Newton's Three Laws: Definitions and Examples. Newton's laws Newton's laws and their formulas

The load in the elevator is affected by the force of gravity and the reaction force of the support.

According to Newton's second law:

Let's direct the coordinate axis as shown in the figure and write this vector equality in projections onto the coordinate axis:

whence the reaction force of the support:

The load will act on the elevator floor with a force equal to its weight. According to Newton's third law, this force is equal in absolute value to the force with which the elevator floor acts on the load, i.e. support reaction force:

Gravity acceleration m/s

Substituting the numerical values ​​of physical quantities into the formula, we calculate:

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.

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 bike), 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. During his 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 the 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".

When no forces act on them (or mutually balanced forces act), they are at rest or uniform rectilinear motion.

Historical wording

Modern wording

where p → = m v → (\displaystyle (\vec (p))=m(\vec (v)))- point momentum, v → (\displaystyle (\vec (v))) is its speed, and t (\displaystyle t)- time . With this formulation, as with the previous one, it is believed that the mass of a material point is unchanged in time.

Attempts are sometimes made to extend the scope of the equation d p ​​→ d t = F → (\displaystyle (\frac (d(\vec (p)))(dt))=(\vec (F))) and in the case of bodies of variable mass. However, along with such a broad interpretation of the equation, it is necessary to significantly modify the previously accepted definitions and change the meaning of such fundamental concepts as material point, momentum and force .

Remarks

When several forces act on a material point, taking into account the principle of superposition, Newton's second law is written as:

Newton's second law, like all classical mechanics, is valid only for the motion of bodies with speeds much less than the speed of light. When bodies move at speeds close to the speed of light, the relativistic generalization of the second law is used, obtained in the framework of the special theory of relativity.

It should be noted that it is impossible to consider a special case (when F → = 0 (\displaystyle (\vec(F))=0)) of the second law as an equivalent of the first, since the first law postulates the existence of the ISO, and the second is formulated already in the ISO.

Historical wording

Newton's original formulation:

Newton's third law

This law describes how two material points interact. Let there be a closed system consisting of two material points, in which the first point can act on the second with some force , and the second - on the first with force . Newton's third law states: the force of action F → 1 → 2 (\displaystyle (\vec (F))_(1\to 2)) equal in absolute value and opposite in direction to the reaction force F → 2 → 1 (\displaystyle (\vec (F))_(2\to 1)).

Newton's third law is a consequence of the homogeneity, isotropy, and mirror symmetry of space.

Newton's third law, like the rest of the laws of Newtonian dynamics, gives practically correct results only when the speeds of all bodies of the system under consideration are negligibly small compared to the speed of propagation of interactions (the speed of light).

Modern wording

The law states that forces arise only in pairs, and any force acting on a body has a source of origin in the form of another body. In other words, strength is always the result interactions tel. The existence of forces that have arisen independently, without interacting bodies, is impossible.

Historical wording

Newton gave the following formulation of the law:

Consequences of Newton's laws

Newton's laws are the axioms of classical Newtonian mechanics. From them, as a consequence, the equations of motion of mechanical systems are derived, as well as the "conservation laws" indicated below. Of course, there are laws (for example, universal gravitation or Hooke) that do not follow from Newton's three postulates.

Equations of motion

The equation F → = m a → (\displaystyle (\vec (F))=m(\vec (a))) is a differential equation: acceleration is the second derivative of the coordinate with respect to time. This means that the evolution (displacement) of a mechanical system in time can be unambiguously determined if its initial coordinates and initial velocities are specified.

Note that if the equations describing our world were first-order equations, then such phenomena as inertia, oscillations, waves would disappear from our world.

Law of conservation of momentum

The law of conservation of momentum states that the vector sum of the impulses of all the bodies of the system is a constant value if the vector sum of the external forces acting on the system of bodies is equal to zero.

Law of conservation of mechanical energy

Newton's laws and forces of inertia

The use of Newton's laws involves setting a certain ISO. However, in practice one has to deal with non-inertial frames of reference. In these cases, in addition to the forces referred to in Newton's second and third laws, the so-called inertia forces.

