Physics is entertaining. Lemon battery

Ya. I. Perelman

Entertaining physics

FROM THE EDITOR

The proposed edition of “Entertaining Physics” basically repeats the previous ones. Ya. I. Perelman worked on the book for many years, improving the text and supplementing it, and for the last time during the author’s lifetime the book was published in 1936 (thirteenth edition). When releasing subsequent editions, the editors did not set as their goal a radical revision of the text or significant additions: the author selected the main content of “Entertaining Physics” in such a way that, while illustrating and deepening the basic information from physics, it is not outdated to this day. In addition, so much time has passed since 1936 that the desire to reflect the latest achievements in physics would have led to a significant increase in the book and to a change in its “face”. For example, the author’s text on the principles of space flight is not outdated, and there is already so much factual material in this area that one can only refer the reader to other books specifically devoted to this topic. The fourteenth and fifteenth editions (1947 and 1949) were published under the editorship of prof. A. B. Mlodzeevsky. Associate Professor took part in the preparation of the sixteenth edition (1959-1960). V. A. Ugarov. When editing all publications published without an author, outdated figures were only replaced, projects that did not justify themselves were removed, and individual additions and notes were made.

This book is an independent collection that is not a direct continuation of the first book of Entertaining Physics. The success of the first collection prompted the author to process the rest of the material he had accumulated, and thus this second, or rather another book, covering the same departments of physics, was compiled.

In the proposed book, as in the first, the compiler strives not so much to impart new knowledge as to revive and refresh the simplest information on physics that the reader already has. The purpose of the book is to stimulate the activity of the scientific imagination, to teach one to think in the spirit of physics and to develop the habit of versatile application of one’s knowledge. Therefore, in “Entertaining Physics” the description of spectacular experiments is given a secondary place; physical puzzles, interesting problems, instructive paradoxes, intricate questions, unexpected comparisons from the field of physical phenomena, etc. come to the fore. In search of such material, the compiler turns to the range of phenomena of everyday life, to the field of technology, to nature, to the pages of scientific - science fiction novels - in a word, to everything that, being outside the textbook and physics classroom, is capable of attracting the attention of an inquisitive reader.

Intending the book not for study, but for reading, the compiler tried, as far as he could, to give the imposition an outwardly interesting form, based on the fact that interest in the subject increases attention, enhances the work of thought and, therefore, contributes to more conscious assimilation. To revive interest in physical calculations, some articles in this collection introduced computational material (which was almost not done in the first book). In general, this collection of material selection is intended for a slightly more prepared reader than the first book of “Entertaining Physics,” although the difference in this regard between both books is so insignificant that they can be read in any order and independently of one another. The third book “ Entertaining physics does not exist. Instead, its author compiled the following books: “Entertaining Mechanics”, “Do You Know Physics?” and, in addition, a separate book devoted to astronomy: “Entertaining Astronomy.”

1936 Y. Perelman

Chapter first

BASIC LAWS OF MECHANICS

Cheapest way to travel

The witty French writer of the 17th century, Cyrano de Bergerac, in his satirical “History of the States on the Moon” (1652), talks, among other things, about such an amazing incident that allegedly happened to him. While engaged in physical experiments, he was once incomprehensibly lifted high into the air along with his flasks. When, a few hours later, he managed to descend to the ground again, then, to his amazement, he found himself no longer in his native France or even in Europe, but on the mainland of North America, in Canada! The French writer, however, finds his unexpected flight across the Atlantic Ocean quite natural. He explains it by the fact that while the involuntary traveler was separated from the earth's surface, our planet continued to rotate to the east; that is why, when he sank, the continent of America was under his feet instead of France.

It would seem, what a cheap and easy way to travel! One has only to rise above the Earth and stay in the air for at least a few minutes to Descend in a completely different place, far to the West. Instead of undertaking tedious journeys across continents and oceans, you can hang motionless above the Earth and wait until it itself offers the traveler a destination.

Unfortunately, this amazing method is nothing more than a fantasy. Firstly, having risen into the air, we, in essence, are not yet separated from the globe: we remain connected to its gaseous shell, hanging in its atmosphere, which also participates in the rotation of the Earth around its axis. The air (or rather, its lower, denser layers) rotates with the Earth, carrying with it everything that is in it: clouds, airplanes, all flying birds, insects, etc. If the air did not participate in the rotation of the globe, then , standing on Earth, we would constantly feel a strong wind, in comparison with which the most terrible hurricane would seem like a gentle breeze). After all, it makes absolutely no difference whether we stand still and the air moves past us, or, on the contrary, the air is motionless and we move in it; in both cases we feel the same strong wind. A motorcyclist moving at a speed of 100 km per hour feels a strong headwind even in completely calm weather.

Figure 1. Is it possible to see how the globe rotates from a balloon? (The figure is not to scale.)

This is the first thing. Secondly, even if we could rise to the highest layers of the atmosphere, or if the Earth were not surrounded by air at all, we would not be able to take advantage of that cheap way of traveling that the French satirist fantasized about. In fact, separating from the surface of the rotating Earth, we continue to move by inertia at the same speed, that is, at the same speed as the Earth moves below us. When we go down again, we find ourselves in the very place from which we were previously separated, just as, after jumping up in the carriage of a moving train, we return to our original place. True, we will move by inertia in a straight line (tangentially), and the Earth below us will move in an arc; but for short periods of time this does not change matters.

"Earth, stop!"

The famous English writer Herbert Wells has a fantastic story about how a certain clerk worked miracles. A very narrow-minded young man, by the will of fate, turned out to be the owner of an amazing gift: as soon as he expressed any wish, it was immediately fulfilled. However, the tempting gift, as it turned out, brought neither its owner nor other people anything but trouble. The end of this story is instructive for us.

After a protracted night of drinking, the miracle clerk, fearing to come home at dawn, decided to use his gift to prolong the night. How to do it? We must order the luminaries of the sky to stop their running. The clerk did not immediately decide on such an extraordinary feat, and when a friend advised him to stop the Moon, he looked at her carefully and said thoughtfully:

“- It seems to me that she is too far away for this... What do you think?

But why not try? - insisted Meydig (that was the friend’s name - Ya.P.). - Of course, it will not stop, you will only stop the rotation of the Earth. Hope this doesn't hurt anyone!

Hm,” said Fotheringay (clerk – Ya.P.), “Okay, I’ll try.” Well…

He stood in a commanding pose, extended his hands over the world and solemnly said:

Earth, stop! Stop spinning! Before he had time to finish these words, the friends were already flying into space at a speed of several dozen miles per minute.

Despite this, he continued to think. In less than a second he had time to think and express to himself the following wish:

Whatever happens, may I be alive and unharmed!

It is impossible not to admit that this desire was expressed at the right time. A few more seconds - and he fell on some freshly dug up earth, and around him, without bringing him any harm, stones, fragments of buildings, and metal objects of various kinds rushed; Some unfortunate cow was also flying, crashing when it hit the ground. The wind blew with terrible force; he could not even raise his head to look around.

“Incomprehensible,” he exclaimed in a broken voice. - What's happened? Storm, or what? I must have done something wrong.

Having looked around as far as the wind and the fluttering tails of his jacket would allow him, he continued:

Everything seems to be in order in the sky. Here comes the Moon. Well, and everything else... Where is the city? Where are the houses and streets? Where did the wind come from? I did not order the wind to be.

Fotheringay tried to get to his feet, but this proved completely impossible, and so he moved forward on all fours, holding on to rocks and ledges of the ground. However, there was nowhere to go, since, as far as one could see from under the tails of the jacket, thrown by the wind over the head of the reptile wizard, everything around was one picture of destruction.

Something in the universe has seriously gone bad, he thought, and what exactly is unknown.

It really has gone bad. No houses, no trees, no living creatures of any kind - nothing was visible. Only shapeless ruins and various fragments lay around, barely visible among a whole hurricane of dust.

The culprit of all this did not understand, of course, what was going on. And yet it was explained very simply. Having stopped the Earth immediately, Fotheringay did not think about inertia, and yet, with a sudden stop in the circular motion, it would inevitably throw everything on it from the surface of the Earth. That is why houses, people, trees, animals - in general, everything that was not inextricably linked with the main mass of the globe flew tangentially to its surface at the speed of a bullet. And then it all fell to Earth again, breaking into pieces.

Fotheringay realized that the miracle he had performed was not particularly successful. Therefore, he was overcome by a deep disgust for all kinds of miracles, and he promised himself not to perform them anymore. But first it was necessary to correct the trouble he had caused. This trouble turned out to be no small one. The storm was raging, clouds of dust covered the Moon, and in the distance the sound of approaching water could be heard; In the light of lightning, Fotheringhay saw a whole wall of water moving with terrible speed towards the place where he lay. He became decisive.

Stop! - he cried, turning to the water. - Not a step further!

Then he repeated the same order to thunder, lightning and wind.

Everything was quiet. He squatted down and thought.

How can this not cause some kind of chaos again, he thought and then said: “Firstly, when everything that I now command is fulfilled, may I lose the ability to perform miracles and be the same as ordinary people.” No need for miracles. Too dangerous a toy. And secondly, let everything be the same: the same city, the same people, the same houses, and I myself am the same as I was then.”

Letter from an airplane

Imagine that you are in an airplane flying quickly over the ground. Below are familiar places. Now you will fly over the house where your friend lives. “It would be nice to send him greetings,” flashes through your mind. You quickly write a few words on a piece of notebook paper, tie the note to some heavy object, which we will later call “cargo,” and, after waiting for the moment when the house is right under you, you release the cargo from your hands.

You are fully confident, of course, that the load will fall in the garden of the house. However, it falls in the wrong direction, even though the garden and house are located right below you!

Watching it fall from the plane, you would see a strange phenomenon: the weight goes down, but at the same time continues to remain under the plane, as if sliding along an invisible thread tied to it. And when the load reaches the ground, it will be far ahead of the place you have planned.

The same law of inertia manifests itself here, which prevents you from taking advantage of the tempting advice to travel the Bergerac way. While the cargo was on the plane, it moved with the car. You let him go. But, having separated from the aircraft and falling down, the cargo does not lose its original speed, but, while falling, continues at the same time to move in the air in the same direction. Both movements, vertical and horizontal, add up, and as a result, the load flies down a curved line, remaining under the aircraft the entire time (unless, of course, the aircraft itself changes direction or speed of flight). The load flies, in essence, in the same way as a horizontally thrown body flies, for example a bullet thrown from a horizontally directed gun: the body describes an arcuate path, ultimately ending on the ground.

Note that everything said here would be absolutely true if there were no air resistance. In fact, this resistance slows down both the vertical and horizontal movement of the cargo, as a result of which the cargo does not remain directly under the aircraft all the time, but lags somewhat behind it.

The deviation from the plumb line can be very significant if the aircraft is flying high and at high speed. In calm weather, a load falling from an airplane flying at a speed of 100 km per hour at an altitude of 1000 m will fall 400 meters ahead of a place lying vertically below the airplane (Fig. 2).

The calculation (if we neglect air resistance) is simple. From the formula for the path with uniformly accelerated motion

we will get that

This means that from a height of 1000 m a stone must fall within

i.e. 14 sec.

During this time, he will have time to move horizontally by

Bombing

After what has been said, it becomes clear how difficult the task of a military pilot who is tasked with dropping a bomb on a certain place is: he has to take into account the speed of the aircraft, the influence of air on the falling body, and, in addition, the speed of the wind. In Fig. 3 schematically shows the various paths described by a dropped bomb under certain conditions. If there is no wind, the dropped bomb lies along the AP curve; why this is so - we explained above. With a tailwind, the bomb is carried forward and moves. along the AG curve. With a headwind of moderate strength, the bomb falls along the AD curve if the wind above and below are the same; if, as often happens, the wind below has the direction opposite to the upper wind (headwind at the top, tailwind at the bottom), the fall curve changes its appearance and takes line shape A E.

Figure 2. A load thrown from a flying airplane does not fall vertically, but along a curve.

Figure 3. The path along which bombs dropped from an airplane fall. AR - in calm weather; AG - with a tailwind, AD - with a headwind, AE - with a headwind at the top and a tailwind at the bottom.

