Strength (physical quantity). We measure strength

The word "power" is so all-encompassing that to give it a clear concept is an almost impossible task. The variety from muscle strength to the strength of the mind does not cover the full range of concepts invested in it. Force considered as physical quantity, has clearly certain value and definition. The force formula defines a mathematical model: the dependence of force on the main parameters.

The history of force research includes the definition of dependence on parameters and the experimental proof of dependence.

Force in physics

Force is a measure of the interaction of bodies. The mutual action of bodies on each other fully describes the processes associated with a change in the speed or deformation of bodies.

As a physical quantity, force has a unit of measurement (in the SI system - Newton) and a device for measuring it - a dynamometer. The principle of operation of the force meter is based on comparing the force acting on the body with the elastic force of the dynamometer spring.

A force of 1 newton is taken to be the force under which a body of mass 1 kg changes its speed by 1 m in 1 second.

Strength is defined as:

• direction of action;
• application point;
• module, absolute value.

Describing the interaction, be sure to indicate these parameters.

Types of natural interactions: gravitational, electromagnetic, strong, weak. Gravitational gravity with its variety - gravity) exist due to the influence of gravitational fields surrounding any body that has mass. The study of gravitational fields has not been completed so far. It is not yet possible to find the source of the field.

A larger number of forces arise due to the electromagnetic interaction of the atoms that make up the substance.

pressure force

When a body interacts with the Earth, it exerts pressure on the surface. The force of which has the form: P = mg, is determined by the mass of the body (m). Acceleration free fall(g) has various meanings at different latitudes of the earth.

The vertical pressure force is equal in modulus and opposite in direction to the elastic force arising in the support. The force formula changes depending on the movement of the body.

Change in body weight

The action of a body on a support due to interaction with the Earth is often referred to as the weight of the body. Interestingly, the amount of body weight depends on the acceleration of movement in the vertical direction. In the case when the direction of acceleration is opposite to the acceleration of free fall, an increase in weight is observed. If the acceleration of the body coincides with the direction of free fall, then the weight of the body decreases. For example, while in an ascending elevator, at the beginning of the ascent, a person feels an increase in weight for a while. It is not necessary to assert that its mass is changing. At the same time, we share the concepts of "body weight" and its "mass".

Elastic force

When the shape of the body changes (its deformation), a force appears that tends to return the body to its original shape. This force was given the name "elastic force". It arises as a result of the electrical interaction of the particles that make up the body.

Consider the simplest deformation: tension and compression. Stretching is accompanied by an increase linear dimensions bodies, compression - their reduction. The value characterizing these processes is called body elongation. Let's denote it by "x". The elastic force formula is directly related to elongation. Each body subjected to deformation has its own geometric and physical parameters. The dependence of the elastic resistance to deformation on the properties of the body and the material from which it is made is determined by the coefficient of elasticity, let's call it stiffness (k).

The mathematical model of elastic interaction is described by Hooke's law.

The force arising from the deformation of the body is directed against the direction of displacement of individual parts of the body, is directly proportional to its elongation:

• F y = -kx (in vector notation).

The "-" sign indicates the opposite direction of deformation and force.

In scalar form negative sign is absent. The elastic force, the formula of which is as follows F y = kx, is used only for elastic deformations.

Interaction of a magnetic field with current

Influence magnetic field on the D.C. In this case, the force with which the magnetic field acts on a current-carrying conductor placed in it is called the Ampère force.

The interaction of the magnetic field with causes a force manifestation. The Ampere force, the formula of which is F = IBlsinα, depends on (B), the length of the active part of the conductor (l), (I) in the conductor and the angle between the direction of the current and the magnetic induction.

Thanks to the last dependence, it can be argued that the vector of the magnetic field can change when the conductor is rotated or the direction of the current changes. The left hand rule allows you to set the direction of action. If a left hand position in such a way that the magnetic induction vector enters the palm, four fingers are directed along the current in the conductor, then bent 90 ° thumb shows the direction of the magnetic field.

The use of this effect by mankind has been found, for example, in electric motors. The rotation of the rotor is caused by a magnetic field created by a powerful electromagnet. The force formula allows you to judge the possibility of changing the engine power. With an increase in current or field strength, the torque increases, which leads to an increase in motor power.

Particle Trajectories

The interaction of a magnetic field with a charge is widely used in mass spectrographs in the study of elementary particles.