Usually we are talking about the forces of inertia of two different types. The force of the first type ( d'Alembert's inertia force) is a vector quantity equal to the product of the mass of a material point and its acceleration, taken with a minus sign. Forces of the second type ( Euler forces of inertia) are used to obtain the formal possibility of writing the equations of motion of bodies in non-inertial frames of reference in a form that coincides with the form of Newton's second law. By definition, the Euler force of inertia is equal to the product of the mass of a material point and the difference between the values ​​of its acceleration in that non-inertial frame of reference for which this force is introduced, on the one hand, and in any inertial frame of reference, on the other. The forces of inertia thus defined are not forces in the true sense of the word, they are called fictitious , seeming or pseudo-forces .

Newton's laws in the logic of the course of mechanics

There are methodologically different ways of formulating classical mechanics, that is, choosing its fundamental postulates, on the basis of which laws-consequences and equations of motion are then derived. Giving Newton's laws the status of axioms based on empirical material is only one of such ways ("Newtonian mechanics"). This approach is adopted in high school, as well as in most university courses in general physics.

An alternative approach, used mainly in theoretical physics courses, is Lagrangian mechanics. Within the framework of the Lagrangian formalism, there is one and only formula (recording the action) and one and only postulate (the bodies move so that the action is stationary), which is a theoretical concept. All Newton's laws can be deduced from this, however, only for Lagrangian systems (in particular, for conservative systems). However, it should be noted that all known fundamental interactions are described precisely by Lagrangian systems. Moreover, within the framework of the Lagrangian formalism, one can easily consider hypothetical situations in which the action has some other form. In this case, the equations of motion will no longer resemble Newton's laws, but classical mechanics itself will still be applicable.

Historical outline

The practice of using machines in the manufacturing industry, the construction of buildings, shipbuilding, and the use of artillery made it possible by the time of Newton to accumulate a large number of observations on mechanical processes. The concepts of inertia, force, acceleration became more and more clear during the 17th century. The works of Galileo, Borelli, Descartes, Huygens on mechanics already contained all the necessary theoretical prerequisites for Newton to create a logical and consistent system of definitions and theorems in mechanics.

Original text (lat.)

LEX I
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quantenus a viribus impressis cogitur statum illum mutare.

LEX II
Mutationem motus proportionalem esse vi motrici impressae et fieri secundum lineam rectam qua vis illa imprimitur.

Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.

See the previous sections for the Russian translation of these wordings of the laws.

Newton also gave rigorous definitions of such physical concepts as amount of movement(not quite clearly used by Descartes) and power. He introduced into physics the concept of mass as a measure of the inertia of a body and, at the same time, its gravitational properties (previously, physicists used the concept weight).

In the middle of the 17th century, the modern technique of differential and integral calculus did not yet exist. The corresponding mathematical apparatus in the 1680s was simultaneously created by Newton himself (1642-1727), as well as by Leibniz (1646-1716). Euler (1707-1783) and Lagrange (1736-1813) completed the mathematization of the foundations of mechanics.

