Madam, why are your children so gray? Darling, I tell them the truth at night instead of fairy tales.

The task of a cargo carrier is as old as the world - the carrier wants to bring as much cargo as possible during the flight, as long as the horse can bear it. Everything is logical and understandable - he transported more, earned more, but the road along which he transports the cargo (we don’t take tundra) also costs money: someone designed it, built it and now takes tender care of it. Since a road is a technical structure, there are also conditions for its use - standards and rules. The quality of engineers, materials and the amount of money spent on design and construction varies greatly in different countries and territories, as does the quality of roads. And the rules are different everywhere. In international transportation, truck axle load standards are a very pressing issue, because the cargo travels through different countries. In every country and even region, the police or transport inspectorate sternly looks into the distance and guards its roads, does not allow tanks to travel (they spoil it a little) and weighs passing vehicles. The traffic police severely punish those trucks that damage their roads by exceeding the axle loads. During international cargo transportation, very strict control of the weight and dimensions of vehicles is carried out at the borders. No country wants to let in strangers who didn’t pay for the roads (didn’t pay taxes in this country), and driving through them will ruin them. The main restrictions relate to the total weight vehicle and loads on each axle separately.

The carrier, understandably, wants to avoid fines and other persecution and find out the axle loads before falling into the clutches of the police.

How to find out the load on a car's axle?

Axle load is the force with which a truck's axle pushes on the scale, measured in kilograms or tons. Children's question— how to find out the weight? You just have to weigh it. In words, sitting in a cozy office, everything is very simple. Let's move on to practice and living a difficult life becomes easier and easier.... after all, you don't need to weigh 100 grams. butterscotch, and a 19-meter piece weighing about 40 tons, it’s difficult to do this on grandma’s steelyard.

IN freight transport, especially in Russia, the role of the weigher - the “extreme” - is assigned to the driver. You there, dear, control the loading and if anything happens, load it so that there is no overload. Truck drivers are a people of few words; they only speak when extreme cases. Any question is answered with eyebrows, and the driver, admittedly, has few opportunities for control. That’s why they don’t tell anyone anything and just say “whatever happens,” because they see that office workers are constantly running away from the problem.

The result is a tractor, there is a semi-trailer, here is the load - how to determine the axle loads so as not to become a victim of transport control? There are several shamanic ways to do this:

• The most mysterious one is to jump around the fire, hit a tambourine and just guess or “by eye”.
• The easiest way is to go to the weight control point and weigh yourself. But this point still needs to be found, you also need to go to it by road and not fly by air, and if you weren’t caught on the road for weighing, they will take a bribe. Oddly enough, this simple method is used extremely rarely. Do you often go to the clinic to measure how hard you press on the scale? The bottom line is this: weighing trucks is time-consuming, expensive, and the best part is that there are no such scales at the loading site. And when the cargo is loaded and you’re out on the road, it’s not particularly interesting anymore (it’s too late to rush around).
• The most civilized option is to order a tractor equipped with an axle load monitoring system when purchasing.

  Usually this is done only on tractors; trailers are often re-coupled and they are rarely compatible with the electronics of the tractors. Of course, everything is changing and there are systems called “Weight Distribution Monitoring System”. This system shows the actual axle load of the entire road train. The on-board computer display can display the values ​​of the vertical force on each axle and the weight of the load. To calculate the load value, an air pressure sensor built into the air bag is used. Truck manufacturers claim that to obtain information about the axle load of a semi-trailer, it is enough that the trailer is equipped with an EBS electronic braking system (in practice this is not enough). The “weight distribution monitoring system” is very convenient to use, but as often happens in technology, it is not widely used.

  
  

• The most practical one - if you have air suspension on both the tractor and the semi-trailer, then it’s easy to install ordinary pressure gauges yourself in the air spring line on each axle. Then you will have to do the adjustment of these pressure gauges yourself: determining which position of the arrow corresponds to which weight, this is not difficult, but again, few people do it. In my opinion, this is the simplest, cheapest, fastest and most practical method, because pressure gauges are inexpensive and readings are taken quickly, during the loading process. The difficulty of this method for determining axle loads is that the front (steering) axles of tractors are extremely rarely equipped with air suspension: there is nowhere to build a pressure gauge.
• The most handy one is to attach special sensors to the truck. The sensors themselves and electronic controllers for them are sold by many companies. Sensors are electronic and electro-mechanical. Electronic ones are built in as pressure gauges in a pneumatic system; they transmit a signal to the controller, which processes this signal and displays the received load on the controller screen. The electromechanical sensor is similar to a “floor level” crane; this sensor is mounted on the frame of a tractor or semi-trailer, and the movable rod is mounted on the axle. The difficulties of this method: you need to buy sensors and a controller, run wiring, build in sensors, calibrate the entire system... it's a hassle, and in the end we get a homemade gun. This method is used mainly in mining dump trucks, where the electronic controller not only records the loads on the axles, but also transmits readings of the weight of the load via cellular communication to the dispatch service, because space registrations flourish in bulk cargo, and this is very important there.
• The most elegant one is called “checkered”:

  
  A 22.5-inch load wheel usually has 48 checkers around its perimeter. The semi-trailer is loaded with 17.5 tons of cargo; as can be seen in the photo, 4 “checkered” parts come into contact with the road. Problem: determine how many checkers will come into contact with the road at a critical load of 24 tons? You can guess and count the number of checkers in contact when the trailer is empty and the second time, when a known amount of cargo is loaded into the trailer, determine how much one checker “weighs”. If there are no checkers on the wheel (you are piloting a Formula 1 car), then you can put two pieces of red wire where the wheel contacts the road and measure the distance between them with a tape measure for an empty and loaded trailer, and then determine how much one centimeter “weighs”.

• The laziest one is to ask a physicist you know for help, tell him the weight of the tractor, the weight of the semi-trailer, the coordinates of the centers of gravity, that the pressure in the wheel is 9 atmospheres, the number of wheels on the axle is 2 or 4, and he can easily calculate everything in 5 minutes. That's why he's a physicist, not a mare driver. The method is excellent, but its applicability is limited; carrying a live calculator with you in the cab is a little expensive.
• Most " correct» - be able to calculate the loads on the axles of the road train BEFORE loading. It’s a no-brainer that calculating the axle load is necessary before loading, because this is the only way to solve the problem of overload and fines. All of the above shamanic methods of determining the load are exclusively historical in nature and only control functions, because the cargo is already in the cargo compartment and in order to change something, the cargo must either be moved (if there is somewhere) or unloaded. That is why these methods are unpopular and truck manufacturers do not pay much attention to them; control is a tool of the driver and not the manager (organizer) of transportation. And so, in the act of calculating the axle load, another character appears - the transportation manager, who is also a dispatcher, logistician, transportation organizer. What is typical for the transportation organizer, he decides how to load the cargo and communicates with the senders before the cargo enters the cargo space of the semi-trailer. The transportation organizer knows in advance the dimensions and weight of the cargo, he has the vehicle parameters at hand and can calculate the axle loads (or may not). During the negotiations, the transportation organizer can “strangle” the customer with compelling arguments until any overloads occur. Therefore, a logistician is the top of the food transport chain, an iceberg of logistics, he does not believe in the black cat and horoscopes, he knows how to use a computer and read the thoughts of drivers and customers.

Here we weighed our tractor:

weighing data on dynamic scales, axle loads of the MAN TGX tractor (click on image to enlarge)

Here is the result of weighing a loaded road train:

Polish plumb line on the Belarusian-Polish border. In transport jargon, a “plumb line” is a receipt for weighing results, but we live in the 21st century, so the plumb line has become electronic; the picture shows a photo of the border service screen. The weight on the semi-trailer axles is different.
The plumb line shows that the road train weighs 33,400 kg. Has axle loads of 6600, 8650, 5950, 6100, 6100.
This road train (consisting of a MAN TGX18.400 tractor and a loaded SCHMITZ SRR24 semi-trailer) weighs 14,600 kg when unloaded and has axle loads of: 5300, 3600, 1900, 1900, 1900.

Why are the loads on the rear axles of a semi-trailer not the same? There may be several reasons for this:

This is how Dmitry wrote to us: “The speed of travel on the scales was not the same when hitting the sensor with the 3rd axle and then 4.5, or the material of the air springs of the 3rd axle of the road train is less elastic than the 4th and 5th axles. (another manufacturer of pneumatic elements).”
Anyone who knows the true reasons, write to us at e-mail, we will be very grateful.

