Starting off and accelerating the train when leaving the station. Starting and accelerating the train when leaving the station If the electric locomotive moves abruptly
Let no one think that Newton's great creation
can be overthrown by the theory of relativity
or some other theory.
Newton's clear and broad ideas
will forever retain their significance as the foundation on which
our modern physical concepts are built...
1948 Albert Einstein
BOX OF QUALITY PROBLEMS IN PHYSICS: INERTIA
Didactic materials on physics for students, as well as their parents;-) and, of course, for creative teachers.
For those who love to learn!
I present to your attention 40
qualitative problems in physics on the topic of: "Inertia". Let's pay tribute to the integration: biophysics, fiction, important nuances for car owners, passengers and pedestrians… According to the established tradition of green pages, let’s treat ourselves masterpieces of world painting... We will give detailed answers to some problems ;-) and ... a lyrical digression from the history of physics:
Galileo's principle of inertia - Newton's first law of mechanics.
Task No. 1
Coming out of the water, the dog shakes itself. What phenomenon helps her in this case to free her wool from water? Explain your answer.
Task No. 2
“Pantry of the Sun”, 1945, Mikhail Mikhailovich Prishvin
“...Travka didn’t have to wait long. With her subtle hearing, she heard the clack of a hare's paw, inaccessible to human hearing, through the puddles on the swamp path. These puddles appeared on Nastya’s morning tracks. The Rusak would certainly now appear at the Lying Stone itself.
The grass behind the juniper bush crouched down and strained its hind legs for a mighty throw, and when it saw the ears, it rushed.
Just at this time, the hare, a big, old, seasoned hare, hobbling barely, decided to suddenly stop and, even standing up on his hind legs, to listen to how far away the fox was barking.
So they came together at the same time: The grass rushed, and the hare stopped.
And the Grass was carried through the hare.
While the dog was righting itself, the hare was already flying with huge leaps along the Mitrashina path straight to the Blind Elan ... "
Why was Grass carried through the hare?
Answer: When the hare suddenly stopped, the dog Travka, by inertia, continued its movement forward and jumped over the hare.
Task No. 3
The hare, escaping from the wolf pursuing him, makes sharp jumps to the side. Why is it difficult for a wolf to catch a hare, although he runs faster?
Answer: At the moment when the hare makes a sharp turn, the wolf, by inertia, continues to move forward and cannot grab the hare.
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Komarov Alexey Nikanorovich(1879–1977) is considered the founder of the Russian animalistic school. Alexey Nikanorovich Komarov illustrated scientific and children's books, created drawings for stamps, postcards, and visual aids. Several generations of children grew up learning from textbooks with his wonderful drawings.
For the curious: Winter coat of a brown hare slightly lighter than summer (unlike white hares, brown hares are never snow-white in winter); the head, tips of the ears and the front of the back remain dark in winter. Winter coat of a white hare– dazzling white, with the exception of the black tips of the ears. However... in areas where there is no stable snow cover, hares do not turn white for the winter ;-)
Task No. 4
Ripe pods of leguminous plants, quickly opening, describe arcs. What phenomenon underlies this method of seed dispersal?
Answer: Ripe pods of leguminous plants, quickly opening, describe arcs - at this time, the seeds, breaking away from their places of attachment, move tangentially to the sides by inertia and fall significantly further than the mother plant.
Inertia in wildlife:: Flying fish
For the curious: In the tropical zones of the Atlantic and Indian oceans, the flight of so-called flying fish is often observed, which, fleeing from sea predators, jump out of the water and, with a favorable wind, make a gliding flight, covering distances of up to 200-300 m at an altitude of 5-7 m. The fish rises to air due to fast and strong vibrations of the caudal fin. First, the fish rushes along the surface of the water, then a strong blow of the tail lifts it into the air. Spread out long pectoral fins support the body of the fish like a glider. The flight of a flying fish is stabilized by its caudal fins; fish move by inertia.