Notes

1. Isaac Newton. Mathematical principles of natural philosophy. Translation from Latin and notes by A. N. Krylov / ed. Polaka L. S. - M .: Nauka, 1989. - S. 40-41. - 690 p. - (Classics of science). - 5,000 copies. - ISBN 5-02-000747-1.
2. Targ S. M. Newton's laws of mechanics// Physical Encyclopedia: [in 5 volumes] / Ch. ed. A. M. Prokhorov. - M.: Great Russian Encyclopedia, 1992. - T. 3: Magnetoplasmic - Poynting's theorem. - S. 370. - 672 p. - 48,000 copies. - ISBN 5-85270-019-3.
3. Inertia// Physical Encyclopedia / Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1990. - T. 2. - S. 146. - 704 p. - ISBN 5-85270-061-4.
4. inertial frame of reference// Physical Encyclopedia (in 5 volumes) / Edited by Acad. A. M. Prokhorova. - M.: Soviet Encyclopedia, 1988. - T. 2. - S. 145. - ISBN 5-85270-034-7.
5. “An additional characteristic (in comparison with the geometrical characteristics) of a material point is the scalar quantity m - the mass of the material point, which, generally speaking, can be both constant and variable. … In classical Newtonian mechanics, a material point is usually modeled by a geometric point with its inherent constant mass) being a measure of its inertia.” p. 137 Sedov LI , Tsypkin AG Fundamentals of macroscopic theories of gravitation and electromagnetism. M: Nauka, 1989.
6. Markeev A.P. Theoretical mechanics. - M. : CheRO, 1999. - S. 87. - 572 p."The mass of a material point is considered a constant value, independent of the circumstances of the movement."
7. Golubev Yu. F. Fundamentals of theoretical mechanics. - M. : MGU, 2000. - S. 160. - 720 p. - ISBN 5-211-04244-1. « Axiom 3.3.1. The mass of a material point retains its value not only in time, but also during any interactions of a material point with other material points, regardless of their number and the nature of interactions.
8. Zhuravlev V.F. Fundamentals of theoretical mechanics. - M. : Fizmatlit, 2001. - S. 9. - 319 p. - ISBN 5-95052-041-3.“The mass [of a material point] is assumed to be constant, independent of either the position of the point in space or time.”
9. Markeev A.P. Theoretical mechanics. - M. : CheRO, 1999. - S. 254. - 572 p.“... Newton's second law is valid only for a point of constant composition. The dynamics of systems of variable composition requires special consideration.”
10. "In Newtonian mechanics... m=const and dp/dt=ma". Irodov I. E. Basic laws of mechanics. - M.: Higher school, 1985. - S. 41. - 248 p..
11. Kleppner D., Kolenkow R. J. An Introduction to Mechanics. - McGraw-Hill, 1973. - P. 112. - ISBN 0-07-035048-5."For a particle in Newtonian mechanics, M is a constant and (d/dt)(M v) = M(d v/dt) = M a».
12. Sommerfeld A. Mechanics = Sommerfeld A. mechanic. Zweite, revidierte auflage, 1944. - Izhevsk: Research Center "Regular and Chaotic Dynamics", 2001. - S. 45-46. - 368 p. - ISBN 5-93972-051-X.

In the absence of external force influences, the body will continue to move uniformly in a straight line.

The acceleration of a moving body is proportional to the sum of the forces applied to it and inversely proportional to its mass.

Every action has an equal and opposite reaction.

Newton's laws, depending on how you look at them, represent either the end of the beginning or the beginning of the end of classical mechanics. In any case, this is a turning point in the history of physical science - a brilliant compilation of all the knowledge accumulated up to that historical moment about the motion of physical bodies within the framework of a physical theory, which is now commonly called classical mechanics. It can be said that the history of modern physics and the natural sciences in general started from Newton's laws of motion.

However, Isaac Newton did not take the laws named after him out of thin air. They, in fact, became the culmination of a long historical process of formulating the principles of classical mechanics. Thinkers and mathematicians - we will only mention Galileo ( cm. Equations of uniformly accelerated motion) - for centuries they tried to derive formulas for describing the laws of motion of material bodies - and constantly stumbled over what I personally call unspoken conventions for myself, namely, both fundamental ideas about what principles the material world is based on, which are so firmly entered the minds of people that seem undeniable. For example, the ancient philosophers did not even think that celestial bodies can move in orbits other than circular ones; at best, the idea arose that planets and stars revolve around the Earth in concentric (that is, nested in each other) spherical orbits. Why? Yes, because since the time of the ancient thinkers of ancient Greece, it never occurred to anyone that the planets can deviate from perfection, the embodiment of which is a strict geometric circle. It was necessary to have the genius of Johannes Kepler in order to honestly look at this problem from a different angle, analyze the data of real observations and withdraw of them, that in reality the planets revolve around the Sun along elliptical trajectories ( cm. Kepler's laws).