Non-stop railway

When you are standing on a stationary station platform and a courier train rushes past it, jumping into the carriage while it is moving is, of course, tricky. But imagine that the platform below you is also moving, at the same speed and in the same direction as the train. Will it be difficult for you to get into the carriage then?

Not at all: you will enter as calmly as if the carriage were standing still. Since both you and the train are moving in one direction at the same speed, then in relation to you the train is completely at rest. True, its wheels rotate, but it will seem to you that they are spinning in place. Strictly speaking, all those objects that we usually consider stationary - for example, a train standing at a station - move with us around the axis of the globe and around the Sun; however, in practice we can ignore this movement, since it does not bother us at all.

Consequently, it is quite conceivable to arrange so that the train, passing by stations, picks up and drops off passengers at full speed, without stopping. Devices of this kind are often installed at exhibitions to enable the public to quickly and conveniently view their attractions spread over a vast area. The extreme points of the exhibition area, like an endless ribbon, are connected by a railway; Passengers can enter and exit the carriages at any time and anywhere while the train is running at full speed.

This curious device is shown in the accompanying drawings. In Fig. 4 letters A and B mark the outermost stations. At each station there is a round stationary platform surrounded by a large rotating ring-shaped disk. A rope runs around the rotating disks of both stations, to which the cars are attached. Now watch what happens when the disk rotates. The cars run around the disks at the same speed as their outer edges rotate; therefore, passengers can move from the discs to the carriages without the slightest danger or, conversely, leave the train. After exiting the carriage, the passenger walks along the rotating disk to the center of the circle until he reaches a stationary platform; and it is no longer difficult to move from the inner edge of the movable disk to the stationary platform, since here, with a small radius of the circle, the peripheral speed is also very small). Having reached the internal fixed platform, the passenger can only cross the bridge to the ground outside the railway (Fig. 5).

Figure 4. Diagram of a non-stop railway between stations A and B. The station structure is shown in the following figure.

Figure 5. Non-stop railway station.

The absence of frequent stops results in huge savings in time and energy consumption. In city trams, for example, most of the time and almost two-thirds of all energy is spent gradually accelerating when leaving a station and slowing down when stopping).

At railway stations, it would be possible to do even without special moving platforms in order to receive and disembark passengers while the train is at full speed. Imagine that an express train is rushing past an ordinary stationary station; we wish that he would accept new passengers here without stopping. For now, let these passengers take seats on another train standing on a spare parallel track, and let this train begin to move forward, developing the same speed as the express one. When both trains are side by side, they will be motionless relative to each other: it is enough to throw over the bridges that would connect the cars of both trains, and passengers of the auxiliary train will be able to safely transfer to the courier train. Stops at stations will become, as you see, unnecessary.

Moving sidewalks

Another device, hitherto used only at exhibitions, is based on the principle of the relativity of motion: the so-called “moving sidewalks.” They were first implemented at an exhibition in Chicago in 1893, then at the Paris World Exhibition in 1900. Here is a drawing of such a device (Fig. 6). You see five closed lanes-sidewalks, moving through a special mechanism, one inside the other at different speeds.

The outermost lane goes quite slowly - at a speed of only 5 km per hour; This is the normal speed of a pedestrian, and it is not difficult to enter such a slowly creeping lane. Next to it, inside, a second lane runs at a speed of 10 km per hour. Jumping onto it straight from a stationary street would be dangerous, but jumping onto it from the front page costs nothing. Indeed: in relation to this first stripe, crawling at a speed of 5 km, the second, running at a speed of 10 km per hour, does only 5 km per hour; This means that moving from the first to the second is as easy as moving from the ground to the first. The third lane is already moving at a speed of 15 km per hour, but it is, of course, not difficult to switch to it from the second lane. It’s just as easy to move from the third lane to the next, fourth, running at a speed of 20 km/h, and, finally, from there to the fifth, already rushing at a speed of 25 km/h. This fifth lane takes the passenger to the point he needs; from here, successively moving back from strip to strip, he lands on motionless ground.

Figure 6. Moving sidewalks.

Difficult Law

None of the three fundamental laws of mechanics probably causes as much confusion as the famous “Newton's third law” - the law of action and reaction. Everyone knows it, they know how to apply it correctly even in other cases, and yet few people are free from some ambiguities in its understanding. Perhaps, reader, you were lucky enough to immediately understand him, but I confess that I fully comprehended him only ten years after my first acquaintance with him.

Talking with different people, I was more than once convinced that the majority is ready to recognize the correctness of this law only with significant reservations. They readily admit that it is true for motionless bodies, but they do not understand how it can be applied to the interaction of moving bodies... Action, says the law, is always equal and opposite to reaction. This means that if a horse pulls a cart, then the cart pulls the horse back with the same force. But then the cart must remain in place: why is it still moving? Why don't these forces balance each other if they are equal?

These are the usual perplexities associated with this law. So the law is wrong? No, he is absolutely true; we just misunderstand it. The forces do not balance each other simply because they are applied to different bodies: one to the cart, the other to the horse. Forces are equal, yes, but do equal forces always produce equal effects? Do equal forces impart equal accelerations to all bodies? Doesn’t the effect of a force on a body depend on the body, on the amount of “resistance” that the body itself provides to the force?

If you think about it, it becomes clear why the horse drags the cart, although the cart pulls him back with the same force. The force acting on the cart and the force acting on the horse are equal at each moment; but since the cart moves freely on wheels, and the horse rests on the ground, it is understandable why the cart rolls towards the horse. Also think about the fact that if the cart did not counteract the driving force of the horse, then... it would be possible to do without the horse: the weakest force would have to set the cart in motion. The horse is then needed to overcome the opposition of the cart.

All this would be better understood and would give rise to less bewilderment if the law were expressed not in the usual short form: “action is equal to reaction,” but, for example, like this: “the opposing force is equal to the acting force.” After all, here only the forces are equal, but the actions (if we understand, as is usually understood, by the “action of a force” the movement of a body) are usually different, because the forces are applied to different bodies.

In the same way, when the polar ice squeezed the Chelyuskin’s hull, its sides pressed on the ice with equal force. The disaster occurred because the powerful ice was able to withstand such pressure without collapsing; the hull of the ship, although made of steel, but not a solid body, succumbed to this force, was crushed and crushed. (More details about the physical causes of the death of “Chelyuskin” are described further, in a separate article, on page 44).

Even the fall of bodies strictly obeys the law of reaction. The apple falls to the Earth because it is attracted by the globe; but with exactly the same force the apple attracts our entire planet to itself. Strictly speaking, the apple and the Earth fall on each other, but the speed of this fall is different for the apple and for the Earth. Equal forces of mutual attraction give the apple an acceleration of 10 m/sec2, and the earth the same amount of acceleration as the mass of the earth exceeds the mass of the apple. Of course, the mass of the globe is an incredible number of times greater than the mass of an apple, and therefore the Earth receives a displacement so insignificant that it can practically be considered equal to zero. That is why we say that the apple falls to the Earth, instead of saying: “the apple and the Earth fall on each other”).

Why did Svyatogor the hero die?

Remember the folk epic about Svyatogor the hero, who decided to raise the Earth? Archimedes, according to legend, was also ready to accomplish the same feat and demanded a fulcrum for his leverage. But Svyatogor was strong even without leverage. He was only looking for something to grab onto, something to put his heroic hands to. “As soon as I found the traction, I would lift the whole Earth!” The opportunity presented itself: the hero found on the ground a “saddle bag” that “will not hide, will not fold, will not rise.”

If Svyatogor had known the law of action and reaction, he would have realized that his heroic force applied to the earth would cause an equal, and therefore equally colossal, counterforce that could pull him into the ground.

In any case, it is clear from the epic that popular observation has long noticed the resistance exerted by the earth when they lean on it. People unconsciously applied the law of reaction thousands of years before Newton first proclaimed it in his immortal book, The Mathematical Foundations of Natural Philosophy (i.e., physics).

Is it possible to move without support?

When walking, we push off with our feet from the ground or floor; You cannot walk on a very smooth floor or on ice from which your foot cannot push off. When moving, the locomotive is pushed away from the rails by its “driving” wheels: if the rails are lubricated with oil, the locomotive will remain in place. Sometimes even (in icy conditions) in order to move the train, the rails in front of the driving wheels of the locomotive are sprinkled with sand from a special device. When wheels and rails (at the dawn of railways) were made with gears, it was assumed that the wheels should push off the rails. The steamboat is pushed away from the water by the blades of the side wheel or propeller. The plane also pushes away from the air using a propeller. In a word, no matter what medium an object moves in, it relies on it during its movement. But can a body begin to move without having any support outside itself?

It would seem that striving to carry out such a movement is the same as trying to lift oneself by the hair. As is known, such an attempt has so far only been successful for Baron Munchausen. Meanwhile, it is precisely this seemingly impossible movement that often occurs before our eyes. True, a body cannot set itself entirely in motion by internal forces alone, but it can force some part of its substance to move in one direction, and the rest in the opposite direction. How many times have you seen a flying rocket, but have you thought about the question: why is it flying? In a rocket we have a clear example of precisely the kind of motion that interests us now.

Why does a rocket take off?

Even among people who have studied physics, one often hears a completely wrong explanation for the flight of a rocket: it flies because it is repelled from the air by its gases formed when gunpowder burns in it. That's what they thought in the old days (rockets are an old invention). However, if you were to launch a rocket in airless space, it would fly no worse, or even better, than in the air. The true reason for the rocket's movement is completely different. It was very clearly and simply stated by the First March revolutionary Kibalchich in his suicide note about the flying machine he invented. Explaining the design of combat missiles, he wrote:

“Into a tin cylinder, closed at one base and open at the other, a cylinder of pressed gunpowder is tightly inserted, having a void in the form of a channel along its axis. The combustion of gunpowder begins from the surface of this channel and spreads over a certain period of time to the outer surface of the pressed gunpowder; the gases formed during combustion produce pressure in all directions; but the lateral pressures of the gases are mutually balanced, while the pressure on the bottom of the tin shell of gunpowder, not balanced by the opposite pressure (since the gases have a free outlet in this direction), pushes the rocket forward.”

The same thing happens here as when a cannon is fired: the projectile flies forward, and the cannon itself is pushed back. Remember the “recoil” of a gun and any firearm in general! If a cannon were hanging in the air, not supported by anything, after firing it would move backwards with a certain speed, which is the same number of times less than the speed of the projectile, how many times the projectile is lighter than the cannon itself. In Jules Verne’s science fiction novel “Upside Down,” the Americans even decided to use the recoil force of a gigantic cannon to carry out a grandiose undertaking - “straighten the earth’s axis.”

A rocket is the same cannon, only it spews not shells, but powder gases. For the same reason, the so-called “Chinese wheel” rotates, which you probably happened to admire when setting up fireworks: when gunpowder burns in tubes attached to the wheel, gases flow out in one direction, and the tubes themselves (and with them the wheel) get the opposite movement. In essence, this is just a modification of a well-known physical device - the Segner wheel.

It is interesting to note that before the invention of the steamboat there was a design for a mechanical vessel based on the same beginning; the supply of water on the ship was supposed to be released using a strong pressure pump in the stern; as a result, the ship had to move forward, like those floating tins that are available to prove the principle in question in school physics classrooms. This project (proposed by Remsey) was not implemented, but it played a well-known role in the invention of the steamboat, as it gave Fulton his idea.

Figure 7. The oldest steam engine (turbine), attributed to Heron of Alexandria (2nd century BC).

Figure 8. Steam car attributed to Newton.

Figure 9. Toy steamer made of paper and eggshells. The fuel is alcohol poured into a thimble. The steam escaping from the hole in the “steam boiler” (a blown egg) causes the steamboat to sail in the opposite direction.

We also know that the most ancient steam engine, invented by Heron of Alexandria back in the 2nd century BC, was designed on the same principle: steam from the boiler (Fig. 7) flowed through a tube into a ball mounted on a horizontal axis; then flowing out of the cranked tubes, the steam pushed these tubes in the opposite direction, and the ball began to rotate. Unfortunately, the Heron steam turbine in ancient times remained only a curious toy, since the cheapness of slave labor did not encourage anyone to put the machines into practical use. But the principle itself has not been abandoned by technology: in our time it is used in the construction of jet turbines.