Alfred Edmund Brehm(Alfred Edmund Brehm; 02.02.1829–11.11.1884) - German zoologist and traveler, author of the famous popular science work "Life of animals".
For lovers of animal art, I suggest you take a look at the green pages:
§ Who is Tsutsik? A tiny study
tsutsik can be different :-)
§ Friedrich Wilhelm Kuhnert
Lions, elephants, tigers, birds...
§ Mystery paintings by artist Stephen Gardner (Part I)
pandas, black bears (baribals), owls, wolves
§ Mystery paintings by artist Stephen Gardner (Part II)
horses, coyotes, cougars, walruses
§ Mystery paintings by artist Stephen Gardner (Part III)
sea turtles, whales, killer whales, dolphins
Problem #5
“Frog Traveler”, 1887, Vsevolod Mikhailovich Garshin
“...Then the frog could no longer stand it and, forgetting all caution, screamed with all her might:
- It's me! I!
And with that scream she flew upside down to the ground. The ducks squawked loudly; one of them wanted to pick up the poor companion on the fly, but missed. The frog, shaking all four legs, quickly fell to the ground; but since the ducks flew very quickly, she fell not directly on the place where she screamed and where there was a hard road, but much further, which was great happiness for her, because she splashed into a dirty pond at the edge of the village.
She soon emerged from the water and immediately again vehemently screamed at the top of her lungs:
- It's me! I came up with this!..."
Why did the frog fall to the ground in a different place from where it started to fall?
Answer: The frog, falling down, maintained its horizontal speed by inertia, so it fell in a different place from where it began to fall.
Problem #6
Why do buildings and bridges collapse during an earthquake? Why is it recommended, if possible, to leave the building and move to an open space during earthquakes?
Answer: The main cause of destruction during earthquakes is strong tremors and earth tremors reaching the earth's surface. Due to the inertia and rigidity of the structure of ground structures, they collapse.
The whole earth shook, a ridge of clouds rushed.
The shaking of the earth carried away cities...
All the shackles of heaven were able to open.
The joints of the earth were shaken by rampant shaking,
He squeezed the poor land into such a vice,
That he broke huge rocks into pieces...
Nizami
Nizami Ganjavi Abu Muhammad Ilyas ibn Yusuf (about 1141 - about 1209) is a classic of Persian poetry, one of the greatest poets of the medieval East.
Basin Pyotr Vasilievich(1793–1877) – Russian genre painter and portrait painter.
Problem No. 7
Why is it prohibited to tow a car with faulty brakes using a flexible cable?
Problem No. 8
Why does the driver reduce the speed of the car when turning?
Problem No. 9
Why is it necessary to securely secure loads in the back of a truck?
Problem No. 10
Why can’t you cross the street in front of nearby traffic?
Problem No. 11
Why shouldn't you jump off the running board of a bus or tram?
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Zuev Agap Sergeevich(01/31/1922–1985) - Soviet, Russian painter. Member of the Union of Artists of the USSR.
Problem No. 12
Why do both wheels brake when stopping a motorcycle quickly? What can happen if you brake only with the front wheel?
Problem No. 13
Why should the rear red light on a car turn on when the driver of the car presses the brake pedal?
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Pimenov Yuri Ivanovich(1903–1977) – Soviet painter and graphic artist. People's Artist of the USSR. Laureate of Lenin and two Stalin prizes of the second degree.
Problem No. 14
Explain the reason that when a car brakes sharply, its front part goes down.
Answer: During sharp braking, the front part of the car continues to move by inertia, turning around its front wheels at a small angle, which leads to its lowering.
Problem No. 15
What changes occurred in the movement of the car if the passenger was pressed against the back of the seat; to the right side of the seat back?
Answer: The car began to increase speed; began to turn left.
Problem No. 16
Explain the purpose of seat belts and airbags in a car. Why does the effectiveness of airbags depend on whether the driver and front seat passenger are wearing seat belts? Why can the deployment of airbags in the event of an accident cause serious injury to the driver and passenger of the car if they were not wearing seat belts?