The action of the field in this case causes the appearance of a force called the Lorentz force. When a charged particle moving at a certain speed enters a magnetic field, the formula of which has the form F = vBqsinα causes the particle to move in a circle.

In this mathematical model v is the particle velocity modulus, electric charge which - q, B is the magnetic induction of the field, α is the angle between the directions of speed and magnetic induction.

The particle moves in a circle (or an arc of a circle), since the force and speed are directed at an angle of 90 ° to each other. A change in the direction of the linear velocity causes an acceleration to appear.

The rule of the left hand, discussed above, also takes place when studying the Lorentz force: if the left hand is placed in such a way that the vector of magnetic induction enters the palm, four fingers extended in a line are directed along the speed of a positively charged particle, then bent by 90 ° the thumb will show the direction of the force.

Plasma issues

The interaction of a magnetic field and matter is used in cyclotrons. Problems related to laboratory study plasma, do not allow to contain it in closed vessels. High can only exist at high temperatures. Plasma can be kept in one place in space by means of magnetic fields, twisting the gas in the form of a ring. Controlled ones can also be studied by twisting high-temperature plasma into a filament using magnetic fields.

An example of the action of a magnetic field in vivo on ionized gas - aurora borealis. This majestic spectacle is observed beyond the Arctic Circle at an altitude of 100 km above the earth's surface. The mysterious colorful glow of gas could only be explained in the 20th century. The earth's magnetic field near the poles cannot prevent the solar wind from penetrating the atmosphere. The most active radiation directed along the lines of magnetic induction causes ionization of the atmosphere.

Phenomena associated with the movement of charge

Historically, the main quantity characterizing the flow of current in a conductor is called the current strength. Interestingly, this concept has nothing to do with force in physics. The strength of the current, the formula of which includes the charge flowing per unit of time through transverse section conductor looks like:

• I = q/t, where t is the flow time of charge q.

In fact, the current strength is the amount of charge. Its unit of measurement is Ampere (A), unlike N.

Determination of the work of a force

Force action on a substance is accompanied by the performance of work. The work of a force is a physical quantity numerically equal to the product of the force and the displacement passed under its action, and the cosine of the angle between the directions of the force and displacement.

The desired work of the force, the formula of which is A = FScosα, includes the magnitude of the force.

The action of the body is accompanied by a change in the speed of the body or deformation, which indicates simultaneous changes in energy. The work done by a force is directly related to its magnitude.

How is strength measured? In what units is force measured?

Back in school, we taught that the concept of strength Introduced into physics by a man who had an apple fall on his head. By the way, it fell due to gravityquot ;. Newton seems to have been his last name. So he called the unit of measurement of force. Although he could have called it an apple, it still hit him on the head!

According to the International System of Units (SI), force is measured in Newtons.

According to Technical System Units, force is measured in ton-force, kilogram-force, gram-force, etc.

According to the CGS System of Units, the unit of force is the dyne.

In the USSR, for some time, to measure force, they used such a unit of measurement as the wall.

In addition, in physics there are so-called natural units, according to which the force is measured in Planck forces.

• • What is the strength in, brother?
  • Newtons bro...

  (Physics stopped being taught at school?)

Force is one of the most widely known concepts in physics. Under force is understood as a quantity that is a measure of the impact on the body from other bodies and various physical processes.

With the help of force, not only the movement of objects in space can occur, but also their deformation.

The action of any force on a body obeys Newton's 3 laws.

Unit of measurement force in the international system of units SI is newton. It is marked with the letter H.

1N is a force, under the influence of which on a physical body with a mass of 1 kg, this body acquires an acceleration equal to 1 ms.

An instrument used to measure force is dynamometer.

It is also worth noting that a number of physical quantities are measured in other units.

For example:

Current strength is measured in Amps.

The intensity of light is measured in Candela.

In honor of the outstanding scientist and physicist Isaac Newton, who did a lot of research into the nature of the existence of processes that affect the speed of a body. Therefore, in physics it is customary to measure the force in newtons(1 N).

In physics, such a concept as force measured in newtons. They gave the name Newtons, in honor of the famous and outstanding physicist named Isaac Newton. In physics, there are 3 Newton's laws. The unit of force is also called the newton.

