Isaac Newton (1642-1727) collected and published the basic laws of classical mechanics in 1687. Three famous laws were included in the work, which was called "Mathematical Principles of Natural Philosophy."

For a long time this world was shrouded in deep darkness
Let there be light, and then Newton appeared.

(Epigram 18th century)

But Satan did not wait long for revenge -
Einstein came, and everything was as before.

(Epigram 20th century)

What happened when Einstein came, read in a separate article about relativistic dynamics. In the meantime, we will give formulations and examples of solving problems for each Newton's law.

Newton's first law

Newton's first law states:

There are such frames of reference, called inertial ones, in which bodies move uniformly and rectilinearly if no forces act on them or the action of other forces is compensated.

Simply put, the essence of Newton's first law can be formulated as follows: if we push a cart on an absolutely flat road and imagine that we can neglect the frictional forces of the wheels and air resistance, then it will roll at the same speed indefinitely.

Inertia- this is the ability of a body to maintain speed both in direction and in magnitude, in the absence of influences on the body. Newton's first law is also called the law of inertia.

Before Newton, the law of inertia was formulated in a less clear form by Galileo Galilei. The scientist called inertia "indestructibly imprinted movement." Galileo's law of inertia states that in the absence of external forces, a body is either at rest or moves uniformly. The great merit of Newton is that he was able to combine the principle of relativity of Galileo, his own works and the work of other scientists in his "Mathematical Principles of Natural Philosophy".

It is clear that such systems, where the cart was pushed, and it rolled without the action of external forces, do not actually exist. Forces always act on bodies, and it is almost impossible to completely compensate for the action of these forces.

For example, everything on Earth is in a constant field of gravity. When we move (whether we walk, ride a car or bicycle), we need to overcome many forces: rolling friction and sliding friction, gravity, Coriolis force.

Newton's second law

Remember the cart example? At this point we attached to her force! It is intuitively clear that the cart will roll and soon stop. This means that its speed will change.

In the real world, the speed of a body most often changes rather than remains constant. In other words, the body is moving with acceleration. If the speed increases or decreases uniformly, then the motion is said to be uniformly accelerated.

If the piano falls from the roof of the house down, then it moves with uniform acceleration under the influence of constant acceleration of free fall g. Moreover, any arc of an object thrown out of a window on our planet will move with the same free fall acceleration.

Newton's second law establishes a relationship between mass, acceleration, and the force acting on a body. Here is the formulation of Newton's second law:

The acceleration of a body (material point) in the inertial frame of reference is directly proportional to the force applied to it and inversely proportional to the mass.

If several forces act on the body at once, then the resultant of all forces, that is, their vector sum, is substituted into this formula.

In this formulation, Newton's second law is applicable only for movement at a speed much less than the speed of light.

There is a more universal formulation of this law, the so-called differential form.

In any infinitesimal period of time dt the force acting on the body is equal to the derivative of the momentum of the body with respect to time.

What is Newton's third law? This law describes the interaction of bodies.

Newton's 3rd law tells us that for every action there is a reaction. And, in the literal sense:

Two bodies act on each other with forces opposite in direction but equal in magnitude.

Formula expressing Newton's third law:

In other words, Newton's third law is the law of action and reaction.

An example of a task on Newton's laws

Here is a typical problem on the application of Newton's laws. Its solution uses Newton's first and second laws.

The paratrooper opened his parachute and descended at a constant speed. What is the force of air resistance? The mass of the paratrooper is 100 kilograms.

Solution:

The movement of the parachutist is uniform and rectilinear, therefore, according to Newton's first law, the action of forces on it is compensated.

The force of gravity and the force of air resistance act on the paratrooper. Forces are directed in opposite directions.

According to Newton's second law, the force of gravity is equal to the acceleration of free fall, multiplied by the mass of the paratrooper.

Answer: The force of air resistance is equal to the force of gravity in absolute value and is opposite in direction.

