Gravity calculation. Determination of the gravitational constant

Gravity is the amount by which a body is attracted to the earth under the influence of its attraction. This indicator directly depends on the weight of a person or the mass of an object. The more weight, the higher it is. In this article, we will explain how to find the force of gravity.

From a school physics course: the force of gravity is directly proportional to the weight of the body. You can calculate the value using the formula F \u003d m * g, where g is a coefficient equal to 9.8 m / s 2. Accordingly, for a person who weighs 100 kg, the force of attraction is 980. It is worth noting that in practice everything is a little different, and many factors affect gravity.

Factors affecting gravity:

  • distance from the ground;
  • the geographical location of the body;
  • Times of Day.
Remember that at the north pole the constant g is not 9.8 but 9.83. This is possible due to the presence of mineral deposits in the earth that have magnetic properties. The coefficient increases slightly in places of iron ore deposits. At the equator, the coefficient is 9.78. If the body is not on the ground or in motion, then to determine the force of attraction, it is necessary to know the acceleration of the object. To do this, you can use special devices - a stopwatch, speedometer or accelerometer. To calculate the acceleration, determine the final and initial speeds of the object. Subtract the initial speed from the final value, and divide the resulting difference by the time it took the object to travel the distance. You can calculate acceleration by moving an object. To do this, you need to move the body from rest. Now multiply the distance by two. Divide the resulting value by the time squared. This method of calculating acceleration is suitable if the body is initially at rest. If there is a speedometer, then to determine the acceleration, it is necessary to square the initial and final speeds of the body. Find the difference between the squares of the final and initial speeds. Divide the result by the time multiplied by 2. If the body moves in a circle, then it has its own acceleration, even at a constant speed. To find the acceleration, square the speed of the body and divide by the radius of the circle along which it is moving. The radius must be specified in meters.


Use the accelerometer to determine the instantaneous acceleration. If you get a negative acceleration value, it means that the object is slowing down, that is, its speed is decreasing. Accordingly, with a positive value, the object accelerates, and its speed increases. Remember, a factor of 9.8 can only be used if gravity is determined for an object that is on the ground. If the body is mounted on a support, the resistance of the support should be taken into account. This value depends on the material from which the support is made.


If the body is not dragged in a horizontal direction, then it is worth taking into account the angle at which the object deviates from the horizon. As a result, the formula will look like this: F=m*g – Fthrust*sin. The force of gravity is measured in newtons. For calculations, use the speed measured in m/s. To do this, divide the speed in km/h by 3.6.

It is necessary to know the point of application and the direction of each force. It is important to be able to determine exactly what forces act on the body and in what direction. Force is denoted as , measured in Newtons. In order to distinguish between forces, they are designated as follows

Below are the main forces acting in nature. It is impossible to invent non-existent forces when solving problems!

There are many forces in nature. Here we consider the forces that are considered in the school physics course when studying dynamics. Other forces are also mentioned, which will be discussed in other sections.

Gravity

Every body on the planet is affected by the Earth's gravity. The force with which the Earth attracts each body is determined by the formula

The point of application is at the center of gravity of the body. Gravity always pointing vertically down.


Friction force

Let's get acquainted with the force of friction. This force arises when bodies move and two surfaces come into contact. The force arises as a result of the fact that the surfaces, when viewed under a microscope, are not smooth as they seem. The friction force is determined by the formula:

A force is applied at the point of contact between two surfaces. Directed in the direction opposite to the movement.

Support reaction force

Imagine a very heavy object lying on a table. The table bends under the weight of the object. But according to Newton's third law, the table acts on the object with exactly the same force as the object on the table. The force is directed opposite to the force with which the object presses on the table. That is up. This force is called the support reaction. The name of the force "speaks" react support. This force arises whenever there is an impact on the support. The nature of its occurrence at the molecular level. The object, as it were, deformed the usual position and connections of the molecules (inside the table), they, in turn, tend to return to their original state, "resist".