Problem No. 17
Warning road signs inform drivers that they are approaching a dangerous section of the road, driving along which requires taking measures appropriate to the situation. There are three warning road signs in front of you. Give each of them an explanation and indicate what measures the driver of the vehicle should take upon seeing such a sign.
Warning road signs
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Answer: Sign number: 1.15 – Slippery road. A section of road with increased slipperiness of the roadway. . Sign number: 1.23 – Children. A section of road near a children's institution (school, health camp, etc.), on the roadway of which children may appear. The driver must reduce speed. Sign number: 1.27 – Wild animals. The sign warns that wild animals may run onto the road. The driver must reduce speed.
Problem No. 18
Why are passengers required to fasten their seat belts before takeoff and landing?
Problem No. 19
Why should passengers standing on a bus, tram or trolleybus hold on to the handrails?
Problem No. 20
In which direction do bus passengers deviate when the speed suddenly increases? during a sudden stop?
Problem No. 21
What change occurred in the movement of the water bus if passengers suddenly deviated to the right?
Problem No. 22
In which direction does a tripping person fall? a person who slipped? Why?
Problem No. 23
“Chuk and Gek”, 1939, Arkady Petrovich Gaidar
“...The whole next day the road went through forests and mountains. On the climbs, the coachman jumped off the sleigh and walked along the snow next to him. But on the steep slopes the sleigh raced with such speed that it seemed to Chuk and Gek as if they, along with the horses and sleigh, were falling to the ground straight from the sky.
Finally, in the evening, when both people and horses were quite tired, the coachman said:
- Well, here we are! Behind this toe there is a turn. Here, in the clearing, is their base... Hey, but-oh!... Pile up!
Squealing merrily, Chuk and Huck jumped up, but the sleigh was jerked, and they plopped down into the hay..."
Why did the boys flop into the hay when the sleigh was pulled?
Answer: The boys' bodies, by inertia, remained at rest, and their legs began to move forward along with the sleigh, so Chuk and Gek fell back and plopped into the hay.
Problem No. 24
Why do ice jams form at river bends during ice drift?
Problem No. 25
Why, when rafting timber, a large number of logs are thrown ashore at the bends of the river? Why are rafts of trees only allowed in many countries?
Belov Kondraty Petrovich(03/23/1900–05/04/1988) – Soviet painter. People's Artist of the RSFSR. In 1949 landscape "Timber rafting on the Irtysh" was included in the exhibition of Soviet art exhibited in a number of foreign countries. Art critics called him the first complete and expressive portrait of Siberia.
For the curious: Timber rafting- the traditional and cheapest way to transport it to woodworking enterprises. The most intensive felling is usually carried out in winter, since this causes less damage to the forest. On sleighs pulled by tractors or powerful cars, the forest is transported to the bank of the frozen river. Then, during the spring flood, rafters launch it into the water. With mole rafting, the forest floats further on its own. When rafting, rafts are tied from logs. Trees floating freely along the river quickly get wet and sink to the bottom. A large number of logs are thrown ashore at the bends of the river. In addition, when a large number of trees are lowered at the same time, their trunks cause irreparable damage to the river fauna, cutting off algae and thereby depriving fish and amphibians of food. When sunken trunks rot, substances toxic to fish also pass into the water. Finally, trunks sticking out from the river bottom pose a great danger to river vessels. Tree trunks that are not caught from the river in a timely manner become unsuitable for industrial use. That's why In many countries, rafting of trees is allowed only by rafts.
Problem No. 26
Why is it prohibited to suddenly lift a load with a crane?
Problem No. 27
When an electric locomotive suddenly starts moving a train, the coupling may break. In which train is a rupture most likely to occur, loaded or unladen? Why?
Problem No. 28
How is the free surface of oil located in the tank when the electric locomotive picks up speed? When does he slow down? Support your answer with drawings.
