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Body impulse. Jet propulsion in nature and technology

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 define the momentum of a body and relate the change in this quantity to the force that acts on the body.

Conservation laws are a very powerful tool for solving mechanical problems. They are used when the dynamics equations 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 homogeneous, and the law of conservation of momentum arises due to the homogeneity of space. Moreover, in nuclear physics As a result of the 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.

Let's consider Newton's second law in vector form:

Remember that acceleration is the rate of change of velocity:

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 impulse form:

The quantity to the left of the equal sign is called the impulse of the force. Thus,

The change in the momentum of the body is equal to the impulse 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 a force acts on a body for some time not only when the speed of the body changes, but also when the mass of the body 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. This equation is called the Meshchersky equation, or the Tsiolkovsky equation.

Let's take a closer look at the value we introduced. This quantity is usually called the momentum of the body. So,

Body impulse is physical quantity, equal to the product of the mass of the body and its speed.

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

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

Rice. 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 conserved 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)

Rice. 2. The ball does not bounce elastically

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

Thus, in this lesson you were introduced to the concept of momentum, the law of conservation of momentum and Newton's second law written in impulse form. In addition, you considered the problem of a ball that bounces perfectly elastically off a wall.

Bibliography

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

Question: We found that when a ball hits a wall in an absolutely elastic way, 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 to explain this?

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 a photon falls is equal to the angle of reflection.

Question: Airplanes, when they fly, are pushed away from the air by a propeller. What does a rocket push off from when flying?

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

Law of conservation of momentum

In subsection (5.8), the concept of 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 convenient to use 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 momentum of a complex body (system of bodies) is equal to the vector sum of the impulses of its parts:

p = p 1 +p 2 +…(9.13)

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

dp = F dt.(9.14)

Momentum change system of bodies is equal to the impulse of external forces acting on it.

Let's look at some examples illustrating the operation of this law.

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

In Fig. 9.10, b shows a javelin thrower. The speed that a javelin 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.

Rice. 9.10. a) Sportswoman on a skateboard; b) javelin thrower

Rice. 9.11.

Shot put

Therefore, before throwing the javelin, the athlete raises his hand far back. A similar process is analyzed in more detail in the example of an athlete putting a shot put, Fig. 9.11.

From equality (9.14) follows one important thing for practical application consequence called law of conservation of momentum. Let us consider a system of bodies that is not acted upon by external forces. Such a system is called closed.

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

There are no external forces for such a system (F= 0 and dp = 0). Therefore it takes place law of conservation of momentum.

Vector sum of impulses of bodies, included in a 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 =p 2(9.15)

The law of conservation of momentum is a fundamental law of nature that knows no exceptions. It is absolutely strictly 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 for a short action interval the force impulse can be considered equal to zero:

F dt 0→dp 0.

Short duration processes include

Collisions of moving bodies

Body disintegration into parts (explosion, shot, throw).

Examples

Action films often feature scenes in which, after being hit by a bullet, a person is thrown back as the shot progresses. It looks quite impressive on the screen. Let's check if this is possible? Let the mass of people M= 70 kg and at the moment the bullet hits it is at rest. Let us take the mass of the bullet to be equal to t = 9 g, and its speed v = 750 m/s. If we assume that after being hit by a bullet, a person begins to move (in reality, this can be prevented by the friction force between the soles and the floor), then for the man-bullet system we can write the law of conservation of momentum: p 1 = p 2. Before being hit by a bullet, the person does not move and, in accordance with (9.9), the impulse of the system р 1 = m∙v+0. We will assume that the bullet gets stuck in the body. Then the final momentum of the system R 2 = (M + t)∙i, Where And- the speed that a person received when hit by a bullet. Substituting these expressions into the law of conservation of momentum, we obtain:

The result obtained shows that there can be no question of a person flying several meters away (by the way, a body thrown upward 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 1 And M 2 move towards each other at speeds correspondingly v 1, v 2(Fig. 9.12). Determine the total speed of their movement, considering the collision absolutely inelastic(with an absolutely inelastic impact, the bodies “couple” and move further as one whole).

Rice. 9.12. Absolutely inelastic collision of hockey players

Let us apply the law of conservation of momentum to a system consisting of two hockey players. System impulse before collision p 1 =M 1 ∙v 1- M 2 v 2. There is a “-” sign in this formula because the speed v 1 And v 2 directed towards each other. Speed direction v 1 is considered positive, and the direction of speed v 2- negative. After an inelastic collision, the bodies move with a common speed v and momentum of the system р 2 = (M l + M 2)∙v. Let's write the law of conservation of momentum and find the speed v:

Speed direction v is determined by its sign.

Let us pay attention to one important circumstance: the law of conservation of momentum can only be applied to free bodies. If the movement of one of the bodies is limited by external connections, then the overall 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 given to the movement of a body that occurs when some part of it is separated 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 equal to zero. When burning a portion of fuel mass T Gases are formed, which are ejected through the nozzle at a speed and. According to the law of conservation of momentum, the total momentum of the rocket and fuel preserved: p 2 = p 1→ t∙i +(M - m)∙v = 0, where v- the speed received by the rocket. From this equation we find: v = ─t∙i /(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's speed continuously increases.