Scale data

According to the Operating Manual for scales for static weighing M 014.060.00 RE, the maximum permissible error when weighing objects is:

• operation from 200 kg to 5,000 kg is +/- 10 kg.
• from 5,000 kg to 15,000 kg - +/- 20 kg;

How does it happen?

When checking the car at the transport control post, it was recorded that the permissible axle load was exceeded. At the same time, the total weight of the road train was 37.5 tons (weight of the tractor, semi-trailer, container and cargo in the container). The driver was ordered to pay a fine of 2,500 rubles. The driver paid the fine and kept the receipt. But later the company was sent a notification about the initiation of a case on the Administrative Offenses Code of the Russian Federation 12.21-1 in relation to a legal entity. Liability under this article is from 400-500 thousand rubles. To carry out such transportation, a special permit is required.
The carrier reasons as follows: we accepted the container for transportation, what kind of cargo is in it, we know only from the documents, and how the cargo is placed we do not know and cannot control, the container is under seal. The total weight of the road train was checked - 37.5 tons, we do not reach the permitted 40 tons. Therefore, no special permission was issued.
Who has won?

Practice calculations and load distribution in a semi-trailer

Calculator for calculating the axle loads of a freight road train consisting of a truck tractor and a semi-trailer.

Forwarder or carrier? Three secrets and international cargo transportation

Forwarder or carrier: who to choose? If the carrier is good and the forwarder is bad, then the first. If the carrier is bad and the forwarder is good, then the latter. This choice is simple. But how can you decide when both candidates are good? How to choose from two seemingly equivalent options? The fact is that these options are not equivalent.

Horror stories of international transport

BETWEEN A HAMMER AND A HILL.

It is not easy to live between the customer of transportation and the very cunning and economical owner of the cargo. 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 its recipient customers.

AN ENCHANTED PLACE - PTO KOZLOVICHY.

According to legends 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 create, they find fault in every possible way and charge exorbitant prices. And it is true. But not all...

ON THE NEW YEAR'S TIME WE BROUGHT POWDERED MILK.

Loading with groupage cargo at a consolidation warehouse in Germany. One of the cargoes is milk powder from Italy, the delivery of which was ordered by the Forwarder.... A classic example of the work of a forwarder-“transmitter” (he doesn’t delve into anything, he just transmits along the chain).

Documents for international transport

International road transport of goods is very organized and bureaucratic; as a result, a bunch of unified documents are used to carry out international road transport of goods. It doesn’t matter if it’s a customs carrier or an ordinary one - he won’t travel without documents. Although this is not very exciting, we tried to simply explain the purpose of these documents and the meaning that they have. They gave an example of filling out TIR, CMR, T1, EX1, Invoice, Packing List...

Axle load calculation for road freight transport

The goal is to study the possibility of redistributing loads on the axles of the tractor and semi-trailer when the location of the cargo in the semi-trailer changes. And applying 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 load $(\large (gr))$. All variables related to each of these objects will be marked with the superscript $T$, $(\large (p.p.))$ and $(\large (gr))$ respectively. For example, the tare weight of a tractor will be denoted as $m^(T)$.

Why don't you eat fly agarics? The customs officer exhaled a sigh of 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 will completely terminate the agreement with the IRU as not meeting the requirements of the Customs Union and is putting forward financial claims that are not childish.
IRU in response: “The explanations of the Federal Customs Service of Russia regarding the alleged debt of ASMAP in the amount of 20 billion rubles are a complete fiction, since all the old TIR claims have been fully settled..... What do we, common 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 sea transport, volume is most often decisive, for air transport - weight. For road transport of goods, a complex indicator is important. Which parameter for calculations will be chosen in a particular case depends on specific gravity of the cargo (Stowage Factor) .

Methods for measuring cargo masses are set out in GOST 8.424-81, GOST 8.484-83. Let's look at some of them.

Determination of the mass of cargo during static weighing of loaded and empty wagons, a car, a trailer or a semi-trailer with uncoupling

The “net” mass of cargo Mn is found as Mn = Mb - Mt, where Mb is the “gross” mass of a loaded car, wagon, trailer, semi-trailer; Mt is the mass of an empty car, wagon, trailer, semi-trailer. The error values ​​for determining Mn are taken according to Table 1

Table 1. Limit errors for determining the value of Mn on truck scales

Depending on the price of scale division, on the values ​​of Mt, Mb, Mn for cars, trailers, semi-trailers and according to Table 2 for cars.

Table 2. Limit errors for determining the value of Мн on carriage scales

With release when loading on scales

An empty wagon, car, trailer or semi-trailer is placed on the scale platform. The mass of Mn is compensated, after which they are loaded and the mass of Mn is measured. The maximum errors in measuring the cargo mass Mn depending on the scale division price, the values ​​of Mn and Mb for truck scales are given in Table 3,

Table 3. Maximum errors in determining the value of Мн when loading on truck scales

and for carriage scales - and table 4.

4. Limit errors in determining the value of Мн when loading on carriage scales

Weighing without release

The mass of Mn is found as Mn = Mb - Mt.

The values ​​of Mb and Mt are determined by direct measurement. The maximum errors in measuring masses Mn, depending on the scale division price and the values ​​of masses Mn, Mb, Mt, are determined for truck scales according to Table 5, and for carriage scales - according to Table 6 (below).

Without release when loading on scales

An empty vehicle, trailer, or semi-trailer is placed on the weighing platform, then the mass of the vehicle is compensated using a tare compensation device. After this, they are loaded and the mass of the load Mn is measured. The maximum errors in measuring masses Mn depending on the scale division price, the values ​​of masses Mn, Mb for truck scales are given in Table 7.

Weighing a loaded wagon with uncoupling

The mass of the cargo is found as Mn = Mb - Mt where Mt is the mass indicated on the car stencil. The maximum errors depending on the loading of the car at scale division prices of 50... 100 kg are determined based on the graphs (Fig. 1).

Weighing a loaded wagon without uncoupling

Perform in the same way as indicated in paragraph 5, using graphs (Fig. 1). The above is true for trains with the number of cars not exceeding 25.

Table 5. Maximum errors in determining the value of Мн on truck scales when weighing without uncoupling

Consider the movement of a car. For example, if a car travels 15 km in every quarter hour (15 minutes), 30 km in every half hour (30 minutes), and 60 km in every hour, it is considered to be moving uniformly.

Uneven movement.

If a body travels equal distances in any equal intervals of time, its motion is considered uniform.

Uniform movement is very rare. The Earth moves almost uniformly around the Sun; every year the Earth makes one revolution around the Sun.

Almost never does a car driver manage to maintain uniform motion - for various reasons he has to either speed up or slow down. The movement of the clock hands (minute and hour) only seems uniform, which is easy to verify by observing the movement of the second hand. She moves and then stops. The other two arrows move in exactly the same way, only slowly, and therefore their jerks are not visible. Gas molecules hitting each other stop for a while and then accelerate again. During subsequent collisions, with other molecules, they again slow down their movement in space.

These are all examples of uneven motion. This is how the train moves, leaving the station, passing larger and larger tracks in equal periods of time. A skier or skater covers equal distances in different times in competitions. This is how a plane takes off, a door opens, or a falling snowflake moves.

If a body passes in equal intervals of time different ways, then its movement is called uneven.

Uneven movement can be observed experimentally. The picture shows a cart with a dropper from which drops fall at regular intervals. When the cart moves under the influence of a load, we see that the distances between the traces of the drops are not the same. And this means that in the same periods of time the cart travels different paths.

Speed. Units of speed.

We often say that some bodies move faster, others slower. For example, a tourist is walking along the highway, a car is rushing, an airplane is flying in the air. Let us assume that they all move uniformly, nevertheless, the movement of these bodies will be different.

A car moves faster than a pedestrian, and an airplane moves faster than a car. In physics, the quantity that characterizes the speed of movement is called velocity.

Suppose that a tourist travels 5 km in 1 hour, a car 90 km, and the speed of an airplane is 850 km per hour.

Velocity during uniform motion of a body shows how far the body has traveled per unit time.

Thus, using the concept of speed, we can now say that the tourist, the car and the plane are moving at different speeds.

With uniform motion, the speed of the body remains constant.

If a cyclist travels a distance of 25 m in 5 seconds, then his speed will be 25m/5s = 5m/s.

To determine the speed during uniform motion, the distance traveled by the body in a certain period of time must be divided by this period of time:

speed = path/time.