Problem No. 29
The train approaches the station and slows down. In which direction is it easier to drag a heavy suitcase along the floor of the carriage at this time - along the train or in the opposite direction?
Answer: Along the train.
Problem #30
Why does the chuck continue to rotate after turning off the motor of a drilling machine (electric drill)?
Inertia in military equipment:: Artillery
It’s not thunder that rumbles in the clouds and it’s not lightning that burns -
Our guns speak with a mighty voice!
Don’t touch, enemy, your native land, don’t touch the land of labor!
Holy vengeance leads to battle! Aim straight! Fire! Fire! Fire!…
"March of Artillery", 1944
words: Sergey Alexandrovich Vasiliev
music: Anatoly Grigorievich Novikov
Usypenko Fedor Pavlovich(1917–2000) – Soviet painter, member of the Union of Artists of the USSR. People's Artist of the RSFSR.
For the curious: The phenomenon of inertia was used in the design of fuses for artillery shells. When a projectile, hitting an obstacle, suddenly stops, the explosive capsule, placed inside the projectile but not rigidly connected to its body, continues to move by inertia and hits the tip of the fuse connected to the body. In the same way, the significant acceleration received by the projectile at the moment of firing is used to remove the fuse, eliminating the danger of the projectile exploding during storage, transportation, or when loading the gun.
Problem No. 31
All the grains of the grindstone move along with it around the circle. But as soon as the grain breaks off from the stone, its movement becomes linear. Why?
Problem No. 32
In order for the mercury column in a medical thermometer to drop, the thermometer is “shaken” - lowered down, and then abruptly stopped. What is the reason for the mercury column to drop?
Answer: At the moment of a sharp stop of the thermometer body, the mercury, by inertia, continues to move and falls.
Problem No. 33
Why does a cyclist increase his speed when approaching a rise in the road?
Problem No. 34
Why do they take a running start when jumping long and high? Why is it easier to jump over a puddle, stream, or ditch with a running start?
Problem No. 35
Why does the impact of steam hammers on the anvil shake the soil much less with heavy anvils than with lighter ones? Why should an anvil be significantly more massive than a hammer?
Problem No. 36
Why can’t a full cup of tea or a bowl of soup be quickly and abruptly placed on the table without spilling?
Problem No. 37
There are two ways to split logs. In the first case, the log is struck with a fast-moving axe. In the second, they drive the ax into the log with a weak blow, and then, swinging the ax with the impaled log, they hit the butt against the block. Explain the mechanical phenomena observed in this case.
Answer: When chopping wood, hitting a log with an axe, it continues to move due to inertia and enters deep into the motionless log. When the butt of an ax that is partially embedded in a log is struck against a block on which firewood is cleaved, the ax stops, but the log continues to move due to inertia and splits.
Problem No. 38
What happens to the rider if the horse stumbles while jumping over an obstacle?
Answer: When the horse suddenly stops, the rider, moving by inertia, will fall forward over the horse's head.
Problem No. 39
Why does a ruler suspended on paper rings break when struck sharply, but the rings remain intact?
Problem No. 40
Place a postcard on the glass and place a coin on the postcard. Click on the card. Why does the card fly off and the coin fall into the glass?
Answer: Due to the inertia of the coin and insufficient interaction between the coin and the card.
And in conclusion... a little from history of physics…
Give me matter and motion and I will build the Universe.
1640 Rene Descartes
Rene Descartes(Rene Descartes; 03/31/1596–02/11/1650) - French philosopher, mathematician, mechanic, physicist and physiologist, creator of analytical geometry and modern algebraic symbolism.
Galileo's principle of inertia - Newton's first law of mechanics
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about the essence of movement and the system of the world... Movement
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Galileo Galilei(Galileo Galilei; 02/15/1564–01/08/1642) - Italian physicist, mechanic, astronomer, philosopher and mathematician. Galileo Galilei is rightly called the founding father of experimental physics.