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And here is another physics problem to understand the operation of Newton's third law.

The mosquito hits the windshield of a car. Compare the forces acting on a car and a mosquito.

Solution:

According to Newton's third law, the forces with which bodies act on each other are equal in absolute value and opposite in direction. The force with which the mosquito acts on the car is equal to the force with which the car acts on the mosquito.

Another thing is that the action of these forces on bodies differ greatly due to the difference in masses and accelerations.

Isaac Newton: myths and facts from life

At the time of the publication of his main work, Newton was 45 years old. For my long life the scientist made a huge contribution to science, laying the foundation of modern physics and determining its development for years to come.

He was engaged not only in mechanics, but also in optics, chemistry and other sciences, he drew well and wrote poetry. Not surprisingly, Newton's personality is surrounded by many legends.

Below are some facts and myths from the life of I. Newton. Let us clarify right away that a myth is not reliable information. However, we admit that myths and legends do not appear on their own and some of the above may well turn out to be true.

• Fact. Isaac Newton was a very modest and shy person. He immortalized himself thanks to his discoveries, but he himself never aspired to fame and even tried to avoid it.
• Myth. There is a legend according to which it dawned on Newton when an apple fell on him in the garden. It was the time of the plague epidemic (1665-1667), and the scientist was forced to leave Cambridge, where he constantly worked. It is not known for sure whether the fall of the apple was really such a fatal event for science, since the first mention of this appears only in the biographies of the scientist after his death, and the data of different biographers diverge.
• Fact. Newton studied and then worked hard at Cambridge. On duty, he needed to conduct classes with students for several hours a week. Despite the recognized merits of the scientist, Newton's classes were poorly attended. It happened that no one came to his lectures at all. Most likely, this is due to the fact that the scientist was completely absorbed in his own research.
• Myth. In 1689 Newton was elected a member of the Cambridge Parliament. According to legend, in more than a year of sitting in parliament, the eternally absorbed scientist took the floor to speak only once. He asked to close the window as there was a draft.
• Fact. It is not known how the fate of the scientist and all modern science would have developed if he had obeyed his mother and started doing housework on the family farm. Only thanks to the persuasion of teachers and his uncle, young Isaac went to study further instead of planting beets, scattering manure across the fields and drinking in local pubs in the evenings.

Dear friends, remember - any problem can be solved! If you're having trouble solving a physics problem, look at the basic physics formulas. Perhaps the answer is in front of your eyes, and you just need to consider it. Well, if there is absolutely no time for independent studies, a specialized student service is always at your service!

At the very end, we suggest watching a video tutorial on the topic "Newton's Laws".

In the well-known game of tug-of-war, both parties act on each other (through the rope) with by equal forces, as follows from the law of action and reaction. This means that it is not the party that pulls harder, but the one that rests more against the Earth that will win (tug the rope).

How to explain that a horse is pulling a sled if, as follows from the law of action and reaction, the sled pulls the horse back with the same force in modulus F 2, with which the horse pulls the sled forward (force F 1)? Why are these forces not balanced?

The fact is that, firstly, although these forces are equal and directly opposite, they are applied to different bodies, and secondly, forces from the side of the road also act on the sleigh and on the horse (Fig. 9).

Force F 1 from the side of the horse is applied to the sledge, which, in addition to this force, experiences only a small friction force f 1 skid on snow; so the sleigh starts moving forward. To the horse, in addition to the strength of the sleigh F 2 directed backwards, applied from the side of the road against which it rests with its feet, forces f 2 directed forward and greater than the force from the side of the sled. Therefore, the horse also begins to move forward. If you put the horse on the ice, then the force from the slippery ice will not be enough; and the horse will not move the sleigh. The same will happen with a very heavily loaded wagon, when the horse, even resting on its feet, will not be able to create sufficient force to move the wagon from its place. After the horse has moved the sleigh and a uniform movement of the sleigh has been established, the force f 1 will be balanced by the forces f 2 (Newton's first law).