Speed ​​is denoted by v, path by s, time by t. The formula for finding speed will look like this:

The speed of a body during uniform motion is a quantity equal to the ratio of the path to the time during which this path is covered.

In the International System (SI), speed is measured in meters per second (m/s).

This means that the unit of speed is taken to be the speed of such uniform motion that in one second the body travels a distance of 1 meter.

The speed of a body can also be measured in kilometers per hour (km/h), kilometers per second (km/s), centimeters per second (cm/s).

Example. A train, moving uniformly, covers a distance of 108 km in 2 hours. Calculate the speed of the train.

So, s = 108 km; t = 2 h; v = ?

Solution. v = s/t, v = 108 km/2 h = 54 km/h. Simply and easily.

Now, let’s express the speed of the train in SI units, that is, we’ll convert kilometers into meters, and hours into seconds:

54 km/h = 54000 m/ 3600 s = 15 m/s.

Answer: v = 54 km/h, or 15 m/s.

Thus, The numerical value of the speed depends on the selected unit.

Speed, in addition to its numerical value, has a direction.

For example, if you need to indicate where a plane departing from Vladivostok will be in 2 hours, then you need to indicate not only the value of its speed, but also its destination, i.e. its direction. Quantities that, in addition to a numerical value (modulus), also have a direction, are called vector.

Speed ​​is a vector physical quantity.

All vector quantities are designated by the corresponding letters with an arrow. For example, speed is denoted by the symbol v with an arrow, and the velocity module is indicated by the same letter, but without the arrow v.

Some physical quantities have no direction. They are characterized only by a numerical value. These are time, volume, length, etc. They are scalar.

If, when a body moves, its speed changes from one section of the path to another, then such movement is uneven. To characterize the uneven movement of a body, the concept of average speed was introduced.

For example, a train from Moscow to St. Petersburg travels at a speed of 80 km/h. What speed do they mean? After all, the speed of the train at stops is zero, after stopping it increases, and before stopping it decreases.

In this case, the train is moving unevenly, which means that the speed of 80 km/h is the average speed of the train.

It is determined in almost the same way as speed during uniform motion.

To determine average speed of a body during uneven movement, the entire distance traveled must be divided by the entire time of movement:

It should be recalled that only with uniform motion will the s/t ratio be constant over any period of time.

With uneven movement of a body, the average speed characterizes the movement of the body over the entire period of time. It does not explain how the body moved at different points in time during this period.

Table 1 shows the average speeds of movement of some bodies.

Table 1

Average speeds of movement of some bodies, the speed of sound, radio waves and light.

Calculation of the route and time of movement.

If the speed of a body and time during uniform motion are known, then the distance traveled by it can be found.

Since v = s/t, the path is determined by the formula

To determine the distance traveled by a body during uniform motion, the speed of the body must be multiplied by the time of its movement.

Now, knowing that s = vt, we can find the time during which the body moved, i.e.

To determine time during uneven motion, the distance traveled by the body must be divided by the speed of its movement.

If a body moves unevenly, then, knowing its average speed of movement and the time during which this movement occurs, find the path:

Using this formula, you can determine the time when the body moves unevenly:

Inertia.

Observations and experiments show that the speed of a body by itself cannot change.

Experience with trolleys. Inertia.

A soccer ball lies on the field. With a kick, the football player sets it in motion. But the ball itself will not change its speed and will not begin to move until other bodies act on it. A bullet inserted into the barrel of a gun will not fly out until it is pushed out by the powder gases.

Thus, both the ball and the bullet do not have their own speed until they are acted upon by other bodies.

A soccer ball rolling on the ground stops due to friction with the ground.

A body reduces its speed and stops not by itself, but under the influence of other bodies. Under the influence of another body, the direction of speed also changes.

A tennis ball changes direction after hitting the racket. After hitting the hockey player’s stick, the puck also changes its direction of movement. The direction of movement of a gas molecule changes when it hits another molecule or the walls of a container.

Means, a change in the speed of a body (magnitude and direction) occurs as a result of the action of another body on it.

Let's do an experiment. Let's place the board at an angle on the table. Place a pile of sand on the table, a short distance from the end of the board. Place the cart on the inclined board. The cart, having rolled down the inclined board, quickly stops, hitting the sand. The speed of the cart decreases very quickly. Its movement is uneven.

Let's level the sand and release the cart again from the previous height. The cart will now travel a greater distance across the table before it stops. Its speed changes more slowly, and its movement becomes closer to uniform.

If you completely remove sand from the path of the cart, then the only obstacle to its movement will be friction on the table. The cart gets to the stop even slower, and it will travel further than the first and second time.

So, the less the effect of another body on the cart, the longer the speed of its motion is maintained and the closer it is to uniform.

How will a body move if other bodies do not act on it at all? How can this be established experimentally? Thorough experiments to study the motion of bodies were first carried out by G. Galileo. They made it possible to establish that if a body is not acted upon by other bodies, then it is either at rest or moves in a straight line and uniformly relative to the Earth.

The phenomenon of maintaining the speed of a body in the absence of the action of other bodies on it is called inertia.

Inertia- from Latin inertia- immobility, inactivity.

Thus, the movement of a body in the absence of the action of another body on it is called movement by inertia.

For example, a bullet fired from a gun would still fly, maintaining its speed, if it were not acted upon by another body - air (or rather, the gas molecules that are in it.). As a result, the speed of the bullet decreases. The cyclist stops pedaling and continues moving. He would be able to maintain the speed of his movement if the force of friction did not act on him.

So, If the body is not acted upon by other bodies, then it moves at a constant speed.

Interaction of bodies.

You already know that when moving unevenly, the speed of a body changes over time. A change in the speed of a body occurs under the influence of another body.

Experience with trolleys. The carts move relative to the table.

Let's do an experiment. We will attach an elastic plate to the cart. Then we bend it and tie it with thread. The cart is at rest relative to the table. Will the cart move if the elastic plate straightens?

To do this, we will cut the thread. The plate will straighten out. The cart will remain in the same place.

Then we will place another similar cart close to the bent plate. Let's burn the thread again. After this, both carts begin to move relative to the table. They go in different directions.

To change the speed of the cart, a second body was needed. Experience has shown that the speed of a body changes only as a result of the action of another body (the second cart) on it. In our experience, we observed that the second cart also began to move. Both began to move relative to the table.

Boat experience. Both boats begin to move.

Trolleys act on each other, i.e. they interact. This means that the action of one body on another cannot be one-sided; both bodies act on each other, that is, they interact.

We considered the simplest case of interaction of two bodies. Before the interaction, both bodies (carts) were at rest relative to each other and relative to the table.

Boat experience. The boat moves away in the direction opposite to the jump.

For example, the bullet was also at rest relative to the gun before being fired. When interacting (during a shot), the bullet and the gun move in different directions. The result is a phenomenon of recoil.

If a person sitting in a boat pushes another boat away from him, then interaction occurs. Both boats begin to move.

If a person jumps from a boat to the shore, then the boat moves in the direction opposite to the jump. The man acted on the boat. In turn, the boat also affects the person. It acquires a speed that is directed toward the shore.

So, As a result of interaction, both bodies can change their speed.

Body mass. Unit of mass.

When two bodies interact, the velocities of the first and second bodies always change.

Experience with trolleys. One is bigger than the other.

After interaction, one body acquires a speed that can differ significantly from the speed of another body. For example, after shooting from a bow, the speed of the arrow is much greater than the speed that the bow string acquires after the interaction.

Why is this happening? Let's carry out the experiment described in paragraph 18. Only now, let's take carts of different sizes. After the thread has been burned, the carts move away at different speeds. A cart that moves slower after interaction is called more massive. She has more weight. A cart that moves at a higher speed after the interaction has less mass. This means that the carts have different masses.

The speeds acquired by the carts as a result of the interaction can be measured. These speeds are used to compare the masses of interacting carts.

Example. The speeds of the carts before interaction are zero. After the interaction, the speed of one cart became 10 m/s, and the speed of the other 20 m/s. Since the speed acquired by the second cart If the speed of the first one is 2 times greater, then its mass is 2 times less than the mass of the first cart.

If, after interaction, the velocities of the initially stationary carts are the same, then their masses are the same. Thus, in the experiment depicted in Figure 42, after the interaction the carts move apart at equal speeds. Therefore, their masses were the same. If after interaction the bodies acquire different speeds, then their masses are different.

International standard kilogram. In the picture: the US kilogram standard.

