An example of Newton's 3rd law. Examples of application of Newton's third law. Interaction of bodies: gravity, elasticity, friction. Examples of the manifestation of these forces in nature and technology

Ticket No. 2

Newton's laws. Examples of the manifestation of Newton's laws in nature and their
use in technology.

Let's look at an example. Hang the ball on a cord. The ball is at rest relative to the s.o. associated with the Earth. There are various bodies around the ball; it is clear that they do not influence the ball in the same way. If, for example, you move furniture in a room, the ball will remain at rest. But if you cut the cord, the ball will fall down, moving with acceleration. From experience it is clear that the ball is noticeably affected by 2 bodies: the Earth and the cord. But their combined influence ensured a state of rest for the ball. If the cord were removed, the ball would cease to be at rest and begin to move with acceleration towards the ground. If it were possible to remove the earth, the ball would move uniformly accelerated towards the cord.

This leads to the conclusion that the actions of two bodies—the cord and the earth—on the ball compensate each other. The example we have considered and many other examples allow us to draw the conclusion: the body is at rest and uniform relative to the ground if the forces acting on it are compensated. If a body is at rest, its acceleration is 0 and its speed is constant or equal to 0.

We know that motion and rest are relative. Relative to the s.o. associated with the Earth, the ball is at rest. Let's imagine that a car is moving past it with a constant speed, relative to the s.o. associated with the car, the ball is moving P.R.D., and is not at rest.

It turns out that when compensating for the actions of other things on the body, it can not only rest, but also move P.R.D.

These examples and others lead us to one of the basic laws of mechanics - 1 wow Newton's law:

There are such reference systems relative to which a translationally moving body maintains its speed constant if other bodies do not act on it (or the actions of other bodies equalize each other)

The very phenomenon of keeping the speed of a body constant is called inertia . Therefore, reference systems relative to which bodies move at a constant speed are called inertial (when compensating for external influences), and Newton’s first law is law of inertia .

We must, however, keep in mind that there are s.o.s that cannot be considered inertial. These are s.o. that move relative to the inertial s.o. with acceleration. These s.o. are called non-inertial.

If we observe accelerated movement of a body, then we can always prove its cause.

The reason for the acceleration of bodies - the action of other bodies on them. But in reality, every body influences and is influenced. There is a so-called interaction.

Experiments show that when two bodies interact, both bodies receive accelerations directed in opposite directions.

For two given interacting bodies, the ratio of the magnitudes of their accelerations is always the same.

But if we take different bodies, then this ratio will be equal. Consequently, each body has some inherent property, which determines the ratio of its acceleration to the acceleration of its “partner”.

This property is called inertia. When a body moves without acceleration, it is said to move by inertia. Therefore, a body that, during interaction, changed its speed to a smaller value is said to be more inert than another body whose speed changed to a larger value.

The property of inertia inherent in all bodies is that it takes some time to change the speed of the body.

In physics, the properties of the objects being studied are usually characterized by certain quantities. The property of inertia is characterized by a special quantity – mass.

That of two interacting bodies that receives less acceleration, i.e. more inert, has greater mass.

Weight – a measure of inertia, measured on a scale, measured in kilograms (kg)

a 1 /a 2 = m 2 /m 1

Halley's principle of relativity :

In all inertial s.o. under the same initial conditions, all mechanical processes proceed in the same way, i.e. subject to the same laws.

t 1 = t – time does not depend on r.s.

m 1 = m – mass does not depend on r.s.

a’ = V’-V’ 0 /t = V + U – V 0 + U/t = V – V 0 /t =a

3) Acceleration does not depend on the choice of S.k.

4) The force does not depend on the choice of S.K., but is determined only by the interaction of bodies.

That of the bodies is more inert, which has a greater mass. a 1 /a 2 = m 2 /m 1.

Bodies obey not only Newton's first law, but also others. We know that the acceleration of a body is always caused by the action of another body on it - the one with which it interacts.

In physics, the action of one body on another, which causes acceleration, is called by force . For example, the fall of a stone is caused by a force applied to it, the force of gravity.

Force - physical quantity. It can be expressed as a number.

P let's create an experience. We hang a load on a spring. Forces impart acceleration to bodies. But the bodies are at rest, which means a = -g, which means that the force is characterized not only by number, but also by direction - vector quantity .

What is strength? To answer this question, let us turn to experiment: the end of a spring was attached to a cart of known mass m, and the other was thrown over a block. The load moves downward under the influence of gravity and stretches the spring. A spring stretched to a certain length /\l acts on the cart and imparts acceleration to it. Which is equal to a. Let's repeat the experiment with two carts connected together so that their total mass is 2m. Let's measure the acceleration of the carts at the same elongation of the spring /\l (for this we will have to change the load on the thread). The acceleration will be equal to a/2. With 3 and 4 carts, the acceleration will be equal to a/3 and a/4. This means that the value am will be the same.