Newton, the author of the law of action and reaction, is credited with one of the earliest designs of a steam car, based on the same principle: steam from a boiler placed on wheels rushes out in one direction, and the boiler itself, due to recoil, rolls in the opposite direction (Fig. 8) .

Rocket cars, experiments with which were widely written about in 1928 in newspapers and magazines, are a modern modification of Newton's carriage.

For those who like to craft, here is a drawing of a paper steamer, also very similar to Newton’s carriage: in a steam boiler, steam is formed from an emptied egg, heated with cotton wool soaked in alcohol in a thimble; escaping as a stream in one direction, it forces the entire steamer to move in the opposite direction. However, the construction of this instructive toy requires very skillful hands.

How does a cuttlefish move?

It will be strange for you to hear that there are quite a few living creatures for which the imaginary “lifting of oneself by the hair” is their usual way of moving in water.

Figure 10. Swimming movement of cuttlefish.

Cuttlefish and, in general, most cephalopods move in water in this way: they take water into the gill cavity through a side slit and a special funnel in front of the body, and then energetically throw out a stream of water through the said funnel; at the same time, according to the law of reaction, they receive a reverse push sufficient to swim quite quickly with the back side of the body forward. The cuttlefish can, however, direct the funnel tube sideways or backwards and, rapidly squeezing water out of it, move in any direction.

The movement of the jellyfish is based on the same thing: by contracting its muscles, it pushes water out from under its bell-shaped body, receiving a push in the opposite direction. A similar technique is used when moving by salps, dragonfly larvae and other aquatic animals. And we still doubted whether it was possible to move like that!

What could be more tempting than leaving the globe and traveling across the vast universe, flying from Earth to the Moon, from planet to planet? How many science fiction novels have been written on this topic! Who hasn’t taken us on an imaginary journey through the heavenly bodies! Voltaire in Micromegas, Jules Verne in A Trip to the Moon and Hector Servadac, Wells in The First Men on the Moon and many of their imitators made the most interesting journeys to the heavenly bodies - of course, in their dreams.

Is there really no way to make this long-standing dream come true? Are all the ingenious projects depicted with such tempting verisimilitude in novels really impossible? In the future we will talk more about fantastic projects of interplanetary travel; Now let’s get acquainted with the real project of such flights, first proposed by our compatriot K. E. Tsiolkovsky.

Is it possible to fly to the moon by plane? Of course not: airplanes and airships move only because they rely on the air, are pushed away from it, and there is no air between the Earth and the Moon. In global space, there is generally no sufficiently dense medium on which an “interplanetary airship” could rely. This means that we need to come up with a device that would be able to move and be controlled without relying on anything.

We are already familiar with a similar projectile in the form of a toy - a rocket. Why not build a huge rocket, with a special room for people, food supplies, air tanks and everything else? Imagine that people in a rocket are carrying with them a large supply of flammable substances; they can direct the outflow of explosive gases in any direction. You will receive a real controllable celestial ship on which you can sail in the ocean of cosmic space, fly to the Moon, to the planets... Passengers will be able, by controlling explosions, to increase the speed of this interplanetary airship with the necessary gradualness so that the increase in speed is harmless to them. If they want to descend to some planet, they can, by turning their ship, gradually reduce the speed of the projectile and thereby weaken the fall. Finally, passengers will be able to return to Earth in the same way.

Figure 11. Project of an interplanetary airship, designed like a rocket.

Let us remember how recently aviation made its first timid gains. And now the planes are already flying high in the air, flying over mountains, deserts, continents, and oceans. Maybe “astronavigation” will have the same magnificent blossoming in two or three decades? Then man will break the invisible chains that have chained him to his native planet for so long and rush into the boundless expanse of the universe.

Chapter two

FORCE. JOB. FRICTION.

The swan, crayfish and pike problem

The story of how “a swan, a crayfish and a pike began to carry a load of luggage” is known to everyone. But hardly anyone tried to consider this fable from a mechanical point of view. The result is not at all similar to the conclusion of the fabulist Krylov.

Before us is a mechanical problem involving the addition of several forces acting at an angle to one another. The direction of forces is defined in the fable as follows:

... The swan rushes into the clouds,

The crayfish moves back, and the pike pulls into the water.

This means (Fig. 12) that one force, the swan's thrust, is directed upward; the other, pike thrust (OV), - sideways; third, cancer thrust (CR), - back. Let's not forget that there is a fourth force - the weight of the cart, which is directed vertically downwards. The fable states that “the cart is still there,” in other words, that the resultant of all forces applied to the cart is equal to zero.

Is it so? Let's see. A swan rushing towards the clouds does not interfere with the work of the crayfish and pike, and even helps them: the swan’s thrust, directed against gravity, reduces the friction of the wheels on the ground and on the axles, thereby lightening the weight of the cart, and perhaps even completely balancing it - after all the load is small (“the luggage would seem light to them”). Assuming the last case for simplicity, we see that only two forces remain: the thrust of the crayfish and the thrust of the pike. It is said about the direction of these forces that “the crayfish moves back, and the pike pulls into the water.” It goes without saying that the water was not in front of the cart, but somewhere on the side (the Krylov workers were not going to sink the cart!). This means that the forces of the crayfish and the pike are directed at an angle to one another. If the applied forces do not lie on the same straight line, then their resultant cannot in any way be equal to zero.

Figure 12. The problem of Krylov's swan, crayfish and pike, solved according to the rules of mechanics. The resultant (OD) should drag the cart into the river.

Acting according to the rules of mechanics, we build a parallelogram on both forces OB and OS; its diagonal OD gives the direction and magnitude of the resultant. It is clear that this resultant force must move the cart from its place, especially since its weight is fully or partially balanced by the swan’s thrust. Another question is in which direction will the cart move: forward, backward or sideways? This depends on the ratio of forces and on the size of the angle between them.

Readers who have some practice in the addition and expansion of forces will easily understand the case when the force of the swan does not balance the weight of the cart; they will be convinced that the cart cannot remain motionless even then. Under one condition only, the cart may not move under the influence of these three forces: if the friction at its axes and against the road surface is greater than the applied forces. But this does not agree with the statement that “the luggage would seem light to them.”

In any case, Krylov could not confidently assert that “things are still moving,” that “things are still there.” This, however, does not change the meaning of the fable.

Contrary to Krylov

We have just seen that Krylov’s everyday rule: “when there is no agreement among comrades, things will not go well for them” is not always applicable in mechanics. Forces can be directed in more than one direction and, despite this, give a certain result.

Few people know that hard workers - ants, whom the same Krylov praised as exemplary workers, work together precisely in the way ridiculed by the fabulist. And things are generally going well for them. The law of addition of forces comes to the rescue again. By carefully watching the ants while they work, you will soon see that their intelligent cooperation is only apparent: in fact, each ant works for itself, without even thinking about helping others.

Here's how one zoologist describes the work of ants:

“If a dozen ants are dragging large prey across level ground, then everyone acts in the same way, and the result is the appearance of cooperation. But the prey - for example a caterpillar - got caught on some obstacle, on a stem of grass, on a pebble. You can’t drag it further forward, you have to go around it. And here it is clearly revealed that each ant, in its own way and without conforming to any of its comrades, tries to cope with the obstacle (Fig. 13 and 14). One drags to the right, the other to the left; one pushes forward, the other pulls back. They move from place to place, grab the track in another place, and each pushes or pulls in their own way. When it happens that the forces of the workers are formed in such a way that four ants move the caterpillar in one direction, and six in the other, then the caterpillar ultimately moves precisely in the direction of these six ants, despite the opposition of four.”

Let us give (borrowed from another researcher) another instructive example that clearly illustrates this imaginary cooperation of ants. In Fig. Figure 15 shows a rectangular piece of cheese that has been grabbed by 25 ants. The cheese slowly moved in the direction indicated by arrow A, and one might think that the front line of ants was pulling the load towards itself, the back line was pushing it forward, while the side ants were helping both. However, this is not the case, as is easy to verify: use a knife to separate the entire back rank - the burden will crawl much faster! It is clear that these 11 ants were pulling backward, not forward: each of them tried to turn the burden so that, backing away, they would drag it towards the nest. This means that the rear ants not only did not help the front ones, but diligently interfered with them, destroying their efforts. To drag this piece of cheese, the efforts of only four ants would be enough, but inconsistency in actions leads to the fact that 25 ants are dragging the load.

Figure 13. How ants drag a caterpillar.

Figure 14. How ants pull prey. The arrows show the directions of effort of individual ants.

Figure 15. How ants try to drag a piece of cheese to an anthill located in the direction of arrow A.

This feature of the joint actions of ants was noticed long ago by Mark Twain. Talking about a meeting between two ants, one of which found the leg of a grasshopper, he says: “They take the leg by both ends and pull with all their might in opposite directions. Both see that something is wrong, but cannot understand what. Mutual bickering begins; the argument turns into a fight... Reconciliation occurs, and joint and meaningless work begins again, with a comrade wounded in the fight only being a hindrance. Trying with all his might, the healthy comrade drags the burden, and with it the wounded friend, who, instead of giving up the prey, hangs on it.” Jokingly, Twain makes the absolutely correct observation that “an ant works well only when it is observed by an inexperienced naturalist who draws the wrong conclusions.”

Is it easy to break eggshells?

Among the philosophical questions over which the thoughtful Kifa Mokievich from “Dead Souls” racked his wise head was the following problem: “Well, if an elephant was born in an egg, because the shell, tea, would be very thick, you couldn’t hit it with a cannon; we need to invent some new firearm.”

Gogol's philosopher would probably have been quite amazed if he had learned that an ordinary eggshell, despite its thinness, is also far from a delicate thing. It is not so easy to crush an egg between your palms, pressing on its ends; It takes a lot of effort to break the shell under such conditions.

Such an extraordinary strength of an eggshell depends solely on its convex shape and is explained in the same way as the strength of all kinds of vaults and arches.

In the attached fig. 17 shows a small stone vault above the window. The load S (i.e., the weight of the overlying parts of the masonry), pressing on the wedge-shaped middle stone of the arch, presses down with a force, which is indicated in the figure by arrow A. But the stone cannot move down due to its wedge-shaped shape; it only puts pressure on neighboring stones. In this case, force A is decomposed according to the parallelogram rule into two forces, indicated by arrows C and B; they are balanced by the resistance of adjacent stones, in turn sandwiched between neighboring ones. Thus, the force pressing on the vault from the outside cannot destroy it. But it is relatively easy to destroy it by force acting from within. This is a mistake, since the wedge-shaped shape of the stones, which prevents them from falling, does not in the least prevent them from rising.

Figure 16. It takes considerable force to break an egg in this position.

Figure 17. Reason for the strength of the arch.

The shell of an egg is the same vault, only solid. When exposed to external pressure, it does not break down as easily as one would expect from such a brittle material. You can place a fairly heavy table with legs on four raw eggs - and they will not be crushed (for stability, you need to equip the eggs with plaster extensions at the ends; plaster easily sticks to the lime shell).

Now you understand why the hen does not have to worry about breaking the shells of her eggs with the weight of her body. And at the same time, the weak chick, wanting to get out of the natural prison, easily breaks the shell from the inside with its beak.

Easily breaking an egg shell with a side blow of a teaspoon, we have no idea how strong it is when pressure acts on it under natural conditions, and what reliable armor nature has protected the living creature developing in it.

The mysterious strength of light bulbs, seemingly so delicate and fragile, is explained in the same way as the strength of eggshells. Their strength will become even more amazing if we remember that many of them (hollow, not gas-filled) are almost completely empty and nothing from the inside counteracts the pressure of the external air. And the amount of air pressure on an electric light bulb is considerable: with a diameter of 10 cm, the light bulb is compressed on both sides with a force of more than 75 kg (the weight of a person). Experience shows that a hollow light bulb can withstand even 2.5 times greater pressure.

