The law of physics for every action is a reaction. Newton's laws. Causes of friction force

When bodies interact, the forces arising between them are equal in absolute value and directed against each other. This is how Newton's third law works, which is important not only in mechanics, but also in grade 10 topics - electricity and magnetism.

Wording

Isaac Newton, in the mathematical principles of natural philosophy, introduced the principle now known as Newton's third law. According to this principle, for every action there is an equal and opposite reaction. In modern physics, it is formulated differently: material points act on each other with forces of the same nature, the absolute magnitudes of which are equal, but the directions are opposite.

The system of two bodies connected by a thread clearly describes the mechanism of the third law. If one of the bodies is pulled, then a tension force will arise in the thread. It acts in the same way in two opposite directions.

Rice. 1. Thread tension force.

Another example is an object lying on any surface. The object itself presses on the surface with a force $\vec P = m \vec g$, called the weight of the body. On the other hand, the surface acts on the object with the force $\vec N = m \vec g$, which is called the normal reaction force of the support.

Rice. 2. Body weight and ground reaction.

The force of gravity also acts mutually. Just as the Earth pulls on the Moon, the Moon pulls on the Earth. But since the acceleration of free fall for the Moon is much greater than for the Earth, outwardly everything looks as if only the Moon is falling.

Rice. 3. The attraction of bodies to each other.

The formula for Newton's third law is:

$F_(1,2) = – F_(2,1)$, where the minus sign indicates how the forces are directed.

It is valid for inertial reference systems and forces of any nature. So the forces of the Coulomb interaction between point charges are equal in absolute value and opposite in direction, and the Coulomb law itself in mathematical notation looks similar to the law of universal gravitation.

Addition to Newton's other laws

In a closed system, the forces of interaction between material points arise in pairs and balance each other, and the system itself is at rest. This addition to Newton's first and second laws leads to the law of conservation of momentum in a closed system.

If no external force acts on the system, then the total change in the momentum of its points is zero:

$(d \over dt)\sum\limits_(i=1)^n \vec p_n = 0$

Tasks

• The boy kicked the ball, giving it an acceleration equal to $2 m/s^2$. The mass of the ball is 300 grams. Find the strength of their interaction.

Solution

According to Newton's third law, the force with which the boy kicks the ball is equal to the force with which the ball kicks the boy:

$F_(1,2) = – F_(2,1) = F$, where F is the force of interaction.

$F = ma = (0.3 \cdot 2) = 0.6 N$

• The man in the water pushed himself off the side. The mass of a person is 60 kg, the acceleration he received is $1 m/s^2$. Find the force with which the side is repelled from the person. Ignore water resistance.

Solution

According to Newton's third law, the force with which the side acts on a person is equal to the force with which a person acts on the side.

$F_(1,2) = – F_(2,1)$

$F_(1,2) = ma = 60 N$

$F_(2,1) = - 60 N$

What have we learned?

During the lesson, the definition of Newton's third law was formulated, examples illustrating it were considered, a mathematical record of the law was given and an important addition was given, following from it - the conservation of momentum of a closed system. At the end of the lesson, the tasks are analyzed.

Topic quiz

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DEFINITION

Statement of Newton's first law. There are such frames of reference, in relation to which the body maintains a state of rest or a state of uniform rectilinear motion, if other bodies do not act on it or the action of other bodies is compensated.

Description of Newton's first law

For example, the ball on the thread hangs at rest, because the force of gravity is compensated by the tension in the thread.

Newton's first law is valid only in . For example, bodies at rest in the cabin of an aircraft that is moving uniformly can begin to move without any influence from other bodies if the aircraft begins to maneuver. In vehicles, when braking hard, passengers fall, although no one pushes them.

Newton's first law shows that the state of rest and the state do not require external influences for their maintenance. The property of a free body to keep its speed constant is called inertia. Therefore, Newton's first law is also called law of inertia. Uniform rectilinear motion of a free body is called inertial motion.

Newton's first law contains two important statements:

1. all bodies have the property of inertia;
2. inertial reference systems exist.

It should be remembered that in Newton's first law we are talking about bodies that can be taken for.

The law of inertia is by no means obvious, as it might seem at first glance. With his discovery, one long-standing misconception was done away with. Prior to this, for centuries it was believed that in the absence of external influences on the body, it can only be in a state of rest, that rest is, as it were, the natural state of the body. For a body to move at a constant speed, another body must act on it. Everyday experience seemed to confirm this: in order for a wagon to move at a constant speed, it must be pulled all the time by a horse; in order for the table to move along the floor, it must be continuously pulled or pushed, etc. Galileo Galilei was the first to point out that this is not true, that in the absence of external influence, the body can not only rest, but also move rectilinearly and uniformly. Rectilinear and uniform motion is, therefore, the same "natural" state of bodies as rest. In fact, Newton's first law says that there is no difference between a body at rest and uniform rectilinear motion.