Justus Sustermans(Justus Sustermans; 1597–1681) - Flemish painter of the Baroque era.
In the first part of his poem "Movement" Alexander Sergeevich Pushkin describes a dispute between ancient Greek scientists about the essence of movement. In the second part, he refers to the existence of two opposing systems of the world - geocentric(The Earth is motionless, but the Sun moves around the Earth) and heliocentric(The Earth revolves around the Sun) created by Claudius Ptolemy and Nikolai Copernicus.
It’s not for nothing that stubborn is mentioned here ;-) Galileo Galilei.
In 1632, the work was published in Florence Galileo Galilei "Dialogue on the Two Major Systems of the World"(about the geocentric system of Ptolemy and the heliocentric system of the world of Copernicus). In it, Galileo laid the foundations of dynamics - the principle of inertia and the classical principle of relativity.
In 1687 Isaac Newton formulated the laws of dynamics. Not only the movement of planets around the Sun, but also much more complex phenomena have become understandable and calculable. Isaac Newton adopted Galileo's principle of inertia as the first law of dynamics..
Galileo formulated this principle as a consequence of his experiments while studying the fall of bodies on an inclined plane.
Galileo did not distinguish between concepts "force" And "weight", so installed by him principle of inertia did not claim a fundamental law of nature.
Newton put law of inertia (Galilean principle of inertia) at the head of his entire system of mechanics.
In modern formulation principle of inertia States that every body maintains a state of rest or uniform rectilinear motion until the influence of other bodies takes it out of this state.
Isaac Newton(Sir Isaac Newton; 01/04/1643–03/31/1727) - English physicist, mathematician, mechanic and astronomer, one of the creators of classical physics. The author of the fundamental work “Mathematical Principles of Natural Philosophy,” in which he outlined the law of universal gravitation and the three laws of mechanics, which became the basis of classical mechanics.
Thornhill James(James Thornhill; 07/25/1675–05/13/1734) - English painter, founder of historical English painting.
...from the phenomena of motion to the study of the nature of forces and then from these forces to the demonstration of other phenomena: ... the movements of planets, comets, the Moon and the sea...
1686 Isaac Newton
I wish you success in making your own decision.
quality problems in physics!
Literature:
§ Katz Ts.B. Biophysics in physics lessons
§ Lukashik V.I. Physics Olympiad
Moscow: Prosveshchenie Publishing House, 1987
§ Tarasov L.V. Physics in nature
Moscow: Prosveshchenie Publishing House, 1988
§ Perelman Ya.I. Do you know physics?
Domodedovo: publishing house "VAP", 1994
§ Zolotov V.A. Questions and tasks in physics grades 6-7
Moscow: publishing house "Prosveshchenie", 1971
§ Tulchinsky M.E. Qualitative problems in physics
Moscow: Prosveshchenie Publishing House, 1972
§ Kirillova I.G. Reading book on physics grades 6-7
Moscow: Prosveshchenie Publishing House, 1978
§ Erdavletov S.R., Rutkovsky O.O. Interesting geography of Kazakhstan
Alma-Ata: Mektep Publishing House, 1989.
The theory of train motion is an integral part of the applied science of train traction, which studies the issues of train movement and the operation of locomotives. For a clearer understanding of the operating process of an electric locomotive, it is necessary to know the basic provisions of this theory. First of all, let's consider the main forces acting on the train when moving - this is the traction force F, the resistance to movement W, the braking force B. The driver can change the traction force and braking force; the force of resistance to movement cannot be controlled.
How are these forces formed, what do they depend on? We have already said that each driving wheel pair of an electric locomotive has a separate traction motor, which is connected to it by a gear reducer (Fig. 3, a). The small gear wheel of the gearbox (gear) is mounted on the shaft of the traction motor, and the large one is mounted on the axis of the wheelset. The ratio of the number of teeth of the large wheel to the number of teeth of the small one is called the gear ratio. If you start the traction motor, a torque is created on its shaft. The speed of rotation of the wheelset will be 1 time less than the speed of rotation of the engine shaft, but the torque is correspondingly 1 time greater (if you do not take into account the efficiency of the gear drive).
