At the top of the trajectory, the speed of the projectile is parallel to the axis. Let's write the law of conservation of momentum: Let's go from vectors to scalar values. To do this, we will square both sides of the vector equality and use the formulas for: Considering that and also that, we find the speed of the second fragment: Substituting the numerical values \u200b\u200bof physical quantities into the resulting formula, we calculate: The direction of flight of most of the projectile is determined using: Substituting numerical values \u200b\u200binto the formula, we get:
Answer	Most of the projectile will fly at a speed of 249 m / s downward at an angle to the horizontal direction.

EXAMPLE 3

The task

Train weight 3000 tons. Friction coefficient 0.02. What should be a steam locomotive for the train to pick up speed of 60 km / h 2 minutes after the start of movement.

Decision

Since the train is acted upon (by an external force), the system cannot be considered closed, and the law of conservation of momentum in this case is not fulfilled. Let's use the law of impulse change: Since the friction force is always directed in the direction opposite to the movement of the body, the impulse of the friction force will enter the projection of the equation onto the coordinate axis (the direction of the axis coincides with the direction of movement of the train) with a minus sign:

space research. Semiconductor diode, pn - junction and its properties. Application of semiconductor devices. The task of applying 1 law of thermodynamics.

Body impulse - this is the product of body mass by its speed p \u003d mv (kg * m / s) Body impulse - amount of movement. The change in the momentum of the body is equal to the change in the momentum of the force. ∆p \u003d F∆t
The sum of impulses of bodies before interaction is equal to the sum of impulses after interaction OR: The geometric sum of impulses of bodies in a closed system remains constant. m1v1 + m2v2 \u003d const

The law of conservation of momentum is at the heart of jet propulsion - this is a movement in which a part of the body is separated, and the other receives additional acceleration.
Jet propulsion in technology: FOR EXAMPLE (in airplanes and in rockets)
Reactive motion in nature: FOR EXAMPLE (molluscs, octopuses). Space information is of great importance for the further development of science and technology. Space exploration is likely to lead in the near future to revolutionary transformations in many areas of technology and technology, as well as in medicine. The results of developments in the field of space technology will find application in industrial and agricultural work, in the exploration of the depths of the World Ocean and in polar research, in sports competitions, in the manufacture of geological equipment and in other areas. A semiconductor diode is a semiconductor device with one electrical junction and two leads (electrodes). An electron-hole junction is a region of a semiconductor in which a spatial change in the type of conductivity takes place (from an electronic n-region to a hole p-region). Semiconductor devices are used: in the motor transport complex. electronic ignition. electronic control unit. LEDs: sensors, headlights, traffic lights, etc. global positioning system. Cell Phones

6 The law of universal gravitation. The force of gravity. Free fall of bodies. Body weight. Weightlessness. A magnetic field. Magnetic induction, magnetic induction lines. Ampere force and its application. The task of applying formulas of work or DC power.

The law of universal gravitation Newton's is a law that describes gravitational interaction in the framework of classical mechanics. This law was discovered by Newton around 1666. It states that the force of gravitational attraction between two material points of mass and, separated by distance, is proportional to both masses and inversely proportional to the square of the distance between them. The force of gravity - the force acting on any material body located near the surface of the Earth or other astronomical body. Free fall - Equally variable motion under the action of gravity, when other forces acting on the body are absent or negligible. Weight - the force of action of the body on the support (or suspension or other type of attachment), preventing the fall, arising in the field of gravity P \u003d mg. Weightlessness - a state in which the force of interaction of the body with the support (body weight), arising in connection with gravitational attraction, the action of other mass forces, in particular the force of inertia arising during the accelerated motion of the body, is absent. A magnetic field - a force field acting on moving electric charges and on bodies with a magnetic moment, regardless of the state of their motion. Magnetic induction - vector quantity, which is the force characteristic of the magnetic field (its action on charged particles) at a given point in space. Determines with what force the magnetic field acts on a charge moving with speed.
Magnetic induction lines - lines, tangents to which are directed as well as the vector of magnetic induction at a given point of the field.