How many times the speed of the first body is greater (less than) the speed of the second body, how many times the mass of the first body is less (greater) than the mass of the second.

How body speed changes less when interacting, the more mass it has. Such a body is called more inert.

And vice versa than body speed changes more during interaction, the less mass it has, the more less it inert.

This means that all bodies have the characteristic property of changing their speed differently when interacting. This property is called inertia.

Body mass is a physical quantity that characterizes its inertia.

You should know that any body: Earth, man, book, etc. - has mass.

Mass is designated by the letter m. The SI unit of mass is the kilogram ( 1 kg).

Kilogram- this is the mass of the standard. The standard is made of an alloy of two metals: platinum and iridium. The international standard kilogram is stored in Sevres (near Paris). More than 40 exact copies were made from the international standard and sent to different countries. One of the copies of the international standard is located in our country, at the Institute of Metrology named after. D.I. Mendeleev in St. Petersburg.

In practice, other units of mass are used: ton (T), gram (G), milligram (mg).

1 t	= 1000 kg (10 3 kg)	1 g	= 0.001 kg (10 -3 kg)
1 kg	= 1000 g (10 3 g)	1 mg	= 0.001 g (10 -3 g)
1 kg	= 1,000,000 mg (10 6 mg)	1 mg	= 0.000001 kg (10 -6 kg)

In the future, when studying physics, the concept of mass will be revealed more deeply.

Measuring body weight on scales.

To measure body weight, you can use the method described in paragraph 19.

Training scales.

By comparing the velocities acquired by bodies during interaction, they determine how many times the mass of one body is greater (or less) than the mass of the other. It is possible to measure the mass of a body in this way if the mass of one of the interacting bodies is known. In this way, the masses of celestial bodies, as well as molecules and atoms, are determined in science.

In practice, body weight can be found using scales. There are various types of scales: educational, medical, analytical, pharmaceutical, electronic, etc.

Special set of weights.

Let's consider training scales. The main part of such scales is the rocker arm. An arrow is attached to the middle of the rocker - a pointer that moves to the right or left. Cups are suspended from the ends of the rocker. Under what condition will the scales be in equilibrium?

Let us place the carts that were used in the experiment on the scales (see § 18). Since during the interaction the carts acquired the same speeds, we found out that their masses are the same. Therefore, the scales will be in balance. This means that the masses of bodies lying on the scales are equal to each other.

Now, on one pan of the scale, we place the body whose mass we need to find out. We will place weights whose masses are known on the other until the scales are in equilibrium. Consequently, the mass of the body being weighed will be equal to the total mass of the weights.

When weighing, a special set of weights is used.

Various scales are designed for weighing different bodies, both very heavy and very light. So, for example, using carriage scales, you can determine the mass of a carriage from 50 tons to 150 tons. The mass of a mosquito, equal to 1 mg, can be determined using analytical balances.

Density of matter.

We weigh two cylinders of equal volume. One is aluminum and the other is lead.

The bodies around us consist of various substances: wood, iron, rubber, etc.

The mass of any body depends not only on its size, but also on what substance it consists of. Therefore, bodies that have the same volumes, but consist of different substances, have different masses.

Let's do this experiment. Let's weigh two cylinders of the same volume, but consisting of different substances. For example, one is made of aluminum, the other is made of lead. Experience shows that the mass of aluminum is less than lead, that is, aluminum is lighter than lead.

At the same time, bodies with the same masses, consisting of different substances, have different volumes.

An iron beam weighing 1 ton occupies 0.13 cubic meters. And ice weighing 1 ton has a volume of 1.1 cubic meters.

Thus, an iron bar weighing 1 ton occupies a volume of 0.13 m 3, and ice with the same mass of 1 ton occupies a volume of 1.1 m 3. The volume of ice is almost 9 times the volume of the iron bar. This is because different substances can have different densities.

It follows that bodies with a volume of, for example, 1 m 3 each, consisting of different substances, have different masses. Let's give an example. Aluminum with a volume of 1 m3 has a mass of 2700 kg, lead of the same volume has a mass of 11,300 kg. That is, with the same volume (1 m3), lead has a mass that is approximately 4 times greater than the mass of aluminum.

Density shows the mass of a substance taken in a certain volume.

How can you find the density of a substance?

Example. A marble slab has a volume of 2 m 3 and its mass is 5400 kg. It is necessary to determine the density of marble.

So, we know that marble with a volume of 2m3 has a mass of 5400 kg. This means that 1 m 3 of marble will have a mass 2 times less. In our case - 2700 kg (5400: 2 = 2700). Thus, the density of marble will be 2700 kg per 1 m 3.

This means that if the mass of a body and its volume are known, the density can be determined.

To find the density of a substance, you need to divide the mass of the body by its volume.

Density is a physical quantity that is equal to the ratio of the mass of a body to its volume:

density = mass/volume.

Let us denote the quantities included in this expression by letters: the density of the substance is ρ (Greek letter “rho”), the mass of the body is m, its volume is V. Then we obtain a formula for calculating density:

The SI unit of density of a substance is kilogram per cubic meter (1kg/m3).

The density of a substance is often expressed in grams per cubic centimeter (1g/cm3).

If the density of a substance is expressed in kg/m3, then it can be converted to g/cm3 as follows.

Example. The density of silver is 10,500 kg/m3. Express it in g/cm3.

10,500 kg = 10,500,000 g (or 10.5 * 10 6 g),

1m3 = 1,000,000 cm3 (or 10 6 cm3).

Then ρ = 10,500 kg/m 3 = 10.5 * 10 6 / 10 6 g/cm 3 = 10.5 g/cm 3.

It should be remembered that the density of the same substance in solid, liquid and gaseous states is different. Thus, the density of ice is 900 kg/m3, water is 1000 kg/m3, and water vapor is 0.590 kg/m3. Although all these are states of the same substance - water.

Below are tables of densities of some solids, liquids and gases.

table 2

Densities of some solids (at normal atmospheric pressure, t = 20 °C)

Solid	ρ, kg/m 3	ρ, g/cm 3	Solid	ρ, kg/m 3	ρ, g/cm 3
Osmium	22 600	22,6	Marble	2700	2,7
Iridium	22 400	22,4	Window glass	2500	2,5
Platinum	21 500	21,5	Porcelain	2300	2,3
Gold	19 300	19,3	Concrete	2300	2,3
Lead	11 300	11,3	Brick	1800	1,8
Silver	10 500	10,5	Rafinated sugar	1600	1,6
Copper	8900	8,9	Plexiglas	1200	1,2
Brass	8500	8,5	Capron	1100	1,1
Steel, iron	7800	7,8	Polyethylene	920	0,92
Tin	7300	7,3	Paraffin	900	0,90
Zinc	7100	7,2	Ice	900	0,90
Cast iron	7000	7	Oak (dry)	700	0,70
Corundum	4000	4	Pine (dry)	400	0,40
Aluminum	2700	2,7	Cork	240	0,24

Table 3

Densities of some liquids (at normal atmospheric pressure t=20 °C)

Table 4

Densities of some gases (at normal atmospheric pressure t=20 °C)

Calculation of mass and volume based on its density.

Knowing the density of substances is very important for various practical purposes. An engineer, when designing a machine, can calculate the mass of the future machine in advance based on the density and volume of the material. The builder can determine what the mass of the building under construction will be.

Therefore, knowing the density of a substance and the volume of a body, it is always possible to determine its mass.

Since the density of a substance can be found using the formula ρ = m/V, then from here you can find the mass i.e.

m = ρV.

To calculate the mass of a body, if its volume and density are known, the density must be multiplied by the volume.

Example. Determine the mass of a steel part with a volume of 120 cm3.

From Table 2 we find that the density of steel is 7.8 g/cm 3 . Let's write down the conditions of the problem and solve it.

Given:

V = 120 cm 3;

ρ = 7.8 g/cm3;

Solution:

m = 120 cm 3 7.8 g/cm 3 = 936 g.

Answer: m= 936 g

If the mass of a body and its density are known, then the volume of the body can be expressed from the formula m = ρV, i.e. the volume of the body will be equal to:

V = m/ρ.

To calculate the volume of a body if its mass and density are known, the mass must be divided by the density.

Example. The mass of sunflower oil filling the bottle is 930 g. Determine the volume of the bottle.

According to Table 3, we find that the density of sunflower oil is 0.93 g/cm 3 .

Let's write down the conditions of the problem and solve it.