A similar question arises when analyzing the movement of a train under the action of an electric locomotive. And here, as in the previous case, movement is possible only due to the fact that, in addition to the forces of interaction between the pulling body (horse, electric locomotive) and the “trailer” (sleigh, train), the pulling body is affected by forces directed from the side of the road or rails. forward. On a perfectly slippery surface, from which it is impossible to "push off", neither the sleigh with the horse, nor the train, nor the car could move.

Newton's third law explains recoil phenomenon when fired. Let us install on the trolley a cannon model acting with the help of steam (Fig. 10) or with the help of a spring. Let the cart rest first. When fired, the “projectile” (cork) flies in one direction, and the “gun” rolls back in the other.

The recoil of the gun is the result of the recoil. Recoil is nothing but the counteraction from the side of the projectile, acting, according to Newton's third law, on the gun that ejects the projectile. According to this law, the force acting from the side of the gun on the projectile is always equal to the force acting from the side of the projectile on the gun, and is directed opposite to it.

In the famous game of tug-of-war, both parties act on each other (through the rope) with equal forces, as follows from the law of action and reaction. This means that it is not the party that pulls harder, but the one that rests more against the Earth that will win (tug the rope).

Rice. 72. The horse will move and carry the loaded sleigh, because from the side of the road, greater friction forces act on its hooves than on the slippery runners of the sleigh.

How to explain that the horse is pulling the sled if, as follows from the law of action and reaction, the sled pulls the horse back with the same modulus of force as the horse pulls the sled forward (force)? Why are these forces not balanced? The fact is that, firstly, although these forces are equal and directly opposite, they are applied to different bodies, and secondly, forces from the side of the road also act on the sleigh and on the horse (Fig. 72). The force from the side of the horse is applied to the sleigh, which, in addition to this force, experiences only a small friction force of the runners on the snow; so the sleigh starts moving forward. To the horse, in addition to the force from the side of the sleigh directed backwards, forces are applied from the side of the road against which it rests with its feet, forces directed forward and greater than the force from the side of the sleigh. Therefore, the horse also begins to move forward. If you put the horse on the ice, then the force from the slippery ice will be insufficient, and the horse will not move the sled. The same will happen with a very heavily loaded wagon, when the horse, even resting on its feet, will not be able to create sufficient force to move the wagon from its place. After the horse has moved the sleigh and a uniform movement of the sleigh has been established, the force will be balanced by the forces (Newton's first law).

A similar question arises when analyzing the movement of a train under the action of an electric locomotive. And here, as in the previous case, movement is possible only due to the fact that, in addition to the forces of interaction between the pulling body (horse, electric locomotive) and the “trailer” (sleigh, train), the pulling body is affected by forces directed from the side of the road or rails. forward. On a perfectly slippery surface, from which it is impossible to "push off", neither the sleigh with the horse, nor the train, nor the car could move.

Rice. 73. When a test tube with water is heated, the cork flies in one direction, and the “gun” rolls in the opposite direction.

Newton's third law allows you to calculate recoil phenomenon when fired. Let us install on the trolley a cannon model acting with the help of steam (Fig. 73) or with the help of a spring. Let the cart rest first. When fired, the “projectile” (cork) flies in one direction, and the “gun” rolls back in the other. The recoil of the gun is the result of the recoil. Recoil is nothing but the counteraction from the side of the projectile, acting, according to Newton's third law, on the gun that ejects the projectile. According to this law, the force acting from the side of the gun on the projectile is always equal to the force acting from the side of the projectile on the gun, and is directed opposite to it. Thus, the accelerations received by the gun and the projectile are directed oppositely, and in absolute value are inversely proportional to the masses of these bodies. As a result, the projectile and the cannon will acquire oppositely directed velocities that are in the same ratio. Let us denote the velocity obtained by the projectile as , and the velocity obtained by the gun as , and denote the masses of these bodies as and respectively. Then

DEFINITION

Statement of Newton's third law. Two bodies act on each other with equal in magnitude and opposite in direction. These forces are of the same physical nature and are directed along the straight line connecting their points of application.