7 The phenomenon of electromagnetic induction, the use of this phenomenon. The law of electromagnetic induction. Lenz's rule. Work. Fur. energy. Kinetic and potential energy. The law of conservation of fur. energy. EZ: Measuring the total resistance of an electrical circuit in series connection. Electromagnetic induction is the phenomenon of the appearance of an electric torus in a closed loop when the magnetic flux passing through it changes. It was discovered by Michael Faradel. The phenomenon of email Poppy. induction used in electrical and radio engineering devices: generators, transformers, chokes, etc. Faraday's law of electromagnetic induction is the basic law of electrodynamics concerning the principles of operation of transformers, chokes, many types of electric motors and generators. The law says: for any closed loop, the induced electromotive force (EMF) is equal to the rate of change of the magnetic flux passing through this loop, taken with a minus sign. Lenz's rule determines the direction of the induction current and says: the induction current always has such a direction that it weakens the effect of the cause that excites the current. Fur. Work is a physical quantity that is a scalar quantitative measure of the action of a force or forces on a body or system, depending on the numerical value, the direction of the force (forces) and on the movement of a point (points), body or system In physics fur. energy describes the sum of potential and kinetic energies present in the components of a mechanical system. Fur. energy is the energy associated with the movement of an object or its position, the ability to perform mechanical work. The law of conservation of fur. energy states that if a body or system is exposed to only conservative forces (both external and internal), then the total mechanical energy of this body or system remains constant. In an isolated system, where only conservative forces act, the total mechanical energy is conserved. Potential is the potential of the body, it embodies the kind of work the body CAN do! And kinetic is the force that is already doing the work. Law of energy conservation - the law of nature, established empirically and consisting in the fact that for an isolated physical system, a scalar physical quantity can be introduced, which is a function of the parameters of the system and is called energy, which is conserved over time. Since the law of conservation of energy does not refer to specific quantities and phenomena, but reflects a general, applicable everywhere and always, regularity, then it can be called not a law, but the principle of conservation of energy. Potential energy- energy which is determined by the mutual position of interacting bodies or parts of the same body. Kinetic energy - the case when the body moves under the influence of force, it not only can, but also does some work

8 Mechanical vibrations, characteristics of mech. oscillations: amplitude, period, frequency. Free and forced vibrations. Resonance. Self-induction. Inductance. Coil magnetic field energy. The problem of applying the law of conservation of momentum Mechanical oscillation is called exactly or approximately repetitive motion, in which the body is displaced one way or the other from the equilibrium position. If the system is capable of oscillating motion, then it is called oscillatory. Oscillatory system properties: The system has a stable equilibrium position. When the system is removed from the equilibrium position, an internal restoring force arises in it. The system is inert. Therefore, it does not stop in a position of equilibrium, but passes it. Oscillations arising in the system under the action of internal forces are called free... All free vibrations are damped. (For example: string vibrations after hitting) Oscillations made by bodies under the action of external periodically changing forces are called forced (for example: oscillation of a metal workpiece when a blacksmith is hammering). Resonance - a phenomenon in which the amplitude of forced vibrations has a maximum at a certain value of the frequency of the driving force. Often this value is close to the natural frequency, in fact it can coincide, but this is not always the case and is not the cause of resonance. Self-induction - this is the phenomenon of induction EMF in a conducting circuit when the current flowing through the circuit changes. When the current in the loop changes, the magnetic flux through the surface bounded by this loop also changes proportionally. A change in this magnetic flux, by virtue of the law of electromagnetic induction, leads to the excitation of inductive EMF (self-induction) in this circuit. Inductance - the coefficient of proportionality between the electric current flowing in any closed loop and the magnetic flux created by this current through the surface, the edge of which is this loop. Around the conductor with current there is a magnetic field that has energy.