Given:

ρ = 0.93 g/cm 3

Solution:

V = 930/0.93 g/cm 3 = 1000 cm 3 = 1 l.

Answer: V= 1 l.

To determine the volume, a formula is used, as a rule, in cases where the volume is difficult to find using simple measurements.

Force.

Each of us constantly encounters various cases of the action of bodies on each other. As a result of interaction, the speed of movement of a body changes. You already know that the speed of a body changes the more, the smaller its mass. Let's look at some examples that prove this.

By pushing the trolley with our hands, we can set it in motion. The speed of the trolley changes under the influence of the human hand.

A piece of iron lying on a plug lowered into water is attracted by a magnet. A piece of iron and a cork change their speed under the influence of a magnet.

By acting on the spring with your hand, you can compress it. First, the end of the spring moves. Then the movement is transferred to the rest of its parts. A compressed spring, when straightened, can, for example, set a ball in motion.

When the spring was compressed, the acting body was the human hand. When a spring straightens, the acting body is the spring itself. She sets the ball in motion.

You can use your racket or hand to stop or change the direction of movement of a flying ball.

In all the examples given, one body, under the influence of another body, begins to move, stops, or changes the direction of its movement.

Thus, the speed of a body changes when it interacts with other bodies.

Often it is not indicated which body and how it acted on this body. It simply says that a force acts on a body or a force is applied to it. This means that force can be considered as the reason for the change in speed.

By pushing the trolley with our hands, we can put it into action.

Experiment with a piece of iron and a magnet.

Spring experiment. We set the ball in motion.

Experience with a racket and a flying ball.

A force acting on a body can not only change the speed of its body, but also its individual parts.

A board lying on supports bends when a person sits on it.

For example, if you press your fingers on an eraser or a piece of plasticine, it will shrink and change its shape. It is called deformation.

Deformation is any change in the shape and size of the body.

Let's give another example. A board lying on supports bends if a person or any other load sits on it. The middle of the board moves a greater distance than the edges.

Under the influence of a force, the speed of different bodies at the same time can change equally. To do this, it is necessary to apply different forces to these bodies.

So, to move a truck, more force is needed than for a car. This means that the numerical value of the force can be different: greater or less. What is strength?

Force is a measure of the interaction of bodies.

Force is a physical quantity, which means it can be measured.

In the drawing, the force is shown as a straight line segment with an arrow at the end.

Force, like speed, is vector quantity. It is characterized not only by numerical value, but also by direction. The force is denoted by the letter F with an arrow (as we remember, the arrow denotes the direction), and its module is also denoted by the letter F, but without the arrow.

When talking about force, it is important to indicate to which point of the body the force is applied.

In the drawing, force is depicted as a straight line segment with an arrow at the end. The beginning of the segment - point A is the point of application of force. The length of the segment conventionally denotes the modulus of force on a certain scale.

So, the result of a force acting on a body depends on its modulus, direction and point of application.

The phenomenon of gravity. Gravity.

Let's release the stone from our hands - it will fall to the ground.

If you let go of a stone from your hands, it will fall to the ground. The same thing will happen with any other body. If a ball is thrown horizontally, it does not travel straight and evenly. Its trajectory will be a curved line.

The stone flies along a curved line.

The artificial Earth satellite also does not fly in a straight line, it flies around the Earth.

An artificial satellite moves around the Earth.

What is the reason for the observed phenomena? Here's the thing. These bodies are acted upon by a force - the force of gravity towards the Earth. Due to gravity towards the Earth, bodies raised above the Earth and then lowered fall. And also, because of this attraction, we walk on the Earth, and do not fly into endless Space, where there is no air to breathe.

The leaves of the trees fall to the Earth because the Earth attracts them. Due to gravity towards the Earth, water flows in rivers.

The Earth attracts any bodies to itself: houses, people, the Moon, the Sun, water in the seas and oceans, etc. In turn, the Earth is attracted to all these bodies.

Attraction exists not only between the Earth and the listed bodies. All bodies attract each other. The Moon and Earth are attracted to each other. The attraction of the Earth to the Moon causes the ebb and flow of water. Huge masses of water rise in the oceans and seas twice a day by many meters. You are well aware that the Earth and other planets move around the Sun, attracted to it and to each other.

The attraction of all bodies in the Universe to each other is called universal gravity.

The English scientist Isaac Newton was the first to prove and establish the law of universal gravitation.

According to this law, The greater the mass of these bodies, the greater the force of attraction between bodies. The forces of attraction between bodies decrease if the distance between them increases.

For everyone living on Earth, one of the most important values ​​is the force of gravity towards the Earth.

The force with which the Earth attracts a body towards itself is called gravity.

Gravity is denoted by the letter F with the index: Fgravity. It is always directed vertically downwards.

The globe is slightly flattened at the poles, so bodies located at the poles are located a little closer to the center of the Earth. Therefore, gravity at the pole is slightly greater than at the equator, or at other latitudes. The force of gravity at the top of a mountain is slightly less than at its foot.

The force of gravity is directly proportional to the mass of a given body.

If we compare two bodies with different masses, then the body with a larger mass is heavier. A body with less mass is lighter.

How many times the mass of one body is greater than the mass of another body, the same number of times the force of gravity acting on the first body is greater than the force of gravity acting on the second. When the masses of bodies are the same, then the forces of gravity acting on them are also the same.

Elastic force. Hooke's law.

You already know that all bodies on Earth are affected by gravity.

A book lying on the table is also affected by gravity, but it does not fall through the table, but is at rest. Let's hang the body on a thread. It won't fall.

Hooke's law. Experience.

Why do bodies lying on a support or suspended on a thread rest? Apparently, gravity is balanced by some other force. What kind of power is this and where does it come from?

Let's conduct an experiment. Place a weight in the middle of a horizontal board, placed on supports. Under the influence of gravity, the weight will begin to move down and bend the board, i.e. the board is deformed. In this case, a force arises with which the board acts on the body located on it. From this experiment we can conclude that, in addition to the force of gravity directed vertically downward, another force acts on the weight. This force is directed vertically upward. She balanced the force of gravity. This force is called elastic force.

So, the force that arises in a body as a result of its deformation and tends to return the body to its original position is called the elastic force.

The elastic force is denoted by the letter F with the index Fup.

The more the support (board) bends, the greater the elastic force. If the elastic force becomes equal to the force of gravity acting on the body, then the support and the body stop.

Now let's hang the body on a thread. The thread (suspension) stretches. An elastic force arises in the thread (suspension), as well as in the support. When the suspension is stretched, the elastic force is equal to the force of gravity, then the stretching stops. Elastic force occurs only when bodies are deformed. If the deformation of the body disappears, then the elastic force also disappears.

Experience with a body suspended by a thread.

There are deformations different types: tension, compression, shear, bending and torsion.

We have already become familiar with two types of deformation - compression and bending. You will study these and other types of deformation in more detail in high school.

Now let's try to find out what the elastic force depends on.

English scientist Robert Hooke , a contemporary of Newton, established how elastic force depends on deformation.

Let's consider experience. Let's take a rubber cord. We will fix one end of it in a tripod. The original length of the cord was l 0. If you hang a cup with a weight on the free end of the cord, the cord will lengthen. Its length will become equal to l. The cord extension can be found like this:

If you change the weights on the cup, the length of the cord will also change, and therefore its elongation Δl.

Experience has shown that the modulus of the elastic force when stretching (or compressing) a body is directly proportional to the change in the length of the body.

This is Hooke's law. Hooke's law is written as follows:

Fcontrol = -kΔl,

Body weight is the force with which the body, due to attraction to the Earth, acts on a support or suspension.

where Δl is the elongation of the body (change in its length), k is the proportionality coefficient, which is called rigidity.

The rigidity of a body depends on the shape and size, as well as on the material from which it is made.

Hooke's law is valid only for elastic deformation. If, after the cessation of the forces deforming the body, it returns to its original position, then the deformation is elastic.

You will study Hooke's law and types of deformations in more detail in high school.

Body weight.

IN Everyday life The concept of "weight" is used very often. Let's try to find out what this value is. In experiments, when a body was placed on a support, not only the support was compressed, but also the body, attracted by the Earth.

A deformed, compressed body presses on the support with a force called body weight . If a body is suspended on a thread, then not only the thread is stretched, but also the body itself.

Body weight is the force with which the body, due to attraction to the Earth, acts on a support or suspension.

Body weight is a vector physical quantity and is denoted by the letter P with an arrow above this letter, directed to the right.