Sailing against the wind

It is difficult to imagine how sailing ships can go “against the wind” - or, as sailors say, go “close-hauled”. True, a sailor will tell you that you cannot sail directly against the wind, but you can only move at an acute angle to the direction of the wind. But this angle is small - about a quarter of a right angle - and it seems, perhaps, equally incomprehensible: whether to sail directly against the wind or at an angle to it of 22°.

In reality, however, this is not indifferent, and we will now explain how it is possible to move towards it at a slight angle by the force of the wind. First, let's look at how the wind generally acts on the sail, that is, where it pushes the sail when it blows on it. You probably think that the wind always pushes the sail in the direction it blows. But this is not so: wherever the wind blows, it pushes the sail perpendicular to the plane of the sail. Indeed: let the wind blow in the direction indicated by the arrows in Fig. 18; the line AB represents the sail. Since the wind presses evenly on the entire surface of the sail, we replace the wind pressure with a force R applied to the middle of the sail. We will split this force into two: force Q, perpendicular to the sail, and force P, directed along it (Fig. 18, right). The last force pushes the sail nowhere, since the friction of the wind on the canvas is insignificant. The force Q remains, which pushes the sail at right angles to it.

Knowing this, we can easily understand how a sailing ship can sail at an acute angle towards the wind. Let line KK (Fig. 19) represent the keel line of the ship. The wind blows at an acute angle to this line in the direction indicated by a series of arrows. Line AB represents a sail; it is placed so that its plane bisects the angle between the direction of the keel and the direction of the wind. Trace in Fig. 19 for the disintegration of forces. We represent the wind pressure on the sail by force Q, which, we know, must be perpendicular to the sail. Let us divide this force into two: force R, perpendicular to the keel, and force S, directed forward along the keel line of the vessel. Since the movement of the ship in the direction R encounters strong resistance from the water (the keel in sailing ships is very deep), the force R is almost completely balanced by the resistance of the water. There remains only one force S, which, as you can see, is directed forward and, therefore, moves the ship at an angle, as if towards the wind. Usually this movement is performed in zigzags, as shown in Fig. 20. In the language of sailors, such a movement of the ship is called “tacking” in the strict sense of the word.

Figure 18. The wind pushes the sail always at right angles to its plane.

Figure 19. How to sail against the wind.

Figure 20. Tacking a sailing ship.

Could Archimedes lift the Earth?

“Give me a foothold and I will lift the Earth!” - legend attributes this exclamation to Archimedes, the brilliant mechanic of antiquity, who discovered the laws of the lever.

Figure 21. “Archimedes lifts the Earth with a lever.” Engraving from Varignon's book (1787) on mechanics.

“Once Archimedes,” we read from Plutarch, “wrote to King Hieron of Syracuse, to whom he was a relative and friend, that with this force one can move any load. Carried away by the strength of the evidence, he added that if there had been another Earth, he would have moved ours by moving to it.”

Archimedes knew that there is no load that could not be lifted with the weakest force if you use a lever: you just need to apply this force to a very long arm of the lever, and force the short arm to act on the load. That's why he thought that by pressing on the extremely long arm of the lever, he could also lift a load with the force of his hands, the mass of which is equal to the mass of the globe.

But if the great mechanic of antiquity had known how enormous the mass of the globe is, he would probably have refrained from his proud exclamation. Let us imagine for a moment that Archimedes was given that “other Earth”, that point of support that he was looking for; Let us further imagine that he has made a lever of the required length. Do you know how long it would take him to lift a load equal in mass to the globe by at least one centimeter? At least thirty thousand billion years!

Indeed. The mass of the Earth is known to astronomers; a body with such a mass would weigh around 6,000,000,000,000,000,000,000 tons on Earth.

If a person can directly lift only 60 kg, then in order to “raise the Earth”, he will need to put his hands on the long arm of the lever, which is 100,000,000,000,000,000,000,000 times larger than the short one!

A simple calculation will convince you that while the end of the short arm rises 1 cm, the other end will describe a huge arc of 1000,000,000,000,000,000 km in the universe.

Such an unimaginably long distance would have to be taken by the hand of Archimedes, pressing on the lever, in order to “raise the Earth” by only one centimeter! How long will it take for this? If we assume that Archimedes was able to lift a load of 60 kg to a height of 1 m in one second (an efficiency of almost a whole horsepower!), then even then it will take 1000,000,000,000,000,000,000 seconds to “raise the Earth” by 1 cm, or thirty thousand billion years! Throughout his long life, Archimedes, pressing on the lever, would not have “raised the Earth” even by the thickness of the thinnest hair...

No tricks of the brilliant inventor would have helped him to noticeably shorten this period. The “Golden Rule of Mechanics” states that on any machine, a gain in force is inevitably accompanied by a corresponding loss in the length of movement, that is, in time. Even if Archimedes had brought the speed of his hand to the greatest speed possible in nature - up to 300,000 km per second (the speed of light), then even with such a fantastic assumption he would have “raised the Earth” by 1 cm only after ten million years of work .

Jules Vernov's strongman and Euler's formula

Do you remember Jules Verne's strongman-athlete Mathifa? “Magnificent head, proportional to gigantic height; chest like a blacksmith's bellows; legs - like good logs, arms - real lifting specks, with fists like hammers...” Probably, from the exploits of this strongman described in the novel “Mathias Sapdorf”, you remember the amazing incident with the ship “Trabokolo”, when our giant with the mighty force hands delayed the descent of the entire ship.

Here is how the novelist talks about this feat:

“The ship, already freed from the supports that supported it on the sides, was ready for launching. It was enough to remove the moorings for the ship to begin to slide down. Already half a dozen carpenters were working under the keel of the ship. The spectators followed the operation with lively curiosity. At that moment, a pleasure yacht appeared, rounding the coastal ledge. To enter the port, the yacht had to pass in front of the shipyard where the Trabocolo launch was being prepared, and as soon as she gave the signal, it was necessary, in order to avoid any accidents, to delay the launch in order to get back to work after the yacht had entered the canal. If the ships - one standing across, the other moving with great speed - had collided, the yacht would have perished.

The workers stopped hammering. All eyes were fixed on the graceful ship, the white sails of which seemed gilded in the slanting rays of the Sun. Soon the yacht found itself right opposite the shipyard, where a thousand-strong crowd of curious people froze. Suddenly a cry of horror was heard: the Trabocolo swayed and began to move at the very moment when the yacht turned starboard towards him! Both ships were ready to collide; there was neither time nor opportunity to prevent this clash. The Trabocolo quickly slid down the slope... White smoke, which appeared as a result of friction, swirled in front of its bow, while the stern was already plunging into the water of the bay (the ship was descending stern first - Ya. P.).

Suddenly a man appears, grabs the mooring line hanging at the front of the Trabocolo, and tries to hold it, bending to the ground. In one minute he wraps the moorings around an iron pipe driven into the ground and, at the risk of being crushed, holds the rope in his hands with superhuman strength for 10 seconds. Finally the moorings break. But these 10 seconds were enough: the Trabocolo, plunging into the water, only slightly touched the yacht and rushed forward.

The yacht was saved. As for the person for whom no one even had time to come to the rescue - everything happened so quickly and unexpectedly - it was Matifu.”

Mechanics teaches that when a rope wound around a bollard slides, the friction force reaches a large value. The higher the number of turns of the rope, the greater the friction; the rule of increasing friction is such that, with an increase in the number of revolutions in an arithmetic progression, friction increases in a geometric progression. Therefore, even a weak child, holding the free end of a rope wound 3-4 times on a stationary shaft, can balance the enormous force.

At river steamship piers, teenagers use this technique to stop steamships with hundreds of passengers approaching the piers. It is not the phenomenal strength of their hands that helps them, but the friction of the rope on the pile.

The famous 18th century mathematician Euler established the dependence of the friction force on the number of turns of the rope around the pile. For those who are not intimidated by the condensed language of algebraic expressions, we present this instructive Euler formula:

Here F is the force against which our effort f is directed. The letter e indicates the number 2.718... (the base of natural logarithms), k is the coefficient of friction between the rope and the stand. The letter a denotes the “winding angle,” i.e., the ratio of the length of the arc covered by the rope to the radius of this arc.

Let's apply the formula to the case described by Jules Verne. The result will be amazing. The force F in this case is the traction force of the ship sliding along the dock. The weight of the ship from the novel is known: 50 tons. Let the slope of the slipway be 0.1; then it was not the full weight of the ship that acted on the rope, but 0.1 of it, i.e. 5 tons, or 5000 kg.

Substituting all these values ​​into the above Euler formula gives the equation

The unknown f (i.e., the amount of force required) can be determined from this equation using logarithms:

Lg 5000 = lg f + 2n lg 2.72, whence f = 9.3 kg.

So, to accomplish the feat, the giant only had to pull the rope with a force of only 10 kilograms!

Do not think that this figure - 10 kg - is only theoretical and that in reality much more effort will be required. On the contrary, our result is even exaggerated: with a hemp rope and a wooden pile, when the friction coefficient k is greater, the force required is ridiculously insignificant. If only the rope was strong enough and could withstand tension, then even a weak child could, having wound the rope 3-4 times, not only repeat the feat of the Jules Verne hero, but also surpass him.

What determines the strength of the knots?

In everyday life, without even knowing it, we often take advantage of the benefits that Euler’s formula indicates to us. What is a knot if not a string wound around a roller, the role of which in this case is played by another part of the same string? The strength of any kind of knots - ordinary, “gazebo”, “sea”, ties, bows, etc. - depends solely on friction, which here is greatly enhanced due to the fact that the lace wraps around itself, like a rope around a cabinet. This is easy to verify by following the bends of the lace in the knot. The more bends, the more times the twine wraps around itself, the greater the “winding angle” and, therefore, the stronger the knot.

The tailor unconsciously takes advantage of the same circumstance when sewing on a button. He wraps the thread many times around the area of ​​​​material captured by the stitch and then breaks it; If only the thread is strong, the button will not come off. The rule that is already familiar to us applies here: with an increase in the number of thread turns in an arithmetic progression, the sewing strength increases in a geometric progression.

If there were no friction, we could not use buttons: the threads would unravel under their weight and the buttons would fall off.

If there was no friction

You see how friction manifests itself in various and sometimes unexpected ways in the environment around us. Friction takes part, and a very significant one at that, where we don’t even suspect it. If friction suddenly disappeared from the world, many ordinary phenomena would proceed in a completely different way.

The French physicist Guillaume writes very colorfully about the role of friction:

“We’ve all had to go out in icy conditions: how much effort it took us to keep ourselves from falling, how many funny movements we had to do in order to stand! This forces us to recognize that usually the ground we walk on has a precious quality that allows us to maintain our balance without much effort. The same thought occurs to us when we ride a bicycle on a slippery pavement or when a horse slips on the asphalt and falls. By studying such phenomena, we come to the discovery of the consequences that friction leads to. Engineers strive to eliminate it in cars as much as possible - and do a good job. In applied mechanics, friction is spoken of as an extremely undesirable phenomenon, and this is correct, but only in a narrow, special area. In all other cases, we should be grateful to friction: it gives us the opportunity to walk, sit and work without fear of books and inkwell falling to the floor, or the table sliding until it hits a corner, or the pen slipping from our fingers.

Friction is such a common phenomenon that, with rare exceptions, we do not have to call on it for help: it comes to us on its own.

Friction promotes stability. Carpenters level the floor so that the tables and chairs remain where they were placed. Dishes, plates, glasses placed on the table remain motionless without any special worries on our part, unless it happens on a ship during rocking.

Let us imagine that friction can be completely eliminated. Then no bodies, be they the size of a boulder or small as grains of sand, will ever be able to rest on one another: everything will slide and roll until it ends up on the same level. If there were no friction, the Earth would be a sphere without irregularities, like a liquid.”

To this we can add that in the absence of friction, nails and screws would slip out of the walls, not a single thing could be held in the hands, no whirlwind would ever stop, no sound would cease, but would echo endlessly, reverberating incessantly, for example , from the walls of the room.

An object lesson that convinces us of the enormous importance of friction is given to us every time by black ice. Caught by her on the street, we find ourselves helpless and always at risk of falling. Here is an instructive excerpt from the newspaper (December 1927):

“London 21. Due to heavy ice, street and tram traffic in London is noticeably difficult. About 1,400 people were admitted to hospitals with broken arms, legs, etc.”