Force is measured in newtons. The unit of force is 1 Newton (1 N). The very name of the unit of measurement of force comes from the name of the famous scientist, whose name was Isaac Newton. He created the 3 laws of classical mechanics, which are called Newton's 1st, 2nd and 3rd laws. In the SI system, the unit of force is called the Newton (N). Latin the force is denoted by newton (N). Previously, when there was no SI system yet, the unit for measuring force was called the dyne, which was formed from the carrier of one instrument for measuring force, which was called a dynamometer.

Force in the system of international units (SI) is measured in Newtons (N). According to Newton's second law, the force is equal to the product of the body's mass and its acceleration, respectively, Newton (N) \u003d KG x M / C 2. (KILOGRAM MULTIPLY BY METER, DIVIDE BY SECOND IN SQUARE).

We are all accustomed in life to use the word power in comparative characteristic talking men stronger than women, the tractor is stronger than the car, the lion is stronger than the antelope.

Force in physics is defined as a measure of the change in the speed of a body that occurs when bodies interact. If force is a measure, and we can compare the application of different forces, then it is a physical quantity that can be measured. In what units is force measured?

Force units

In honor of the English physicist Isaac Newton, who did tremendous research into the nature of existence and use various kinds force, the unit of force in physics is 1 newton (1 N). What is a force of 1 N? In physics, one does not simply choose units of measurement, but makes a special agreement with those units that have already been adopted.

We know from experience and experiments that if a body is at rest and a force acts on it, then the body under the influence of this force changes its speed. Accordingly, to measure the force, a unit was chosen that would characterize the change in the speed of the body. And do not forget that there is also the mass of the body, since it is known that with the same force the impact on various items will be different. We can throw the ball far, but the cobblestone will fly away a much shorter distance. That is, taking into account all the factors, we come to the definition that a force of 1 N will be applied to the body if a body with a mass of 1 kg under the influence of this force changes its speed by 1 m / s in 1 second.

Gravity unit

We are also interested in the unit of gravity. Since we know that the Earth attracts to itself all the bodies on its surface, then there is a force of attraction and it can be measured. And again, we know that the force of attraction depends on the mass of the body. The greater the mass of the body, the stronger the Earth attracts it. It has been experimentally established that The force of gravity acting on a body of mass 102 grams is 1 N. And 102 grams is approximately one tenth of a kilogram. And to be more precise, if 1 kg is divided into 9.8 parts, then we will just get approximately 102 grams.

If a force of 1 N acts on a body weighing 102 grams, then a force of 9.8 N acts on a body weighing 1 kg. The acceleration of free fall is denoted by the letter g. And g is 9.8 N/kg. This is the force that acts on a body of mass 1 kg, accelerating it every second by 1 m / s. It turns out that the body falling from high altitude, during the flight is gaining a very high speed. Why then do snowflakes and raindrops fall quite calmly? They have a very small mass, and the earth pulls them towards itself very weakly. And the air resistance for them is quite large, so they fly to the Earth with not very high, rather the same speed. But meteorites, for example, when approaching the Earth, gain very high speed and upon landing, a decent explosion is formed, which depends on the size and mass of the meteorite, respectively.

Today we will talk about the unit of measurement of luminous intensity. This article will reveal to readers the properties of photons, which will allow them to determine why light comes in different brightnesses.

Particle or wave?

At the beginning of the twentieth century, scientists were puzzled by the behavior of light quanta - photons. On the one hand, interference and diffraction spoke of their wave essence. Therefore, light was characterized by properties such as frequency, wavelength, and amplitude. On the other hand, they convinced the scientific community that photons transfer momentum to surfaces. This would be impossible if the particles did not have mass. Thus, physicists had to admit: electromagnetic radiation is both a wave and a material object.

Photon energy

As Einstein proved, mass is energy. This fact proves our central luminary, the Sun. A thermonuclear reaction turns a mass of highly compressed gas into pure energy. But how to determine the power of the emitted radiation? Why in the morning, for example, is the luminous intensity of the sun lower than at noon? The characteristics described in the previous paragraph are interconnected by specific relationships. And they all point to the energy that electromagnetic radiation carries. This value changes in big side at:

• decrease in wavelength;
• increasing frequency.

What is the energy of electromagnetic radiation?

A photon is different from other particles. Its mass, and therefore its energy, exists only as long as it moves through space. When colliding with an obstacle, a quantum of light increases it internal energy or gives it a kinetic momentum. But the photon itself ceases to exist. Depending on what exactly acts as an obstacle, various changes occur.