Newton's first law

Given such a serious historical failure, Newton's first law is formulated in an unequivocally revolutionary way. He argues that if any material particle or body is simply not touched, it will continue to move in a straight line with a constant speed by itself. If a body moves uniformly in a straight line, it will continue to move in a straight line at a constant speed. If the body is at rest, it will remain so until external forces are applied to it. To simply move the physical body from its place, you need to necessarily apply external force. Take an airplane: it will never budge until the engines are started. It would seem that the observation is self-evident, however, as soon as we digress from rectilinear motion, it ceases to seem so. When a body moves inertially along a closed cyclic trajectory, its analysis from the standpoint of Newton's first law only makes it possible to accurately determine its characteristics.

Imagine something like an athletics hammer - a ball at the end of a string that you spin around your head. The nucleus in this case does not move in a straight line, but in a circle, which means that, according to Newton's first law, something is holding it; this “something” is the centripetal force that you apply to the nucleus, spinning it. In fact, you yourself can feel it - the handle of an athletics hammer noticeably presses on your palms. If you open your hand and release the hammer, it - in the absence of external forces - will immediately set off in a straight line. It would be more accurate to say that this is how the hammer will behave in ideal conditions (for example, in outer space), since under the influence of the force of the Earth's gravitational attraction, it will fly strictly in a straight line only at the moment when you release it, and in the future the flight path will be all deviate more towards the earth's surface. If you try to really release the hammer, it turns out that the hammer released from the circular orbit will set off strictly in a straight line, which is tangent (perpendicular to the radius of the circle along which it was spun) with a linear speed equal to the speed of its circulation along the “orbit”.

Now we replace the core of the athletics hammer with a planet, the hammer with the Sun, and the string with the force of gravitational attraction: here is the Newtonian model of the solar system.

Such an analysis of what happens when one body revolves around another in a circular orbit at first glance seems to be something self-evident, but do not forget that it absorbed a number of conclusions of the best representatives of scientific thought of the previous generation (suffice it to recall Galileo Galilei). The problem here is that when moving along a stationary circular orbit, a celestial (and any other) body looks very serene and appears to be in a state of stable dynamic and kinematic equilibrium. However, if you look at it, only module(absolute value) of the linear velocity of such a body, while its direction constantly changing under the influence of gravitational attraction. This means that the celestial body is moving uniformly accelerated. By the way, Newton himself called acceleration "a change in motion."

Newton's first law also plays another important role from the point of view of our scientific attitude to the nature of the material world. He tells us that any change in the nature of the movement of the body indicates the presence of external forces acting on it. Relatively speaking, if we observe iron filings, for example, jumping up and sticking to a magnet, or, taking clothes out of the dryer of a washing machine, we find out that things stuck together and dried to one another, we can feel calm and confident: these effects have become a consequence of the action of natural forces (in the examples given, these are the forces of magnetic and electrostatic attraction, respectively).

Newton's second law

If Newton's first law helps us determine whether a body is under the influence of external forces, then the second law describes what happens to a physical body under their influence. The greater the sum of external forces applied to the body, this law says, the greater acceleration acquires a body. This time. At the same time, the more massive the body, to which an equal sum of external forces is applied, the less acceleration it acquires. This is two. Intuitively, these two facts seem self-evident, and in mathematical form they are written as follows:

F = ma

where F- power, m - weight, a - acceleration. This is probably the most useful and most widely used for applied purposes of all physical equations. It is enough to know the magnitude and direction of all forces acting in a mechanical system, and the mass of the material bodies of which it consists, and it is possible to calculate its behavior in time with exhaustive accuracy.

It is Newton's second law that gives all classical mechanics its special charm - it begins to seem as if the entire physical world is arranged like the most accurate chronometer, and nothing in it escapes the gaze of an inquisitive observer. Give me the spatial coordinates and velocities of all material points in the Universe, as if Newton tells us, show me the direction and intensity of all the forces acting in it, and I will predict you any future state of it. And such a view of the nature of things in the universe existed until the advent of quantum mechanics.

