Interaction of bodies examples from life. Interaction of bodies in physics

>> Interaction of bodies

Why does the Moon move around the Earth and not fly into outer space? What body is called charged? How do charged bodies interact with each other? How often do we encounter electromagnetic interaction? These are only some of the questions that we have to deal with in this paragraph. Let's get started!

1. Make sure that the bodies interact

In everyday life, we constantly encounter various types of influences of some bodies on others. To open the door, you need to “act” on it with your hand; the impact of your foot causes the ball to fly into the goal; even when you sit down on a chair, you act on it (Fig. 1.35, p. 38).

At the same time, when we open the door, we feel its impact on our hand, the effect of the ball on our foot is especially noticeable if you play football barefoot, and the effect of the chair prevents us from falling to the floor. That is, an action is always an interaction: if one body acts on another, then the other body acts on the first.

Rice. 1.35. Examples of interaction between bodies

You can clearly see that the action is not one-sided. Carry out a simple experiment: while standing on skates, lightly push your friend. As a result, not only your friend will begin to move, but you yourself will begin to move.

These examples confirm the conclusion of scientists that in nature we always deal with interaction, and not with unilateral action.

Let's take a closer look at some types of interactions.

2. Remember about gravitational interaction

Why does any object, be it a pencil released from a hand, a leaf of a tree or a drop of rain, fall and move downwards (Fig. 1.36)? Why does an arrow fired from a bow not fly straight but eventually fall to the ground? Why does the Moon move around the Earth? The reason for all these phenomena is that the Earth attracts other bodies to itself, and these bodies also attract the Earth to themselves. For example, the gravity of the Moon causes tides on Earth (Fig. 1.37). Our planet and all the other planets in the solar system are attracted to the Sun and to each other.

Rice. 1.36. Raindrops fall down under the influence of the Earth's gravity

In 1687, the outstanding English physicist Isaac Newton (Fig. 1.38) formulated a law according to which there is mutual attraction between all bodies in the Universe.

Rice. 1.37. Tides are a consequence of the Moon's gravity

This mutual attraction of material objects is called gravitational interaction. Based on experiments and mathematical calculations, Newton established that the intensity of gravitational interaction increases with increasing masses of interacting bodies. That is why it is easy to be convinced that you and I are attracted by the Earth, but we do not feel the attraction of our desk neighbor at all.

3. Getting to know the macromagnetic interaction

There are other types of interactions. For example, if you rub a balloon with a piece of silk, it will begin to attract various light objects: fibers, grains of rice, pieces of paper (Fig. 1.39). Such a ball is said to be electrified, or charged.

Charged bodies interact with each other, but the nature of their interaction can be different: they either attract or repel each other (Fig. 1.40).

Rice. 1.38. Famous English scientist Isaac Newton (1643-1727)

The first serious studies of this phenomenon were carried out by the English scientist William Gilbert (1544-1603) at the end of the 16th century.

Rice. 1.39. An electrified ball attracts a sheet of paper

Rice. 1.40. Two charged balls interact with each other: a - attract; b - repulse

Gilbert called the interaction between charged bodies electric (from the Greek word elektron - amber), since the ancient Greeks noticed that amber, if rubbed, begins to attract small objects to itself.

You know well that the compass needle, if allowed to rotate freely, always stops with one end pointing north and the other south (Fig. 1.41). This is due to the fact that the compass needle is a magnet, our planet Earth is also a magnet, and a huge one, and two magnets always interact with each other. Take any two magnets, and as soon as you try to bring them closer to each other, you will immediately feel attraction or repulsion. This interaction is called magnetic.

Physicists have found that the laws describing electrical and magnetic interactions are the same. Therefore, in science it is customary to talk about a single electromagnetic interaction.

We encounter electromagnetic interactions literally at every step - after all, when we walk, we interact with the road surface (we push off), and the nature of this interaction is electromagnetic. Thanks to electromagnetic interactions we move, sit, and write. We also see, hear, smell and touch with the help of electromagnetic interaction (Fig. 1.42). The operation of most modern devices and household appliances is based on electromagnetic interaction.

Let's say more: the existence of physical bodies, including you and me, would be impossible without electromagnetic interaction. But what does the interaction of charged balls and magnets have to do with all this? - you ask. Don't rush: by studying physics, you will definitely be convinced that this connection exists.

4. We face unresolved problems

Our description will be incomplete if we do not mention two more types of interactions that were discovered only in the middle of the last century.

Rice. 1.41 The compass needle is always oriented north

Rice. 1.42 We see, we hear, we understand thanks to electromagnetic interaction

They are called strong and weak interactions and act only within the microcosm. Thus, there are four different types of interactions. Is it too much? Of course, it would be much more convenient to deal with a single universal type of interaction. Moreover, there is already an example of combining various interactions - electric and magnetic - into a single electromagnetic one.