However, it should be remembered that the force of gravity is applied to the body and the weight is applied to the support or suspension.

If the body and the support are stationary or moving uniformly and rectilinearly, then the weight of the body in its numerical value is equal to the force of gravity, i.e.

P = F heavy

It should be remembered that gravity is the result of the interaction between the body and the Earth.

So, body weight is the result of the interaction of the body and the support (suspension). The support (suspension) and the body are deformed, which leads to the appearance of an elastic force.

Units of force. The relationship between gravity and body weight.

You already know that force is a physical quantity. In addition to the numerical value (modulus), it has a direction, i.e. it is a vector quantity.

Force, like any physical quantity, can be measured and compared with force taken as a unit.

Units of physical quantities are always chosen arbitrarily. So, any force can be taken as a unit of force. For example, one can take the elastic force of a spring stretched to a certain length as a unit of force. The unit of force can also be taken as the force of gravity acting on a body.

Do you know that force causes a change in the speed of a body. That is why The unit of force is the force that changes the speed of a body weighing 1 kg by 1 m/s in 1 s.

This unit is named after the English physicist Newton. Newton (1 N). Other units are often used - kilonewtons (kN), millinewtons (mN):

1 kN = 1000 N, 1 N = 0.001 kN.

Let's try to determine the magnitude of the force in 1 N. It has been established that 1 N is approximately equal to the force of gravity that acts on a body weighing 1/10 kg, or more precisely 1/9.8 kg (i.e., about 102 g).

It must be remembered that the force of gravity acting on a body depends on the geographical latitude at which the body is located. The force of gravity changes as the height above the Earth's surface changes.

If we know that the unit of force is 1 N, then how to calculate the force of gravity that acts on a body of any mass?

It is known that, how many times the mass of one body is greater than the mass of another body, the same number of times the force of gravity acting on the first body is greater than the force of gravity acting on the second body. Thus, if a body weighing 1/9.8 kg is subject to a force of gravity equal to 1 N, then a body weighing 2/9.8 kg will be subject to a force of gravity equal to 2 N.

On a body weighing 5/9.8 kg - the force of gravity is 5 N, 5.5/9.8 kg - 5.5 N, etc. On a body weighing 9.8/9.8 kg - 9. 8 N.

Since 9.8/9.8 kg = 1 kg, then a force of gravity equal to 9.8 N will act on a body weighing 1 kg. The value of the force of gravity acting on a body weighing 1 kg can be written as follows: 9.8 N/kg.

This means that if a force equal to 9.8 N acts on a body weighing 1 kg, then a force equal to 2 times greater will act on a body weighing 2 kg. It will be equal to 19.6 N, and so on.

Thus, to determine the force of gravity acting on a body of any mass, it is necessary to multiply 9.8 N/kg by the mass of this body.

Body weight is expressed in kilograms. Then we get that:

Ftie = 9.8 N/kg m.

The value 9.8 N/kg is denoted by the letter g, and the formula for gravity will be:

where m is mass, g is called acceleration of free fall. (The concept of acceleration due to gravity will be taught in 9th grade.)

When solving problems where great accuracy is not required, g = 9.8 N/kg is rounded to 10 N/kg.

You already know that P = Ftie, if the body and the support are stationary or moving uniformly and linearly. Therefore, body weight can be determined by the formula:

Example. There is a kettle with water weighing 1.5 kg on the table. Determine the force of gravity and the weight of the teapot. Show these forces in Figure 68.

Given:

g ≈ 10 N/kg

Solution:

Ftie = P ≈ 10 N/kg 1.5 kg = 15 N.

Answer: Ftie = P = 15 N.

Now let's depict the forces graphically. Let's choose a scale. Let 3 N be equal to a segment 0.3 cm long. Then a force of 15 N must be drawn with a segment 1.5 cm long.

It should be taken into account that the force of gravity acts on the body, and therefore is applied to the body itself. The weight acts on the support or suspension, that is, it is applied to the support, in our case to the table.

Dynamometer.

The simplest dynamometer.

In practice, it is often necessary to measure the force with which one body acts on another. To measure force, a device called dynamometer (from Greek dynamis- force, metreo- I measure).

Dynamometers come in various designs. Their main part is a steel spring, which is given different shapes depending on the purpose of the device. The design of a simple dynamometer is based on comparing any force with the elastic force of a spring.

The simplest dynamometer can be made from a spring with two hooks mounted on a board. A pointer is attached to the lower end of the spring, and a strip of paper is glued to the board.

Mark on paper with a dash the position of the pointer when the spring is not tensioned. This mark will be the zero division.

Manual dynamometer - strength meter.

Then we will hang a load weighing 1/9.8 kg, i.e. 102 g, from the hook. A gravity force of 1 N will act on this load. Under the influence of this force (1 N), the spring will stretch and the pointer will move down. We mark its new position on paper and put the number 1. After that, we hang a load weighing 204 g and put a mark 2. This means that in this position the elastic force of the spring is 2 N. Having suspended a load weighing 306 g, we put a mark 3, and so on .d.

In order to apply tenths of a Newton, it is necessary to apply divisions - 0.1; 0.2; 0.3; 0.4, etc. For this, the distances between each whole mark are divided into ten equal parts. This can be done, taking into account that the elastic force of the spring Fupr increases as many times as its elongation Δl increases. This follows from Hooke's law: Fupr = kΔl, i.e. the elastic force of a body when stretched is directly proportional to the change in the length of the body.

Traction dynamometer.

A graduated spring will be the simplest dynamometer.

Using a dynamometer, not only gravity is measured, but also other forces, such as elastic force, friction force, etc.

For example, to measure the strength of various human muscle groups, it is used medical dynamometers.

To measure the muscular strength of the arm when clenching the hand into a fist, a manual dynamometer - strength meter .

Mercury, hydraulic, electric and other dynamometers are also used.

IN Lately Electric dynamometers are widely used. They have a sensor that converts the strain into an electrical signal.

To measure large forces, such as, for example, traction forces of tractors, prime movers, locomotives, sea and river tugs, special traction dynamometers . They can measure forces up to several tens of thousands of newtons.

In each such case, it is possible to replace several forces actually applied to the body by one force equivalent in its effect to these forces.

A force that produces the same effect on a body as several simultaneously acting forces is called the resultant of these forces.

Let us find the resultant of these two forces acting on the body along one straight line in one direction.

Let's turn to experience. We hang two weights weighing 102 g and 204 g from the spring, one below the other, i.e., weighing 1 N and 2 N. Note the length to which the spring is stretched. Let's remove these weights and replace them with one weight, which the spring stretches to the same length. The weight of this load turns out to be 3 N.

From experience it follows that: the resultant of forces directed along one straight line in the same direction, and its module is equal to the sum of the modules of the component forces.

In the figure, the resultant of the forces acting on the body is denoted by the letter R, and the component forces are denoted by the letters F 1 and F 2. In this case

Let us now find out how to find the resultant of two forces acting on a body along one straight line in different directions. The body is a dynamometer table. Let's place a weight weighing 5 N on the table, i.e. Let's act on it with a force of 5 N directed downwards. Let's tie a thread to the table and act on it with a force equal to 2 N, directed upward. Then the dynamometer will show a force of 3 N. This force is the resultant of two forces: 5 N and 2 N.

So, the resultant of two forces directed along one straight line in opposite directions is directed towards the larger force in magnitude, and its module is equal to the difference in the modules of the component forces(rice.):

If two equal and oppositely directed forces are applied to a body, then the resultant of these forces is zero. For example, if in our experiment the end is pulled with a force of 5 N, then the dynamometer needle will be set to zero. The resultant of the two forces in this case is zero:

The sled has rolled down the mountain and soon stops.

The sled, having rolled down the mountain, moves unevenly along a horizontal path, its speed gradually decreases, and after a while it stops. The man, having taken a running start, slides on his skate across the ice, but no matter how smooth the ice is, the man still stops. The bicycle also stops when the cyclist stops pedaling. We know that the cause of such phenomena is force. In this case it is the friction force.

When one body comes into contact with another, an interaction occurs that prevents their relative motion, which is called friction. And the force characterizing this interaction is called friction force.

Friction force- this is another type of force, different from the previously discussed gravity and elastic force.

Another reason for friction is mutual attraction of molecules of contacting bodies.

The occurrence of friction force is mainly due to the first reason, when the surfaces of bodies are rough. But if the surfaces are well polished, then upon contact some of their molecules are located very close to each other. In this case, the attraction between the molecules of the contacting bodies begins to manifest itself noticeably.