An example of jet propulsion is the recoil of a rifle shot. Let a rifle whose mass m 1 = 4.5 kg, shoots a bullet weighing t 2 = 11 g, ejected at speed v 1 = 800 m/s. From the law of conservation of momentum, we can calculate the recoil velocity:

This significant recoil velocity will occur if the rifle is not restrained 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 his shoulder and the shooter's entire body absorbs the recoil. With a shooter mass of 70 kg, the recoil speed in this case will be equal to 11.8 cm/s, which is quite acceptable.

space research. Semiconductor diode, pn junction and its properties. Application of semiconductor devices. Problem on applying the 1st law of thermodynamics.

Body impulse– is the product of a body’s mass and its speed p = mv (kg * m/s) The momentum of a body is the amount of motion. The change in the momentum of the body is equal to the change in the impulse of the force. ∆p = F∆t
The sum of the momenta of bodies before interaction is equal to the sum of impulses after interaction OR: The geometric sum of the momenta of bodies in a closed system remains constant. m1v1 + m2v2 = const

The law of conservation of momentum underlies jet motion - this is a movement in which part of the body is separated, and the other receives additional acceleration.
Jet propulsion in technology: FOR EXAMPLE (in airplanes and rockets)
Jet propulsion in nature: FOR EXAMPLE (molluscs, octopuses). Great importance has space information for the further development of science and technology. Space research will apparently lead in the near future to revolutionary changes in many areas of engineering and technology, as well as in medicine. Results of developments in the field space technology will find application in industrial and agricultural work, in exploring 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 there is a spatial change in the type of conductivity (from the electronic n-region to the 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 Law universal gravity. Gravity. Free fall of bodies. Body weight. Weightlessness. A magnetic field. Magnetic induction, magnetic induction lines. Ampere force and its application. The task is to apply formulas for work or power of direct current.

Law of Gravity Newton's law that describes gravitational interaction within 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 a distance is proportional to both masses and inversely proportional to the square of the distance between them. Gravity- a force acting on any material body located near the surface of the Earth or another astronomical body. Free fall- uniformly variable motion under the influence of gravity, when other forces acting on the body are absent or negligibly small. Weight- the force of the body on the support (or suspension or other type of fastening), preventing a fall, arising in the field of gravity P=mg. Weightlessness- a state in which the force of interaction of a body with a support (body weight), arising in connection with gravitational attraction, the action of other mass forces, in particular the inertial force that arises during the accelerated movement of a body, is absent. A magnetic field- a force field acting on moving electric charges and on bodies with magnetic moment, regardless of their state of motion. Magnetic induction- vector quantity, which is a power characteristic magnetic field(its action on charged particles) at a given point in space. Determines the force with which a magnetic field acts on a charge moving at speed.
Magnetic induction lines- lines, the tangents to which are directed in the same way as the magnetic induction vector at a given point in the field.

7 The phenomenon of electromagnetic induction, the use of this phenomenon. Law of electromagnetic induction. Lenz's rule. Job. Fur. energy. Kinetic and potential energy. Law of conservation of fur. energy. E.Z: Measuring the total resistance of an electrical circuit in a series connection. Electromagnetic induction is the phenomenon of the appearance of an electric torus in a closed circuit when the magnetic flux passing through it changes. It was discovered by Michael Faradel. The phenomenon of electric 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 states: the induction current always has such a direction that it weakens the effect of the cause that excites the current. Fur. Job- 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, 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 available in the components of a mechanical system. Fur. energy- this is the energy associated with the movement of an object or its position, the ability to perform mechanical work. Law of conservation of fur. energy states that if a body or system is subjected to only conservative forces (both external and internal), then the total mechanical energy of that body or system remains constant. IN isolated system, where only conservative forces act, the total mechanical energy is conserved. Potential is the potential of the body, it personifies what kind of work the body CAN do! And kinetic is the force that is already doing work. Law of energy conservation- a 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 system parameters and is called energy, which is conserved over time. Since the law of conservation of energy does not apply to specific quantities and phenomena, but reflects a general pattern that is applicable everywhere and always, it can be called not a law, but the principle of conservation of energy. Potential energy- energy that is determined by the relative position of interacting bodies or parts of the same body. Kinetic energy- the case when a body moves under the influence of force, it not only can, but also does some work

8 Mechanical vibrations, mechanical characteristics. vibrations: amplitude, period, frequency. Free and forced vibrations. Resonance. Self-induction. Inductance. The energy of the magnetic field of the coil. The task of applying the law of conservation of momentum Mechanical oscillation is a precisely or approximately repeating movement in which the body is displaced in one direction or the other from the equilibrium position. If a system is capable of oscillating movements, then it is called oscillatory. Properties of an oscillatory system: The system has a stable equilibrium position. When a system is removed from an equilibrium position, an internal restoring force arises in it. The system is inert. Therefore, it does not stop at the equilibrium position, but passes through it. Oscillations arising in the system under the influence internal forces, are called free. All free vibrations are damped (for example: string vibration after impact) Vibrations performed by bodies under the influence of external periodically changing forces are called forced (for example: vibration of a metal workpiece when a blacksmith works with a hammer). Resonance- a phenomenon in which the amplitude of forced oscillations has a maximum at a certain value of the frequency of the driving force. Often this value is close to the frequency of natural oscillations, in fact it may coincide, but this is not always the case and is not the cause of resonance. Self-induction- this is the phenomenon of the occurrence of induced emf in a conducting circuit when the current flowing through the circuit changes. When the current in a circuit changes, the magnetic flux through the surface bounded by this circuit also changes proportionally. A change in this magnetic flux, due to the law of electromagnetic induction, leads to the excitation of an inductive EMF (self-induction) in this circuit. Inductance- proportionality coefficient between electric shock, flowing in some closed circuit, and the magnetic flux created by this current through the surface, the edge of which is this circuit. Around the conductor with current there is a magnetic field that has energy.