For many decades, scientists have been trying to create a theory of such unification. Some steps have already been taken. In the 60s of the 20th century, it was possible to create a theory of the so-called electroweak interaction, within the framework of which electromagnetic and weak interactions were combined. But the complete (“great”) unification of all types of interaction is still far away. Therefore, each of you has a chance to make a scientific discovery of world significance!

Let's sum it up

Interaction in physics is the action of bodies or particles on each other. We briefly described two types of interaction out of four known to science: gravitational and electromagnetic.

The attraction of bodies to the Earth, planets to the Sun and vice versa are examples of the manifestation of gravitational interaction.

An example of electrical interaction is the interaction of an electrified balloon with pieces of paper. An example of magnetic interaction is the interaction of a compass needle with the Earth, which is also a magnet, as a result of which one end of the needle always points to the north, and the other to the south.

Electrical and magnetic interactions are manifestations of a single electromagnetic interaction.

Control questions

1. Give examples of interaction between bodies.

2. What types of interactions exist in nature?

3. Give examples of gravitational interaction.

4. Who discovered the law according to which there is mutual attraction between all bodies in the Universe?

5. Give examples of electromagnetic interaction.

Exercise

Write a short essay on the topic “My experience confirming the interaction of bodies” (it could even be poetry!).

Physics and technology in Ukraine

Lev Vasilievich Shubnikov (1901-1945) lived a significant part of his short life in Kharkov, where he headed the low temperature laboratory. The level of accuracy of many measurements in the laboratory was not inferior to modern ones. In the laboratory in the 30s, oxygen, nitrogen and other gases were obtained in liquid form. Shubnikov was the founder of the study of metals in the so-called superconducting state, when the electrical resistance of the material is zero. The highest reward for a scientist is when the name of the phenomenon he discovered is used instead of a technical term by the name of the scientist himself. “Shubnikov-de Haas effect”; “Shubnikov phase”; “Obreimov-Shubnikov method” are just a few examples of the contribution of the famous Ukrainian scientist to the construction of modern physics.

Physics. 7th grade: Textbook / F. Ya. Bozhinova, N. M. Kiryukhin, E. A. Kiryukhina. - X.: Publishing house "Ranok", 2007. - 192 p.: ill.

In order for a body to rest or move uniformly and rectilinearly, it either does not need to be acted upon at all, or it needs to be acted on in such a way that the total action of all bodies is compensated. The time has come to figure out what must happen in order for the body to begin to change speed, that is, to acquire acceleration. To do this, you will need to remember some physical quantities that we encountered in physics lessons in previous grades.

As is known, the speed of a body changes only if another body acts on it. For example, the free fall of a weight as a result of the action of the Earth on it. When falling, the speed increases, which means its change is due to this action (Fig. 1).

Rice. 1. Free fall

But at the same time, the speed of the second body also changes. Try to push off on the ice from a friend standing next to you. You will notice that your friend will also begin to move. Bodies interact. There is no such thing as unilateral action.

To characterize the interaction of bodies, it is necessary to introduce a physical quantity, such a quantity is force.

Force - this is a vector quantity that characterizes the action of one body on another (the interaction of bodies). Force is a measure of interaction. The SI unit of force is the newton.

N (newton)

Since a body experiences acceleration as a result of the action of a force, it is necessary to establish a connection between the acceleration that the body acquired and the force that caused this acceleration.

If forces of various magnitudes are applied to a trolley on which a special structure with a suspended weight (Fig. 2) is installed, which deflects when the trolley accelerates, you can notice that the deflection of the weight will increase with increasing applied force. That is, the acceleration that a body acquires as a result of the action of a force on it is directly proportional to the magnitude of this force (Fig. 3). Acceleration is directed in the same direction as force.

Rice. 2. Study of the relationship between force and acceleration of a body

Rice. 3. The acceleration that a body acquires as a result of a force acting on it is directly proportional to the magnitude of this force

Acceleration also depends on body weight.

If you change the mass of the cart (Fig. 4), to which a constant force is applied, you will notice that the deflection of the weight decreases as the mass increases. That is, acceleration is inversely proportional to the mass of the body.

Rice. 4. The acceleration that a body acquires as a result of the action of a force on it is inversely proportional to the mass of this body

Newton's second law combines the two conclusions obtained above.

Newton's second law: acceleration acquired by a body as a result of the action of a force on it F, is directly proportional to the magnitude of this force and inversely proportional to the mass of the body.

If several forces act on a body, then the resultant of these forces is found, that is, a certain total total force that has a certain direction and numerical value. That is, virtually all cases of application of various forces at a specific moment in time can be reduced to the action of one resultant force.

