Newton's first law describes. Newton's laws, law of universal gravitation, Hooke's law, friction force

1. Definition

Newton's third law reads: The interactions of two bodies on each other are equal and directed in opposite directions.

The essence of Newton's third law: for every action there is a reaction.

The difference between the 3rd law of Newton's 1st and 2nd laws. In Newton's first and second laws, only one body is considered. In the 3rd law, the interaction of two bodies with forces that are identical in absolute value and opposite in direction is considered. These forces are called interaction forces. They are directed along the same straight line and are attached to different bodies.

2. Formula of Newton's third law

From experience:

1. |a_1m_1|=|a_2m_2|
2. Accelerations of interacting bodies are directed along one straight line in opposite directions.

\overrightarrow(a)_1m_1=-\overrightarrow(a)_2m_2 or F1=-F2

• F1 is the force with which the first body acts on the second,
• F2- the force with which the second body acts on the first.

Examples: All bodies in the universe interact with each other if one body pulls on another. Or two bodies repel obeying this law.

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 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.

In this lesson, we will study Newton's third law, which describes the forces of interaction between two bodies. We also recall the basic information about Newton's first and second laws. In addition, we will recall the main experimental law of dynamics, consider the principle of relativity of Galileo. At the end of the lesson, we will learn how to apply Newton's third law when analyzing qualitative problems.

It is known 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.

Let's do an experiment. Let's take two dynamometers (Fig. 1). We will put one of them with a ring on something motionless, for example, on a nail in the wall, and we will connect the second with the first hooks. Pull the ring of the second dynamometer. Both devices will show the same tension force in modulus.

Rice. 1. Experience with dynamometers

Another example. Imagine that you and your friend are skateboarding, and the friend is riding the same skateboard as his brother (Fig. 2).

Rice. 2. Acquisition of acceleration through interaction

Your mass is, the mass of a friend with a brother is. If you repel each other, then you acquire accelerations that are directed along one straight line in opposite directions. The ratio of the masses of the participants in this process is inversely proportional to the ratio of the acceleration module.

Consequently:

According to Newton's second law:

The power with which you are affected by a friend with a brother

The force with which you act on a friend with a brother

Since the accelerations are opposite, then:

This equality expresses Newton's third law: bodies act on each other with forces that have the same modules and opposite directions (Fig. 3).

Rice. 3. Newton's third law

Basic experimental law of dynamics

When deriving Newton's third law, we saw that when two bodies interact, the ratio of two accelerations that the first and second body acquires is a constant value. Moreover, the ratio of these accelerations does not depend on the nature of the interaction (Fig. 4), therefore, it is determined by the bodies themselves, by some of its characteristics.

Rice. 4. The acceleration ratio does not depend on the nature of the interaction

This feature is called inertia. The measure of inertia is mass. Therefore, the ratio of accelerations acquired by bodies as a result of interaction with each other is equal to the inverse ratio of the masses of these bodies. This fact is illustrated by an experiment in which two carts with different masses () repel each other with the help of an elastic plate (Fig. 5). As a result of this interaction, a cart with a smaller mass will acquire a greater acceleration.

Rice. 5. Interaction of two bodies with different masses

Rice. 6. Basic experimental law of dynamics

The law that describes the ratio of body masses and accelerations acquired as a result of interaction is called the main experimental law of dynamics(Fig. 6).

A simpler formulation of Newton's third law sounds like this: the force of action is equal to the force of reaction.

The force of action and the force of reaction are always forces of the same nature. For example, in the previous experiment, the force of the first dynamometer on the second and the force of the second dynamometer on the first are elastic forces; the forces of action of one charged body on another and vice versa are forces of an electrical nature.

Each of the interaction forces is applied to different bodies. Consequently, the forces of interaction between bodies cannot compensate each other, although formally:

Rice. 7. The paradox of the resultant force

Let's demonstrate an experiment that confirms Newton's third law. Before the start of the experiment, the scales are in balance: the forces acting on the left are equal to all the forces acting on the right (Fig. 8).

Rice. 8. Forces acting on the left are equal to all forces acting on the right

Let's place the weight in a vessel with water, without touching its walls and bottom. A buoyant force acts on the weight from the side of the water, directed vertically upwards. But, according to Newton's third law, forces necessarily arise in pairs. This means that from the side of the small weight, the force of Archimedes, equal in absolute value, but oppositely directed, will begin to act on the water, which will “push” the vessel down. This means that the balance will be disturbed in the direction of the vessel with a weight (Fig. 9).