9 Fur. waves. Wavelength, wave propagation speed and relationships between them. Thermonuclear reaction. The use of atomic energy. Prospects and problems of nuclear power development. EZ: Determination of the refractive index of a glass plate. Fur. waves are perturbations propagating in an elastic medium (deviations of particles of the medium from the equilibrium position). If the vibrations of the particles and the propagation of the wave occur in the same direction, the wave is called longitudinal, and if these movements occur in perpendicular directions, it is called transverse. Longitudinal waves, accompanied by tensile and compressive deformations, can propagate in any elastic media: gases, liquids and solids. Transverse waves propagate in those media where elastic forces appear during shear deformation, i.e., in solids. When a wave propagates, energy is transferred without the transfer of matter. The speed with which the disturbance propagates in an elastic medium is called the wave speed. It is determined by the elastic properties of the medium. The distance that a wave propagates over a time equal to the period of oscillation in it is called the wavelength (lambda). Wavelength - the distance that the wave manages to overcome while moving in space at the speed of light in one period, which in turn is the reciprocal of the frequency. The higher the frequency, the shorter the wavelength. Thermonuclear reaction - a kind of nuclear reaction, in which light atomic nuclei combine into heavier ones due to the kinetic energy of their thermal motion. The development of an industrial society is based on the constantly growing level of production and consumption of various types of energy (drastically reduces the use of natural resources

10 The emergence of the atomistic hypothesis of the structure of matter and its experimental evidence: diffusion, Brownian motion. The main provisions of the ICT. Mass, sizes of molecules. Electromotive force. Ohm's law for a complete circuit. The task of applying the formula fur. work

Diffusionis the phenomenon of the propagation of particles of one substance between the particles of another

Brownian motion- this is the movement of particles insoluble in a liquid under the action of liquid molecules.Molecular-kinetic theory is the doctrine of the structure and properties of matter based on the idea of \u200b\u200bthe existence of atoms and molecules as the smallest particles of chemical substances At the heart of molecular kinetic theory there are three main provisions:. All substances - liquid, solid and gaseous - are formed from the smallest particles - molecules, which themselves consist of atoms. .Atoms and molecules are in continuous chaotic motion. The particles interact with each other by forces of an electrical nature. The gravitational interaction between particles is negligible. m 0 is the mass of the molecule (kg). The size of the molecule is very small. Electromotive force forces, that is, any forces of non-electrical origin, acting in quasi-stationary circuits of direct or alternating current.

Ohm's law for a complete circuit- the current in the circuit is proportional to the EMF acting in the circuit and is inversely proportional to the sum of the resistances of the circuit and the internal resistance of the source.

11 Electromagnetic waves to and from properties. The principle of radio communication. The invention of radio, modern means of communication. Temperature and its measurement Absolute temperature. Temperature is a measure of the average kinetic energy of the movement of molecules. EZ: Measuring the optical power of the collecting lens.

Electromotive force is a scalar physical quantity that characterizes the work of third-party forces, that is, any forces of non-electrical origin, acting in quasi-stationary circuits of direct or alternating current. The device of general schemes for organizing radio communications. A characteristic of a radio information transmission system in which telecommunication signals are transmitted by radio waves in an open space. Radio - a kind of wireless information transmission, in which radio waves are used as a carrier of information, freely propagating in space. On May 7, 1895, Russian physicist Alexander Stepanovich Popov (1859 - 1905/06) demonstrated the world's first radio receiver. Modern means of communication is a telephone, walkie-talkie, etc. Temperature - a physical quantity characterizing the thermal state of bodies. Temperature is measured in degrees.

Absolute temperature is an unconditional measure of temperature and one of the main characteristics

thermodynamics. Temperatureis a measure of the average kinetic energy of molecules, energy

proportional to temperature.

12 Work in thermodynamics. Internal energy. The first and second laws of thermodynamics. Alternator. Transformer. Production and transmission of electricity, energy saving at home and at work. EZ: Measuring the acceleration of gravity at a given point on the earth.

In thermodynamics the movement of the body as a whole is not considered, it is about the movement of parts of the macroscopic body relative to each other. As a result, the volume of the body can change, and its speed remains equal to zero. ... Work in thermodynamics is defined in the same way as in mechanics, but it is not equal to

a change in the kinetic energy of the body, and a change in its internal energy. Internal energy body (denoted as E or U) - the total energy of this body minus the kinetic energy of the body as a whole and the potential energy of the body in the external field of forces. Consequently, the internal energy consists of the kinetic energy of the chaotic movement of molecules, the potential energy of interaction between them and intramolecular energy. The first law of thermodynamics The change ΔU of the internal energy of a non-isolated thermodynamic system is equal to the difference between the amount of heat Q transferred to the system and the work A performed by the system over external bodies.