9 Fur. waves. Wavelength, wave speed and relationships between them. Thermonuclear reaction. Application of atomic energy. Prospects and problems of nuclear energy development. E.Z: determination of the refractive index of a glass plate. Fur. waves are disturbances propagating in an elastic medium (deviations of particles of the medium from the equilibrium position). If particle oscillations and wave propagation occur in one 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 matter being transferred. The speed with which a disturbance propagates in an elastic medium is called wave speed. It is determined by the elastic properties of the medium. The distance over which a wave propagates in a time equal to the period of oscillation in it is called the wavelength (lambda). Wavelength- the distance that a wave manages to cover when 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 type of nuclear reaction in which light atomic nuclei combine into heavier ones due to kinetic energy their thermal movement. The development of industrial society is based on an ever-increasing level of production and consumption various types energy.(Dramatically reduces the use natural resources

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

Diffusion- this is the phenomenon of the distribution of particles of one substance between 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 the existence of atoms and molecules as the smallest particles chemical substances Based on 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. Particles interact with each other by forces that are electrical in nature. The gravitational interaction between particles is negligible. m 0 - molecule mass (kg). The molecule size is very small. Electromotive force strength, that is, any strength non-electrical origin, operating in quasi-stationary circuits of direct or alternating current.

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

11 Electromagnetic waves and from properties. The principle of radio communication. Invention of radio, modern means of communication. Temperature and its measurement Absolute temperature. Temperature is a measure of the average kinetic energy of molecular motion. E.Z: Measuring the optical power of a collecting lens.

Electromotive force- scalar physical quantity characterizing the work of third parties strength, that is, any strength non-electrical origin, operating in quasi-stationary circuits of direct or alternating current. Design of general circuits for organizing radio communications. Characteristics of a radio information transmission system in which telecommunication signals are transmitted via radio waves in open space. Radio- a type of wireless information transmission in which radio waves, freely propagating in space, are used as an information carrier. On May 7, 1895, Russian physicist Alexander Stepanovich Popov (1859 - 1905/06) demonstrated the world's first radio receiver. Modern means of communication- this 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. Temperature- 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 in everyday life and at work. E.Z: Acceleration measurement free fall at a given point on earth.

In thermodynamics the movement of the body as a whole is not considered, we are talking about the movement of parts of a macroscopic body relative to each other. As a result, the volume of the body may change, but 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 a body, but 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, internal energy consists of the kinetic energy of the chaotic movement of molecules, the potential energy of interaction between them and intramolecular energy. 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 on external bodies.

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 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, application 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 (efficiency) of a heat engine is the ratio of the work A´ performed by the engine to the amount of heat received from the heater:

The continuous development of energy, automobile and other types of transport, the increase in the consumption of coal, oil and gas in industry and for domestic needs increases the possibilities of meeting human vital needs. However, at present, the amount of chemical fuel burned annually in various heat engines is so large that protecting 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- a field of science and technology that combines 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. Ocean-going ships use radar systems for navigation. On airplanes, radars are used to solve a number of problems, including determining the flight altitude relative to the ground.

Body impulse is a quantity equal to the product of a body's mass and its speed.

The impulse is indicated by a letter and has the same direction as the speed.

Pulse unit:

The momentum of the body is calculated by the formula: , where

The change in the momentum of the body is equal to the impulse of the force acting on it:

For a closed system of bodies it is true law of conservation of momentum:

in a closed system, the vector sum of the momenta of bodies before interaction is equal to the vector sum of momenta of bodies after interaction.

The law of conservation of momentum underlies jet propulsion.

Jet propulsion- this is the movement of the body that occurs after separation of its part from the body.

To calculate the speed of a rocket, write down the law of conservation of momentum

and get the formula for rocket speed: =, where M is the mass of the rocket,

10. Rutherford's experiments on the scattering of α-particles. Nuclear model of the atom. Bohr's quantum postulates.

The first model of the atom was proposed by the English physicist Thomson. According to Thomson, an atom is a positively charged ball, inside of which there are negatively charged electrons.

Thomson's model of the atom was incorrect, which was confirmed by the experiments of the English physicist Rutherford in 1906.

In these experiments, a narrow beam of α particles emitted radioactive substance, was directed onto thin gold foil. A screen was placed behind the foil, capable of glowing under the impacts of fast particles.

It was found that most α-particles deviate from straight-line propagation after passing through the foil, i.e. dissipate. And some alpha particles are generally thrown back.

Rutherford explained the scattering of α-particles by the fact that the positive charge is not distributed evenly over the ball, as Thomson assumed, but is concentrated in the central part of the atom - atomic nucleus. When passing near the nucleus, an alpha particle having a positive charge is repelled from it, and when it hits the nucleus, it is thrown back.

Rutherford suggested that the atom was structured like a planetary system.

But Rutherford could not explain stability (why electrons do not emit waves and fall towards a positively charged nucleus).