Description of Newton's third law

For example, a book lying on a table acts on the table with a force directly proportional to its own and directed vertically downwards. According to Newton's third law, the table at the same time acts on the book with absolutely the same force, but directed not downwards, but upwards.

When an apple falls from a tree, it is the Earth that acts on the apple with the force of its gravitational attraction (as a result of which the apple moves uniformly accelerated towards the surface of the Earth), but at the same time the apple also attracts the Earth to itself with the same force. And the fact that it seems to us that it is the apple that falls to the Earth, and not vice versa, is a consequence. The mass of an apple compared to the mass of the Earth is small to incomparability, therefore it is the apple that is noticeable to the observer's eyes. The mass of the Earth, in comparison with the mass of an apple, is huge, so its acceleration is almost imperceptible.

Likewise, if we kick the ball, the ball kicks us back. Another thing is that the ball has a much smaller mass than the human body, and therefore its impact is practically not felt. However, if you kick a heavy iron ball, the response is well felt. In fact, every day we “kick” a very, very heavy ball – our planet – many times every day. We push it with every step we take, only at the same time it is not she who flies away, but we. And all because the planet is millions of times larger than us in mass.

Thus, Newton's third law states that forces as a measure of interaction always appear in pairs. These forces are not balanced, as they are always applied to different bodies.

Newton's third law is valid only in and is valid for forces of any nature.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

Exercise

Compare the acceleration moduli of two balls of the same radius during interaction if the first ball is made of steel and the second is made of lead.