Resultant They call a force that would impart to a body the same acceleration as the vector sum of all forces acting on the body.

Thus, Newton's second law can be formulated like this: the resultant of all forces acting on a body is equal to the product of the mass of the body and the acceleration acquired as a result of the action of these forces.

Types of interaction in physics

There are four types of interactions in nature.

1. Gravitational(gravitational force) is the interaction between bodies that have mass. It is significant on the scale of cosmic bodies. For example, we feel our attraction to the Earth, since it has a huge mass, but we do not feel the attraction to the table, chair and other bodies with relatively small mass.

2. Electromagnetic. The composition of any atom includes charged particles, therefore, such interaction is fundamental and we encounter it always and everywhere. It is the electromagnetic interaction that is responsible for such mechanical forces as the friction force (Fig. 5) and the elastic force.

Rice. 5. The nature of friction force

As the intermolecular distance increases, the forces of intermolecular attraction and repulsion decrease - only the attractive forces decrease more slowly than the repulsive forces - therefore, total elastic forces arise, which are directed towards the intermolecular forces of attraction (Fig. 6).

Rice. 6. The nature of elastic force

Compared to gravitational interaction, electromagnetic interaction is much stronger, but, unlike the first, it is valid for bodies with an electric charge.

3. Strong. This interaction was discovered about 100 years ago. It was then that scientists began to wonder how protons, which are positively charged and part of the nucleus, are held there (Fig. 7), because similarly charged bodies must repel each other. The strong force holds protons in the nucleus. This interaction is short-range, that is, it acts over a distance on the order of the size of the nucleus.

Rice. 7. The strong force keeps protons in the nucleus

4. Weak. Such interaction is responsible for some types of interaction among elementary particles, for some types of β-decay and for other processes occurring inside the atom, atomic nucleus (Fig. 8).

Rice. 8. Alpha, beta and gamma decays

Many physicists believe that there is one general interaction in nature, and the above interactions are only its manifestations, and are trying to obtain the so-called unified field theory, in which all these four types will be reduced to one. At the moment, it has been possible to combine electromagnetic, strong and weak interactions.

Newton's second law in NSO. Centrifugal force

Newton's laws are fulfilled in inertial frames of reference, but it is possible to achieve that these laws will also be fulfilled in non-inertial frames of reference (NSF).

Scientists have agreed to believe that in NSO, in addition to the usual forces responsible for the appearance of acceleration in a body, there are inertial forces - a special type of force. They are associated with the acceleration with which a non-inertial system moves relative to an inertial one.

In NSO, Newton's second law takes on the following form:

where is acceleration in a non-inertial reference frame; - inertia force

where is the absolute acceleration of the inertial reference frame

In NSO, Newton's third law regarding inertial forces is not satisfied.

An example of inertia force is centrifugal force. During a sharp turn of the car, a person is pressed into a seat. From the point of view of this person, a centrifugal force acts on him, and from the point of view of an observer on the ground, the person continues to move by inertia, while the car seat tends to turn (Fig. 9).

Rice. 9. Centrifugal force

How to find the resultant force

Resultant (resultant) is a force whose result is equivalent to the total action of all forces applied to the body (Fig. 10).

Rice. 10. Finding the resultant

The forces do not necessarily have to mutually increase each other. Imagine that you are sledding in winter (Fig. 11). In the first situation, the forces that your friends provide add up. In the second, one of the friends does not want to give up the sled and pulls it in the other direction. In this case, the force modules are subtracted.

Rice. 11. Illustration for example

Let's consider an example when the forces are directed not along one straight line, but in different directions. In Fig. 11 shows a body that is on an inclined plane and is held on it due to the action of friction. In addition to this force, the body is affected by the force of gravity () and the ground reaction force (). If the body is in an equilibrium position, then the vector sum of all forces is equal to zero, that is, the resultant is equal to zero.

Consequently, the acceleration that the body acquires is also zero.

Rice. 11. Forces acting on the body

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.

Internet portal Studopedia.org ().
Internet portal Abitura.com ().
Internet portal School-collection.edu.ru ().
Internet portal Class-fizika.narod.ru ().
Internet portal Fizika-lekcii.ucoz.ua ().

Homework

According to classical physics, in the world we know, bodies and particles constantly interact with each other. Even if we observe objects at rest, this does not mean that nothing is happening. It is thanks to the holding forces between molecules, atoms and elementary particles that you can see an object in the form of matter of the physical world that is accessible and understandable to us.

Interaction of bodies in nature and life

As we know from our own experience, when you fall on something, hit something, collide with something, it turns out to be unpleasant and painful. You push a car or an unwary passer-by crashes into you. In one way or another you interact with the world around you. In physics, this phenomenon was defined as “interaction of bodies.” Let us consider in detail what types modern classical science divides them into.