Experiment with a block and a dynamometer. We measure the friction force.

The friction force can be reduced many times if a lubricant is introduced between the rubbing surfaces. A layer of lubricant separates the surfaces of the rubbing bodies. In this case, it is not the surfaces of the bodies that come into contact, but the layers of lubricant. Lubrication is in most cases liquid, and the friction of liquid layers is less than that of solid surfaces. For example, on ice skates, the low friction when sliding on ice is also due to the effect of lubrication. A thin layer of water forms between the skates and the ice. In technology, various oils are widely used as lubricants.

At sliding one body on the surface of another will experience friction, which is called sliding friction. For example, such friction will occur when sleds and skis move on snow.

If one body does not slide, but rolls on the surface of another, then the friction that arises in this case is called rolling friction . Thus, when the wheels of a carriage or car move, or when logs or barrels roll on the ground, rolling friction appears.

The force of friction can be measured. For example, to measure the sliding friction force of a wooden block on a board or table, you need to attach a dynamometer to it. Then move the block evenly along the board, holding the dynamometer horizontally. What will the dynamometer show? Two forces act on the block in the horizontal direction. One force is the elastic force of the dynamometer spring, directed in the direction of movement. The second force is the frictional force directed against the movement. Since the block moves uniformly, this means that the resultant of these two forces is zero. Consequently, these forces are equal in magnitude, but opposite in direction. The dynamometer shows the elastic force (traction force), equal in magnitude to the friction force.

Thus, By measuring the force with which the dynamometer acts on a body during its uniform motion, we measure the friction force.

If you put a load on a block, for example a weight, and measure the friction force using the method described above, it will turn out to be greater than the friction force measured without the load.

The greater the force pressing the body to the surface, the greater the friction force that arises.

By placing a block of wood on round sticks, the rolling friction force can be measured. She turns out less strength sliding friction.

Thus, at equal loads, the rolling friction force is always less than the sliding friction force . That is why, even in ancient times, people used rollers to drag large loads, and later they began to use a wheel.

Rest friction.

Rest friction.

We became acquainted with the frictional force that arises when one body moves along the surface of another. But is it possible to talk about the force of friction between solid bodies in contact if they are at rest?

When a body is at rest on an inclined plane, it is held on it by the force of friction. Indeed, if there were no friction, the body would slide down the inclined plane under the influence of gravity. Let us consider the case when the body is at rest on a horizontal plane. For example, there is a closet on the floor. Let's try to move it. If you press the cabinet weakly, it will not budge. Why? The acting force in this case is balanced by the frictional force between the floor and the legs of the cabinet. Since this force exists between bodies at rest relative to each other, this force is called the static friction force.

In nature and technology, friction has great importance. Friction can be beneficial or harmful. When it is useful, they try to increase it, when it is harmful, they try to decrease it.

Without static friction, neither people nor animals would be able to walk on the ground, since when we walk we push off from the ground. When the friction between the sole of the shoe and the ground (or ice) is low, for example, in icy conditions, it is very difficult to push off from the ground, your feet slip. To prevent feet from slipping, the sidewalks are sprinkled with sand. This increases the friction force between the sole of the shoe and the ice.

Without friction, objects would slip out of your hands.

The force of friction stops the car when braking, but without friction it would not be able to stand still, it would skid. To increase friction, the surface of the car tires is made with ribbed protrusions. In winter, when the road is especially slippery, it is sprinkled with sand and cleared of ice.

Many plants and animals have various organs that serve for grasping (plant antennae, elephant trunks, prehensile tails of climbing animals). They all have a rough surface to increase friction.

Insert. Inserts are made of hard metals - bronze, cast iron or steel. Their inner surface is covered with special materials, most often babbitt (an alloy of lead or tin with other metals), and lubricated. Bearings in which the shaft slides along the surface of the liner when rotating are called plain bearings.

We know that the rolling friction force under the same load is significantly less than the sliding friction force. The use of ball and roller bearings is based on this phenomenon. In such bearings, the rotating shaft does not slide on a stationary bearing shell, but rolls along it on steel balls or rollers.

The structure of the simplest ball and roller bearings is shown in the figure. The bearing inner ring, made of solid steel, is mounted on the shaft. The outer ring is fixed in the machine body. When the shaft rotates, the inner ring rolls on balls or rollers located between the rings. Replacing plain bearings in a machine with ball or roller bearings can reduce the friction force by 20-30 times.

Ball and roller bearings are used in a variety of machines: cars, lathes, electric motors, bicycles, etc. Without bearings (they use frictional force), it is impossible to imagine modern industry and transport.

The charter of inland water transport requires mandatory determination and indication in the waybill of the cargo consignment when accepting it for transportation. This is necessary in order to accurately determine how much cargo has been accepted and must be delivered to the recipient, which makes it possible to establish transport responsibility for the safety of transportation, correctly calculate freight charges, rationally use the carrying capacity of ships and the cargo capacity of warehouses, as well as for quantitative accounting of completed transportation.

Methods for determining the mass of a consignment

To ensure that there are no liberties in resolving this issue, Articles 64-66 of the “Charter of Inland Water Transport” establish the procedure and methods for determining the mass of a consignment of cargo.

In accordance with the standards, all methods are divided into 3 groups:

• determination of the mass of a consignment by weighing;
• calculation methods;
• at the request of the sender.

The choice of method is influenced by a number of factors:

• type of cargo;
• container type;
• method of transportation;
• belonging to the berth where cargo is accepted for transportation.

It should be noted that when choosing a method, the basic principle must be observed: the weight of the consignment must be determined in the same way as it can be determined at the point of destination or transshipment from one type of transport to another. This is due to two factors.

Firstly, the method for determining the mass of a consignment at the point of departure and destination must be the same. Only under this condition can one judge the presence or absence of partial loss of cargo in transit, because different methods for determining mass may not give identical results, which will lead to claims from the cargo owner.

Secondly, the departure port selects the method based on the technical capabilities of the destination port. This is determined by the fact that destination ports are, as a rule, peripheral and their technical capabilities are lower than the technical capabilities of departure ports.

Determining the mass of a consignment by weighing

Weighing- the most accurate and most expensive way to determine the mass of a cargo shipment, increasing fleet downtime by 15-20%. In accordance with Art. 50 UVVT, in order to determine the mass of cargo, the required number of scales installed at the side of the vessel must be located at the berths of general and non-public use, and at elevators - in the chain of mechanization of transshipment operations.

This method is used in all cases of transportation of grain cargo (except for those transported in standard containers), salt transported in bulk, coal and other bulk cargo, when transporting mass when doubt arises about the correctness, and in some other cases. The weight of the cargo consignment is determined by weighing in all cases if loading is carried out on non-public berths, and by the port if the cargo is received and loaded on public berths.

Transport organizations have the right (Article 65 of the UVVT) to check the weight of the cargo determined by the sender. In the case when cargo is accepted for transportation, which then must be transferred to another vehicle with a weight check, then this right becomes the responsibility of the carrier.

For weighing, various types of scales can be used: commodity, automobile, carriage, bunker. The choice of scales for each berth is determined by technical equipment and transportation rules. The number of scales for each berth is determined by calculation depending on their productivity. The permissible error when weighing should be no more than 0.1%.

It should be noted that when determining the mass of cargo by weighing, the basic principle must be observed: the scales at the point of departure and destination must be of the same type. This is due to the fact that different types of scales give different errors.

Since weighing is a labor-intensive and expensive method, in practice, calculation methods for determining the mass of cargo are more often used.

Determining the mass of a consignment based on the standard mass of individual packages

Until 1956, the weight of a consignment was determined for all cargo only by weighing. Since 1956, work has been carried out to standardize packaging and therefore some types of products are produced in standard weight packaging (sugar, flour, cereals, etc.). According to Article 65 of the Air Transport Regulations, cargo in standard weight packaging is not weighed when accepted for transportation. The mass of a consignment is determined as the product of the mass of one cargo item by the number of items.

Q n = N n q cm , kg,

where Q n is the mass of the cargo consignment, kg;
N n — number of places in a consignment, units;
q cm — standard weight of one cargo item, kg;
An entry is made in the invoice: “According to standard.”

According to a stencil or non-standard weight of individual cargo items

When cargo is transported in non-standard containers (shoes, clothing, equipment, machines, etc.), the mass of the cargo shipment is determined as the sum of the mass of each item.