1. If the obstacle is solid, then most often the light heats it up. The following scenarios are also possible: the photon changes the direction of motion, stimulates chemical reaction or causes one of the electrons to leave its orbit and go to another state (photoelectric effect).
2. If the obstacle is a single molecule, for example, from a rarefied gas cloud into open space, then the photon makes all its bonds oscillate more strongly.
3. If the obstacle is a massive body (for example, a star or even a galaxy), then the light is distorted and changes the direction of motion. This effect is based on the ability to "look" into the distant past of the cosmos.

Science and Humanity

Scientific data often seem to be something abstract, inapplicable to life. This also happens with the characteristics of light. If a we are talking about experimenting or measuring the radiation of stars, scientists need to know the absolute values ​​(they are called photometric). These concepts are usually expressed in terms of energy and power. Recall that power refers to the rate of change of energy per unit of time, and in general it shows the amount of work that the system can produce. But man is limited in his ability to sense reality. For example, the skin feels heat, but the eye does not see the photon. infrared radiation. The same problem with units of luminous intensity: the power that radiation actually shows is different from the power that the human eye can perceive.

Spectral sensitivity of the human eye

We remind you that the discussion below will focus on average indicators. All people are different. Some do not perceive individual colors at all (colorblind). For others, the culture of color does not coincide with the generally accepted scientific point vision. For example, the Japanese do not distinguish between green and blue, and the British - blue and blue. In these languages different colors denoted by one word.

The unit of luminous intensity depends on the spectral sensitivity of the average human eye. The maximum daylight falls on a photon with a wavelength of 555 nanometers. This means that in the light of the sun a person sees best. green color. Night vision maximum is a photon with a wavelength of 507 nanometers. Therefore, under the moon, people see blue objects better. At dusk, everything depends on the lighting: the better it is, the more “green” the maximum color that a person perceives becomes.

The structure of the human eye

Almost always, when it comes to vision, we say what the eye sees. This is an incorrect statement, because the brain perceives first of all. The eye is only an instrument that conveys information about luminous flux to the main computer. And, like any tool, the entire color perception system has its limitations.

In the human retina there are two various types cells - cones and rods. The former are responsible for daytime vision and perceive colors better. The latter provide night vision, thanks to the sticks, a person distinguishes between light and shadow. But they do not perceive colors well. The sticks are also more sensitive to movement. That is why, if a person walks through a moonlit park or forest, he notices every swaying of the branches, every breath of the wind.

The evolutionary reason for this separation is simple: we have one sun. The moon shines by reflected light, which means that its spectrum does not differ much from the spectrum of the central luminary. Therefore, the day is divided into two parts - illuminated and dark. If people lived in a system of two or three stars, then our vision would probably have more components, each of which was adapted to the spectrum of one luminary.

I must say, on our planet there are creatures whose eyesight is different from human. Desert dwellers, for example, detect infrared light with their eyes. Some fish can see near ultraviolet, as this radiation penetrates the deepest into the water column. Our pet cats and dogs perceive colors differently, and their spectrum is reduced: they are better adapted to chiaroscuro.

But people are all different, as we mentioned above. Some representatives of mankind see near infrared light. This is not to say that they would not need thermal cameras, but they are able to perceive slightly redder shades than most. Others have developed the ultraviolet part of the spectrum. Such a case is described, for example, in the film "Planet Ka-Pax". The protagonist claims that he came from another star system. The examination revealed that he had the ability to see ultraviolet radiation.

Does this prove that Prot is an alien? No. Some people can do it. In addition, the near ultraviolet is closely adjacent to the visible spectrum. No wonder some people take a little more. But Superman is definitely not from Earth: the X-ray spectrum is too far from the visible for such vision to be explained from a human point of view.

Absolute and relative units for determining the luminous flux

Spectral sensitivity independent quantity that indicates the flux of light in known direction, is called "candela". already with a more "human" attitude is pronounced the same way. The difference is only in the mathematical designation of these concepts: the absolute value has a subscript "e", relative to the human eye - "υ". But do not forget that the sizes of these categories will vary greatly. This must be taken into account when solving real problems.