It is impossible to test the law of inertia empirically, because it is impossible to create such conditions under which the body would be free from external influences. However, the opposite can always be traced. Anyway. When a body changes the speed or direction of its movement, you can always find the cause - the force that caused this change.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

In the school physics course, Newton's three laws are studied, which are the basis of classical mechanics. Today, every schoolchild is familiar with them, but in the time of the great scientist, such discoveries were considered revolutionary. Newton's laws will be briefly and clearly described below, they help not only to understand the basis of mechanics and the interaction of objects, but also help to write data as an equation.

For the first time, Issac Newton described the three laws in his work “The Mathematical Principles of Natural Philosophy” (1867), which detailed not only the scientist’s own conclusions, but all the knowledge on this topic discovered by other philosophers and mathematicians. Thus, labor became fundamental in the history of mechanics, and later of physics. It considers the movement and interaction of massive bodies.

Interesting to know! Isaac Newton was not only a talented physicist, mathematician and astronomer, but was also considered a genius in mechanics. He served as President of the Royal Society of London.

Each statement illuminates one of the spheres of interaction and movement of objects in nature, although the appeal to them was somewhat abolished by Newton, and they were accepted as points without a certain size (mathematical).

It was this simplification that made it possible to ignore natural physical phenomena: air resistance, friction, temperature, or other physical indicators of the object.

The data obtained could only be described in terms of time, mass, or length. It is because of this that Newton's formulations provide only suitable but approximate values ​​that cannot be used to describe the exact response of large or variable objects.

The movement of massive objects that are involved in the definitions is usually calculated in inertial, represented as a three-dimensional coordinate system, and at the same time it does not increase its speed and does not turn around its axis.

It is often called Newton's frame of reference, but at the same time, the scientist never created or used such a system, but used an irrational one. It is in this system that bodies can move as Newton describes it.

First Law

It's called the law of inertia. There is no practical formula for it, but there are several formulations. Physics textbooks offer the following formulation of Newton's first law: there are inertial frames of reference, in relation to which an object, if it is free from the influence of any forces (or they are instantly compensated), is completely at rest or moves in a straight line and with the same speed. What does this definition mean and how to understand it?

In simple terms, Newton's first law is explained as follows: any body, if it is not touched and not affected in any way, will remain constantly at rest, that is, it will stand in place forever. The same thing happens when it moves: it will move uniformly along a given trajectory indefinitely, until something affects it.

A similar statement was voiced by Galileo Galilei, but could not clarify and accurately describe this phenomenon. In this formulation, it is important to understand correctly what inertial frames of reference are. In very simple words, this is a system in which the action of this definition is performed.

In the world you can see a huge variety of such systems if you watch the movement:

• trains on a given section at the same speed;
• moons around the earth;
• ferris wheels in the park.

As an example, consider a skydiver who has already opened his parachute and is moving in a straight line and at the same time uniformly with respect to the surface of the Earth. The movement of a person will not stop until the earth's gravity is compensated by the movement and air resistance. As soon as this resistance decreases, the attraction will increase, which will lead to a change in the speed of the parachutist - his movement will become rectilinear and uniformly accelerated.

It is in relation to this formulation that there is an apple legend: Isaac was resting in the garden under an apple tree and was thinking about physical phenomena when a ripe apple fell off the tree and fell into the grass. It was the even fall that forced the scientist to study this issue and eventually give a scientific explanation for the movement of an object in a certain frame of reference.

Interesting to know! In addition to the three phenomena in mechanics, Isaac Newton also explained the motion of the Moon as a satellite of the Earth, created the corpuscular theory of light, and decomposed the rainbow into 7 colors.

Second law

This scientific rationale concerns not just the movement of objects in space, but their interaction with other objects and the results of this process.

The law says: an increase in the speed of an object with some constant mass in an inertial frame of reference is directly proportional to the force of impact and inversely proportional to the constant mass of the moving object.

Simply put, if there is a certain moving body, the mass of which does not change, and an extraneous force suddenly begins to act on it, then it will begin to accelerate. But the acceleration rate will directly depend on the impact and inversely depend on the mass of the moving object.

For example, consider a snowball that rolls down a mountain. If the ball is pushed in the direction of motion, then the acceleration of the ball will depend on the power of the impact: the larger it is, the greater the acceleration. But, the greater the mass of this ball, the less will be the acceleration. This phenomenon is described by a formula that takes into account acceleration, or "a", the resultant mass of all acting forces, or "F", as well as the mass of the object itself, or "m":

It should be clarified that this formula can exist only if the resultant of all forces is not less and not equal to zero. The law applies only to bodies that move at a speed less than light.

Useful video: Newton's first and second laws

third law

Many have heard the expression: "For every action there is a reaction." It is often used not only for general educational purposes, but also for educational purposes, explaining that there is a great one for every force.

This formulation came from another scientific statement by Isaac Newton, or rather, his third law, which explains the interaction of various forces in nature with respect to any body.