Q n = ∑ q i tr. , kg,

where q i tr. - the weight of each piece is applied with paint directly on the container or on various tags attached to each piece of cargo.

In transport documents, in the “name of cargo” column, a list of goods is given and their weight is indicated, then the total weight is summed up and recorded in the “batch weight” column and the note “According to the stencil” is made.

According to the conventional weight of individual cargo packages

The weight of some specific cargo (cars, furniture, animals, plants, etc.) is accepted for transportation without weighing according to the conventional weight of individual cargo items. This is due to the fact that it is not advisable to determine the actual mass of this category of cargo due to their relatively small mass with a significant occupied volume, and also due to the fact that their mass decreases during transportation (animals).

The notional weight is greater than the actual weight and thus makes it possible to obtain increased freight charges corresponding to the actual cost of transporting these goods.

To ensure that there is no arbitrariness when determining the mass of a consignment using this method, the conditional mass is determined and approved in Appendix No. 5 of price list 14-01. Formula for determining the mass of a consignment:

Q n = n · q arb. , kg,

where q cond. — weight of one piece, kg;
n — number of places, units;
“Conditionally” is written in transport documents.

Determining the mass of a consignment by measuring the stacks

Based on size and average density (volumetric mass), the mass of bulk and timber cargo is determined. As a result of measuring the stack, the volume of the stack is obtained. Measurements can be made both on shore and in the hold of the ship. The mass is determined by multiplying the volume of the stack found as a result of measurement by its volumetric mass.

Q n = V γ, kg,

where γ is the density of the cargo, t/m 3 ;
V is the volume of the stack, m3.

The conversion of volumetric measures into mass measures for individual types of cargo is given in Appendix No. 6 of price list 14-01.

When determining the mass of timber cargo, 1 m 3 of dense wood is taken as a volumetric measure of round timber and lumber, and a folded cubic meter is taken as a volumetric measure of the balance sheets of a mine stand and firewood.

If the volume of timber cargo is determined in dense wood, then their mass is determined by the formula:

Q p = γ pl · V pl. , T,

where γpl is the density of dense wood t/m 3;
Vpl - volume of dense wood, m3.

If the volume of timber cargo is set in a folded measure, then their mass will be determined by the formula:

Q p = K skl: γ pl V skl, t,

where Kcl = 0.64 is the conversion factor from folded cubic meters to cubic meters of dense wood;
V cl - folded volume of wood, m 3.

If raw wood and firewood, rafted during the current navigation and loaded into the vessel from the water, round timber and sawn timber after the first of October of the previous year are presented for transportation.

When transporting sand and sand-gravel mixture in vessels adapted for hydromechanized loading and unloading, the weight is determined based on the average height of the unfilled part of the bunker; ten measurements are taken from the edge of the hopper to the surface of the load (h i) along each side at equal intervals:

h with p = 20 Σ h i i - l 20, m

You can then determine the height of the load and its volume.

h r = h σ - h avg, m,

where h σ is the height of the hopper;
h r — load height, m;
In traditional documents, in the column “method of determining mass”, “By measuring stacks” is written.

According to the vessel's draft

This method determines the mass of bulk and bulk cargo (except for grain, the mass of which is determined by weighing). In this case, two methods are used to determine the mass: according to the load size table or load scale and calculated.

For this purpose, the average draft of the vessel is determined. Draft measurements are taken at six points: three points on the port side (bow, middle, stern) and three on the starboard side. The average draft is determined by the formula:

T s r = T n l. b + 2 T s r l. b + T k l. b + T n p. b + 2 T s r p. b + T k p. b 8, m

where Tn, Tav, Tk are the draft of the bow, middle and stern, respectively, for the left and right sides, m.

In order to more accurately determine the mass of a cargo consignment, the draft of the middle part of the vessel, where the largest amount of cargo is located, is doubled.

Based on the average draft of the vessel when loaded and unladen, the weight of the loaded cargo is determined using the cargo size chart or the load scale.

The mass of the shipment Q n will be equal to:

Q n = Q 2 – Q 1, t,

Where Q 2 and Q 1 are the loading of the vessel, loaded and empty, t;
T 0, T gr—register values ​​of sediment, m;
₸ 0, ₸ gr - average value of sediment, m;
Q p—register load capacity, t;
In this case, the value of Q 1 > 0 indicates that the ship may have ballast, fuel, reserve drinking water etc.

If there is a cargo scale for the vessel, then the mass of the cargo shipment is determined from it.

The load scale is a passport characteristic of the vessel and is presented in the form of a table.

In cases where the ship does not have a cargo size chart or a cargo scale, the mass of the batch can be determined by calculation. The basis for determining the mass of loaded (unloaded) cargo based on the vessel's draft by calculation is the principle of the difference in the displacement of a loaded and unladen vessel.

Q n = D gr – D o, t,

where D gr, D o - displacement when loaded and empty, i.e.

The vessel's displacement is determined by the formula:

D c = γδ L BT, m,

where L is the length of the vessel, m;
B is the width of the vessel, m;
T—vessel draft, m;
δ—displacement completeness coefficient is defined as the ratio of the volume of the underwater part of the vessel to the volume of the parallelepiped that describes the underwater part of the vessel;

γ—water density, t/m3;
γ = 1- for fresh water;
γ = 1.003-1.031 - for salt water (varies depending on the sea basin).

Based on this, the mass of the cargo shipment will be equal to:

Q n = δγ LB (T gr – T 0), i.e.

This formula is valid for determining the mass of cargo when transported in a basin with the same water density by vessels with contours that do not change in height or when the vessel is loaded to its full capacity. In relative cases, it is necessary to take into account the change in displacement coefficient and water density. Then the formula will take the form:

Q n = LB (δ gr γ 2 T gr – δ o γ 1 T 0), t,

where δ gr, δ o are the displacement coefficients when loaded and empty;
γ 2, γ 1 - density of water at the point of loading and unloading, t/m 3.

When determining the mass of cargo by draft, it is necessary to take into account changes in reserves of fuel, ballast, drinking water, etc. during transshipment operations. The formula will be:

Q n = (D gr - ∑q gr) – (D 0 - ∑q 0), t,

where ∑q gr, ∑q 0 is the amount of reserves of fuel, drinking water and ballast before and after loading.

When determining the mass of cargo by the vessel's draft, the most labor-intensive and not always sufficiently accurate process is the process of measuring the vessel's draft (waves).

In transport documents it is written: “By draft”.

Determination of the mass of a consignment of cargo transported in bulk in ships

The weight of a shipment can be determined in three ways:

• according to calibration tables of coastal tanks;
• by calculation;
• according to the cargo tables of ships.

The first method is the simplest. The low tide height in the tank is determined before and after loading; for each, the volumes are determined using calibration tables, the difference of which will give the volume of cargo loaded into the ship. Then the mass of the cargo consignment will be equal to:

Q n = V n γ n, t,

V n - volume of petroleum product, m 3;
γ n is the density of the oil product, t/m3.

In the absence of calibration tables for coastal cylindrical tanks, the mass of petroleum products can be obtained by calculation:

Q n = πR 2 hγ n, t,

where R is the radius of the tank, m;
h—filling height, m;
γ n is the density of the oil product, t/m3.

This method is used in cases where the distance from coastal reservoirs is no more than 2 km; if more than 2 km, then it is prohibited to use this method (losses in pipelines).

In the absence of calibration tables for shore tanks or when these tanks are located more than 2 km from the ship, the mass of the cargo consignment can be determined from the ships' cargo tables.

The essence of the method is as follows: the filling height is measured in all tanks of the ship before and after loading, then the volume in each tank is determined, multiplied by the density of the corresponding cargo, and the resulting values ​​are summed up. This is how the total mass of the cargo loaded into the ship is found.

Determination of the mass of a consignment at the request of the sender

This is the simplest of all methods. It is used to determine the mass of low-value bulk cargo.

The shipper is responsible for the correct determination of the mass of the consignment. At the destination, the cargo is released without checking the weight. However, you need to pay attention to the following points:

• if the shipper incorrectly stated the weight of the cargo, then according to Art. 198 UVVT, a fine is collected from him according to the tariff (in the amount of double the freight charge accrued for an unspecified amount of cargo). In addition, freight charges are charged for an unspecified amount of cargo;
• If an accident occurs as a result of an incorrectly specified mass, then, in addition to the above payments, the cargo owner pays all expenses for eliminating the accident.

In transport documents it is written: “At the request of the sender.”

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