Enumeration and comparison of absolute and relative values

To understand what the power of light is measured in, it is necessary to compare the "absolute" and "human" values. On the right are purely physical concepts. On the left are the values ​​into which they turn when passing through the system of the human eye.

1. The power of radiation becomes the power of light. Concepts are measured in candela.
2. Energy brightness turns into brightness. The values ​​are expressed in candela per square metre.

Surely the reader saw familiar words here. Many times in their lives, people say: "Very bright sun, let's go into the shade" or "Make the monitor brighter, the movie is too gloomy and dark." We hope the article will slightly clarify where this concept came from, as well as what the unit of luminous intensity is called.

Features of the concept of "candela"

We have already mentioned this term above. We also explained why the same word is called absolutely different concepts physics related to power electromagnetic radiation. So, the unit of measure for the intensity of light is called the candela. But what is it equal to? One candela is the intensity of light in a known direction from a source that emits strictly monochromatic radiation with a frequency of 5.4 * 10 14, and the energy force of the source in this direction is 1/683 watts per unit solid angle. The reader can easily convert frequency into wavelength, the formula is very easy. We will prompt: the result lies in visible area.

The unit of measurement for the intensity of light is called the "candela" for a reason. Those who know English language, remember that candle is a candle. Previously, many areas human activity measured in natural parameters, for example, horsepower, millimeters of mercury. So it is not surprising that the unit of measurement for the intensity of light is the candela, one candle. Only a candle is very peculiar: with a strictly specified wavelength, and producing a specific number of photons per second.

If the body is accelerating, then something acts on it. But how to find this "something"? For example, what kind of forces act on a body near the surface of the earth? This is the force of gravity directed vertically downward, proportional to the mass of the body and for heights much smaller than the radius of the earth $(\large R)$, almost independent of the height; it is equal to

$(\large F = \dfrac (G \cdot m \cdot M)(R^2) = m \cdot g )$

$(\large g = \dfrac (G \cdot M)(R^2) )$

so-called acceleration of gravity. In the horizontal direction, the body will move at a constant speed, but the movement in the vertical direction according to Newton's second law:

$(\large m \cdot g = m \cdot \left (\dfrac (d^2 \cdot x)(d \cdot t^2) \right) )$

after canceling $(\large m)$ we get that the acceleration in the direction $(\large x)$ is constant and equals $(\large g)$. This is the well-known motion of a freely falling body, which is described by the equations

$(\large v_x = v_0 + g \cdot t)$

$(\large x = x_0 + x_0 \cdot t + \dfrac (1)(2) \cdot g \cdot t^2)$

How is strength measured?

In all textbooks and smart books, it is customary to express force in Newtons, but except in the models that physicists operate with, Newtons are not used anywhere. This is extremely inconvenient.

newton newton (N) - derived unit of force in international system units (SI).
Based on Newton's second law, the unit newton is defined as the force that changes the speed of a body with a mass of one kilogram by 1 meter per second in one second in the direction of the force.

Thus, 1 N \u003d 1 kg m / s².

Kilogram-force (kgf or kg) - gravitational metric unit of force, equal to strength, which acts on a body with a mass of one kilogram in the gravitational field of the earth. Therefore, by definition, the kilogram-force is equal to 9.80665 N. The kilogram-force is convenient in that its value is equal to the weight of a body with a mass of 1 kg.
1 kgf \u003d 9.80665 newtons (approximately ≈ 10 N)
1 N ≈ 0.10197162 kgf ≈ 0.1 kgf

1 N = 1 kg x 1m/s2.

Law of gravitation

Every object in the universe is attracted to every other object with a force proportional to their masses and inversely proportional to the square of the distance between them.

$(\large F = G \cdot \dfrac (m \cdot M)(R^2))$

It can be added that any body reacts to the force applied to it by acceleration in the direction of this force, in magnitude inversely proportional to the mass of the body.