Newton's third law

For this law, most likely, Newton earned himself honor and respect from not only natural scientists, but also humanities scientists and simply the general public. They like to quote him (on business and without business), drawing the widest parallels with what we are forced to observe in our everyday life, and pull almost by the ears to substantiate the most controversial provisions during discussions on any issues, starting with interpersonal and ending with international relations and global politics. Newton, however, invested in his subsequently called the third law a completely specific physical meaning and hardly conceived it in any capacity other than as an accurate means of describing the nature of force interactions. This law states that if body A acts with a certain force on body B, then body B also acts on body A with an equal and opposite force. In other words, standing on the floor, you act on the floor with a force proportional to the mass of your body. According to Newton's third law, the floor at the same time acts on you with absolutely the same force, but directed not down, but strictly up. It is not difficult to verify this law experimentally: you constantly feel how the earth presses on your soles.

Here it is important to understand and remember that Newton is talking about two forces of a completely different nature, and each force acts on “its own” object. When an apple falls from a tree, it is the Earth that exerts its gravitational attraction on the apple (as a result of which the apple rushes to the Earth's surface with uniform acceleration), but at the same time the apple also attracts the Earth to itself with equal force. And the fact that it seems to us that it is the apple that falls to the Earth, and not vice versa, is already a consequence of Newton's second law. The mass of an apple compared to the mass of the Earth is low to the point of incomparability, so it is precisely its acceleration 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. (In the case of an apple falling, the center of the Earth shifts upward to a distance less than the radius of the atomic nucleus.)

Taken together, Newton's three laws have given physicists the tools they need to begin a comprehensive observation of all phenomena occurring in our universe. And despite all the tremendous advances in science since Newton, to design a new car or send a spacecraft to Jupiter, you still use Newton's three laws.

See also:

Isaac Newton, 1642-1727

An Englishman who is generally considered by many to be the greatest scientist of all times and peoples. Born into a family of small estate nobles in the vicinity of Woolsthorpe (Lincolnshire, England). He did not find his father alive (he died three months before the birth of his son). Having remarried, the mother left the two-year-old Isaac in the care of his grandmother. Many researchers of his biography attribute the peculiar eccentric behavior of an already adult scientist to the fact that until the age of nine, when the death of his stepfather followed, the boy was completely deprived of parental care.

For a while, young Isaac studied the wisdom of agriculture at a trade school. As is often the case with later great men, there are still many legends about his eccentricities in that early period of his life. So, in particular, they say that once he was sent to graze to guard cattle, which safely dispersed in an unknown direction, while the boy sat under a tree and enthusiastically read a book that interested him. Like it or not, but the teenager's craving for knowledge was soon noticed - and sent back to the Grantham gymnasium, after which the young man successfully entered Trinity College, Cambridge University.

Newton quickly mastered the curriculum and moved on to studying the works of the leading scientists of the time, in particular the followers of the French philosopher René Descartes (1596-1650), who held a mechanistic view of the universe. In the spring of 1665, he received his bachelor's degree - and then the most incredible events in the history of science happened. In the same year, the last bubonic plague broke out in England, the tolling of funeral bells was increasingly heard, and the University of Cambridge was closed. Newton returned to Woolsthorpe for almost two years, taking with him only a few books and his remarkable intelligence to boot.

When the University of Cambridge reopened two years later, Newton had already (1) developed differential calculus, a separate branch of mathematics, (2) outlined the foundations of modern color theory, (3) derived the law of universal gravitation, and (4) solved several mathematical problems that had come before him. no one could decide. As Newton himself said, “In those days I was in the prime of my inventive powers, and Mathematics and Philosophy have never since captivated me as much as they did then.” (I often ask my students, telling them once again about Newton's achievements: “What you did you manage to do it during the summer holidays?”)

Shortly after returning to Cambridge, Newton was elected to the Academic Council of Trinity College, and a statue of him still adorns the university church. He gave a course of lectures on color theory, in which he showed that color differences are explained by the main characteristics of the light wave (or, as they now say, wavelength) and that light has a corpuscular nature. He also designed a mirror telescope, an invention that brought him to the attention of the Royal Society. Long-term studies of light and colors were published in 1704 in his fundamental work "Optics" ( Optics).