Figure 22. Above - loaded sleds on an icy road; two horses carry 70 tons of cargo. Below is an icy road; A - track; B - skid; C - compacted snow; D - earthen base of the road.

“In a collision near Hyde Park between three cars and two tram cars, the cars were completely destroyed due to the explosion of gasoline...”

"Paris 21. Ice in Paris and its suburbs caused numerous accidents..."

However, the negligible friction on ice can be successfully exploited technically. Already ordinary sleds serve as an example of this. This is even better evidenced by the so-called ice roads, which were arranged for transporting timber from the cutting site to the railway or to rafting points. On such a road (Fig. 22), which has smooth ice rails, two horses pull a sleigh loaded with 70 tons of logs.

The physical cause of the Chelyuskin disaster

From what has been said now, one should not rush to the conclusion that friction on ice is negligible under all circumstances. Even at temperatures close to zero, friction with ice is often quite significant. In connection with the work of icebreakers, the friction of the ice of the polar seas on the steel plating of the ship was carefully studied. It turned out that it was unexpectedly large, no less than the friction of iron on iron: the coefficient of friction of the new steel ship plating on ice is 0.2.

To understand what significance this figure has for ships when sailing in ice, let’s look at Fig. 23; it depicts the direction of forces acting on the side MN of the ship under ice pressure. The ice pressure force P is decomposed into two forces: R, perpendicular to the board, and F, directed tangential to the board. The angle between P and R is equal to the angle a of the inclination of the side to the vertical. The friction force Q of ice on the side is equal to the force R multiplied by the friction coefficient, i.e. by 0.2; we have: Q = 0.2R. If the friction force Q is less than F, the latter force drags the pushing ice under the water; the ice slides along the side without having time to cause harm to the ship. If the force Q is greater than F, friction interferes with the sliding of the ice floe, and the ice, with prolonged pressure, can crush and push through the side.

Figure 23. “Chelyuskin”, lost in ice. Bottom: forces acting on the side of the MN ship under ice pressure.

When is the Q "F"? It's easy to see that

therefore there must be an inequality:

and since Q = 0.2R, the inequality Q «F leads to another:

0.2R “R tg a, or tg a” 0.2.

Using the tables, we find the angle whose tangent is 0.2; it is equal to 11°. This means Q “F when a” is 11°. This determines what inclination of the ship’s sides to the vertical ensures safe navigation in ice: the inclination must be at least 11°.

Let us now turn to the death of “Chelyuskin”. This steamer, not an icebreaker, successfully navigated the entire northern sea route, but found itself trapped in ice in the Bering Strait.

The ice carried the Chelyuskin far to the north and crushed it (in February 1934). The two-month heroic stay of the Chelyuskinites on the ice floe and their rescue by heroic pilots is preserved in the memory of many. Here is a description of the disaster itself:

“The strong metal of the hull did not give in immediately,” the head of the expedition, O. Yu. Schmidt, reported on the radio. “You could see how the ice floe was being pressed into the side and how the sheets of plating above it were swelling, bending outward. The ice continued its slow but irresistible advance. The swollen iron sheets of the hull sheathing tore along the seams. Rivets flew with a crash. In an instant, the left side of the steamer was torn off from the bow hold to the aft end of the deck...”

After what has been said in this article, the reader should understand the physical cause of the disaster.

Practical consequences follow from this: when constructing ships intended for navigation in ice, it is necessary to give the sides their proper slope, namely at least 11°.

Self-balancing stick

Place a smooth stick on the index fingers of your outstretched hands, as shown in Fig. 24. Now move your fingers towards each other until they come together tightly. Strange thing! It turns out that in this final position the stick does not tip over, but maintains its balance. You do the experiment many times, changing the initial position of your fingers, but the result is always the same: the stick turns out to be balanced. If you replace the stick with a drawing ruler, a cane with a knob, a billiard cue, or a floor brush, you will notice the same feature. What is the solution to the unexpected ending? First of all, the following is clear: since the stick is balanced on the joined fingers, then it is clear that the fingers have converged under the center of gravity of the stick (the body remains in balance if a plumb line drawn from the center of gravity passes within the boundaries of the support).

When the fingers are spread apart, the greater load falls on the finger that is closer to the center of gravity of the stick. As pressure increases, friction also increases: a finger closer to the center of gravity experiences more friction than a finger further away. Therefore, the finger close to the center of gravity does not slide under the stick; Only the finger that is farthest from this point always moves. As soon as the moving finger is closer to the center of gravity than the other, the fingers change roles; such an exchange is made several times until the fingers come together closely. And since only one of the fingers moves each time, namely the one that is farther from the center of gravity, it is natural that in the final position both fingers converge under the center of gravity of the stick.

Figure 24. Experiment with a ruler. On the right is the end of the experiment.

Figure 25. Same experiment with a floor brush. Why are the scales out of balance?

Before you finish this experiment, repeat it with a floor brush (Fig. 25, above) and ask yourself this question; If you cut the brush in the place where it is supported by your fingers, and put both parts on different cups of scales (Fig. 25, below), then which cup will win - with the stick or with the brush?

It would seem that since both parts of the brush balanced each other on the fingers, they should also be balanced on the scales. In reality, the cup with the brush will overtighten. The reason is not difficult to guess if we take into account that when the brush was balanced on the fingers, the weight forces of both parts were applied to the unequal arms of the lever; in the case of scales, the same forces are applied to the ends of the equal-armed lever.

For the “Pavilion of Entertaining Science” in the Leningrad Cultural Park, I ordered a set of sticks with different positions of the center of gravity; the sticks were separated into two usually unequal parts exactly at the place where the center of gravity was located. Putting these parts on the scales, visitors were surprised to see that the short part was heavier than the long part.

Chapter Three

ROUNDABOUT CIRCULATION.

Why doesn't the spinning top fall?

Of the thousands of people who played with a top as children, not many will be able to answer this question correctly. How, in fact, can we explain the fact that a rotating top, placed vertically or even inclined, does not tip over, contrary to all expectations? What force holds him in such a seemingly unstable position? Doesn't heaviness affect him?

There is a very interesting interaction of forces taking place here. The theory of the spinning top is not simple, and we will not go deeper into it. Let us outline only the main reason why the rotating top does not fall.

In Fig. 26 shows a top rotating in the direction of the arrows. Notice part A of its rim and part B opposite it. Part A tends to move away from you, part B towards you. Now observe what kind of movement these parts receive when you tilt the axis of the top towards you. With this push you force part A to move up, part B to move down; both parts receive a push at right angles to their own motion. But since during the rapid rotation of the top the peripheral speed of the parts of the disk is very high, the insignificant speed you report, adding up to the large circular speed of the point, gives a resultant very close to this circular speed - and the movement of the top almost does not change. This makes it clear why the top seems to resist an attempt to topple it. The more massive the top and the faster it rotates, the more stubbornly it resists tipping over.

Figure 26. Why doesn't the top fall?

Figure 27. A spinning top, when thrown, retains the original direction of its axis.

The essence of this explanation is directly related to the law of inertia. Each particle of the top moves in a circle in a plane perpendicular to the axis of rotation. According to the law of inertia, at every moment the particle tends to move from the circle onto a straight line tangent to the circle. But every tangent is located in the same plane as the circle itself; therefore, each particle tends to move so as to remain at all times in a plane perpendicular to the axis of rotation. It follows that all planes in the top, perpendicular to the axis of rotation, tend to maintain their position in space, and therefore the common perpendicular to them, i.e., the axis of rotation itself, also tends to maintain its direction.

We will not consider all the movements of the top that occur when an external force acts on it. This would require too much detailed explanation, which would probably seem boring. I just wanted to explain the reason for the desire of any rotating body to maintain the direction of the axis of rotation unchanged.

This property is widely used by modern technology. Various gyroscopic (based on the property of a top) devices - compasses, stabilizers, etc. - are installed on ships and aircraft.

Such is the useful use of a seemingly simple toy.

The art of jugglers

Many amazing tricks of the varied juggling program are also based on the property of rotating bodies to maintain the direction of the axis of rotation. Let me quote an excerpt from a fascinating book by the English physicist Prof. John Perry's Spinning Top.

Figure 28. How a coin tossed with rotation flies.

Figure 29. A coin tossed without rotation lands in a random position.

Figure 30. A thrown hat is easier to catch if it has been given rotation around its axis.

“One day I was demonstrating some of my experiments to an audience drinking coffee and smoking tobacco in the magnificent Victoria Concert Hall in London. I tried to interest my listeners as much as I could, and talked about how a flat ring must be given rotation if one wants to throw it so that one can indicate in advance where it will fall; They do the same thing if they want to throw a hat to someone so that he can catch this object with a stick. You can always rely on the resistance that a rotating body exerts when the direction of its axis is changed. I further explained to my listeners that, having polished the barrel of a cannon smoothly, one can never count on the accuracy of the sight; As a result, rifled muzzles are now made, that is, spiral-shaped grooves are cut out on the inside of the cannon muzzle into which the protrusions of the cannonball or projectile fit, so that the latter should receive a rotational movement when the force of the explosion of gunpowder forces it to move along the cannon channel. Thanks to this, the projectile leaves the gun with a precisely defined rotational movement.

That was all I could do during this lecture, as I have no dexterity in throwing hats or discus. But after I had finished my lecture, two jugglers appeared on the stage, and I could not wish for a better illustration of the above-mentioned laws than that given by each individual trick performed by these two artists. They threw spinning hats, hoops, plates, umbrellas to each other... One of the jugglers threw a whole row of knives into the air, caught them again and threw them up again with great accuracy; my audience, having just heard the explanation of these phenomena, rejoiced with pleasure; she noticed the rotation that the juggler imparted to each knife, releasing it from his hands, so that he could probably know in what position the knife would return to him again. I was then amazed that almost without exception all the juggling tricks performed that evening were an illustration of the principle stated above.”

New solution to the Columbus problem

Columbus solved his famous problem of how to place an egg too simply: he broke its shell. This decision is, in essence, incorrect: having broken the shell of the egg, Columbus changed its shape and, therefore, placed not an egg, but another body; after all, the whole essence of the problem is in the shape of an egg: by changing the shape, we replace the egg with another body. Columbus did not provide a solution for the body for which it was sought.

Figure 31. Solution to the Columbus problem: the egg rotates while standing on its end.

Meanwhile, you can solve the problem of the great navigator without changing the shape of the egg at all, if you use the property of the top; To do this, it is enough just to put the egg into a rotational movement around its long axis - and it will stand for some time on a blunt or even sharp end without tipping over. The Figure shows how to do this: the egg is given a rotational movement with your fingers. Taking your hands away, you will see that the egg continues to spin upright for some time: the problem is solved.

For the experiment, you must definitely take boiled eggs. This restriction does not contradict the conditions of Columbus’s problem: having proposed it, Columbus immediately took an egg from the table, and, presumably, not raw eggs were served to the table. You will hardly be able to get a raw egg to spin upright, because the internal liquid mass is a brake in this case. This, by the way, is a simple way to distinguish raw eggs from hard-boiled ones - a technique known to many housewives.

"Destroyed" gravity

“Water does not pour out from a vessel that rotates, it does not pour out even when the vessel is turned upside down, because rotation interferes with this,” wrote Aristotle two thousand years ago. In Fig. 32 depicts this spectacular experiment, which, no doubt, is familiar to many: by rotating a bucket of water quickly enough, as shown in the figure, you achieve that the water does not spill out even in that part of the way where the bucket is turned upside down.

In everyday life, it is customary to explain this phenomenon by “centrifugal force,” meaning by it that imaginary force that is supposedly applied to the body and determines its desire to move away from the center of rotation. This force does not exist: this desire is nothing more than a manifestation of inertia, and any movement by inertia is carried out without the participation of force. In physics, centrifugal force means something else, namely, the real force with which a rotating body pulls the thread holding it or presses on its curved path. This force is applied not to a moving body, but to an obstacle that prevents it from moving rectilinearly: to a thread, to rails on a curved section of track, etc.