Types of interaction between bodies

In nature, there are four types of interaction between bodies. The first, well-known, is the gravitational interaction of bodies. The mass of bodies determines how strong gravity is.

It must be large enough for us to notice it. Otherwise, observing and recording this type of interaction is quite difficult. Space is the place where gravitational forces can be observed in the example of cosmic bodies with enormous mass.

Relationship between gravity and body mass

Directly, the energy of interaction between bodies is directly proportional to the mass and inversely proportional to the square of the distance between them. This is according to the definition of modern science.

The attraction of you and all objects on our planet is due to the fact that there is a force of interaction between two bodies with mass. Therefore, an object thrown upward is attracted back to the surface of the Earth. The planet is quite massive, so the force of action is noticeable. Gravity causes the interaction of bodies. The mass of bodies makes it possible to manifest and register it.

The nature of gravity is not clear

The nature of this phenomenon today causes a lot of controversy and speculation; apart from actual observation and the visible relationship between mass and attraction, the force causing gravity has not been identified. Although today a number of experiments are being carried out related to the detection of gravitational waves in outer space. A more accurate assumption was once made by Albert Einstein.

He formulated the hypothesis that gravitational force is a product of the curvature of the fabric of space-time by bodies located in it.

Subsequently, when space is displaced by matter, it tends to restore its volume. Einstein proposed that there is an inverse relationship between force and the density of matter.

An example of a clear demonstration of this dependence is black holes, which have an incredible density of matter and gravity that can attract not only cosmic bodies, but also light.

It is thanks to the influence of the nature of gravity that the force of interaction between bodies ensures the existence of planets, stars and other space objects. In addition, the rotation of some objects around others is present for the same reason.

Electromagnetic forces and progress

The electromagnetic interaction of bodies is somewhat reminiscent of gravitational interaction, but much stronger. The interaction of positively and negatively charged particles is the reason for its existence. Actually, this causes the emergence of an electromagnetic field.

It is generated by the body(s) or absorbed or causes the interaction of charged bodies. This process plays a very important role in the biological activity of a living cell and the redistribution of substances in it.

In addition, a clear example of the electromagnetic manifestation of forces is ordinary electric current, the magnetic field of the planet. Humanity uses this power quite extensively to transmit data. These are mobile communications, television, GPRS and much more.

In mechanics, this manifests itself in the form of elasticity and friction. A clear experiment demonstrating the presence of this force is known to everyone from a school physics course. This is rubbing an ebonite shelf with a silk cloth. Particles with a negative charge that appear on the surface provide attraction for light objects. An everyday example is a comb and hair. After several movements of the plastic through the hair, an attraction arises between them.

It is worth mentioning the compass and the Earth's magnetic field. The arrow is magnetized and has ends with positively and negatively charged particles, as a result, it reacts to the magnetic field of the planet. It turns its “positive” end in the direction of negative particles and vice versa.

Small in size but huge in strength

As for the strong interaction, its specificity is somewhat reminiscent of the electromagnetic type of forces. The reason for this is the presence of positive and negatively charged elements. Like electromagnetic force, the presence of opposite charges leads to the interaction of bodies. The mass of the bodies and the distance between them are very small. This is an area of the subatomic world where such objects are called particles.

These forces act in the region of the atomic nucleus and provide communication between protons, electrons, baryons and other elementary particles. Given their size, compared to large objects, the interaction of charged bodies is much stronger than with the electromagnetic type of force.

Weak forces and radioactivity

The weak type of interaction is directly related to the decay of unstable particles and is accompanied by the release of different types of radiation in the form of alpha, beta and gamma particles. As a rule, substances and materials with similar characteristics are called radioactive.

This type of force is called weak due to the fact that it is weaker than the electromagnetic and strong types of interaction. However, it is more powerful than gravitational interaction. The distances in this process between particles are very small, on the order of 2·10−18 meters.

The fact of discovering force and defining it among the fundamental ones happened quite recently.

With the discovery in 1896 by Henri Becquerel of the phenomenon of radioactivity of substances, in particular uranium salts, the study of this type of interaction of forces began.

Four forces created the universe

The entire Universe exists thanks to four fundamental forces discovered by modern science. They gave birth to space, galaxies, planets, stars and various processes in the form in which we observe it. At this stage, the definition of the fundamental forces in nature is considered complete, but perhaps over time we will learn about the presence of new forces, and knowledge of the nature of the universe will become one step closer to us.

Interaction of bodies

You can give any number of examples of body interaction. When you, while in a boat, begin to pull another rope, your boat will certainly move forward. By acting on the second boat, you force it to act on your boat.