Absolutely any body, even a very light one (for example, a pencil lying on a table), deforms the support at the micro level. Therefore, a support reaction occurs.

There is no special formula for finding this force. They designate it with the letter, but this force is just a separate type of elastic force, so it can also be denoted as

The force is applied at the point of contact of the object with the support. Directed perpendicular to the support.


Since the body is represented as a material point, the force can be depicted from the center

Elastic force

This force arises as a result of deformation (changes in the initial state of matter). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress the spring, we decrease it. When we twist or shift. In all these examples, a force arises that prevents deformation - the elastic force.

Hooke's law


The elastic force is directed opposite to the deformation.

Since the body is represented as a material point, the force can be depicted from the center

When connected in series, for example, springs, the stiffness is calculated by the formula

When connected in parallel, the stiffness

Sample stiffness. Young's modulus.

Young's modulus characterizes the elastic properties of a substance. This is a constant value that depends only on the material, its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. The value of Young's modulus is tabular.

Learn more about the properties of solids.

Body weight

Body weight is the force with which an object acts on a support. You say it's gravity! The confusion occurs in the following: indeed, often the weight of the body is equal to the force of gravity, but these forces are completely different. Gravity is the force that results from interaction with the Earth. Weight is the result of interaction with the support. The force of gravity is applied at the center of gravity of the object, while the weight is the force that is applied to the support (not to the object)!

There is no formula for determining weight. This force is denoted by the letter .

The support reaction force or elastic force arises in response to the impact of an object on a suspension or support, therefore the body weight is always numerically the same as the elastic force, but has the opposite direction.



The reaction force of the support and the weight are forces of the same nature, according to Newton's 3rd law they are equal and oppositely directed. Weight is a force that acts on a support, not on a body. The force of gravity acts on the body.

Body weight may not be equal to gravity. It can be either more or less, or it can be such that the weight is zero. This state is called weightlessness. Weightlessness is a state when an object does not interact with a support, for example, the state of flight: there is gravity, but the weight is zero!



It is possible to determine the direction of acceleration if you determine where the resultant force is directed

Note that weight is a force, measured in Newtons. How to correctly answer the question: "How much do you weigh"? We answer 50 kg, naming not weight, but our mass! In this example, our weight is equal to gravity, which is approximately 500N!

Overload- the ratio of weight to gravity

Strength of Archimedes

Force arises as a result of the interaction of a body with a liquid (gas), when it is immersed in a liquid (or gas). This force pushes the body out of the water (gas). Therefore, it is directed vertically upwards (pushes). Determined by the formula:

In the air, we neglect the force of Archimedes.

If the Archimedes force is equal to the force of gravity, the body floats. If the Archimedes force is greater, then it rises to the surface of the liquid, if it is less, it sinks.



electrical forces

There are forces of electrical origin. Occur in the presence of an electric charge. These forces, such as the Coulomb force, Ampère force, Lorentz force, are discussed in detail in the Electricity section.

Schematic designation of the forces acting on the body

Often the body is modeled by a material point. Therefore, in the diagrams, various points of application are transferred to one point - to the center, and the body is schematically depicted as a circle or rectangle.

In order to correctly designate the forces, it is necessary to list all the bodies with which the body under study interacts. Determine what happens as a result of interaction with each: friction, deformation, attraction, or maybe repulsion. Determine the type of force, correctly indicate the direction. Attention! The number of forces will coincide with the number of bodies with which the interaction takes place.

The main thing to remember

1) Forces and their nature;
2) Direction of forces;
3) Be able to identify the acting forces

Distinguish between external (dry) and internal (viscous) friction. External friction occurs between solid surfaces in contact, internal friction occurs between layers of liquid or gas during their relative motion. There are three types of external friction: static friction, sliding friction and rolling friction.