Newton's second law :

The force acting on a body is equal to the product of the mass of the body and the acceleration imparted by this force.

Acceleration co-directed with strength!

Several forces can act on a body. The acceleration in this case turns out to be the same as would be imparted to it by one single force equal to the geometric sum of all applied forces. This amount is usually called resultant or resulting by force.

A force equal to the geometric sum of all forces applied to a body is called the resultant or resultant force.

Like the first law, Newton's second law is valid only if the motion is considered relative to inertial frames of reference.

The unit of force is the force that imparts an acceleration of 1 m/s to a body weighing 1 kg. This unit is called newton .

Using the same experience, by measuring the accelerations of two bodies interacting in some way with each other, we can find the ratio of their masses according to the formula. To find the mass of an individual body, you need to take a body whose mass is taken as 1 - the standard of mass.

Then conduct an experiment in which a body whose mass is measured interacts with a body whose mass is known. Then both of them, the body and the standard, will receive accelerations that can be measured, then write down the ratio: a fl /a t = m t /m fl or m t = a fl *m fl /a t

Body mass determines the ratio of the acceleration modulus of the mass standard to the acceleration modulus of the body during their interaction. However, a more convenient method is weighing.The kilogram is taken as a unit of mass.

The actions of bodies on each other always have the nature of interaction. Each body acts on the other and imparts acceleration to it. The ratio of the acceleration modules is equal to the inverse ratio of their masses. The accelerations of the two bodies are directed in opposite directions.

m 1 a 1 = -m 2 a 2

since F = ma, then it can be written like this:

F 1 = F 2 – 3 th Newton's law.

Bodies act on each other with forces equal in magnitude and opposite in direction.

3 th Newton's law consists of 5 And statements:

1) Forces are born in pairs

2) The forces are equal in magnitude

3) Paired forces are directed in opposite directions

4) The resulting forces lie on the same straight line

Emerging forces of the same nature

Just like Newton's first and second laws, the third law is valid when motion is considered relative to inertial frames of reference.

Experiment: take two carts, an elastic steel plate is attached to one of them. Let's bend the plate and tie it with thread, and place the second cart next to the first so that it is in close contact with the other end of the plate. Let's cut the thread. The plate will accelerate, and we will see that both carts will begin to move. This means that both received accelerations. Since the masses of the carts are the same, the accelerations are also the same in magnitude. (V 1 = V 2; S 1 = S 2)

If we put some kind of load on one cart, we will see that the movements will no longer be the same. This means that their accelerations are not the same: the acceleration of the loaded cart is less, but its mass is greater. The product of mass and acceleration, that is, the force acting on each of the carts, is the same in absolute value.

The basic laws of classical mechanics were collected and published by Isaac Newton (1642-1727) in 1687. Three famous laws were included in a work 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.

(18th century epigram)

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

(20th century epigram)

Read what happened when Einstein came 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 reference systems, 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 forces of wheel friction and air resistance, then it will roll at the same speed for an infinitely long time.

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: in the absence of external forces, a body is either at rest or moving uniformly. Newton's great merit is that he was able to combine Galileo's principle of relativity, his own works and the works 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, actually do not 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 (it doesn’t matter whether we walk, ride a car or ride a bicycle), we need to overcome many forces: rolling friction and sliding friction, gravity, Coriolis force.

Newton's second law

Remember the example about the cart? At this moment we applied to her force! Intuitively, the cart will roll and soon stop. This means 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 a piano falls down from the roof of a house, then it moves uniformly under the influence of constant acceleration due to gravity g. Moreover, any arced object thrown out of a window on our planet will move with the same free fall acceleration.

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

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

If several forces act on a 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 body's momentum 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.

Example of a problem using Newton's laws

Here is a typical problem using Newton's laws. Its solution uses Newton's first and second laws.

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

Solution:

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

The paratrooper is affected by gravity and air resistance. The forces are directed in opposite directions.

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

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

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Here's another physical problem to help you understand the operation of Newton's third law.

A 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 magnitude and opposite in direction. The force that the mosquito exerts on the car is equal to the force that the car exerts on the mosquito.

Another thing is that the effects of these forces on bodies are very different due to differences in masses and accelerations.