If you kick a soccer ball, you will immediately feel the kick back on your foot. When two billiard balls collide, they change their speed, i.e. Both balls get acceleration. All this is a manifestation of the general law of interaction between bodies.

The actions of bodies on each other are in the nature of interaction not only during direct contact of bodies. Place, for example, two strong magnets with different poles facing each other on a smooth table, and you will immediately find that they will begin to move towards each other. The Earth attracts the Moon (universal gravity) and forces it to move along a curved path; in turn, the Moon also attracts the Earth (also the force of universal gravity). Although, naturally, in the frame of reference associated with the Earth, the acceleration of the earth caused by this force cannot be detected directly, it manifests itself in the form of tides.

Let us find out through experiment how the forces of interaction between two bodies are related. Rough measurements of forces can be made using the following experiments:

1 experience. Let's take two dynamometers, hook their hooks to each other, and holding the rings, we will stretch them, monitoring the readings of both dynamometers.

We will see that for any stretch, the readings of both dynamometers will be the same; This means that the force with which the first dynamometer acts on the second is equal to the force with which the second dynamometer acts on the first.

2 experience. Let's take a strong enough magnet and an iron bar and place them on the rollers to reduce friction on the table. We attach identical soft springs to the magnet and the bar, with their other ends hooked on the table. The magnet and the bar will attract each other and stretch the springs.

Experience shows that by the time the movement stops, the springs are stretched equally. This means that forces that are equal in magnitude and opposite in direction act on both bodies from the side of the springs.

Since the magnet is at rest, the force is equal in magnitude and opposite in direction to the force with which the block acts on it.

In the same way, the forces acting on the block from the magnet and the spring are equal in magnitude and opposite in direction.

Experience shows that the forces of interaction between two bodies are equal in magnitude and opposite in direction even in cases where the bodies are moving.

3 experience. Two people A and B stand on two carts that can roll on rails. They hold the ends of the rope in their hands. It is easy to find that no matter who pulls the rope, A or B, or both, the carts always begin to move at the same time and, moreover, in opposite directions. By measuring the accelerations of the carts, one can verify that the accelerations are inversely proportional to the masses of each of the carts (including the person). It follows that the forces acting on the carts are equal in magnitude.

Newton's first law. Inertial reference systems

As the first law of dynamics, Newton accepted the law established by Galileo: a material point maintains a state of rest or uniform linear motion until the influence of other bodies takes it out of this state.

Newton's first law shows that rest or uniform linear motion does not require any external influences to maintain it. This reveals a special dynamic property of bodies, called their inertia.

Accordingly, Newton's first law is called the law of inertia, and the movement of a body in the absence of influences from other bodies is called motion by inertia.

Mechanical motion is relative: its character for the same body can be different in different reference systems moving relative to each other. For example, an astronaut on board an artificial Earth satellite is motionless in the reference frame associated with the satellite. At the same time, in relation to the Earth, it moves together with the satellite in an elliptical orbit, i.e. not evenly or straight.

It is natural, therefore, that Newton’s first law should not be satisfied in every frame of reference. For example, a ball lying on the smooth floor of a ship's cabin, which moves in a straight line and uniformly, can begin to move along the floor without any influence on it from any bodies. To do this, it is enough that the speed of the ship begins to change.

The reference system in relation to which a material point, free from external influences, is at rest or moves uniformly and rectilinearly is called an inertial reference system. The content of the first law, Newton's first law, is essentially reduced to two statements: firstly, that all bodies have the property of inertia and, secondly, that there are inertial frames of reference.

Any two inertial reference systems can move relative to each other only translationally and, moreover, uniformly and rectilinearly. It has been experimentally established that the heliocentric reference system is practically inertial, the origin of which is located at the center of mass of the Solar system (approximately at the center of the Sun), and the axes are drawn in the direction of three distant stars, chosen, for example, so that the coordinate axes are mutually perpendicular.

The laboratory reference system, whose coordinate axes are rigidly connected to the Earth, is not inertial mainly due to the daily rotation of the Earth. However, the Earth rotates so slowly that the maximum normal acceleration of points on its surface during daily rotation does not exceed 0.034 m/. Therefore, in most practical problems, the laboratory frame of reference can be approximately considered inertial.

Inertial frames of reference play a special role not only in mechanics, but also in all other branches of physics. This is due to the fact that, according to Einstein's principle of relativity, the mathematical expression of any physical law must have the same form in all inertial frames of reference.

Force is a vector quantity that is a measure of the mechanical action on the body in question from other bodies. Mechanical interaction can occur both between directly contacting bodies (for example, during friction, when bodies press on each other), and between remote bodies. A special form of matter that connects particles of matter into single systems and transmits the action of one particle to another at a finite speed is called a physical field, or simply a field.