New ideas about the special properties of the atom were formulated by the Danish physicist Bohr in two postulates.

1st postulate. An atomic system can only be in special stationary or quantum states, each of which has a corresponding energy; In a stationary state, the atom does not radiate.

2nd postulate. When an atom transitions from one stationary state to another, a quantum of electromagnetic radiation is emitted or absorbed.

The energy of the emitted photon is equal to the difference in the energies of the atom in two states:

Planck's constant.

MINISTRY OF GENERAL AND VOCATIONAL EDUCATION OF THE ROSTOV REGION

STATE EDUCATIONAL INSTITUTION OF SECONDARY

PROFESSIONAL EDUCATION OF THE ROSTOV REGION

"SALSKY INDUSTRIAL TECHNIQUE"

METHODOLOGICAL DEVELOPMENT

training session

in the discipline "Physics"

Subject: "Pulse. Law of conservation of momentum. Jet propulsion".

Developed by the teacher: Titarenko S.A.

Salsk

2014

Topic: “Impulse. Law of conservation of momentum. Jet propulsion".

Duration: 90 minutes.

Lesson type: Combined lesson.

Lesson objectives:

educational:

reveal the role of conservation laws in mechanics;

give the concept of “body impulse”, “closed system”, “reactive movement”;

teach students to characterize physical quantities (body impulse, force impulse), apply a logical scheme when deriving the law of conservation of momentum, formulate the law, write it in the form of an equation, explain the principle of reactive motion;

apply the law of conservation of momentum when solving problems;

promote the acquisition of knowledge about methods scientific knowledge nature, modern physical picture of the world, dynamic laws of nature (law of conservation of momentum);

educational:

learn how to prepare a workplace;

maintain discipline;

develop the ability to apply acquired knowledge when performing independent tasks and subsequent formulation of the conclusion;

to cultivate a sense of patriotism in relation to the work of Russian scientists in the field of motion of a body with variable mass (jet motion) - K. E. Tsiolkovsky, S. P. Korolev;

developing:

expand students' horizons by making interdisciplinary connections;

develop the ability to correctly use physical terminology during frontal oral work;

form:

scientific understanding of the structure of the material world;

the universal nature of the knowledge gained through interdisciplinary connections;

methodical:

stimulate cognitive and creative activity;

strengthen the motivation of students using various teaching methods: verbal, visual and modern technical means, to create conditions for learning the material.

As a result of studying the material in this lesson, the student must
know/understand :
- the meaning of the impulse of a material point as a physical quantity;
- a formula expressing the relationship of momentum with other quantities (speed, mass);
- classifying sign of impulse (vector quantity);
- units of impulse measurement;
- Newton's second law in impulse form and its graphical interpretation; the law of conservation of momentum and the limits of its application;
- the contribution of Russian and foreign scientists who had the greatest influence on the development of this branch of physics;

be able to:
- describe and explain the results of observations and experiments;
- give examples of the manifestation of the law of conservation of momentum in nature and technology;
- apply the acquired knowledge to solve physical problems using the concept of “momentum of a material point”, the law of conservation of momentum.

Educational technologies:

advanced learning technology;

technology of immersion in the topic of the lesson;

ICT.

Teaching methods:

verbal;

visual;

explanatory and illustrative;

heuristic;

problem;

analytical;

self-test;

mutual verification.

Form: theoretical lesson.

Forms of organization educational activities : collective, small groups, individual.

Interdisciplinary connections:

physics and mathematics;

physics and technology;

physics and biology;

physics and medicine;

physics and computer science;

Intrasubject connections:

Newton's laws;

weight;

inertia;

mechanical movement.

Equipment:

PC, screen,

blackboard, chalk,

balloon, inertia cars, water toy, aquarium with water, Segner wheel model.

Equipment:

didactic:

reference notes for students, test tasks, reflection sheet;

methodical:

working programs a, calendar-thematic plan;

methodological manual for teachers on the topic “ Pulse. Law of conservation of momentum. Examples of problem solving";

Information Support:

PC with Windows OS and Microsoft Office installed;

multimedia projector;

Microsoft PowerPoint presentations, videos:

- manifestation of the law of conservation of momentum when bodies collide;

- recoil effect;

Kinds independent work:

classroom: solving problems on the use of FSI , work with supporting notes;

extracurricular: working with notes and additional literature .

Progress of the lesson:

I. Introductory part

1. Organizational time – 1-2 minutes.

a) checking those present, students’ readiness for class, availability of uniform, etc.

2. Announcement of the topic, its motivation and goal setting – 5-6 min.

a) announcement of the rules of work in the lesson and announcement of assessment criteria;

b) d homework assignment;

c) initial motivation for learning activities (involving students in the process of goal setting).

3. Update background knowledge(frontal survey) – 4-5 min.

II. Main part- 60min.

1. Studying new theoretical material

a) Presentation of the new lecture material according to plan:

1). Definition of concepts: “body impulse”, “force impulse”.

2). Solving qualitative and quantitative problems for calculating the momentum of a body, the impulse of force, the masses of interacting bodies.

3). Law of conservation of momentum.

4). Limits of applicability of the law of conservation of momentum.

5). Algorithm for solving problems on ZSI. Special cases of the law of conservation of momentum.