Let's consider the conditions necessary for an electric locomotive to start moving.
If the wheels of the electric locomotive did not touch the rails, then after starting the traction motors they would simply rotate, remaining in the same place. However, due to the fact that the wheels of the locomotive come into contact with the rails when torques M are transmitted to the axles of the wheel pairs, an adhesion force appears between the surfaces of the wheels and the rails.
In passing, we note that initially, when creating the first locomotives - steam locomotives, they generally doubted the possibility of their movement along a “smooth” rail track. Therefore, it was proposed to create gearing between the wheels of the locomotive and the rails (Blenkinson locomotive). A locomotive was also built (Brunton locomotive), which moved along the rails with the help of special devices that were alternately pushed off the track. Fortunately, these doubts were not justified.
The moment M (see Fig. 3) applied to the wheel forms a pair of forces with the shoulder R. The force FK is directed against the movement. It tends to move the reference point of the wheel relative to the rail in the direction opposite to the direction of movement. This is prevented by the reaction force of the rail, the so-called adhesion force Fcu, which arises under the action of pressing the wheel on the rail at the support point. According to Newton's third law, it is equal and opposite to the force FK. This force forces the wheel, and therefore the electric locomotive, to move along the rail.
At the point of contact of the wheel with the rail there are two points, one of which belongs to the bandage Ab, and the other to the rail Ar. For an electric locomotive standing still, these points merge into one. If, during the transfer of torque to the wheel, point Ab moves relative to point Lp, then in the next instant the points of the bandage will begin to alternately come into contact with point Lp. In this case, the locomotive does not start moving, and if it was already moving, then its speed sharply decreases, the wheel loses its support and begins to slip relative to the rail - slipping.
In the case when points Ap and Ab do not have a relative displacement, at each subsequent moment of time they leave contact, but at the same time the following points continuously come into contact: BB with Br, Wb with BP, etc.
The point of contact between the wheel and the rail represents the instantaneous center of rotation. Obviously, the speed with which the instantaneous center of rotation moves along the rails is equal to the speed of the forward motion of the locomotive.
To move an electric locomotive, it is necessary that the adhesion force at the point of contact between the wheel and the rail feu, equal but opposite in direction to the force FK, does not exceed a certain limit value. Until it reaches it, the force FC creates a reactive torque FCVLR, which, according to the condition of uniform motion, must be equal to the torque.
The sum of the adhesion forces at the points of contact of all wheels of the electric locomotive determines the total force, called the tangential traction force FK. It is not difficult to imagine that there is a certain maximum traction force, limited by adhesion forces, at which boxing does not yet occur.
The emergence of adhesion force can be somewhat simplified as follows. There are irregularities on the seemingly smooth surfaces of rails and wheels. Since the contact area (contact surface) of the wheel and the rail is very small, and the load from the wheels on the rails is significant, large pressures arise at the point of contact. The irregularities of the wheel are pressed into the irregularities on the surface of the rails, resulting in the adhesion of the wheel to the rail.
It has been established that the adhesion force is directly proportional to the pressing force - the load from all moving wheels on the rails. This load is called the adhesion weight of the locomotive.
To calculate the maximum traction force that a locomotive can develop without exceeding the adhesion force, in addition to the adhesion weight, it is also necessary to know the adhesion coefficient. By multiplying the adhesion weight of the locomotive by this coefficient, the traction force is determined.
The work of many scientists and practitioners is devoted to the problem of maximizing the use of adhesion between wheels and rails. It has not yet been finally resolved.