The interaction between distant bodies is carried out through the gravitational and electromagnetic fields they create (for example, the attraction of planets to the Sun, the interaction of charged bodies, conductors with current, etc.). The mechanical action on a given body from other bodies manifests itself in two ways. It is capable of causing, firstly, a change in the state of mechanical motion of the body in question, and secondly, its deformation. Both of these manifestations of force can serve as a basis for measuring forces. For example, measuring forces using a spring dynamometer based on Hooke's law for longitudinal tension. Using the concept of force in mechanics, we usually talk about the movement and deformation of a body under the influence of forces applied to it.

In this case, of course, each force always corresponds to some body acting on the object under consideration with this force.

The force F is completely defined if its magnitude, direction in space and point of application are given. The straight line along which the force is directed is called the line of action of the force.

A field acting on a material point with a force F is called a stationary field if it does not change over time t, i.e. if at any point in the field the force F does not depend explicitly on time:

For the field to be stationary, it is necessary that the bodies creating it are at rest relative to the inertial frame of reference used when considering the field.

Simultaneous action of several forces on a material point M is equivalent to the action of one force, called the resultant, or resultant, force and equal to their geometric sum.

It represents the closing polygon of forces

Weight. Pulse

In classical mechanics, the mass of a material point is a positive scalar quantity, which is a measure of the inertia of this point. Under the influence of a force, a material point does not change its speed instantly, but gradually, i.e. acquires a finite acceleration, which is smaller, the greater the mass of the material point. To compare the masses of two material points, it is enough to measure the modules and accelerations acquired by these points under the action of the same force:

Typically, body weight is found by weighing on a lever scale.

In classical mechanics it is believed that:

a) The mass of a material point does not depend on the state of motion of the point, being its constant characteristic.

b) Mass is an additive quantity, i.e. the mass of a system (for example, a body) is equal to the sum of the masses of all material points that are part of this system.

c) The mass of a closed system remains unchanged during any processes occurring in this system (law of conservation of mass).

The density ρ of a body at a given point M is the ratio of the mass dm of a small element of the body, including point M, to the value dV of the volume of this element:

The dimensions of the element under consideration must be so small that by changing the density within its limits many times greater intermolecular distances can be achieved.

A body is called homogeneous if the density is the same at all its points. The mass of a homogeneous body is equal to the product of its density and volume:

Mass of a heterogeneous body:

where ρ is a function of coordinates, and integration is carried out over the entire volume of the body. The average density (ρ) of an inhomogeneous body is the ratio of its mass to volume: (ρ)=m/V.

The center of mass of a system of material points is called point C, the radius vector of which is equal to:

where and are the mass and radius vector of the i-th material point, n is the total number of material points in the system, and m= is the mass of the entire system.

Center of mass speed:

Vector quantity equal to the product of the mass of a material point and its speed is called momentum, or momentum, of this material point. The momentum of a system of material points is the vector p, equal to the geometric sum of the momenta of all material points of the system:

The momentum of the system is equal to the product of the mass of the entire system and the speed of its center of mass:

Newton's second law

The basic law of the dynamics of a material point is Newton’s second law, which talks about how the mechanical motion of a material point changes under the influence of forces applied to it. Newton's second law states: the rate of change of momentum ρ of a material point is equal to the force F acting on it, i.e.

where m and v are the mass and speed of the material point.

If several forces simultaneously act on a material point, then the force F in Newton’s second law must be understood as the geometric sum of all acting forces - both active and reaction reactions, i.e. resultant force.

The vector quantity F dt is called the elementary impulse of force F for a short time dt of its action. The impulse of force F for a finite period of time from to is equal to a certain integral:

where F, in general, depends on time t.

According to Newton's second law, the change in the momentum of a material point is equal to the momentum of the force acting on it:

dp = F dt and ,

Where – the value of the momentum of the material point at the end () and at the beginning () of the time period under consideration.

Since in Newtonian mechanics the mass m of a material point does not depend on the state of motion of the point, then

Therefore, the mathematical expression of Newton's second law can also be represented in the form

where is the acceleration of a material point, r is its radius vector. Accordingly, the formulation of Newton's second law states: the acceleration of a material point coincides in direction with the force acting on it and is equal to the ratio of this force to the mass of the material point.

The tangential and normal acceleration of the material are determined by the corresponding components of the force F

where is the magnitude of the velocity vector of the material point, and R is the radius of curvature of its trajectory. The force imparting normal acceleration to a material point is directed towards the center of curvature of the point’s trajectory and is therefore called centripetal force.

If several forces simultaneously act on a material point , then its acceleration

Where . Consequently, each of the forces simultaneously acting on a material point imparts to it the same acceleration as if there were no other forces (the principle of independence of the action of forces).