6). Application of the law of conservation of momentum in science, technology, nature, medicine.

b) Conducting demonstration experiments

c) Viewing a multimedia presentation.

d) Consolidation of the material during the lesson (solving problems on the use of digital information, solving qualitative problems);

e) Filling out the supporting notes.

III. Control of material absorption - 10 min.

IV. Reflection. Summing up – 6-7 min. (Time reserve 2 min.)

Preliminary preparation of students

Students are given the task to prepare a multimedia presentation and message on the topics: “The Law of Conservation of Momentum in Engineering”, “The Law of Conservation of Momentum in Biology”, “The Law of Conservation of Momentum in Medicine”.

During the classes.

I. Introductory part

1. Organizational moment.

Checking absenteeism and student readiness for class.

2. Announcement of the topic, its motivation and goal setting .

a) announcement of the rules of work in the lesson and announcement of assessment criteria.

Lesson rules:

On your desks there are supporting notes that will become the main working element in today's lesson.

The supporting outline indicates the topic of the lesson and the order in which the topic will be studied.

In addition, today in class we will use rating system, i.e. each of you will try to earn as much as possible with your work in class larger number points, points will be awarded for correctly solved problems, correct answers to questions, correct explanation of observed phenomena, in total for a lesson you can score a maximum of 27 points, i.e. a correct, complete answer to each question is 0.5 points, solving the problem is scored 1 point.

You will calculate the number of your points for the lesson yourself and write it down on the reflection card., so if you type from 19-27 points – “excellent”; from 12–18 points – “good”; from 5-11 points – “satisfactory” rating

b) homework:

Learn lecture material.

Collection of problems in physics, ed. A.P. Rymkevich No. 314, 315 (p. 47), No. 323,324 (p. 48).

V) initial motivation for learning activities (involving students in the goal-setting process):

I would like to draw your attention to an interesting phenomenon that we call impact. The effect produced by a blow always surprised a person. Why does a heavy hammer placed on a piece of metal on an anvil only press it to the support, while the same hammer flattens it with a hammer blow?

What is the secret of the old circus trick, when a crushing blow of a hammer on a massive anvil does not harm the person on whose chest this anvil is installed?

Why can we easily catch a flying tennis ball with our hand, but we cannot catch a bullet without damaging our hand?

In nature, there are several physical quantities that can be conserved; we will talk about one of them today: momentum.

Impulse translated into Russian means “push”, “blow”. This is one of the few physical quantities that can be conserved during the interaction of bodies.

Please explain the observed phenomena:

EXPERIENCE #1: there are 2 toy cars on the demonstration table, No. 1 is at rest, No. 2 is moving, as a result of interaction, both cars change the speed of their movement - No. 1 gains speed, No. 2 decreases the speed of its movement. (0.5 points)

EXPERIENCE #2: cars move towards each other, after a collision they change their speed . (0.5 points)

What do you think: what are the goals of our lesson today? What should we learn? (Students’ expected answer: get acquainted with the physical quantity “momentum”, learn to calculate it, find the relationship of this physical quantity with other physical quantities.)(0.5 points)

3. Updating the body of knowledge.

You and I already know that if a certain force is applied to a body, then as a result of this.....(the body changes its position in space (performs mechanical movement))

An answer to a question earns 0.5 points (maximum 7 points for correct answers to all questions)

Define mechanical motion.

Sample answer: a change in the position of a body in space relative to other bodies is called mechanical motion.

What's happened material point?

Sample answer: a material point is a body whose dimensions can be neglected in the conditions of a given problem (the dimensions of the bodies are small compared to the distance between them or the body travels a distance much greater than the geometric dimensions of the body itself)

-Give examples of material points.

Sample answer: a car on the way from Orenburg to Moscow, a man and the Moon, a ball on a long thread.

What is mass? Its units of measurement are in SI?

Sample answer: mass is a measure of the inertia of a body, a scalar physical quantity, denoted Latin letter m, SI units are kg (kilogram).

What does the expression mean: “the body is more inert”, “the body is less inert”?

Sample answer: more inert - changes speed slowly, less inert - changes speed faster.

Define force, name its units of measurement and basic

characteristics.

Sample answer: force is a vector physical quantity, which is a quantitative measure of the action of one body on another (a quantitative measure of the interaction of two or more bodies), characterized by modulus, direction, point of application, measured in SI in Newtons (N).

-What powers do you know?

Sample answer: gravity, elastic force, ground reaction force, body weight, friction force.

As you understand: the resultant of the forces applied to the body is equal to

10 N?

Sample answer: the geometric sum of forces applied to the body is 10 N.

What will happen to a material point under the influence of a force?

Sample answer: the material point begins to change the speed of its movement.

How does the speed of a body depend on its mass?

Sample answer: because mass is a measure of the inertia of a body, then a body of greater mass changes its speed more slowly, a body of less mass changes its speed faster.

What reference systems are called inertial?

Sample answer: inertial frames of reference are those frames of reference that move rectilinearly and uniformly or are at rest.

State Newton's first law.

Sample answer: There are such reference systems relative to which translationally moving bodies maintain their speed constant or are at rest if no other bodies act on them or the actions of these bodies are compensated.

- Formulate Newton's third law.

\Sample answer: the forces with which the bodies act on each other are equal in magnitude and directed along one straight line in opposite directions.

State Newton's second law.

Where And speeds of 1 and 2 balls before interaction, And - speed of the balls after interaction, And - mass of balls.