Rolling friction is determined by the formula

The resistance force arises when a body moves in a liquid or gas. The magnitude of the resistance force depends on the size and shape of the body, the speed of its movement and the properties of the liquid or gas. At low speeds, the resistance force is proportional to the speed of the body

At high speeds it is proportional to the square of the speed

Consider the mutual attraction of an object and the Earth. Between them, according to the law of gravity, a force arises

Now let's compare the law of gravity and the force of gravity

The value of free fall acceleration depends on the mass of the Earth and its radius! Thus, it is possible to calculate with what acceleration objects on the Moon or on any other planet will fall, using the mass and radius of that planet.

The distance from the center of the Earth to the poles is less than to the equator. Therefore, the acceleration of free fall at the equator is slightly less than at the poles. At the same time, it should be noted that the main reason for the dependence of the acceleration of free fall on the latitude of the area is the fact that the Earth rotates around its axis.

When moving away from the surface of the Earth, the force of gravity and the acceleration of free fall change inversely with the square of the distance to the center of the Earth.


Why does a ball thrown in a horizontal direction (Fig. 28) end up on the ground after a while? Why does a stone released from the hands (Fig. 29) fall down? Why does a person jumping up soon find himself down again? All these phenomena have the same reason - the attraction of the Earth.
The earth attracts all bodies to itself: people, trees, water, houses, the moon, etc.

The force of gravity towards the earth is called gravity. The force of gravity is always directed vertically downwards. It is designated as follows:

F T- gravity.

When a body falls down under the influence of attraction to the Earth, it is affected not only by the Earth, but also by air resistance. In cases where the force of air resistance is negligible compared to the force of gravity, the fall of the body is called free.

For observation free fall various bodies (for example, pellets, feathers, etc.), they are placed in a glass tube (Newton's tube), from which air is pumped out. If at first all these objects are at the bottom of the tube, then after it is quickly turned over, they are on top, after which they begin to fall down (Fig. 30). Watching them fall, you can see that both the lead pellet and the light feather reach the bottom of the tube at the same time. Having traveled the same path in the same time, these bodies hit the bottom with the same speed. This happens because gravity has the following remarkable property: for every second it increases the speed of any freely falling body (regardless of its mass) always by the same amount.

Measurements show that near the surface of the Earth, the speed of any freely falling body increases by 9.8 m/s for every second of fall. This value is denoted by the letter g and call free fall acceleration.

Knowing the acceleration of free fall, you can find the force with which the Earth attracts any body located near it to itself.

To determine the force of gravity acting on a body, it is necessary to multiply the mass of this body by the acceleration of free fall:

F T = mg.

From this formula it follows that g = F T /m. But F T measured in newtons, a m- in kilograms. Therefore, the value g can be measured in newtons per kilogram:

g= 9.8 N/kg ≈10 N/kg.

As the height above the Earth increases, the free fall acceleration gradually decreases. For example, at an altitude of 297 km it turns out to be not 9.8 N/kg, but 9 N/kg. The decrease in free fall acceleration means that the force of gravity also decreases as the height above the Earth increases. The farther the body is from the Earth, the weaker it attracts it.

1. What causes all bodies to fall to the ground? 2. What force is called gravity? 3. In what case is the fall of a body called free? 4. What is the free fall acceleration near the Earth's surface? 5. What is the formula for gravity? 6. What will happen to the force of gravity, acceleration and time of fall if the mass of the falling body doubles? 7. How do gravity and free fall acceleration change with distance from the Earth?
Experimental tasks. 1. Pick up a piece of paper and release it. Watch him fall. Now crumple this sheet and release again. How will the nature of his fall change? Why? 2. Take a metal circle (for example, a coin) in one hand, and a slightly smaller paper circle in the other. Release them at the same time. Will they fall at the same time? Now take a metal circle in your hand and put a paper circle on top of it (Fig. 31). Release the mugs. Why are they falling at the same time now?