Solution

Let's make a drawing The impact force with which the second ball acts on the first: and the impact force with which the first ball acts on the second: According to Newton's third law, these forces are opposite in direction and equal in magnitude, so it can be written down. There are as many examples of the interaction of bodies as you like. When you, being in one boat, begin to pull the other by the rope, then your boat will certainly move forward (Fig. 1). By acting on the second boat, you make it act on your boat. If you kick a soccer ball, you will immediately feel the backlash on your leg. When two billiard balls collide, both balls change their speed, that is, they receive accelerations. When the cars collide with each other during the formation of the train, the buffer springs are compressed at both cars. All these are manifestations of the general law of interaction of bodies. The actions of bodies on each other are in the nature of interaction not only with direct contact of the bodies. Put, for example, on a smooth table two strong magnets with opposite poles towards each other, and you will immediately find that the magnets will begin to move towards each other. The Earth attracts the Moon (universal gravitational force) and makes it move along a curvilinear trajectory; in turn, the Moon also attracts the Earth (also the force of universal gravitation). Although, of course, in the reference frame associated with the Earth, the acceleration of the Earth caused by this force cannot be directly detected (even the much greater acceleration caused by the attraction of the Earth by the Sun cannot be directly detected), it manifests itself in the form of tides. Noticeable changes in the velocities of both interacting bodies are observed, however, only in cases where the masses of these bodies do not differ greatly from each other. If the interacting bodies differ significantly in mass, only one of them, which has a smaller mass, receives a noticeable acceleration. So, when a stone falls, the Earth noticeably accelerates the movement of the stone, but the acceleration of the Earth (and the stone also attracts the Earth) cannot be practically detected, since it is very small. Forces of interaction of two bodies Let us find out with the help of experience how the forces of interaction of two bodies are interconnected. Rough measurements of the interaction forces can be made in the following experiments. 1 experience. Let's take two dynamometers, hook their hooks to each other and, holding the rings, we will stretch them, following the readings of both dynamometers (Fig. 2). We will see that under any stretching, the readings of both dynamometers will coincide; hence, 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. Take a sufficiently strong magnet and an iron bar and put them on the rollers to reduce friction on the table (Fig. 3). We attach identical soft springs to the magnet and the bar, hooked at the other ends on the table. The magnet and the bar will be attracted to each other and stretch the springs. Experience shows that by the time the movement stops, the springs are stretched in exactly the same way. This means that both bodies from the side of the springs are subject to the same modulus and opposite forces: \(\vec F_1 = -\vec F_2 \qquad(1)\) Since the magnet is at rest, the force \(\vec F_2\) is equal in absolute value and opposite in direction to the force \(\vec F_4\) with which the bar acts on it: \(\vec F_1 = \vec F_4 \qquad(2)\) In the same way, the forces acting on the bar from the side of the magnet and the spring are equal in absolute value and opposite in direction: \(\vec F_3 = -\vec F_1 \qquad(3)\) From equalities (1), (2), (3) it follows that the forces with which the magnet and the bar interact are equal in absolute value and opposite in direction: \(\vec F_3 = -\vec F_4 \qquad(1)\) Experience shows that the forces of interaction between two bodies are equal in absolute value and opposite in direction even in those cases when the bodies are moving. 3 experience. There are two people on two carts that can roll on rails. A And IN(Fig. 4). They hold the ends of the rope in their hands. It is easy to discover that no matter who pulls ("selects") the rope, A or IN or both together, the carts always move at the same time and, moreover, in opposite directions. By measuring the accelerations of 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 absolute value. Newton's third law Based on these and similar experiments, Newton's third law can be formulated. The forces with which the bodies act on each other are equal in magnitude and directed along one straight line in opposite directions. This means that if the body A from the side of the body IN force \(\vec F_A\) acts (Fig. 5), then simultaneously on the body IN from the side of the body A the force \(\vec F_B\) acts, and \(\vec F_A = -\vec F_B \qquad(5)\) Using Newton's second law, we can write equality (5) as follows: \(m_1 \cdot \vec a_1 = -m_2 \cdot \vec a_2 \qquad (6)\) Hence it follows that \(\frac(a_1)(a_2) = \frac(m_2)(m_1)= \mbox(const) \qquad (7)\) The ratio of the modules a 1 and a 2 of the accelerations of the interacting bodies is determined by the inverse ratio of their masses and is completely independent of the nature of the forces acting between them. (Here we mean that no other forces, except for the forces of interaction, act on these bodies.) This can be verified by the following simple experiment. Let's put two carts of the same mass on smooth rails and on one of them we will fix a small electric motor, on the shaft of which a thread tied to another cart can be wound, and on the other we will put a weight, the mass of which is equal to the mass of the engine (Fig. 6). When the engine is running, both carts rush towards each other with the same accelerations and pass the same paths. If the mass of one of the carts is made twice as large, then its acceleration will be half that of the other, and in the same time it will cover half the distance. The