Substituting the last two equalities into the formula of Newton’s third law and carrying out the transformations, we obtain:

, those.

The law of conservation of momentum is formulated as follows: the geometric sum of the impulses of a closed system of bodies remains a constant value for any interaction of the bodies of this system with each other.

Or:

If the sum of external forces is zero, then the momentum of the system of bodies is conserved.

The forces with which the bodies of the system interact with each other are called internal, and the forces created by bodies that do not belong to a given system are called external.

A system that is not affected by external forces, or the sum of external forces is zero, is called closed.

In a closed system, bodies can only exchange impulses, but the total value of the impulse does not change.

Limits of application of the law of conservation of momentum:

Only in closed systems.

If the sum of the projections of external forces on a certain direction is equal to zero, then in the projection only on this direction we can write: pstart X = pend X (the law of conservation of the momentum component).

If the duration of the interaction process is short, and the forces arising during the interaction are large (impact, explosion, shot), then during this short time the impulse of external forces can be neglected.

An example of a closed system along the horizontal direction is a cannon from which a shot is fired. The phenomenon of recoil (rollback) of a gun when fired. Firefighters experience the same impact when directing a powerful stream of water at a burning object and struggling to hold the fire nozzle.

Today you should learn methods for solving qualitative and quantitative problems on this topic and learn how to apply them in practice.

Despite the fact that this topic is loved by many, it has its own characteristics and difficulties. The main difficulty is that there is no single a universal formula that could be used to solve a particular problem on a given topic. In each problem, the formula is different, and it is you who must obtain it by analyzing the conditions of the proposed problem.

To make it easier for you to solve problems correctly, I suggest using ALGORITHM FOR SOLVING PROBLEMS.

You don't need to learn it by heart, you can use it as a guide by looking in your notebook, but as you solve problems, it will gradually become memorized on its own.

I want to warn you right away: I do not consider problems without a picture, even if solved correctly!

So, we will consider how, using the proposed PROBLEM SOLVING ALGORITHM, problems should be solved.

To do this, let's start with a step-by-step solution to the first problem: (tasks in general view)

Let's consider an algorithm for solving problems using the law of conservation of momentum. (slide with the algorithm, write down in the supporting notes for the drawings)

Algorithm for solving problems on the law of conservation of momentum:

Make a drawing in which to indicate the directions of the coordinate axis, the velocity vectors of the bodies before and after the interaction;

2) Write down the law of conservation of momentum in vector form;

3) Write down the law of conservation of momentum in projection onto the coordinate axis;

4) From the resulting equation, express the unknown quantity and find its value;

SOLVING PROBLEMS (Special cases of FSI on independent decision task #3):

(correct solution to 1 problem – 1 point)

1. 200 kg of sand was poured on top of a trolley weighing 800 kg, rolling along a horizontal track at a speed of 0.2 m/s.

What was the speed of the trolley after this?

2. A car weighing 20 tons moving at speed 0.3 m/s, overtakes a car weighing 30 tons, moving at a speed of 0.2 m/s.

What is the speed of the cars after the coupling is activated?

3. What speed will a cast iron cannonball lying on ice acquire if a bullet flying horizontally at a speed of 500 m/s bounces off it and moves in the opposite direction at a speed of 400 m/s? Bullet weight 10 g, core weight 25 kg. (the task is a backup one, i.e. it is solved if there is time left)

(The solution to the problems is displayed on the screen, students check their solution with the standard, analyze errors)

The law of conservation of momentum is of great importance for the study of jet propulsion.

Underjet propulsionunderstand the movement of a body that occurs when any part of it is separated from the body at a certain speed. As a result, the body itself acquires an oppositely directed impulse.

Inflate a rubber children's balloon without tying the holes and release it from your hands.

What will happen? Why? (0.5 points)

(Suggested answer: The air in the ball creates pressure on the shell in all directions. If the hole in the ball is not tied, then air will begin to come out of it, while the shell itself will move in the opposite direction. This follows from the law of conservation of momentum: the momentum of the ball before interaction is equal to zero, after interaction they must acquire impulses equal in magnitude and opposite in direction, i.e., move in opposite directions.)

The motion of a ball is an example of jet motion.

Video Jet propulsion.

It is not difficult to make working models of jet engine devices.

In 1750, the Hungarian physicist J.A. Segner demonstrated his device, which was called the “Segner wheel” in honor of its creator.

A large “Segner wheel” can be made from a large milk bag: make a hole at the bottom of the opposite walls of the bag by piercing the bag with a pencil. Tie two threads to the top of the bag and hang the bag on some kind of crossbar. Plug the holes with pencils and pour water into the bag. Then carefully remove the pencils.

Explain the observed phenomenon. Where can it be used? (0.5 points)

(Students' expected answer: two jets will burst out of the holes in opposite directions, and a reactive force will arise that will rotate the package. The Segner wheel can be used in an installation for watering flower beds or beds.)

Next model: spinning balloon. In an inflated children's balloon, before tying the hole with thread, insert a juice tube bent at a right angle into it. Pour water into a plate smaller than the diameter of the ball and lower the ball there so that the tube is on the side. The air will come out of the ball, and the ball will begin to rotate through the water under the influence of reactive force.