Rice. 9. The balance will be disturbed in the direction of the vessel with a weight

Thus, Newton's first law states: if the body is not affected by foreign bodies, then it is in a state of rest or uniform rectilinear motion relative to inertial frames of reference. From this it follows that the cause of the change in the speed of the body is the force. Newton's second law explains how a body moves under the action of a force. It establishes a quantitative relationship between acceleration and force.

In Newton's first and second laws, only one body is considered. The third law considers the interaction of two bodies with forces that are identical in modulus and opposite in direction. These forces are called interaction forces. They are directed along the same straight line and are attached to different bodies.

Some features of the interaction of bodies. Galileo's principle of relativity

Conclusions that arise when considering Newton's laws:

1. All forces in nature always arise in pairs (Fig. 10). If one force appeared, then a second force opposite to it will necessarily appear, acting from the side of the first body to the second. Both of these forces are of the same nature.

Rice. 10. All forces in nature always arise in pairs.

2. Each of the interaction forces is applied to different bodies, therefore, the interaction forces between the bodies cannot compensate each other.

3. Accelerations of bodies in different inertial frames of reference are the same. Movements, speeds change, but accelerations do not. The mass of bodies also does not depend on the choice of reference system, which means that the force will not depend on this either. That is, in inertial reference systems, all laws of mechanical motion are the same - this is Galileo's principle of relativity.

Analysis of a qualitative problem

1. Can a person lift himself along a rope thrown over a block if the other end of the rope is tied to the person’s belt, and the block is motionless?

Rice. 11. Illustration for the problem

At first glance, it seems that the force with which a person acts on the rope is equal to the force with which the rope acts on a person (Fig. 11). But the force is applied through the rope to the block, and the force is applied to the person, therefore, the person will be able to lift himself along this rope. Such a system is not closed. The "man - rope" system includes a block.

2. Can a person push a boat if he himself is in this boat and rests his hands on one of the sides?

Rice. 12. Illustration for the problem

In this problem, the “man-boat” system is closed (Fig. 12), that is, the force with which a person presses on the side of the boat is equal to the force with which the side of the boat acts on the person, but is directed in the opposite direction. There will be no movement.

3. Can a person pull himself out of the swamp by his hair?

Rice. 13. Illustration for the problem

The system is also closed. The force with which the hand acts on the hair is equal to the force with which the hair acts on the hand, but is directed in the opposite direction (Fig. 14). A man cannot pull himself out of the swamp by his hair.

Bibliography

1. G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics 10. - M .: Education, 2008.
2. A.P. Rymkevich. Physics. Problem book 10-11. - M.: Bustard, 2006.
3. O.Ya. Savchenko. Problems in physics. - M.: Nauka, 1988.
4. A.V. Peryshkin, V.V. Krauklis. Physics course. T. 1. - M .: State. uch.-ped. ed. min. education of the RSFSR, 1957.

1. Internet portal "raal100.narod.ru" ()
2. Internet portal "physics.ru" ()
3. Internet portal "bambookes.ru" ()
4. Internet portal "bourabai.kz" ()

Homework

1. Questions at the end of paragraph 26 (p. 70) - G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics 10 (see list of recommended reading)
2. Newton's third law was formulated by Newton himself as follows: "For an action there is always an equal and opposite reaction." Is there a physical difference between action and reaction? What are Newton's "action" and "reaction"?
3. Is the statement true: the speed of a body is determined by the force acting on it?
4. A mosquito hit the windshield of a moving car. Compare the forces acting on the mosquito and the car during the impact.

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.

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Remember!!!

• The dynamics of a material point is based on Newton's three laws.
• Newton's first law - law of inertia
• Under the body is meant a material point, the movement of which is considered in an inertial frame of reference.

1. Formulation

“There are such inertial frames of reference, in relation to which the body, if no other forces act on it (or the action of other forces is compensated), is at rest or moves uniformly and rectilinearly.”

2. Definition

Newton's first law - any material point (body) maintains a state of rest or uniform rectilinear motion until the impact from other bodies makes it change this state.

Newton's first law - the law of inertia (Galileo derived the law of inertia)

Law of inertia: If there are no external influences on the body, then this body maintains a state of rest or uniform rectilinear motion relative to the Earth.

Inertial Reference System (ISO)- a system that is either at rest or moves uniformly and rectilinearly relative to some other inertial system. Those. reference frame in which Newton's 1st law is satisfied.

• Body mass is a quantitative measure of its inertia. In SI, it is measured in kilograms.
• Strength- a quantitative measure of the interaction of bodies. Force is a vector quantity and is measured in newtons (N). A force that produces the same effect on a body as several simultaneously acting forces is called the resultant of these forces.