The second law of thermodynamics... It is impossible to transfer heat from a colder system to a hotter one in the absence of other simultaneous changes in both systems or surrounding bodies. an alternator is a device that produces alternating current

A transformer is a device used to lower or increase a current or voltage. Energy saving - the creation of new technologies that consume less energy (new lamps, etc.)

Heat engines. Efficiency of heat engines. Heat engines and ecology. Radar, the use of radar. Experimental task: measuring the wavelength of light using a diffraction grating.

Heat engine - a device that performs work by using internal energy, a heat engine that converts heat into mechanical energy, uses the dependence of the thermal expansion of a substance on temperature.

Coefficient of performance (COP) of a heat engine the ratio of the work A´ performed by the engine to the amount of heat received from the heater is called:

The continuous development of energy, automobile and other types of transport, an increase in the consumption of coal, oil and gas in industry and for household needs increases the possibilities of satisfying human life needs. However, at present, the amount of chemical fuel annually burned in various heat engines is so great that protection of nature from the harmful effects of combustion products is becoming an increasingly difficult problem. The negative impact of heat engines on the environment “is associated with the action of various factors.

Radar - the field of science and technology, combining methods and means of location (detection and measurement of coordinates) and determination of the properties of various objects using radio waves.

Radar-guided missiles are equipped with special autonomous devices to perform combat missions. Oceanic vessels use radar systems for navigation. On airplanes, radars are used to solve a number of tasks, including determining flight altitude relative to the ground.

Lesson number 14

Theme. Body impulse. Impulse conservation law. Jet propulsion.

Goal: to form students' knowledge about physical quantities - the impulse of the body and the impulse of force, and the connection between them; help to understand the law of conservation of momentum; to form knowledge about jet propulsion.

Lesson type: a lesson in the assimilation of new knowledge.

Equipment: a steel ball, a magnet, a glass of water, a sheet of paper, identical balls (2 or 4) on threads, a balloon, a pallet, a children's car, a glass of water and a tap.

^ Lesson outline

Lesson steps	Time, min	Methods and forms of working with the class
I. Organizational stage	2
II. Updating basic knowledge	5	Frontal poll
III. Communication of the topic, purpose and objectives of the lesson	2	Determining the purpose of the lesson according to the study plan of the topic
IV. Motivation for learning activities	2	Reasoned explanation
V. Perception and initial understanding of new material	20	Explanation of the teacher with elements of heuristic conversation
Vi. Securing new material	10	Self-test test
Vii. Lesson summary and homework message	4	Explanation of the teacher, instruction

^ Lesson progress

1. 
   Organizational stage
2. 
   Updating and correcting basic knowledge

The teacher emphasizes that those concepts and physical quantities that students will become familiar with in the lesson are new to them. To create a certain basis for the study of the topic, you should invite students to repeat the previous material.

Questions to the class

1. 
   Formulate Newton's first law of dynamics.
2. 
   Formulate Newton's second law of dynamics.
3. 
   Formulate Newton's third law of dynamics.
4. 
   What system of bodies is called isolated or closed?

1. 
   Communication of the topic, purpose and objectives of the lesson

The teacher informs the topic of the lesson, invites the students to familiarize themselves with the plan of its study written on the board. Then he asks students to formulate the purpose of the lesson on their own and, if necessary, makes adjustments to their answers.

Topic study plan

1. 
   Impulse of power.
2. 
   Body impulse.
3. 
   Isolated system of bodies. Impulse conservation law.
4. 
   Jet propulsion. Rocket movement as jet propulsion.

1. 
   Motivation for learning activities

Newton's laws, in principle, allow solving all problems related to the interaction of bodies. But finding the forces of interaction is often quite difficult, and without this it is impossible to find the acceleration acquired by the body, and, accordingly, its speed and movement. To solve such problems in mechanics, special concepts and quantities have been introduced, with their help, the relationship between them has been established. At the same time, it turned out that the numerical values \u200b\u200bof the introduced quantities do not change in the process of interaction of bodies, therefore the most important relationships between quantities that are preserved are called conservation laws. The energy conservation law in different interpretations has already been considered earlier. Now it's time to get acquainted with the law of conservation of momentum.