connection between the accelerations of interacting bodies and their masses can be established on the basis of such an experiment (Fig. 7). Two rollers of different weights connected by a thread are placed on a horizontal platform. Experience will show that it is possible to find such a position of the rollers when they do not move along it during the rotation of the platform. By measuring the radii of circulation of the rollers around the center of the platform, we determine the ratio of the centripetal accelerations of the rollers: \(\frac(a_1)(a_2) = \frac(\omega \cdot R_1)(\omega \cdot R_2)\) or \(\frac(a_1)(a_2) = \frac(R_1)(R_2)\ ). Comparing this ratio with the inverse ratio of body masses \(\frac(m_2)(m_1)\), we make sure that \(\frac(a_1)(a_2) = \frac(m_2)(m_1)\) at any platform rotation speeds . Note It must be remembered that the forces referred to in Newton's third law attached to different bodies and therefore cannot balance each other. Failure to understand this often leads to misunderstandings. So, sometimes with the help of Newton's third law they try to explain why this or that body is at rest. For example, they say that the chalk rests on the table allegedly because the force of gravity \(\vec F_t\), acting on the body, according to Newton's third law, is equal in absolute value and opposite in direction to the elastic force \(\vec N\) (force reaction of the support) acting on it from the side of the table. In fact, the equality \(\vec F_t + \vec N = 0\) is a consequence of Newton's second law, and not the third: the acceleration is zero, and therefore the sum of the forces acting on the body is zero. Newton's third law only implies that the support reaction force \(\vec N\) is equal in absolute value to the force \(\vec P\) with which the chalk presses on the table (Fig. 8). These forces are applied to different bodies and directed in opposite directions. Examples of the application of Newton's third law. In the famous game of tug-of-war, both parties act on each other (through the rope) with equal forces, as follows from the law of action and reaction. This means that it is not the party that pulls harder, but the one that rests more against the Earth that will win (tug the rope). How to explain that a horse is pulling a sled if, as follows from the law of action and reaction, the sled pulls the horse back with the same force in modulus F 2, with which the horse pulls the sled forward (force F 1)? Why are these forces not balanced? The fact is that, firstly, although these forces are equal and directly opposite, they are applied to different bodies, and secondly, forces from the side of the road also act on the sleigh and on the horse (Fig. 9). Force F 1 from the side of the horse is applied to the sledge, which, in addition to this force, experiences only a small friction force f 1 skid on snow; so the sleigh starts moving forward. To the horse, in addition to the strength of the sleigh F 2 directed backwards, applied from the side of the road against which it rests with its feet, forces f 2 directed forward and greater than the force from the side of the sled. Therefore, the horse also begins to move forward. If you put the horse on the ice, then the force from the slippery ice will not be enough; and the horse will not move the sleigh. The same will happen with a very heavily loaded wagon, when the horse, even resting on its feet, will not be able to create sufficient force to move the wagon from its place. After the horse has moved the sleigh and a uniform movement of the sleigh has been established, the force f 1 will be balanced by the forces f 2 (Newton's first law). A similar question arises when analyzing the movement of a train under the action of an electric locomotive. And here, as in the previous case, movement is possible only due to the fact that, in addition to the forces of interaction between the pulling body (horse, electric locomotive) and the “trailer” (sleigh, train), the pulling body is affected by forces directed from the side of the road or rails. forward. On a perfectly slippery surface, from which it is impossible to "push off", neither the sleigh with the horse, nor the train, nor the car could move. Newton's third law explains recoil phenomenon when fired. Let us install on the trolley a cannon model acting with the help of steam (Fig. 10) or with the help of a spring. Let the cart rest first. When fired, the “projectile” (cork) flies in one direction, and the “gun” rolls back in the other. The recoil of the gun is the result of the recoil. Recoil is nothing but the counteraction from the side of the projectile, acting, according to Newton's third law, on the gun that ejects the projectile. According to this law, the force acting from the side of the gun on the projectile is always equal to the force acting from the side of the projectile on the gun, and is directed opposite to it. On the meaning of Newton's third law The main significance of Newton's third law is revealed in the study of the motion of a system of material points or a system of bodies. This law makes it possible to prove important theorems in dynamics and greatly simplifies the study of the motion of bodies in cases where they cannot be considered as material points. The third law is formulated for point bodies (material points). Its application to real bodies with finite dimensions requires clarification and justification. In this formulation, this law cannot be applied in non-inertial frames of reference either. Literature Physics: Mechanics. Grade 10: Proc. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakishev. – M.: Bustard, 2002. – 496 p. Elementary textbook of physics: Textbook. In 3 volumes / Ed. G.S. Landsberg: T. 1. Mechanics. Heat. Molecular physics - M.: FIZMATLIT, 2003. - 608s. Perhaps you will be interested Astrology Congratulations on the wedding to the groom Diseases Why do people not like their birthday? Career Congratulations on Maslenitsa Astrology Manicure with the zodiac sign Leo Manicure according to the zodiac sign Leo