What determines the value of the adhesion coefficient? First of all, it depends on the material and condition of the contacting surfaces, the shape of the bands and rails. With increasing hardness of tires of wheelsets and rails, the coefficient of adhesion increases. When the rail surface is wet and dirty, the coefficient of adhesion is lower than when it is dry and clean. The influence of the rail surface condition on the adhesion coefficient can be illustrated by the following example. In the Trud newspaper of December 13, 1973, in the article “Snails against the steam locomotive,” it was reported that one of the trains in Italy was forced to stop for several hours. The reason for the delay turned out to be a huge number of snails crawling across the railway track. The driver tried to guide the train through this moving mass, but to no avail: the wheels were slipping and he could not budge. Only after the stream of snails thinned out was the train able to move.
The adhesion coefficient also depends on the design of the electric locomotive - the spring suspension device, the switching circuit of the traction motors, their location, the type of current, the state of the track (the more the rails are deformed or the ballast layer sags, the lower the realized adhesion coefficient) and other reasons. How these reasons influence the implementation of traction force will be discussed further in the relevant paragraphs of the book. The adhesion coefficient also depends on the speed of the train: at the moment the train starts, it is greater; with increasing speed, the realized adhesion coefficient first increases slightly, then falls. As is known, its value varies widely - from 0.06 to 0.5. Due to the fact that the adhesion coefficient depends on many factors, the calculated adhesion coefficient is used to determine the maximum traction force that an electric locomotive can develop without slipping. It represents the ratio of the greatest traction force, reliably realized under operating conditions, to the adhesion weight of the locomotive. The calculated coefficient of adhesion is determined using empirical formulas that depend on speed; they are based on numerous studies and experimental trips, taking into account the achievements of advanced machinists.
When starting from a standstill, i.e. when the speed is zero, the coefficient for direct current electric locomotives and dual power supply is 0.34 (0.33 for electric locomotives of the VL8 series) and 0.36 for alternating current electric locomotives. Thus, for a double-fed electric locomotive VL 82m, the adhesion weight of which is P = 1960 kN (200 tf), the tangential traction force Fk taking into account the design coefficient.
If the surface of the rails is dirty and the adhesion coefficient has decreased, say, to 0.2, then the traction force Pk will be 392 kN (40 tf). When sand is supplied, this coefficient can increase to the previous value and even exceed it. The use of sand is especially effective at low speeds: up to a speed of 10 km/h on wet rails, the adhesion coefficient increases by 70-75%. The effect of using sand decreases with increasing speed.
It is very important to ensure the highest coefficient of adhesion when starting and moving: the higher it is, the greater the traction force the electric locomotive can realize, the greater the mass of the train can be driven.
Resistance to the movement of the train W arises due to friction of the wheels on the rails, friction in the axle boxes, track deformation, air resistance, resistance caused by descents and ascents, curved sections of the track, etc. The resultant of all resistance forces is usually directed against the movement and only on very steep descents coincides with the direction of movement.
Resistance to movement is divided into basic and additional. The main resistance acts constantly and occurs as soon as the train begins to move; additionally due to track slopes, curves, outside air temperature, strong wind, starting off.
It is very difficult to calculate the individual components of the main resistance to train movement. It is usually calculated for cars of each type and locomotives of different series using empirical formulas obtained based on the results of many studies and tests under various conditions. The main drag increases as the speed increases. At high speeds, air resistance predominates in it.
Taking into account the main resistance to the movement of the locomotive, in addition to the tangential traction force of the electric locomotive, the concept of traction force on the automatic coupler Fa is introduced (Fig. 4).
In the process of driving a train, to reduce speed, stop, or maintain its constant speed on descents, brakes are used to create a braking force B. The braking force is generated due to friction of the brake pads on the wheel tires (mechanical braking) or when traction motors operate as generators. As a result of pressing the brake pad to the bandage with force K (see Fig. 3, b), a friction force arises on it.
friction. Due to this, an adhesion force B is formed on the bandage at the point of its contact with the rail, equal to the force T. Force B is braking: it prevents the movement of the train.