Turning to the rotation of the bucket, we will try to understand the reason for this phenomenon, without resorting at all to the ambiguous concept of “centrifugal force”. Let's ask ourselves the question: where will the stream of water go if a hole is made in the wall of the bucket? If there were no gravity, the water jet would, by inertia, be directed along the tangent AK to the circle AB (Fig. 32). Gravity causes the jet to decrease and describe a curve (parabola AR). If the peripheral speed is high enough, this curve will be located outside the circle AB. The stream reveals in front of us the path along which, when the bucket rotates, the water would move if the bucket did not interfere with the pressure on it. Now it is clear that the water does not at all tend to move vertically downwards, and therefore does not pour out of the bucket. It could pour out of it only if the bucket had its hole facing in the direction of its rotation.

Figure 32. Why doesn't water flow out of the rotating bucket?

Now calculate at what speed the bucket must be rotated in this experiment so that the water does not pour out of it. This speed must be such that the centripetal acceleration of the rotating bucket is no less than the acceleration of gravity: then the path along which the water tends to move will lie outside the circle described by the bucket, and the water will not lag behind the bucket anywhere. The formula for calculating the centripetal acceleration W is;

where v is the peripheral speed, R is the radius of the circular path. Since the acceleration of gravity on the earth’s surface is g = 9.8 m/sec2, we have the inequality v2/R» = 9.8. If we set R equal to 70 cm, then

The ability of a liquid to press against the walls of a vessel in which it rotates around a horizontal axis is used in technology for the so-called centrifugal casting. In this case, it is essential that the heterogeneous liquid is stratified by specific gravity: the heavier components are located further from the axis of rotation, the lighter ones occupy a place closer to the axis. As a result, all the gases contained in the molten metal and forming the so-called “shells” in the casting are released from the metal into the inner, hollow part of the casting. Products made in this way are dense and free from shells. Centrifugal casting is cheaper than conventional injection molding and does not require complex equipment.

You as Galileo

For lovers of strong sensations, sometimes a very peculiar entertainment is arranged - the so-called “devil's swing”. There was such a swing in Leningrad. I didn’t have to swing on it myself, and therefore I will give here its description from Fedo’s collection of scientific fun:

“The swing is suspended from a strong horizontal bar thrown across the room at a known height above the floor. When everyone is seated, a specially assigned attendant locks the front door, removes the board used for entry, and, declaring that he will now give the audience the opportunity to take a short air trip, begins to gently swing the swing. After that, he sits back and swings, like a coachman on his heels, or completely leaves the hall.

Meanwhile, the swing's swings become larger and larger; it apparently rises to the height of the crossbar, then goes beyond it, higher and higher, and finally describes a complete circle. The movement accelerates more and more noticeably, and the swingers, although for the most part already warned, experience an undeniable sensation of swinging and rapid movement; It seems to them that they are rushing upside down in space, so that they involuntarily grab the backs of the seats so as not to fall.

But the scope begins to decrease; the swing no longer rises to the height of the crossbar, and after a few seconds it stops completely.

Figure 33. Diagram of the “devil’s swing” device.

In fact, the swing hung motionless all the time while the experiment continued, and the room itself, with the help of a very simple mechanism, turned past the audience around a horizontal axis. Various types of furniture are attached to the floor or walls of the hall; the lamp, soldered to the table in such a way that it appears easily to tip over, consists of an incandescent electric bulb hidden under a large hood. The attendant, who apparently was rocking the swing, giving it light pushes, in essence, matched them with the light vibrations of the hall and only pretended to swing. The whole situation contributes to the complete success of the deception.”

The secret of the illusion, as you can see, is ridiculously simple. And yet, if now, already knowing what the matter was, you found yourself on the “damn swing”, you would inevitably succumb to deception. Such is the power of illusion!

Remember Pushkin's poem "Movement"?

There is no movement, said the bearded sage.

If a rotating platform is given such a curvature that at a certain speed its surface is perpendicular to the resulting one at each point, then a person placed on the floor will feel at all its points as if on a horizontal plane. By mathematical calculation it was found that such a curved surface is the surface of a special geometric body - a paraboloid. It can be obtained by quickly rotating a glass half filled with water around a vertical axis: then the water at the edges will rise, in the center it will fall, and its surface will take the shape of a paraboloid.

If instead of water we pour melted wax into a glass and continue rotating until the wax cools down, then its hardened surface will give us the exact shape of a paraboloid. At a certain rotation speed, such a surface is, for heavy bodies, as if horizontal: a ball placed at any point does not roll down, but remains at this level (Fig. 36).

Now it will be easy to understand the structure of the “enchanted” ball.

Its bottom (Fig. 37) is made up of a large rotating platform, which is given the curvature of a paraboloid. Although the rotation is extremely smooth thanks to the mechanism hidden under the platform, people on the platform would still feel dizzy if the surrounding objects did not move with them; to prevent the observer from detecting movement, the platform is placed inside a large ball with opaque walls, which rotates at the same speed as the platform itself.

Figure 36. If this glass is rotated with sufficient speed, the ball will not roll to the bottom.

Figure 37. “Enchanted” ball (section).

This is the structure of this carousel, which is called the “enchanted” or “magic” sphere. What do you experience when you are on a platform inside the sphere? When it rotates, the floor under your feet is horizontal, no matter where you are on the curve of the platform - at the axis, where the floor is truly horizontal, or at the edge, where it is inclined at 45°. The eyes clearly see the concavity, but the muscular sense indicates that there is a level place under you.

The evidence of both senses contradicts each other in the most dramatic way. If you move from one edge of the platform to the other, it will seem to you as if the entire huge ball, with the ease of a soap bubble, has rolled over to the other side under the weight of your body: after all, at every point you feel as if you are on a horizontal plane. And the position of other people standing obliquely on the platform should seem extremely unusual to you: it will literally seem to you that people are walking on the walls like flies (Fig. 39).

Water poured onto the floor of an enchanted ball would spread in an even layer over its curved surface. It would seem to people that the water here stands in front of them like an inclined wall.

The usual ideas about the laws of gravity seem to be canceled in this amazing ball, and we are transported to a fabulous world of wonders...

The pilot experiences similar sensations when turning. So, if he flies at a speed of 200 km per hour along a curve with a radius of 500 m, then the earth should appear to him to be raised and inclined by 16°.

Figure 38. The true position of people inside the “enchanted” ball.

Figure 39. The position presented to each of the two visitors.

Figure 40. Rotating laboratory - actual position.

Figure 41. Apparent position of the same rotating laboratory.

In Germany, in the city of Göttingen, a similar rotating laboratory was built for scientific research. This (Fig. 40) is a cylindrical room 3 m in diameter, rotating at a speed of up to 50 revolutions per second. Since the floor of the room is flat, when rotating, it seems to an observer standing near the wall that the room is tilted back, and he himself is reclining on the sloping wall (Fig. 41).

Liquid telescope

The best shape for the mirror of a reflecting telescope is parabolic, i.e. exactly the shape that the surface of a liquid in a rotating vessel naturally takes on. Telescope designers spend a lot of painstaking work to give the mirror this shape. Making a mirror for a telescope takes years. The American physicist Wood circumvented these difficulties by constructing a liquid mirror: by rotating mercury in a wide vessel, he obtained an ideal parabolic surface that could play the role of a mirror, since mercury reflects light rays well. Wood's telescope was installed in a shallow well.

The disadvantage of the telescope, however, is that the slightest shock wrinkles the surface of the liquid mirror and distorts the image, as well as the fact that the horizontal mirror makes it possible to directly examine only those luminaries that are at the zenith.

"Devil's Loop"

You may be familiar with the mind-boggling cycling trick sometimes performed in circuses: a cyclist rides in a loop from the bottom up and completes a full circle, despite having to ride upside down at the top of the circle. A wooden path is arranged in the arena in the form of a loop with one or several curls, as shown in our Fig. 42. The artist rides a bicycle down the inclined part of the loop, then quickly takes off on his steel horse up, along its circular part, and makes a full turn, literally down head, and slides safely to the ground.

Figure 42. “Devil's loop.” Below on the left is a diagram for the calculation.

This puzzling bicycle trick seems to be the height of acrobatic art. The puzzled public asks itself in bewilderment: what mysterious force is holding the daredevil upside down? Those who are distrustful are ready to suspect a clever deception here, but meanwhile there is nothing supernatural in the trick. It is entirely explained by the laws of mechanics. A billiard ball launched along this path would do the same with no less success. There are miniature “Devil's loops” in school physics classrooms.

End of free trial.

Ya. I. Perelman

Entertaining physics

FROM THE EDITOR

Proposed edition of “Entertaining Physics” by Ya.I. Perelman repeats the four previous ones. The author worked on the book for many years, improving the text and supplementing it, and for the last time during the author’s lifetime the book was published in 1936 (thirteenth edition). When releasing subsequent editions, the editors did not set as their goal a radical revision of the text or significant additions: the author selected the main content of “Entertaining Physics” in such a way that, while illustrating and deepening the basic information from physics, it is not outdated to this day. In addition, the time after 1936 so much has already passed that the desire to reflect the latest achievements of physics would have led to a significant increase in the book and to a change in its “face”. For example, the author’s text on the principles of space flight is not outdated, and there is already so much factual material in this area that one can only refer the reader to other books specifically devoted to this topic.

The fourteenth and fifteenth editions (1947 and 1949) were published under the editorship of prof. A. B. Mlodzeevsky. Associate Professor took part in the preparation of the sixteenth edition (1959 - 1960). V.A. Ugarov. When editing all publications published without an author, outdated figures were only replaced, projects that did not justify themselves were removed, and individual additions and notes were made.

In this book, the author strives not so much to impart new knowledge to the reader, but to help him “find out what he knows,” that is, to deepen and revive the basic information from physics that he already has, teach him how to consciously manage it and encourage him to use it in many ways. . This is achieved by examining a motley series of puzzles, intricate questions, entertaining stories, amusing problems, paradoxes and unexpected comparisons from the field of physics, related to everyday phenomena or drawn from well-known works of science fiction fiction. The compiler used the latter kind of material especially widely, considering it the most relevant to the purposes of the collection: excerpts from novels and stories by Jules Verne, Wells, Mark Twain and others are given. The fantastic experiences described in them, in addition to their temptingness, can also play an important role in the quality of teaching when teaching. live illustrations.

The compiler tried, as far as he could, to give the presentation an outwardly interesting form and to convey the attractiveness of the subject. He was guided by the psychological axiom that interest in a subject increases attention, facilitates understanding and, consequently, contributes to more conscious and lasting assimilation.

Contrary to the custom established for this kind of collections, in “Entertaining Physics” very little space is devoted to the description of funny and spectacular physical experiments. This book has a different purpose than collections that offer material for experimentation. The main goal of “Entertaining Physics” is to excite the activity of the scientific imagination, to accustom the reader to think in the spirit of physical science and to create in his memory numerous associations of physical knowledge with the most diverse phenomena of life, with everything with which he usually comes into contact. The attitude that the compiler tried to adhere to when revising the book was given by V.I. Lenin in the following words: “A popular writer leads the reader to a deep thought, to a deep teaching, based on the simplest and generally known data, pointing out with the help of simple reasoning or well-chosen main examples conclusions from these data, leading the thinking reader to further and further questions. A popular writer does not assume a reader who does not think, does not want, or cannot think; on the contrary, he assumes in the undeveloped reader a serious intention to work with his head and helps him to do this serious and difficult work, guides him, helps him take his first steps and teaching move on on your own” [V. I. Lenin. Collection cit., ed. 4, vol. 5, p. 285.].

In view of the interest shown by readers in the history of this book, we provide some bibliographic information about it.

“Entertaining Physics” was “born” a quarter of a century ago and was the first-born in the large book family of its author, which now numbers several dozen members.

“Entertaining physics” was lucky enough to penetrate - as letters from readers testify - into the most remote corners of the Union.

The significant distribution of the book, testifying to the keen interest of wide circles in physical knowledge, imposes on the author serious responsibility for the quality of its material. The awareness of this responsibility explains the numerous changes and additions to the text of “Entertaining Physics” during repeated editions. The book, one might say, was written during all 25 years of its existence. In the latest edition, barely half of the text of the first has been preserved, and almost none of the illustrations.