$(\large G)$ is the gravitational constant

$(\large M)$ is the mass of the earth

$(\large R)$ — earth radius

$(\large G = 6.67 \cdot (10^(-11)) \left (\dfrac (m^3)(kg \cdot (sec)^2) \right) )$

$(\large M = 5.97 \cdot (10^(24)) \left (kg \right) )$

$(\large R = 6.37 \cdot (10^(6)) \left (m \right) )$

In the framework of classical mechanics, the gravitational interaction is described by Newton's law of universal gravitation, according to which the force of gravitational attraction between two bodies of mass $(\large m_1)$ and $(\large m_2)$ separated by a distance $(\large R)$ is

$(\large F = -G \cdot \dfrac (m_1 \cdot m_2)(R^2))$

Here $(\large G)$ is the gravitational constant equal to $(\large 6.673 \cdot (10^(-11)) m^3 / \left (kg \cdot (sec)^2 \right) )$. The minus sign means that the force acting on the test body is always directed along the radius vector from the test body to the source of the gravitational field, i.e. gravitational interaction always leads to the attraction of bodies.
The gravity field is potential. This means that it is possible to introduce the potential energy of the gravitational attraction of a pair of bodies, and this energy will not change after moving the bodies along a closed contour. The potentiality of the gravitational field entails the law of conservation of the sum of kinetic and potential energy, which, when studying the motion of bodies in a gravitational field, often greatly simplifies the solution.
In the framework of Newtonian mechanics, the gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space, the gravitational potential and force depend only on the position of the body in this moment time.

Heavier - Lighter

The weight of a body $(\large P)$ is expressed as the product of its mass $(\large m)$ and the acceleration of gravity $(\large g)$.

$(\large P = m \cdot g)$

When on earth the body becomes lighter (presses less on the scales), this comes from a decrease in masses. On the moon, everything is different, the decrease in weight is caused by a change in another factor - $(\large g)$, since the acceleration of gravity on the surface of the moon is six times less than on the earth.

mass of earth = $(\large 5.9736 \cdot (10^(24))\ kg )$

moon mass = $(\large 7.3477 \cdot (10^(22))\ kg )$

gravitational acceleration on Earth = $(\large 9.81\ m / c^2 )$

gravitational acceleration on the moon = $(\large 1.62 \ m / c^2 )$

As a result, the product $(\large m \cdot g )$, and hence the weight, is reduced by a factor of 6.

But it is impossible to designate both these phenomena with the same expression "make it easier". On the moon, bodies do not become lighter, but only less rapidly they fall "less falling"))).

Vector and scalar quantities

A vector quantity (for example, a force applied to a body), in addition to its value (modulus), is also characterized by its direction. A scalar quantity (for example, length) is characterized only by a value. All classical laws of mechanics are formulated for vector quantities.

Picture 1.

On fig. 1 pictured various options location of the vector $( \large \overrightarrow(F))$ and its projections $( \large F_x)$ and $( \large F_y)$ on the axes $( \large X)$ and $( \large Y)$ respectively:

• A. the quantities $( \large F_x)$ and $( \large F_y)$ are non-zero and positive
• b. the quantities $( \large F_x)$ and $( \large F_y)$ are non-zero, while $(\large F_y)$ is positive, and $(\large F_x)$ is negative, because the vector $(\large \overrightarrow(F))$ is directed in the direction opposite to the direction of the axis $(\large X)$
• C.$(\large F_y)$ is a positive non-zero value, $(\large F_x)$ is equal to zero, because the vector $(\large \overrightarrow(F))$ is directed perpendicular to the axis $(\large X)$

Moment of power

Moment of force called the vector product of the radius vector, drawn from the axis of rotation to the point of application of the force, by the vector of this force. Those. according to classical definition moment of force is a vector quantity. Within the framework of our task, this definition can be simplified to the following: the moment of force $(\large \overrightarrow(F))$ applied to a point with coordinate $(\large x_F)$, relative to the axis located at the point $(\large x_0 )$ is a scalar value equal to the product of the modulus of the force $(\large \overrightarrow(F))$ and the arm of the force — $(\large \left | x_F - x_0 \right |)$. And the sign of this scalar value depends on the direction of the force: if it rotates the object clockwise, then the sign is plus, if it is against, then minus.

It is important to understand that we can choose the axis arbitrarily - if the body does not rotate, then the sum of the moments of forces about any axis is zero. The second important note is that if a force is applied to a point through which an axis passes, then the moment of this force relative to this axis zero(since the arm of the force will be zero).