Isaac Newton: myths and facts from life

At the time of 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 studied not only mechanics, but also optics, chemistry and other sciences, drew well and wrote poetry. It is not surprising that 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 man. He immortalized himself thanks to his discoveries, but he himself never sought fame and even tried to avoid it.
Myth. There is a legend according to which Newton had an epiphany 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 mentions of this appear only in the biographies of the scientist after his death, and the data of different biographers differs.
Fact. Newton studied and then worked a lot in Cambridge. Due to his duty, he needed to teach students several hours a week. Despite the scientist's recognized merits, 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 to the Cambridge Parliament. According to legend, during more than a year of sitting in parliament, the scientist, always absorbed in his thoughts, took the floor to speak only once. He asked to close the window because there was a draft.
Fact. It is unknown what the fate of the scientist and all modern science would have been like if he had listened to his mother and started farming on the family farm. It was only thanks to the persuasion of teachers and his uncle that young Isaac went on to study further instead of planting beets, spreading 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 right in front of your eyes and you just need to consider it. Well, if you have absolutely no time for independent studies, a specialized student service is always at your service!

At the very end, we suggest watching a video lesson 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 equal forces, as follows from the law of action and reaction. This means that the winner (tug of war) will be not the party that pulls harder, but the one that pushes harder against the Earth.

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

How can we explain that a horse is pulling a sleigh if, as follows from the law of action and reaction, the sleigh pulls the horse back with the same absolute force as the horse pulls the sleigh 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 road also act on both the sleigh and the horse (Fig. 72). The force from 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 sled begins to move 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, into which it rests with its feet, directed forward and greater than the force from the side of the sleigh. Therefore, the horse also begins to move forward. If you put a horse on 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 cart, when the horse, even pushing its legs, will not be able to create sufficient force to move the cart from its place. After the horse has moved the sled and uniform motion of the sled 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 influence of an electric locomotive. And here, as in the previous case, movement is possible only due to the fact that, in addition to the interaction forces between the pulling body (horse, electric locomotive) and the “trailer” (sleigh, train), the pulling body is acted upon by forces directed from the road or rails forward. On a perfectly slippery surface from which it is impossible to “push off”, neither a sleigh with a horse, nor a train, nor a car could move.

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

Newton's third law allows us to calculate recoil phenomenon when fired. Let's install a model of a cannon on the cart, operating with the help of steam (Fig. 73) or with the help of a spring. Let the cart be at rest at first. When fired, the “projectile” (cork) flies out in one direction, and the “gun” rolls back in the other. The recoil of the gun is the result of recoil. Recoil is nothing more than the reaction from the projectile, acting, according to Newton's third law, on the cannon throwing the projectile. According to this law, the force acting from the cannon on the projectile is always equal to the force acting from the projectile on the cannon and is directed opposite to it. Thus, the accelerations received by the gun and the projectile are directed in opposite directions, and in magnitude are inversely proportional to the masses of these bodies. As a result, the projectile and the gun will acquire oppositely directed velocities that are in the same ratio. Let us denote the speed received by the projectile by , and the speed received by the gun by , and the masses of these bodies will be denoted by and , respectively. Then

You can give as many examples of the interaction of bodies as you like. When you, being in one boat, begin to pull another by the rope, then your boat will definitely move forward (Fig. 1). By acting on the second boat, you force it to act on your boat.

If you kick a soccer ball, you will immediately feel a rebound effect on your foot. When two billiard balls collide, both balls change their speed, i.e., they receive acceleration. When cars bump into each other when forming a train, the buffer springs on both cars are compressed. 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 during direct contact of bodies. Place, for example, two strong magnets with opposite poles facing each other on a smooth table, and you will immediately find that the magnets 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, of course, in the frame of reference 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 Earth's gravity from 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 much from each other. If the interacting bodies differ significantly in mass, only the one with the smaller mass receives 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 between two bodies

Let us find out through experiment how the forces of interaction between two bodies are related. Rough measurements of 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, monitoring the readings of both dynamometers (Fig. 2).

We will see that for any stretch, the readings of both dynamometers will coincide; 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 fairly strong magnet and an iron bar and place them on the rollers to reduce friction on the table (Fig. 3). We attach identical soft springs to the magnet and the bar, which are hooked to the other ends 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 exactly the same. This means that both bodies are acted upon by forces equal in magnitude and opposite in direction from the springs:

\(\vec F_1 = -\vec F_2 \qquad (1)\)

Since the magnet is at rest, the force \(\vec F_2\) is equal in magnitude and opposite in direction to the force \(\vec F_4\) with which the block acts on it:

\(\vec F_1 = \vec F_4 \qquad (2)\)

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

\(\vec F_3 = -\vec F_4 \qquad (1)\)

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

3 experience. Two people stand 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 (“chooses”) the rope, A or IN or both together, the carts always start moving simultaneously 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 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 on the body A from the body side IN the force \(\vec F_A\) acts (Fig. 5), then simultaneously the body IN from the body side 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:

\(m_1 \cdot \vec a_1 = -m_2 \cdot \vec a_2 \qquad (6)\)

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 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 interaction forces, act on these bodies.)