Newton's advocacy of the "wrong" theory of light (at that time wave representations dominated) led to a conflict with Robert Hooke ( cm. Hooke's Law), head of the Royal Society. In response, Newton proposed a hypothesis that combined corpuscular and wave concepts of light. Hooke accused Newton of plagiarism and made claims of priority in this discovery. The conflict continued until Hooke's death in 1702, and made such a depressing impression on Newton that he withdrew from intellectual life for six. However, some psychologists of that time explain this by a nervous breakdown that worsened after the death of his mother.

In 1679, Newton returned to work and gained fame by investigating the trajectories of the planets and their satellites. As a result of these studies, also accompanied by disputes with Hooke about priority, the law of universal gravitation and Newton's laws of mechanics, as we now call them, were formulated. Newton summarized his research in the book "Mathematical Principles of Natural Philosophy" ( Philosophiae naturalis principia mathematica), presented to the Royal Society in 1686 and published a year later. This work, which marked the beginning of the then scientific revolution, brought Newton worldwide recognition.

His religious views, his strong adherence to Protestantism also attracted the attention of Newton to the attention of wide circles of the English intellectual elite, and especially the philosopher John Locke (John Locke, 1632-1704). Spending more and more time in London, Newton became involved in the political life of the capital and in 1696 was appointed superintendent of the Mint. Although this position was traditionally considered a sinecure, Newton approached his work with all seriousness, considering the re-minting of English coins as an effective measure in the fight against counterfeiters. Just at this time, Newton was involved in another priority dispute, this time with Gottfreid Leibniz (1646-1716), over the discovery of differential calculus. At the end of his life, Newton produced new editions of his major works, and also served as President of the Royal Society, while holding a lifetime position as Director of the Mint.

It is a question of the behavior of a body isolated from the influence of other bodies. The second law speaks of the exact opposite situation. It deals with cases where a body or several bodies act on a given one.

Both of these laws describe the behavior of one particular body. But at least two bodies always participate in the interaction. What will happen to both of these bodies? How to describe their interaction? Newton took up the analysis of this situation after formulating his first two laws. Let's do the same research.

Interaction of two bodies

We know that when interacting, both bodies act on each other. It does not happen that one body pushes another, and the second in response would not react in any way. This can happen among differently educated people, but not in nature.

We know that 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 noticeable.

However, if you try to kick a heavy iron ball, you will vividly feel this response. In fact, we kick a very, very heavy ball to 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.

The ratio of forces in the interaction between bodies

So from these considerations it can be seen that when two bodies interact, not only the first acts on the second with some force, but the second in response acts on the first also with some force. The question arises: how are these forces related? Which one is bigger, which one is smaller?

To do this, you need to make some measurements. You will need two dynamometers, but at home I can easily replace them with two steelyards. They measure weight, and weight is also a force, only expressed in units of mass in the case of a steelyard. Therefore, if you have two steelyards, then do the following.

Put one of them with a ring on something motionless, for example, on a nail in the wall, and connect the second to the first with hooks. And pull the ring of the second steelyard. Follow the readings of both instruments. Each of them will show the force with which the other steelyard acts on it.

And although we are only pulling for one of them, it turns out that the testimony of both, as at a confrontation, will coincide. It turns out that the force with which we act on the first steelyard with the second is equal to the force with which the first steelyard acts on the second.

Newton's third law: definition and formula

The force of action is equal to the force of reaction. This is the essence of Newton's third law. Its definition is as follows: the forces with which two bodies act on each other are equal in magnitude and opposite in direction. Newton's third law can be written as a formula:

F_1 = - F_2,

Where F_1 and F_2 are the forces of action on each other, respectively, of the first and second bodies.

The validity of Newton's third law has been confirmed by numerous experiments. This law is valid both for the case when one body pulls another, and for the case when the bodies repel each other. All bodies in the universe interact with each other, obeying this law.

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