Like Newton's laws, conservation laws are the result of theoretical generalizations of research facts. These are the fundamental laws of physics, which are extremely important, since they are applied not only in mechanics,butand in other sections of physics.

1. 
   Perception and initial comprehension of new material

1. Impulse of force

Under the term "impulse" (from lat. "impulsus "- push) in mechanics understand the impulse of force and the impulse of the body.

Question to the class. Do you think the result of the interaction depends on time or is it determined only by the strength of the interaction?

Demonstration 1. Put a steel ball on a horizontal surface and quickly carry a magnet over it. The ball will barely budge (Fig. 1, and). Repeat the experiment by moving the magnet slowly. The ball will move behind the magnet (Fig. 1, b).

Demonstration 2. Put a sheet of paper on the edge of the table and put a glass of water on it. If the sheet is pulled slowly, then the glass moves with it (Fig. 2, and), and if the leaf is pulled, it will pull out from under the glass, and the glass will remain in place (Fig. 2, b).

^ Question to the class. What do these experiments indicate?

The interaction of bodies depends not only on the force, but also on the time of its action, therefore, to characterize the action of the force, a special characteristic was introduced - the impulse of force.

^ Impulse of force - a physical quantity that is a measure of the action of a force for a certain time interval and numerically equal to the product of force and time ee actions:
.

The SI unit is the newton-second (N∙ s). The impulse of force is a vector quantity: the direction of the impulse of the force coincides with the direction of the force acting on the body.

^ 2. Body impulse

Let's imagine that a ball with a mass of 40 g is thrown at a speed of 5 m / s. Such a ball can be stopped by substituting a sheet of thick cardboard or thick cloth. But if the ball is fired from a rifle at a speed of 800 m / s, then even with the help of trex thick boards it is almost impossible to stop it.

^ Question to the class. What conclusion can be drawn from this example?

To characterize the movement, it is not enough to know only body weight and speed. Therefore, as one of the measures of mechanical movement, the body impulse (or momentum) is introduced.

^ Body impulse - a physical quantity, which is a measure of mechanical movement and is numerically determined by the product of the mass of the body by the speed of its movement:
.

The SI unit is kilogram-meter per second (kg∙ m / s). The momentum of a body is a vector quantity, its direction coincides with the direction of the body's velocity.

If the body massm moves with a speed υ, and then over time interacts with another body with a force F , then in the process of this interaction the body will move with acceleration a:

,
.

The last formula demonstrates the relationship between the impulse of force and the change in impulse of the body.

Thus, the change in the momentum of the body is equal to the momentum of the interaction force.

^ 3. An isolated system of bodies. Momentum conservation law

Isolated (or closed) body system is a system of bodies interacting only with each other and not interacting with bodies that are not part of this system.

There are no isolated systems of bodies in the full sense of the word, this is idealization. All bodies in the world interact. But in a number of cases, real systems can be considered as isolated, excluding from consideration those interactions that in this case are insignificant.

Demonstration 3. Elastic impact of two balls of the same mass, suspended by threads (Fig. 3).

So, studying the elastic impact of two identical balls, the system of balls can be considered as isolated, since at the moment of impact the gravity forces of the balls are balanced by the reaction forces of the threads, the resistance forces of the air of the balls are small, they can be neglected.

Give examples of other systems that can be considered isolated.

If we turn again to the system of balls by masses t 1 and t 2 , which at the initial moment of time in the chosen inertial frame of reference have velocities and , then after a moment of time t you can see that their speeds as a result of interaction changed to and .

According to Newton's second law:

Since according to Newton's third law

It can be seen from the obtained expression that the vector sum of the impulses of the bodies included in the closed system remains constant. This is the law of conservation of momentum.

^ 4. Reactive motion. Rocket movement as jet propulsion

Reactive motion is explained by the law of conservation of momentum.