Newton's third law has the following definition: objects affect each other with forces of the same nature (connecting the masses of objects and directed along a straight line), which are equal in their modules and at the same time directed in different directions. This formulation sounds rather complicated, but it is easy to explain the law in simple words: each force has its own opposition or an equal force directed in the opposite direction.

It will be much easier to understand the meaning of the law if, as an example, we take a cannon from which shots are fired. The gun acts on the projectile with the same force with which the projectile acts on the gun. This will be confirmed by a slight movement of the cannon back during the shot, which will confirm the effect of the cannonball on the gun. If we take as an example the same apple that falls to the ground, it becomes clear that the apple and the earth act on each other with equal force.

The law also has a mathematical definition that uses the force of the first body (F1) and the second (F2):

The minus sign indicates that the force vectors of two different bodies are directed in opposite directions. At the same time, it is important to remember that these forces do not compensate each other, since they are directed relative to two bodies, and not one.

Useful video: Newton's 3 laws on the example of a bicycle

Conclusion

These laws of Newton briefly and clearly need to be known to every adult, since they are the basis of mechanics and operate in everyday life, despite the fact that these patterns are not observed under all conditions. They became axioms in classical mechanics, and on the basis of them the equations of motion and energy (conservation of momentum and conservation of mechanical energy) were created.

In contact with

In this section, we will consider Newton's third law, give detailed explanations, get acquainted with significant concepts, derive a formula. We will “dilute” the dry theory with examples and diagrams that will facilitate the assimilation of 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 the bodies interacting with each other are inversely related to the numerical values ​​of the accelerations. So the concept of body mass was introduced.

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

Statement of Newton's third law

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

m 1 a 1 → = - m 2 a 2 →

The minus sign in the formula appeared not by chance. It indicates that the accelerations of two interacting bodies 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 →, which arise during the interaction of bodies.

Consequently:

F 1 → = - F 2 →

So we got the formula of Newton's third law.

Definition 1

The forces with which bodies interact with each other are equal in absolute value 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.

The loader exerts an impact on a certain load with the same modulus of force with which this load acts on the loader. Forces are directed in opposite directions. Their physical nature is the same: the elastic forces of the rope. The acceleration that is reported to each of the bodies from 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 . one . 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

internal forces are forces that act on different parts of the same body.

If we consider a body in motion as a 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 equal to zero.

Example 2

Suppose 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 forces of interaction between these bodies. If we apply Newton's second law to each of these bodies separately, then we get: m 1 a 1 → = F 1 → , m 2 a 1 → = F 2 → + F → .

Newton's first law (law of inertia)

There are reference systems called inertial(hereinafter $-$ ISO), in which any body is at rest or moves uniformly and rectilinearly, if other bodies do not act on it or the action of these bodies is compensated. In such systems, the body will retain its original state of rest or uniform rectilinear motion until the action of other bodies causes it to change this state.

ISO $-$ is a special class of frames of reference, in which the accelerations of bodies are determined only by the real forces acting on the bodies, and not by the properties of frames of reference. As a consequence, if no forces act on the body or their action is compensated $\vec(R_())=\vec(F_1)+\vec(F_2)+\vec(F_3)+…=\vec(0_()) $, then the body either does not change its velocity $\vec(V_())=\vec(const)$ and moves uniformly rectilinearly or is at rest $\vec(V_())=\vec(0_())$.

There are an infinite number of inertial systems. The frame of reference associated with a train moving at a constant speed along a straight section of track is also an inertial frame (approximately), like the frame associated with the Earth. All IFRs form a class of systems that move uniformly and rectilinearly relative to each other. The accelerations of any body in different ISOs are the same.

How to establish that a given frame of reference is inertial? This can only be done by experience. Observations show that, with a very high degree of accuracy, the heliocentric frame can be considered as an inertial frame of reference, in which the origin of coordinates is associated with the Sun, and the axes are directed to certain "fixed" stars. Frames of reference rigidly connected with the Earth's surface, strictly speaking, are not inertial, since the Earth moves in orbit around the Sun and at the same time rotates around its own axis. However, when describing motions that do not have a global (i.e., worldwide) scale, reference systems associated with the Earth can be considered inertial with sufficient accuracy.

Frames of reference are also inertial if they move uniformly and rectilinearly relative to any inertial frame of reference.

Galileo established that it is impossible to determine whether this system is at rest or moving uniformly and rectilinearly by any mechanical experiments set inside an inertial frame of reference. This statement is called Galileo's principle of relativity, or the mechanical principle of relativity.

This principle was subsequently developed by A. Einstein and is one of the postulates of the special theory of relativity. IFRs play an extremely important role in physics, since, according to Einstein's principle of relativity, the mathematical expression of any law of physics has the same form in each IFR.

Non-inertial frame of reference$-$ reference system, which is not inertial. In these systems, the property described in the law of inertia does not work. In fact, any frame of reference moving relative to inertial with acceleration will be non-inertial.