The author received requests from other readers to refrain from revising the text, so as not to force them “to purchase each re-edition because of a dozen new pages.” Such considerations can hardly relieve the author from the obligation to improve his work in every possible way. “Entertaining Physics” is not a work of fiction, but a scientific work, albeit a popular one. Its subject - physics - even in its initial foundations is constantly enriched with fresh material, and the book must periodically include it in its text.

On the other hand, one often hears reproaches that “Entertaining Physics” does not devote space to such topics as the latest advances in radio technology, the fission of the atomic nucleus, modern physical theories, etc. Reproaches of this kind are the fruit of a misunderstanding. “Entertaining Physics” has a very specific goal; consideration of these issues is the task of other works.

“Entertaining Physics,” in addition to her second book, contains several other works by the same author. One is intended for a relatively unprepared reader who has not yet begun the systematic study of physics, and is entitled “Physics at Every Step” (published by “Detizdat”). The other two, on the contrary, refer to those who have already completed their high school physics course. These are “Entertaining mechanics” and “Do you know physics?”. The last book is like the completion of “Entertaining Physics”.

1936 Ya. Perelman

Chapter first. SPEED. ADDITION OF MOVEMENTS.

How fast are we moving?

A good runner runs a sports distance of 1.5 km in about 3 minutes. 50 sec. (world record 1958 - 3 minutes 36.8 seconds). To compare with the usual pedestrian speed - 1.5 m per second - you need to do a small calculation; then it turns out that the athlete runs 7 m per second. However, these speeds are not entirely comparable: a pedestrian can walk for a long time, for hours, doing 5 km per hour, but an athlete is able to maintain a significant running speed only for a short time. An infantry military unit moves at a run three times slower than the record holder; she does 2 meters per second, or more than 7 kilometers per hour, but has the advantage over the athlete that she can make much greater transitions.

It is interesting to compare the normal gait of a person with the speed of such proverbial slow animals as a snail or a turtle. The snail fully lives up to the reputation attributed to it by the saying: it moves 1.5 mm per second, or 5.4 m per hour - exactly a thousand times less than a person! Another classically slow animal, the turtle, is not much faster than the snail: its usual speed is 70 m per hour.

Agile next to a snail and a turtle, a person will appear before us in a different light if we compare his movement with other, even not very fast, movements in the surrounding nature. True, it easily overtakes the flow of water in most lowland rivers and does not lag far behind the moderate wind. But a person can successfully compete with a fly flying 5 m per second only on skis. A person cannot drive a hare or a hunting dog even on a horse. A person can compete in speed with an eagle only on an airplane.

Such a sea exists in a country known to mankind since ancient times. This is the famous Dead Sea of ​​Palestine. Its waters are unusually salty, so much so that not a single living creature can live in them. The hot, rainless climate of Palestine causes strong evaporation of water from the surface of the sea. But only pure water evaporates, while dissolved salts remain in the sea and increase the salinity of the water. That is why the water of the Dead Sea does not contain 2 or 3 percent salt (by weight), like most seas and oceans, but 27 percent or more; Salinity increases with depth. So, a quarter of the contents of the Dead Sea are salts dissolved in its water. The total amount of salts in it is estimated at 40 million tons.
The high salinity of the Dead Sea determines one of its features: the water of this sea is much heavier than ordinary sea water. It is impossible to drown in such a heavy liquid: the human body is lighter than it.
The weight of our body is noticeably less than the weight of an equal volume of densely salty water and, therefore, according to the law of swimming, a person cannot drown in the Dead Sea; he floats in it, just as a chicken egg floats in salt water (which sinks in fresh water)
Humorist Mark Twain, who visited this lake-sea, describes with comic detail the extraordinary sensations that he and his companions experienced while swimming in the heavy waters of the Dead Sea:
“It was a fun swim! We couldn't drown. Here you can stretch out on the water to your full length, lying on your back and folding your arms across your chest, with most of your body remaining above the water. At the same time, you can completely raise your head... You can lie very comfortably on your back, raising your knees to your chin and clasping them with your hands, but you will soon turn over, since your head is outweighed. You can stand on your head and from the middle of your chest to the end of your legs you will remain out of the water, but you will not be able to maintain this position for long. You cannot swim on your back, moving any noticeably, since your legs stick out of the water and you have to push off only with your heels. If you swim face down, then you move not forward, but backward. The horse is so unstable that it can neither swim nor stand in the Dead Sea - it immediately lies on its side.”
In Fig. 49 you see a man sitting quite comfortably on the surface of the Dead Sea; the large specific gravity of water allows him to read a book in this position, protected by an umbrella from the burning rays of the sun.
The water of Kara-Bogaz-Gol (a bay of the Caspian Sea) and the equally salty water of Lake Elton, containing 27% salts, have the same extraordinary properties.
Those patients who take salt baths have to experience something of this kind. If the salinity of the water is very high, as, for example, in the Starorussky mineral waters, then the patient has to make a lot of effort to stay at the bottom of the bath. I heard a woman being treated in Staraya Russa complain indignantly that the water was “positively pushing her out of the bath.” It seems that she was inclined to blame it not on Archimedes’ law, but on the resort administration...

Figure 49. Man on the surface of the Dead Sea (from a photograph).

Figure 50. Load line on board the ship. Brand designations are made at the waterline level. For clarity, they are also shown separately in enlarged form. The meaning of the letters is explained in the text.
The degree of salinity of water in different seas varies somewhat, and accordingly, ships do not sit equally deep in sea water. Perhaps some of the readers happened to see on board the ship near the waterline the so-called “Lloyd’s Mark” - a sign showing the level of the maximum waterlines in water of varying densities. For example, shown in Fig. 50 load line means the maximum waterline level:
in fresh water (Fresch Water) ................................. FW
in the Indian Ocean (India Summer) ...................... IS
in salt water in summer (Summer) ......................... S
in salt water in winter (Winter) ............................. W
all in. Atlant. ocean in winter (Winter North Atlantic) .. WNA
In our country, these brands have been introduced as mandatory since 1909. Let us note in conclusion that there is a type of water that, even in its pure form, without any impurities, is noticeably heavier than ordinary water; its specific gravity is 1.1, i.e. 10% more than ordinary; therefore, in a pool with such water, a person who did not even know how to swim could hardly drown. Such water was called “heavy” water; its chemical formula is D2O (the hydrogen it contains consists of atoms twice as heavy as ordinary hydrogen atoms, and is designated by the letter D). “Heavy” water is dissolved in small quantities in ordinary water: a bucket of drinking water contains about 8 g.
Heavy water with the composition D2O (there are possibly seventeen varieties of heavy water with different compositions) is currently mined in almost pure form; the admixture of ordinary water is about 0.05%.

How does an icebreaker work?

While taking a bath, do not miss the opportunity to do the following experiment. Before leaving the bathtub, open the bathtub outlet while still lying on the bottom of the bathtub. As more and more of your body begins to protrude above the water, you will feel its gradual heaviness. You will most clearly see that the weight lost by the body in the water (remember how light you felt in the bath!) appears again as soon as the body is out of the water.
When a whale involuntarily undergoes such an experiment, finding itself stranded during low tide, the consequences turn out to be fatal for the animal: it will be crushed by its own monstrous weight. It is not for nothing that whales live in the water element: the buoyant force of liquid saves them from the disastrous effect of gravity.
The above is closely related to the title of this article. The operation of an icebreaker is based on the same physical phenomenon: the part of the ship removed from the water ceases to be balanced by the buoyant action of water and acquires its “land” weight. One should not think that the icebreaker cuts the ice while moving through the continuous pressure of its bow - the pressure of the stem. This is not how icebreakers work, but ice cutters. This method of action is only suitable for ice of relatively small thickness.
Genuine sea icebreakers - such as the Krasin or Ermak - work differently. Through the action of its powerful machines, the icebreaker pushes its bow onto the ice surface, which for this purpose is arranged strongly beveled under water. Once out of the water, the bow of the ship acquires its full weight, and this huge cargo (for the Ermak, this weight reached, for example, 800 tons) breaks off the ice. To enhance the effect, more water is often pumped into the bow tanks of the icebreaker - “liquid ballast”.
The icebreaker operates in this way until the ice thickness exceeds half a meter. More powerful ice is defeated by the shock action of the vessel. The icebreaker retreats back and hits the edge of the ice with its entire mass. In this case, it is no longer the weight that acts, but the kinetic energy of the moving ship; the ship turns like an artillery shell of low speed, but of enormous mass, into a ram.
Ice hummocks several meters high are broken by the energy of repeated impacts from the strong bow of the icebreaker.
A participant in the famous passage of the Sibiryakov in 1932, polar explorer N. Markov, describes the work of this icebreaker as follows:
“Among hundreds of ice rocks, among a continuous sheet of ice, the Sibiryakov began the battle. For fifty-two hours in a row, the machine telegraph needle jumped from “full backward” to “full forward.” Thirteen four-hour sea watches of the Sibiryakov crashed into the ice from acceleration, crushed it with its nose, climbed onto the ice, broke it and moved back again. The ice, three-quarters of a meter thick, barely gave way. With each blow we penetrated a third of the hull.”
The USSR has the largest and most powerful icebreakers in the world.

Where are the sunken ships?

It is a common belief, even among sailors, that ships sunk in the ocean do not reach the seabed, but hang motionless at some depth, where the water is “correspondingly compacted by the pressure of the overlying layers.”
This opinion was apparently shared even by the author of “20 Thousand Leagues Under the Sea”; in one of the chapters of this novel, Jules Verne describes a sunken ship hanging motionless in the water, and in another he mentions ships “rotting, hanging freely in the water.”
Is this statement correct?
There seems to be some basis for it, since the water pressure in the depths of the ocean really reaches enormous levels. At a depth of 10 m, water presses with a force of 1 kg per 1 cm2 of a submerged body. At a depth of 20 m this pressure is already 2 kg, at a depth of 100 m - 10 kg, 1000 m - 100 kg. The ocean in many places has a depth of several kilometers, reaching more than 11 km in the deepest parts of the Great Ocean (Mariana Trench). It is easy to calculate the enormous pressure that water and objects immersed in it must experience at these enormous depths.
If an empty, corked bottle is lowered to a considerable depth and then removed again, it will be discovered that the water pressure has driven the cork inside the bottle and the entire vessel is full of water. The famous oceanographer John Murray in his book “The Ocean” says that the following experiment was done: three glass tubes of various sizes, sealed at both ends, were wrapped in canvas and placed in a copper cylinder with holes for the free passage of water. The cylinder was lowered to a depth of 5 km. When it was removed from there, it turned out that the canvas was filled with a snow-like mass: it was crushed glass. Pieces of wood, lowered to such a depth, after being removed, sank in the water like a brick - they were so compressed.
It would seem natural to expect that such a monstrous pressure should so compact the water at great depths that even heavy objects will not sink in it, just as an iron weight does not sink in mercury.
However, such an opinion is completely unfounded. Experience shows that water, like all liquids in general, is difficult to compress. Water compressed with a force of 1 kg per 1 cm2 is compressed by only 1/22,000 of its volume and is compressed approximately the same with a further increase in pressure per kilogram. If we wanted to bring water to such a density that iron would float in it, it would be necessary to compact it 8 times. Meanwhile, to compact only in half, that is, to reduce the volume by half, a pressure of 11,000 kg per 1 cm2 is required (if only the mentioned compression measure took place for such enormous pressures). This corresponds to a depth of 110 km below sea level!
From this it is clear that there is absolutely no need to talk about any noticeable compaction of water in the depths of the oceans. In their deepest place, the water is compacted only by 1100/22000, that is, by 1/20 of its normal density, by only 5%. This can hardly affect the conditions of floating of various bodies in it, especially since solid objects immersed in such water are also subject to this pressure and, therefore, also become compacted.
There can therefore not be the slightest doubt that the sunken ships rest on the ocean floor. “Anything that sinks in a glass of water,” says Murray, “must sink in the deepest ocean.”
I have heard the following objection to this. If you carefully place a glass upside down in water, it may remain in that position as it displaces a volume of water that weighs the same as the glass. A heavier metal glass can be held in a similar position below the water level without sinking to the bottom. In the same way, it seems that a cruiser or other vessel with its keel overturned can stop halfway. If in some rooms of the ship the air is tightly locked, the ship will dive to a certain depth and stop there.
After all, quite a few ships go to the bottom upside down - and it is possible that some of them never reach the bottom, remaining hanging in the dark depths of the ocean. A slight push would be enough to throw such a ship off balance, turn it over, fill it with water and make it fall to the bottom - but where do shocks come from in the depths of the ocean, where peace and quiet always reign and where even the echoes of storms do not penetrate?
All these arguments are based on a physical error. An inverted glass does not submerge itself in water - it must be immersed in water by external force, like a piece of wood or an empty, corked bottle. In the same way, a ship turned upside down with its keel will not begin to sink at all, but will remain on the surface of the water. There is no way he can find himself halfway between the ocean level and its bottom.