OR: into an inflated children's balloon, before tying the hole with a thread, insert a juice tube bent at a right angle, hang the entire structure on the thread, when the air begins to leave the ball through the tube, the ball begins to rotate..

Explain the observed phenomenon. (0.5 points)

Video "Jet Propulsion"

Where does the law of conservation of momentum apply??? Our guys will help us answer this question.

Student reports and presentations.

Topics of messages and presentations:

1. “Application of the law of conservation of momentum in technology and everyday life”

2. “Application of the law of conservation of momentum in nature.”

3. “Application of the law of conservation of momentum in medicine”

Evaluation criteria:

Content of the material and its scientific nature – 2 points;

Accessibility of presentation – 1 point;

Knowledge of the material and its understanding – 1 point;

Design – 1 point.

The maximum score is 5 points.

Let's now try to answer the following questions: (1 point for each correct answer, 0.5 points for an incomplete answer).

"This is interesting"

1. In one of the episodes of the cartoon “Well, wait a minute!” in calm weather, the wolf, in order to catch up with the hare, takes in more air into its chest and blows into the sail. The boat accelerates and... Is this phenomenon possible?

(Students' expected answer: No, because the wolf-sail system is closed, which means the total impulse is zero, in order for the boat to move accelerated, the presence of an external force is necessary. Only external forces can change the impulse of the system. Wolf - air - internal force. )

2. The hero of E. Raspe’s book, Baron Munchausen, said: “Having grabbed my pigtail, I pulled upward with all my might and without much difficulty pulled both myself and my horse out of the swamp, which I held tightly with both legs, like with tongs.”

Is it possible to raise yourself this way? ?

(Students' expected answer: only external forces can change the momentum of a system of bodies, therefore, lift yourself in this way it is forbidden, because in this system only internal forces act. Before the interaction, the momentum of the system was zero. The action of internal forces cannot change the momentum of the system; therefore, after interaction, the momentum will be zero).

3. There is an old legend about a rich man with a bag of gold, who, finding himself on the absolutely smooth ice of a lake, froze, but did not want to part with his wealth. But he could have been saved if he had not been so greedy!

(Suggested answer from students: It was enough to push the bag of gold away from himself, and the rich man himself would slide across the ice in the opposite side according to the law of conservation of momentum.)

III. Control of material absorption:

Test tasks (Annex 1)

(Testing is carried out on sheets of paper, between which carbon paper is placed; at the end of testing, one copy is given to the teacher, the other is given to the neighbor at the desk, mutual verification) (5 points)

IV. Reflection. Summarizing (Appendix 2)

Concluding the lesson, I would like to say that the laws of physics can be applied to solving many problems. Today in class you learned how to put into practice one of the most fundamental laws of nature: the law of conservation of momentum.

I ask you to fill out the “Reflection” sheet, on which you can display the results of today's lesson.

List of used literature:

Literature for teachers

main:

Ed. Pinsky A.A., Kabardina O.F. Physics grade 10: textbook for general education institutions and schools with in-depth study of physics: profile level. - M.: Education, 2013 .

Kasyanov V.A. Physics. 10th grade: textbook for general educationny establishments. – M.: Bustard, 2012.

Physics 7-11. Library of visual aids. Electronic edition. M.: “Bustard”, 2012

additional:

Myakishev G. Ya., Bukhovtsev B. B., Sotsky N. N. Physics-10: Publishing house 15th. – M.: Education, 2006.

Myakishev G. Ya. Mechanics - 10: Ed. 7th, stereotype. – M.: Bustard, 2005.

Rymkevich A.P. Physics. Problem book-10 – 11: Ed. 10th, stereotype. – M.: Bustard, 2006.

Saurov Yu. A. Models of lessons-10: book. for the teacher. – M.: Education, 2005.

Kuperstein Yu. S. Physics-10: basic notes and differentiated problems. – St. Petersburg: September, 2004.

Internet resources used

Literature for students:

Myakishev G.Ya. Physics. Grade 10: textbook for general education institutions: basic and specialized levels. – M.: Prosveshcheniye, 2013 .

Gromov S.V. Physics-10.M. "Enlightenment" 2011

Rymkevich P.A. Collection of problems in physics. M.: “Bustard” 2012.

Annex 1

Option #1.

1.Which of the following quantities is scalar?

A. mass.

B. body impulse.

B. strength.

2. A body of mass m moves with speed. What is the body's momentum?

B. m

IN.

3. What is the name of a physical quantity equal to the product of a force and the time of its action?

A. Body impulse.

B. Projection of force.

B. Force impulse.

4. In what units is force impulse measured?

A. 1 N s

B. 1 kg

V. 1 N

5.What is the direction of the body’s impulse?

A. Has the same direction as the force.

B. In the same direction as the speed of the body.

6.What is the change in momentum of a body if it is acted upon by a force of 15 N for 5 seconds?

A. 3 kg m/s

B. 20 kg m/s

B. 75 kg m/s

7.What is the name of an impact in which part of the kinetic energy of colliding bodies goes towards their irreversible deformation, changing internal energy tel?

A. Absolutely inelastic impact.

B. Absolutely elastic impact

V. Central.

8. Which expression corresponds to the law of conservation of momentum for the case of interaction of two bodies?

A. = m

IN. m =

9.What law is the existence of jet motion based on?