^ Jet propulsion - This is the movement of a body resulting from the separation of a part from it or the ejection of matter by it at a certain speed relative to the body.

Demonstration 4 ... Inflate the balloon and then release. The ball will move due to the gases that "flow out" from it.

Demonstration 5. Put a children's car in the pallet and install a glass of water with a tap on it. If you turn on the tap, water will start flowing out of the glass, and the machine will go.

^ Assignment to the class. Give examples of jet propulsion. (Jet propulsion is carried out by airplanes flying at speeds of several thousand kilometers per hour, shells of the well-known Katyushas, \u200b\u200bspace rockets. Jet propulsion is inherent, for example, in squid, cuttlefish, and octopuses.)

Consider fig. 4. Any rocket consists of a tubular body 1, closed at one end. The second end has a nozzle 2. Each rocket has fuel 3. When the rocket is stationary, its total impulse is zero: the fuel and the body are stationary. Let's assume that the rocket fuel burns out instantly. Rafromhot gases 4 break out under great pressure.

In this case, the rocket body moves in the direction opposite to the movement of hot gases.

Let be mr υ r is the projection of the gas impulse onto the axis OU, and m toυ to is the projection of the impulse of the rocket body. According to the law of conservation of momentum, the sum of the impulses of the rocket body and the outflowing gases is equal to the total impulse of the rocket at the start, which, as is known, is zero. Accordingly 0 = m r υ r + m to υ to

m to υ to = - m rυ r

Hence it follows that the rocket body receives the same impulse in modulus as the gases emitted from the nozzle. Hence,

Here the “-” sign indicates that the direction of the rocket body speed is opposite to the direction of the outgoing gases. Therefore, to move the rocket in a given direction, the jet of gases ejected by the rocket must be directed opposite to the given direction of motion. As you can see, the rocket moves without interacting with other bodies, and therefore can move in space.

^ Assignment to the class. Having analyzed the last formula, answer the question: how can you increase the speed of a rocket?

The rocket speed can be increased in two ways:

1. 
   increase the speed of gases flowing out of the rocket nozzle;
2. 
   increase the mass of burning fuel.

The second method leads to a decrease in the useful mass of the rocket - the mass of the body and the mass of the cargo transported by it.

Vi. Securing new material

^ Self-test test

Please mark the correct answer in your opinion.

1. 
   The body impulse is called:

^ A product of body mass and acceleration

B product of body mass and velocity

IN product of the force acting on the body and the body speed

D product of the force acting on the body and the time of its action

1. 
   Specify the unit of momentum for the body.

1. 
   Specify the unit of impulse force.

1. 
   The change in momentum of the body is equal to:

AND the product of body weight and its speed

B the difference between the initial and final velocity of the body

IN impulse of force

D change in body weight per unit of time

1. 
   Reactive motion occurs:

^ A when bodies are repulsed

B movement of various parts of the body relative to the center of body mass

^ B dividing the body into parts

D separation from the body of a part of its mass with a certain speed of movement relative to the rest

1. 
   Determine in which frames of reference the law of conservation of momentum is fulfilled.

A Inertial B Closed

B Non-inertial D Any

1. 
   Choose an example that demonstrates jet propulsion.

^ A Squid movement

B Pendulum swing

IN Moth flying

D Falling leaves from trees

1. 
   The rocket rises evenly vertically upward. Determine how and why the impulse of the rocket changes.

AND Decreases as the mass of the rocket decreases

B Does not change as the mass decreases and the speed movement increases

IN Increases as the rocket rises higher and higher above the ground

D Does not change because the speed of movement is constant

1. 
   Please indicate correct writing of the law of conservation of momentum.

1	2	3	4	5	6	7	8	9
B	IN	D	IN	D	IN	AND	AND	AND

Vii. Lesson summary and homework message

The teacher sums up the results of the lesson, evaluates the activities of the students.

Homework

1. 
   Learn theoretical material from the textbook.
2. 
   Describe jet propulsion as a physical phenomenon according to the generalized plan of harcharacteristics of a physical phenomenon.
3. 
   Think over, describe and explain the jet propulsion demonstration.