Let's illustrate the above with an example, in Fig.2. Let us assume that the system shown in Fig. 2 is in balance. Consider the support on which the loads are placed. Three forces act on it: $(\large \overrightarrow(N_1),\ \overrightarrow(N_2),\ \overrightarrow(N),)$ points of application of these forces BUT, AT and With respectively. The figure also contains the forces $(\large \overrightarrow(N_(1)^(gr)),\ \overrightarrow(N_2^(gr)))$. These forces are applied to the loads, and according to Newton's 3rd law

$(\large \overrightarrow(N_(1)) = - \overrightarrow(N_(1)^(gr)))$

$(\large \overrightarrow(N_(2)) = - \overrightarrow(N_(2)^(gr)))$

Now consider the condition of equality of the moments of forces acting on the support, relative to the axis passing through the point BUT(and, as we agreed earlier, perpendicular to the plane of the figure):

$(\large N \cdot l_1 - N_2 \cdot \left (l_1 +l_2 \right) = 0)$

Please note that the moment of the force $(\large \overrightarrow(N_1))$ was not included in the equation, since the arm of this force with respect to the considered axis is equal to $(\large 0)$. If, for some reason, we want to choose an axis passing through the point With, then the condition of equality of the moments of forces will look like this:

$(\large N_1 \cdot l_1 - N_2 \cdot l_2 = 0)$

It can be shown that, from a mathematical point of view, the last two equations are equivalent.

Center of gravity

center of gravity of a mechanical system is a point relative to which the total moment of gravity acting on the system is equal to zero.

Center of mass

The center of mass point is remarkable in that if a great many forces act on the particles that form the body (whether it is solid or liquid, a cluster of stars or something else) (only external forces are meant, since all internal forces compensate each other), then the resulting force accelerates this point as if it contained the entire mass of the body $(\large m)$.

The position of the center of mass is determined by the equation:

$(\large R_(c.m.) = \frac(\sum m_i\, r_i)(\sum m_i))$

This is a vector equation, i.e. actually three equations, one for each of the three directions. But consider only the $(\large x)$ direction. What does the following equality mean?

$(\large X_(c.m.) = \frac(\sum m_i\, x_i)(\sum m_i))$

Suppose the body is divided into small pieces with the same mass $(\large m)$, and the total mass of the body will be equal to the number of such pieces $(\large N)$ multiplied by the mass of one piece, for example 1 gram. Then this equation means that you need to take the coordinates $(\large x)$ of all the pieces, add them up and divide the result by the number of pieces. In other words, if the masses of the pieces are equal, then $(\large X_(c.m.))$ will simply be the arithmetic average of the $(\large x)$ coordinates of all the pieces.

Mass and Density

Mass is a fundamental physical quantity. Mass characterizes several properties of the body at once and in itself has a number of important properties.

• Mass is a measure of the substance contained in the body.
• Mass is a measure of the inertia of a body. Inertia is the property of a body to keep its speed unchanged (in inertial system reference), when external influences are absent or compensate each other. In the presence of external influences, the inertia of the body is manifested in the fact that its speed does not change instantly, but gradually, and the slower, the greater the inertia (ie mass) of the body. For example, if a billiard ball and a bus move at the same speed and are braked by the same force, then it takes much less time for the ball to stop than for the bus to stop.
• The masses of bodies are the cause of their gravitational attraction to each other (see the section "Gravity").
• The mass of a body is equal to the sum of the masses of its parts. This is the so-called mass additivity. Additivity makes it possible to use a standard of 1 kg to measure the mass.
• The mass of an isolated system of bodies does not change with time (the law of conservation of mass).
• The mass of a body does not depend on the speed of its movement. Mass does not change when moving from one frame of reference to another.
• Density of a homogeneous body is the ratio of the mass of the body to its volume:

$(\large p = \dfrac (m)(V) )$

Density does not depend on the geometric properties of the body (shape, volume) and is a characteristic of the substance of the body. Density various substances presented in the reference tables. It is advisable to remember the density of water: 1000 kg/m3.

Newton's second and third laws

The interaction of bodies can be described using the concept of force. Force is a vector quantity, which is a measure of the impact of one body on another.
Being a vector, force is characterized by its modulus (absolute value) and direction in space. In addition, the point of application of force is important: the same force in magnitude and direction applied in different points body can have different effects. So, if you take the rim of a bicycle wheel and pull it tangentially to the rim, the wheel will start to rotate. If you drag along the radius, there will be no rotation.

Newton's second law

The product of the body mass and the acceleration vector is the resultant of all forces applied to the body:

$(\large m \cdot \overrightarrow(a) = \overrightarrow(F) )$

Newton's second law relates the vectors of acceleration and force. This means that the following assertions are true.