A. Newton's first law.

B. The law of universal gravitation.

B. Law of conservation of momentum.

10.An example of jet propulsion is

A. The phenomenon of recoil when firing a weapon.

B. Combustion of a meteorite in the atmosphere.

B. Movement under the influence of gravity.

Annex 1

Option #2.

1.Which of the following quantities is vector?

A. body impulse.

B. mass.

V. time.

2.What expression determines the change in the momentum of a body?

A. m

B. t

IN. m

3.What is the name of a physical quantity equal to the product of a body’s mass and its vector instantaneous speed?

A. Force projection.

B. Force impulse.

B. Body impulse.

4.What is the name of the unit of momentum of a body, expressed through the basic units of the International System?

A. 1 kg m/s

B. 1kg m/s 2

B. 1kg m 2 /s 2

5.Where is the change in momentum of the body directed?

A. In the same direction as the speed of the body.

B. In the same direction as the force.

B. To the side opposite to the movement of the body.

6.What is the momentum of a body weighing 2 kg moving at a speed of 3 m/s?

A. 1.5 kg m/s

B. 9 kg m/s

B. 6 kg m/s

7.What is the name of an impact in which the deformation of colliding bodies is reversible, i.e. disappears after termination of interaction?

A. Absolutely elastic impact.

B. Absolutely inelastic impact.

V. Central.

8. Which expression corresponds to the law of conservation of momentum for the case of interaction of two bodies?

A. = m

IN. m =

9. The law of conservation of momentum is satisfied...

A. Always.

B. Mandatory in the absence of friction in any reference frames.

B. Only in a closed system.

10. An example of jet propulsion is...

A. The phenomenon of recoil when diving from a boat into the water.

B. The phenomenon of increased body weight caused by accelerated movement

support or suspension.

B. The phenomenon of attraction of bodies by the Earth.

Answers:

Option #1

Option No. 2

1. A 2. B 3. C 4. A 5. B 6. C 7. A 8. B 9. C 10. A

1 task – 0.5 points

The maximum score for completing all tasks is 5 points.

Appendix 2

Basic summary.

Date ___________.

Lesson topic: “Body impulse. Law of conservation of momentum."

1. Body impulse is ___________________________________________________

2. Calculation formula for body momentum:________________________________

3. Units of measurement of body impulse: ________________________________________

4. The direction of the body’s impulse always coincides with the direction of ___________

5.Impulse force - This __________________________________________________

6. Calculation formula for impulse force :___________________________________

7. Units of measurement impulse of force ___________________________________

8. The direction of the force impulse always coincides with the direction ______________________________________________________________________

9. Write Newton’s second law in impulse form:

______________________________________________________________________

10. Absolutely elastic impact is _______________________________________

______________________________________________________________________

11. Absolutely inelastic impact is _____________________________________

______________________________________________________________________

12. With an absolutely elastic impact, ____________________________ occurs

______________________________________________________________________

16. Mathematical notation of the law: _______________________________________

17. Limits of applicability of the law of conservation of momentum:

_____________________________________________________________________

18. Algorithm for solving problems on the law of conservation of momentum:

1)____________________________________________________________________

2)____________________________________________________________________

3)____________________________________________________________________

4)____________________________________________________________________

19. Special cases of the law of conservation of momentum:

A) absolutely elastic interaction: Projection on the OX axis: 0.3 m/s, catches up with a car weighing 30 tons, moving at a speed of 0.2 m/s. What is the speed of the cars after the coupling is activated?

____________

Answer:

21. Application of the law of conservation of momentum in technology and everyday life:

A) Jet propulsion is ___________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________Examples of jet propulsion: _____________________________________________________________________

_____________________________________________________________________

c) the phenomenon of recoil______________________________________________________________

____________________________________________________________________________________________________________________________________________

22. Application of the law of conservation of momentum in nature:

23. Application of the law of conservation of momentum in medicine:

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

24. This is interesting:

1. There is an old legend about a rich man with a bag of gold, who, finding himself on the absolutely smooth ice of a lake, froze, but did not want to part with his wealth. But he could have been saved if he had not been so greedy! How?__________________________________________________________________

2. In one of the episodes of the cartoon “Well, wait a minute!” in calm weather, the wolf, in order to catch up with the hare, takes in more air into its chest and blows into the sail. The boat accelerates and... Is this phenomenon possible? Why?

3. The hero of E. Raspe’s book, Baron Munchausen, said: “Having grabbed my pigtail, I pulled upward with all my might and without much difficulty pulled both myself and my horse out of the swamp, which I held tightly with both legs, like with tongs.”

Is it possible to raise yourself in this way? Why?

Lesson grade ______________

Appendix 3

Reflection sheet

Last name, first name________________________________________________

Group________________________________________________

1. I worked during the lesson
2. Through my work in class I
3. The lesson seemed to me
4. For the lesson I
5.My mood
6.The lesson material was for me

7.Homework seems to me

active / passive
satisfied/dissatisfied
short / long
not tired / tired
it got better/it got worse
clear / not clear
useful/useless
interesting / boring
easy / difficult
interesting / not interesting

N Draw your mood with an emoticon.

Calculate the number of points you received for the lesson, evaluate your work in the lesson.

If you typed:

from 19-27 points – “excellent”

From 12–18 points – “good”

From 5-11 points – “satisfactory” rating

I scored ________ points

Grade _________

Body impulse. Jet propulsion in nature and technology

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