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) is a derived unit of force in the International System of 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) is a gravitational metric unit of force equal to the force that acts on a body of mass 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 at a given moment in 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. Figure 1 shows different positions 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 the classical definition, the 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 the 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 is 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 FROM 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 FROM, 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 point of the center of mass 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 leads to such an acceleration of 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 an inertial frame of 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. The densities of various substances are presented in 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 the force is important: the same force in modulus and direction, applied at different points of the 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 conditions for 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 legends and experience, everyone who transported goods from Europe by road knows what a terrible place is the 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, as a result - for the implementation of international road transport of goods, a lot 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 already banned the issuance of TIR Carnets without additional guarantees in several federal districts. And she notified that from December 1 of this year she would completely break the contract with the IRU as inappropriate for the requirements of the Customs Union and put forward 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 weight of cargo (Stowage Factor) .

Gravity is the force with which a body is attracted to the Earth due to universal gravitation. Gravity causes all bodies that are not acted upon by other forces to move downward with the acceleration of free fall, g. All bodies in the Universe are attracted to each other, and the greater their mass and the closer they are located, the stronger the attraction. To calculate the force of gravity, the mass of the body should be multiplied by a factor, denoted by the letter g, approximately equal to 9.8 N / kg. Thus, gravity is calculated by the formula

The force of gravity is approximately equal to the force of gravitational attraction to the Earth (the difference between the force of gravity and the gravitational force is due to the fact that the reference frame associated with the Earth is not completely inertial).

Friction force.

Friction force - The force that occurs at the point of contact of bodies and prevents their relative movement. The direction of the friction force is opposite to the direction of motion.

Distinguish between static friction force and sliding friction force. If the body slides on any surface, its movement is hindered by sliding friction force.

, where N— support reaction force, a μ is the coefficient of sliding friction. Coefficient μ depends on the material and quality of processing of the contacting surfaces and does not depend on body weight. The coefficient of friction is determined empirically.

The force of sliding friction is always directed opposite to the motion of the body. When the direction of speed changes, the direction of the friction force also changes.

The force of friction begins to act on the body when they try to move it. If an external force F less product μN, then the body will not move - the beginning of the movement, as they say, is hindered by the rest friction force . The body will start moving only when an external force F exceeds the maximum value that the static friction force can have

Friction of rest - frictional force that prevents the movement of one body on the surface of another. In some cases, friction is useful (without friction it would be impossible for a person, animals to walk on the ground, move cars, trains, etc.), in such cases, friction is increased. But in other cases, friction is harmful. For example, because of it, the rubbing parts of mechanisms wear out, excess fuel is consumed in transport, etc. Then friction is fought by applying lubrication or replacing sliding with pitching.

Friction forces do not depend on the coordinates of the relative position of the bodies, they can depend on the speed of the relative motion of the bodies in contact. Friction forces are non-potential forces.

Weight and weightlessness.

Weight - the force of the body's impact on the support (or suspension or other type of attachment) that prevents falling, arising in the field of gravity. In this case, the resulting elastic forces begin to act on the body with the resulting P directed upwards, and the sum of the forces applied to the body becomes equal to zero.


The force of gravity is directly proportional to the mass of the body and depends on the acceleration of free fall, which is maximum at the poles of the Earth and gradually decreases when moving towards the equator. The flattened shape of the Earth at the poles and its rotation around its axis lead to the fact that at the equator the acceleration of free fall is approximately 0.5% less than at the poles. Therefore, the weight of a body measured with a spring balance will be less at the equator than at the poles. The weight of a body on Earth can vary over a very wide range, and sometimes even disappear.

For example, in a falling elevator, our weight will be 0, and we will be in a state of weightlessness. However, the state of weightlessness can be not only in the cabin of a falling elevator, but also on a space station revolving around the Earth. Rotating in a circle, the satellite moves with centripetal acceleration, and the only force that can give it this acceleration is gravity. Therefore, together with the satellite, revolving around the Earth, we move with an acceleration a = g, directed towards its center. And if we, being on the satellite, stood on the spring scales, then P = 0. Thus, on the satellite, the weight of all bodies is zero.