1. $(\large m \cdot a = F)$, where $(\large a)$ is the acceleration modulus, $(\large F)$ is the resultant force modulus.
2. The acceleration vector has the same direction as the resultant force vector, since the mass of the body is positive.

Newton's third law

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

Superposition principle

Experience shows that if several other bodies act on a given body, then the corresponding forces add up as vectors. More precisely, the principle of superposition is valid.
The principle of superposition of forces. Let forces act on the body$(\large \overrightarrow(F_1), \overrightarrow(F_2),\ \ldots \overrightarrow(F_n))$ If we replace them with one force$(\large \overrightarrow(F) = \overrightarrow(F_1) + \overrightarrow(F_2) \ldots + \overrightarrow(F_n))$ , then the effect will not change.
The force $(\large \overrightarrow(F))$ is called resultant forces $(\large \overrightarrow(F_1), \overrightarrow(F_2),\ \ldots \overrightarrow(F_n))$ or resulting by force.

Freight forwarder or carrier? Three secrets and international cargo transportation

Forwarder or carrier: which one to choose? If the carrier is good and the forwarder is bad, then the first one. If the carrier is bad, and the forwarder is good, then the second one. Such a choice is simple. But how to decide when both applicants are good? How to choose from two seemingly equivalent options? The problem is that these options are not equal.

Scary stories of international transportation

BETWEEN THE HAMMER AND THE ANVIL.

It is not easy to live between a transportation customer and a very cunningly economical cargo owner. One day we received an order. Freight for three kopecks, additional terms on two sheets, the collection is called .... Loading on Wednesday. The car is already in place on Tuesday, and by lunchtime the next day, the warehouse begins to slowly throw into the trailer everything that your forwarder has collected for his customers-recipients.

ENCHANTED PLACE - PTO KOZLOVICHI.

According to legend and experience, everyone who transported goods from Europe by road knows how scary place is PTO Kozlovichi, Brest customs. What chaos the Belarusian customs officers are doing, they find fault in every possible way and tear at exorbitant prices. And it is true. But not all...

HOW UNDER THE NEW YEAR WE CARRIED DRY MILK.

Groupage loading at a consolidation warehouse in Germany. One of the cargoes is powdered milk from Italy, the delivery of which was ordered by the Forwarder .... A classic example of the work of the forwarder-"transmitter" (he does not delve into anything, he only passes along the chain).

Documents for international transport

International road transport of goods is very organized and bureaucratic, a consequence - for the implementation of international road transport loads, a bunch of unified documents are used. It doesn’t matter if it’s a customs carrier or an ordinary one – he won’t go without documents. Although it is not very exciting, we have tried to simply state the purpose of these documents and the meaning that they have. They gave an example of filling in TIR, CMR, T1, EX1, Invoice, Packing List...

Calculation of axle load for trucking

Purpose - to study the possibility of redistributing loads on the axles of the tractor and semi-trailer when changing the location of the cargo in the semi-trailer. And the application of this knowledge in practice.

In the system we are considering, there are 3 objects: a tractor $(T)$, a semi-trailer $(\large ((p.p.)))$ and a cargo $(\large (gr))$. All variables related to each of these objects will be superscripted $T$, $(\large (p.p.))$ and $(\large (gr))$ respectively. For example, the unladen weight of a tractor would be denoted as $m^(T)$.

Why don't you eat mushrooms? Customs exhaled sadness.

What is happening in the international road transport market? The Federal Customs Service of the Russian Federation has banned the issuance of TIR Carnets without additional guarantees for several federal districts. And she notified that from December 1 of this year she would completely terminate the contract with the IRU as inappropriate Customs Union and makes non-childish financial claims.
IRU responded: “The explanations of the Russian Federal Customs Service regarding the alleged debt of ASMAP in the amount of 20 billion rubles are a complete fabrication, since all the old TIR claims have been fully settled ..... What do we, simple carriers, think?

Stowage Factor Weight and volume of cargo when calculating the cost of transportation

The calculation of the cost of transportation depends on the weight and volume of the cargo. For maritime transport, volume is most often decisive, for air transport it is weight. For road transport of goods, a complex indicator plays an important role. Which parameter for calculations will be chosen in a particular case depends on specific gravity cargo (Stowage Factor) .