The differential equation of motion of a material point is called the equation

In projections onto the axes of a rectangular Cartesian coordinate system, this equation has the form

where x, y and z are the coordinates of the moving point.

Newton's third law. Movement of the center of mass

The mechanical action of bodies on each other is manifested in the form of their interaction. This is evidenced by Newton's third law: two material points act on each other with forces that are numerically equal and directed in opposite directions along the straight line connecting these points.

If is the force acting on the i-th material point from the k-th side, and is the force acting on the k-th material point from the i-th side, then, according to Newton’s third law,

Forces are applied to different material points and can be mutually balanced only in those cases when these points belong to the same absolutely rigid body.

Newton's third law is an essential addition to the first and second laws. It allows you to move from the dynamics of a single material point to the dynamics of an arbitrary mechanical system (system of material points). From Newton's third law it follows that in any mechanical system the geometric sum of all internal forces is equal to zero:

where n is the number of material points included in the system, and .

Vector equal to the geometric sum of all external forces acting on the system is called the main vector of external forces:

where is the resultant of external forces applied to the i-th material point.

From Newton’s second and third laws it follows that the first derivative with respect to time t of the momentum p of a mechanical system is equal to the main vector of all external forces applied to the system,

This equation expresses the law of change in the momentum of the system.

Since , where m is the mass of the system, and is the speed of its center of mass, then the law of motion of the center of mass of a mechanical system has the form

, or ,

where is the acceleration of the center of mass. Thus, the center of mass of a mechanical system moves as a material point, the mass of which is equal to the mass of the entire system and which is acted upon by a force equal to the main vector of external forces applied to the system.

If the system under consideration is a rigid body that moves translationally, then the velocities of all points of the body and its center of mass are the same and equal to the velocity v of the body. Accordingly, the acceleration of the body and the basic equation for the dynamics of translational motion of a rigid body have the form

Argues that in inertial systems the acceleration of a body is proportional to the applied force, a physical quantity that is a quantitative measure of interaction. The magnitude of the force characterizing the interaction of bodies can be determined, for example, by the deformation of an elastic body additionally introduced into the system so that the interaction with it completely compensates for the original one. Proportionality factor...

The magnitude and direction of all forces acting in a mechanical system, and the mass of the material bodies of which it consists, and its behavior in time can be calculated with complete accuracy. It is Newton’s second law that gives all of classical mechanics its special charm - it begins to seem as if the entire physical world is structured like the most precise chronometer, and nothing in it escapes the eye...

195. There is a book on the table. What bodies does it interact with? Why is the book at rest?
A book lying on the table interacts with the Earth and the table. It is at rest because these interactions are balanced.

196. The interaction of which bodies determines the movement of clouds; an arrow shot from a bow; a projectile inside a gun barrel when fired; rotation of the wings of a wind turbine?
The interaction of water droplets entering the cloud with air currents and the Earth.
Interacting with the bow string, the Earth and the air.
Interaction with gases formed as a result of the explosion of gunpowder, the gun barrel, its stock and the Earth.
Interaction of the mill wings with the incoming air flow.

197. Give 3-5 names of bodies, as a result of interaction with which the ball can move (or change the direction of its movement).
Footballer's foot, tennis racket, golf club, baseball bat, air flow.

198. What will happen to a spring suspended on threads if the thread AB compressing it is burned with a match (Fig. 38)?
The action of thread A B on the spring will stop, and it will unclench and begin to move.

199. Why is it difficult for a firefighter to hold a fire hose from which water is gushing?
Due to the phenomenon of recoil.

200. Why does the tube deflect when water flows out of it (Fig. 39)?
As a result of the interaction of the flowing water and the tube, the latter will begin to move.

201. Why does the tube not deviate if a piece of cardboard attached to the tube is placed in the path of the water flowing out of it (see problem 200), as shown in Figure 40?
The interaction between the tube and the water is balanced by the interaction between the cardboard and the tube, and so the tube remains at rest.

202. Why does a vessel suspended on a thread rotate when water flows out (Fig. 41)?
The flow of water flowing from the tubes acts on the walls of the tubes. As a result, the vessel rotates.

203. The flask is suspended on a thread (Fig. 42). Will the flask remain at rest when the water in it boils strongly? Explain the phenomenon.
No. see No. 202.

204. In some parks, wooden cylinders (drums) rotating on a horizontal axis are installed on children's playgrounds. In what direction and when is the child running along it?
The child is pushed away from the cylinder, and it moves in the opposite direction.

205. A fish can move forward by throwing out jets of water with its gills. Explain this phenomenon.
This principle of movement is called reactive. The water thrown out by the gills of the fish acts on the fish, which due to this begins to move.