This can be verified by the following simple experiment. Let’s put two carts of equal mass on smooth rails and on one of them we’ll attach a small electric motor, on the shaft of which a thread tied to the other cart can be wound, and on the other we’ll put a weight whose mass is equal to the mass of the engine (Fig. 6). When the engine is running, both carts rush with the same acceleration towards each other and travel 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 through such an experiment (Fig. 7). Two rollers of different masses connected by a thread are placed on a horizontal platform.

Experience will show that it is possible to find a position for the rollers when they do not move along it when the platform rotates. 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 are convinced that \(\frac(a_1)(a_2) = \frac(m_2)(m_1)\) at any speed of rotation of the platform .

Note

We must remember that the forces discussed 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 a particular body is at rest. For example, they claim that the chalk on the table is at rest supposedly because the force of gravity \(\vec F_t\), acting on the body, according to Newton’s third law, is equal in magnitude and opposite in direction to the elastic force \(\vec N\) (force support reaction) 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: acceleration is zero, therefore the sum of the forces acting on the body is zero. From Newton’s third law it only follows that the support reaction force \(\vec N\) is equal in magnitude 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 application of Newton's third law.

How can we explain that a horse is pulling a sleigh if, as follows from the law of action and reaction, the sleigh pulls the horse back with the same absolute force? F 2, with which horse pulls the sleigh forward (strength 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 road also act on both the sleigh and the horse (Fig. 9).

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

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

The recoil of the gun is the result of recoil. Recoil is nothing more than the reaction from the projectile, acting, according to Newton's third law, on the cannon throwing the projectile. According to this law, the force acting from the cannon on the projectile is always equal to the force acting from the projectile on the cannon and is directed opposite to it.

On the meaning of Newton's third law

The main significance of Newton's third law is discovered when studying the motion of a system of material points or a system of bodies. This law makes it possible to prove important theorems of 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 for real bodies with finite dimensions requires clarification and justification. In this formulation, this law cannot be applied to non-inertial frames of reference.

Literature

Physics: Mechanics. 10th grade: Textbook. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakisheva. – M.: Bustard, 2002. – 496 p.
Elementary physics textbook: Study guide. In 3 volumes / Ed. G.S. Landsberg: T. 1. Mechanics. Heat. Molecular physics - M.: FIZMATLIT, 2003. - 608 p.

In this section, we will look at Newton's third law, provide detailed explanations, get acquainted with significant concepts, and derive the formula. We will “dilute” the dry theory with examples and diagrams that will make it easier to understand the topic.

In one of the previous sections, we conducted experiments to measure the accelerations of two bodies after their interaction and obtained the following result: the masses of bodies interacting with each other are inversely related to the numerical values of the accelerations. This is how the concept of body weight was introduced.

m 1 m 2 = - a 2 a 1 or m 1 a 1 = - m 2 a 2

Formulation of Newton's third law

If we give this relationship a vector form, we get:

m 1 a 1 → = - m 2 a 2 →

The minus sign in the formula did not appear by chance. It indicates that the accelerations of two bodies that interact are always directed in opposite directions.

The factors that determine the appearance of acceleration, according to Newton’s second law, are the forces F 1 → = m 1 a 1 → and F 2 → = m 2 a 2 → that arise during the interaction of bodies.

Hence:

F 1 → = - F 2 →

This is how we got the formula of Newton's third law.

Definition 1

The forces with which bodies interact with each other are equal in magnitude and opposite in direction.

The nature of the forces arising during the interaction of bodies is the same. These forces are applied to different bodies, therefore they cannot balance each other. According to the rules of vector addition, we can add only those forces that are applied to one body.

Example 1

The loader exerts an impact on a certain load with the same magnitude force as this load exerts on the loader. The forces are directed in opposite directions. Their physical nature is the same: elastic forces of the rope. The acceleration imparted to each of the bodies in the example is inversely proportional to the mass of the bodies.

We have illustrated this example of the application of Newton's third law with a drawing.

Picture 1 . 9 . 1 . Newton's third law

F 1 → = - F 2 → · a 1 → = - m 2 m 1 a 2 →

The forces acting on the body can be external and internal. Let us introduce the definitions necessary to get acquainted with the topic of Newton's third law.

Definition 2

Inner forces- these are forces that act on different parts of the same body.

If we consider a body in motion as a single whole, then the acceleration of this body will be determined only by an external force. Newton's second law does not consider internal forces, since the sum of their vectors is zero.

Example 2

Let's assume that we have two bodies with masses m 1 and m 2. These bodies are rigidly connected to each other by a thread that has no weight and does not stretch. Both bodies move with the same acceleration a → under the influence of some external force F → . These two bodies move as one.

Internal forces that act between bodies obey Newton's third law: F 2 → = - F 1 →.

The movement of each of the bodies in the coupling depends on the interaction forces between these bodies. If we apply Newton's second law to each of these bodies separately, we get: m 1 a 1 → = F 1 → , m 2 a 1 → = F 2 → + F → .