The maximum value of the braking force is determined by the same conditions as the traction force. To avoid skidding (sliding without rotation of the wheels on the rails) during braking, the condition of friction of the brake pads on the band must be met; it depends on the speed of movement, the specific pressure of the pads on the wheel and their material. This coefficient decreases with increasing speed and specific pressure due to an increase in the temperature of the rubbing surfaces. Therefore, apply bilateral pressure on the wheels when braking.
Depending on the forces applied to the train, three modes of train movement are distinguished: traction (movement under current), coasting (without current), braking.
At the moment of starting and during further movement under current, the train is subject to traction force Fк and resistance to the movement of the train K. The nature of the change in speed depending on time in the section of the OA curve (Fig. 5) is determined by the difference in forces. The greater this difference, the greater the acceleration of the train. Resistance to movement, as already noted, is a variable quantity that depends on speed. It increases with speed. Therefore, if the traction force remains constant, the accelerating traction force will decrease. After a certain point O, the traction force decreases. Then there comes a moment when Fк and the train under current moves at a constant speed (section of the AB curve).
Next, the driver can turn off the engines and continue moving on the coast (BV section) due to the kinetic energy of the train. In this case, the train is only affected by the force of resistance to movement, which reduces its speed if the train is not moving along a steep descent. When the driver turns on the brakes (from point B to point D), two forces act on the train - resistance to movement and braking force B. The speed of the train decreases. The sum of forces B represents the retarding force. It is also possible for a train to move down a steep slope and the driver uses braking force to maintain a constant permissible speed.
All bodies are capable of deformation only to a certain limit. When this limit is reached, the body collapses. For example, a thread breaks when its elongation exceeds a known value; the spring breaks when it is bent too much, etc.
Rice. 87. If you pull the bottom thread slowly, the top thread will break.
Rice. 88. By sharply pulling the bottom thread, you can break it, leaving the top thread intact
To explain why the destruction of a body occurred, it is necessary to consider the movement that preceded the destruction. Let us consider, for example, the reasons for breaking the thread in such an experiment (Fig. 87 and 88). A heavy load is suspended on a thread; a thread of the same strength is attached to the load below. If you pull the lower thread slowly, the upper thread on which the load hangs will break. If you pull the bottom thread sharply, it will be the bottom thread that breaks, not the top thread. The explanation for this experience is as follows. When the load is hanging, the upper thread has already been stretched to a certain length and its tension force balances the force of attraction of the load to the Earth. By slowly pulling the lower thread, we cause the load to move downward. Both threads are stretched, but the top thread is stretched more, since it has already been stretched. That's why it breaks earlier. If you sharply pull the lower thread, then due to the large mass of the load, even with a significant force acting from the thread, it will receive only a slight acceleration, and therefore, in a short time of jerking, the load will not have time to acquire a noticeable speed and move any noticeably. Almost the load will remain in place. Therefore, the upper thread will no longer lengthen and will remain intact; the lower thread will elongate beyond the permissible limit and break.
In a similar way, ruptures and destruction of moving bodies occur in other cases. To avoid ruptures and destruction during sudden changes in speed, it is necessary to use clutches that can stretch significantly without breaking. Many types of couplings, such as steel cables, do not themselves have such properties. Therefore, in cranes, a special spring (“shock absorber”) is placed between the cable and the hook, which can significantly extend without breaking, and thus protects the cable from breaking. Hemp rope, which can withstand significant elongation, does not need a shock absorber.
Fragile bodies, such as glass objects, are also destroyed when they fall on a hard floor. In this case, there is a sharp decrease in the speed of the part of the body that touched the floor, and deformation occurs in the body. If the elastic force caused by this deformation is not sufficient to immediately reduce the speed of the rest of the body to zero, then the deformation continues to increase. And since fragile bodies can withstand only small deformations without destruction, the object breaks.
63.1. Why does the coupling of the train cars sometimes break when an electric locomotive suddenly moves away? In which part of the train is the rupture most likely to occur?
63.2. Why are fragile items placed in shavings during transportation?