206. What is the purpose of webbed feet in waterfowl?
Webbed feet allow increased interaction between water and bird.

207. Why must the rifle butt be pressed tightly against the shoulder when firing?
A loose buttstock can cause shoulder injury as a result of recoil.

208. Why do the projectile and the gun get different speeds when fired?
The mass of the gun is many times greater than the mass of the projectile, and accordingly the speed of the gun will be many times less than the speed of the projectile.

209. A boy jumps from a loaded barge onto the shore. Why is the movement of the barge in the direction opposite to the jump imperceptible?
The mass of the barge is much greater than the mass of the boy, and as a result the speed of the gun is practically zero.

210. At the same distance from the shore there are a boat with a load and the same boat without a load. Which boat is easier to jump ashore from? Why?
It is easier to jump from a loaded boat because it has more mass.

211. a) In a compressed state, the spring on the stand is held with a thread (Fig. 43, a). If the thread is burned at point A, the spring will fly off. Indicate the interaction of which bodies causes the movement of the spring.
b) If, for example, a ball is first placed on the spring, then it will begin to move. The interaction of which bodies will cause the movement of the ball?
c) On the left cart there is a cube made of iron, on the right - from wood (Fig. 43, b). A spring compressed by a thread is placed between the carts. If the thread is burned, the carts will start moving. Which cart will have the highest speed? Why?
a) The interaction of the spring, support and thread.
b) The interaction of the spring, thread, ball and support.
c) m1v1 = m2v2. This means that a cart with a wooden block will gain greater speed, since it has less mass.

212. The left cart (see problem 211, c) acquired a speed of 4 cm/s, the right one - 60 cm/s. Which cart weighs more and by how many times?

213. What is the mass of the left cart (see Problem 212) if the mass of the right cart is 50 g?

214. A pedestrian weighing 90 kg moves at a speed of 3.6 km/h, and a dog weighing 7.5 kg runs at a speed of 12 m/s. Find the ratio of the impulses of the pedestrian and the dog.

215. a) A steel plate is attached to the end of the spring (Fig. 44). The spring is held in a compressed state by a thread. If you burn the thread, the spring straightens and the steel plate simultaneously hits the balls that lie on the table. The masses of the balls are equal, but they are made of different metals (aluminum, lead, steel). What metal are ball 1, ball 2 and ball 3 made of? (In the figure, the position of each ball after impact is indicated by a dotted line.)
b) A spring compressed with the help of a thread is placed between the carts (see Fig. 43, b). If the thread is burned, then as a result of interaction with the spring, the carts will begin to move. How will the speeds acquired by the carts differ if the mass of the left cart is 7.5 kg, and the right cart is 1.5 kg?

216. A spring, the ends of which are tied with a thread, is placed between the carts as shown in Figure 45. There are vessels with sand on the carts. When the thread was burned, the right cart acquired greater speed than the left one. How can this be explained?
The left cart is heavier than the right one.

217. What is the mass of the right cart (see problem 216), if it acquired 0.5 times greater speed than the left cart, whose mass with the load is 450 g?

218. The boy chooses a rope, and the boats approach each other in the lake (Fig. 46). Which of two identical boats acquires greater speed at the moment of approaching each other? Why?
The left boat has greater speed because it is lighter than the right one, in which the child is sitting.

219. When two carts interact, their speeds change to 20 and 60 cm/s. The mass of the larger trolley is 0.6 kg. What is the mass of the smaller cart?

220. The same forces were applied to the balls lying on the table for the same period of time. In this case, a ball weighing 3 kg acquired a speed of 15 cm/s. What speed does the 1 kg ball acquire?

221. A boy weighing 45 kg jumped onto the shore from a stationary inflatable boat weighing 30 kg. At the same time, the boat acquired a speed of 1.5 m/s relative to the shore. What is the boy's speed relative to the boat?

222. A boy whose mass is 46 kg jumped onto the shore at a speed of 1.5 m/s from a stationary raft weighing 1 ton. What speed did the raft acquire relative to the shore?

223. Can two initially motionless bodies, as a result of interaction with each other, acquire numerically equal speeds?
They can, provided that their masses are equal.

224. The air under the pump piston was compressed. Has the mass of air changed?
The air mass has not changed.

225. The weight was lowered into a vessel with water. Has the mass of the weight changed?
The mass of the weight has not changed.

226. While competing in tug-of-war, two boys pull a rope in different directions, each applying a force of 500 N to it. Will a rope break if it can withstand a tension force of only 800 N?
It will not rupture, since a force of only 500 N acts on it.

227. Will the mass of water change when part of it turns into ice or steam?
Its mass will change by an amount equal to the mass of ice or steam.