How the dreams of Jules Verne and Wells came true

Real submarines of our time have in some respects not only caught up with the fantastic Nautilus of Jules Werp, but even surpassed it. True, the speed of current submarine cruisers is half that of the Nautilus: 24 knots versus 50 for Jules Verne (a knot is about 1.8 km per hour). The longest voyage of a modern submarine ship is a trip around the world, while Captain Nemo made a voyage twice as long. But the Nautilus had a displacement of only 1,500 tons, had a crew of only two to three dozen people on board, and was capable of remaining under water without a break for no more than forty-eight hours. The submarine cruiser Surcouf, built in 1929 and owned by the French fleet, had a displacement of 3,200 tons, was manned by a crew of one hundred and fifty people and was capable of staying under water without surfacing for up to one hundred and twenty hours.
This submarine cruiser could make the transition from the ports of France to the island of Madagascar without visiting any port along the way. In terms of comfort of living quarters, Surcouf was perhaps not inferior to Nautilus. Further, the Surcouf had an undoubted advantage over Captain Nemo’s ship in that a waterproof hangar for a reconnaissance seaplane was built on the upper deck of the cruiser. We also note that Jules Verne did not equip the Nautilus with a periscope, which would give the boat the opportunity to view the horizon from under the water.
In one respect only, real submarines will still lag far behind the creation of the French novelist's fantasy: in the depth of immersion. However, it must be noted that at this point Jules Verne’s fantasy crossed the boundaries of plausibility. “Captain Nemo,” we read at one point in the novel, “reached depths of three, four, five, seven, nine and ten thousand meters below the surface of the ocean.” And once the Nautilus even sank to an unprecedented depth - 16 thousand meters! “I felt,” says the hero of the novel, “how the clasps of the iron plating of the underwater vessel were shaking, how its struts were bending, how the windows were moving inward, yielding to the pressure of the water. If our ship did not have the strength of a solid cast body, it would instantly be flattened into a cake.”
The fear is quite appropriate, because at a depth of 16 km (if such a depth existed in the ocean) the water pressure would have reached 16,000: 10 = 1600 kg per 1 cm2 , or 1600 technical atmospheres ; such a force does not crush the iron, but would certainly crush the structure. However, modern oceanography does not know such a depth. The exaggerated ideas about the depths of the ocean that prevailed in the era of Jules Verne (the novel was written in 1869) are explained by the imperfection of methods for measuring depth. In those days, not wire, but hemp rope was used for linting; such a lot was retained by friction against the water, the more strongly the deeper it sank; at a considerable depth, the friction increased to the point that the boat stopped descending altogether, no matter how much the line was poisoned: the hemp rope only became tangled, creating the impression of enormous depth.
Submarines of our time can withstand pressures of no more than 25 atmospheres; this determines the greatest depth of their immersion: 250 m. Much greater depth was achieved in a special apparatus called the “bathysphere” (Fig. 51) and designed specifically for studying the fauna of the ocean depths. This apparatus, however, does not resemble Jules Verne’s Nautilus, but the fantastic creation of another novelist - Wells’s deep-sea balloon, described in the story “In the Depths of the Sea.” The hero of this story descended to the bottom of the ocean to a depth of 9 km in a thick-walled steel ball; the device was submerged without a cable, but with a removable load; Having reached the bottom of the ocean, the ball freed itself from the burden that carried it away and quickly flew up to the surface of the water.
In the bathysphere, scientists have reached a depth of more than 900 m. The bathysphere is lowered on a cable from a ship, with which those sitting in the ball maintain telephone communication.

Figure 51. Steel spherical apparatus “bathysphere” for descent into the deep layers of the ocean. In this apparatus, William Beebe reached a depth of 923 m in 1934. The thickness of the walls of the ball is about 4 cm, the diameter is 1.5 m, and the weight is 2.5 tons.

How was Sadko raised?

In the vast expanse of the ocean, thousands of large and small ships perish every year, especially in wartime. The most valuable and accessible of the sunken ships began to be recovered from the bottom of the sea. Soviet engineers and divers who were part of the EPRON (i.e., “Special Purpose Underwater Expedition”) became famous throughout the world for the successful recovery of more than 150 large vessels. Among them, one of the largest is the icebreaker "Sadko", which sank on the White Sea in 1916 due to the negligence of the captain. After lying on the seabed for 17 years, this excellent icebreaker was raised by EPRON workers and put back into service.
The lifting technique was entirely based on the application of Archimedes' law. Under the hull of the sunken ship, divers dug 12 tunnels in the seabed and stretched a strong steel towel through each of them. The ends of the towels were attached to pontoons that were deliberately sunk near the icebreaker. All this work was carried out at a depth of 25 m below sea level.
The pontoons (Fig. 52) were hollow, impenetrable iron cylinders 11 m long and 5.5 m in diameter. The empty pontoon weighed 50 tons. According to the rules of geometry, it is easy to calculate its volume: about 250 cubic meters. It is clear that such a cylinder should float empty on water: it displaces 250 tons of water, but itself weighs only 50; its carrying capacity is equal to the difference between 250 and 50, i.e. 200 tons. To force the pontoon to sink to the bottom, it is filled with water.
When (see Fig. 52) the ends of the steel slings were firmly attached to the sunken pontoons, compressed air began to be pumped into the cylinders using hoses. At a depth of 25 m, water presses with a force of 25/10 + 1, i.e. 3.5 atmospheres. Air was supplied to the cylinders under a pressure of about 4 atmospheres and, therefore, had to displace water from the pontoons. The lightweight cylinders were pushed with enormous force by the surrounding water onto the surface of the sea. They floated in the water like a balloon in the air. Their combined lifting force with complete displacement of water from them would be equal to 200 x 12, i.e. 2400 tons. This exceeds the weight of the sunken Sadko, so for the sake of a smoother rise, the pontoons were only partially freed from water.

Figure 52. Sadko lifting diagram; shows a cross-section of the icebreaker, pontoons and lines.
Nevertheless, the ascent was carried out only after several unsuccessful attempts. “The rescue party suffered four accidents on it before achieving success,” writes EPRON chief ship engineer T.I. Bobritsky, who led the work. “Three times, tensely waiting for the ship, we saw, instead of a rising icebreaker, pontoons and torn hoses writhing like snakes spontaneously bursting upward, in the chaos of waves and foam. The icebreaker appeared and disappeared again into the depths of the sea twice before it surfaced and finally stayed on the surface.”

"Eternal" water engine

Among the many “perpetual motion” projects, there were many that were based on the floating of bodies in water. A high tower 20 m high is filled with water. At the top and bottom of the tower there are pulleys through which a strong rope is thrown in the form of an endless belt. Attached to the rope are 14 hollow cubic boxes one meter high, riveted from iron sheets so that water cannot penetrate inside the boxes. Our rice. 53 and 54 depict the appearance of such a tower and its longitudinal section.
How does this installation work? Anyone familiar with Archimedes' law will realize that boxes, while in water, will tend to float up. They are carried upward by a force equal to the weight of the water displaced by the boxes, i.e., the weight of one cubic meter of water, repeated as many times as the boxes are immersed in water. From the pictures it can be seen that there are always six boxes in the water. This means that the force that carries the immersed boxes upward is equal to the weight of 6 m3 of water, i.e. 6 tons. They are pulled down by the boxes’ own weight, which, however, is balanced by a load of six boxes hanging freely on the outside of the rope.
So, a rope thrown in this manner will always be subject to a thrust of 6 tons applied to one side and directed upward. It is clear that this force will force the rope to rotate non-stop, sliding along the pulleys, and with each revolution do work of 6000 * 20 = 120,000 kgm.
Now it is clear that if we dot the country with such towers, we will be able to receive from them an unlimited amount of work, sufficient to cover all the needs of the national economy. The towers will rotate the armatures of dynamos and provide electrical energy in any quantity.
However, if you look closely at this project, it is easy to see that the expected movement of the rope should not occur at all.
In order for the endless rope to rotate, the boxes must enter the tower's water pool from the bottom and leave it from the top. But when entering the pool, the box must overcome the pressure of a column of water 20 m high! This pressure per square meter of box area is equal to neither more nor less than twenty tons (the weight of 20 m3 of water). The upward thrust is only 6 tons, that is, it is clearly insufficient to pull the box into the pool.
Among the numerous examples of water “perpetual” engines, hundreds of which were invented by failed inventors, you can find very simple and witty options.

Figure 53. Project of an imaginary “eternal” water engine.

Figure 54. Structure of the tower of the previous figure.
Take a look at fig. 55. Part of a wooden drum mounted on an axis is constantly immersed in water. If Archimedes' law is true, then the part immersed in water should float up and, as long as the buoyant force is greater than the frictional force on the drum axis, the rotation will never stop...

Figure 55. Another project of an “eternal” water engine.
Don't rush to build this “perpetual” engine! You will certainly fail: the drum will not budge. What is the matter, what is the error in our reasoning? It turns out that we did not take into account the direction of the acting forces. And they will always be directed perpendicular to the surface of the drum, that is, along the radius to the axis. From everyday experience, everyone knows that it is impossible to make a wheel rotate by applying force along the radius of the wheel. To cause rotation, a force must be applied perpendicular to the radius, i.e., tangential to the circumference of the wheel. Now it is not difficult to understand why, in this case, the attempt to implement “perpetual” motion will end in failure.
Archimedes' law provided tempting food for the minds of seekers of a "perpetual" motion machine and encouraged them to come up with ingenious devices for using the apparent loss of weight in order to obtain an eternal source of mechanical energy.

Who coined the words "gas" and "atmosphere"?

The word "gas" is one of the words coined by scientists, along with such words as "thermometer", "electricity", "galvanometer", "telephone" and, above all, "atmosphere". Of all the words invented, “gas” is by far the shortest. The ancient Dutch chemist and physician Helmont, who lived from 1577 to 1644 (a contemporary of Galileo), derived “gas” from the Greek word for “chaos.” Having discovered that air consists of two parts, one of which supports combustion and burns out, while the rest does not have these properties, Helmont wrote:
“I called this kind of vapor gas because it is almost no different from the chaos of the ancients.”(the original meaning of the word “chaos” is shining space).
However, the new word was not used for a long time after that and was revived only by the famous Lavoisier in 1789. It became widespread when everyone started talking about the flights of the Montgolfier brothers in the first hot air balloons.
Lomonosov in his writings used another name for gaseous bodies - “elastic liquids” (which remained in use even when I was at school). Let us note, by the way, that Lomonosov is credited with introducing into Russian speech a number of names that have now become standard words in the scientific language:
atmosphere
pressure gauge
barometer
micrometer
air pump
optics, optical
viscosity
e(e)electric
crystallization
e(f)fir
matter
and etc.
The brilliant founder of Russian natural science wrote on this occasion: “I was forced to look for words to name some physical instruments, actions and natural things, which (i.e. words) although at first seem somewhat strange, I hope that over time they will become more familiar through use there will be."
As we know, Lomonosov's hopes were fully justified.
On the contrary, the words subsequently proposed by V. I. Dahl (the famous compiler of the “Explanatory Dictionary”) to replace “atmosphere” - the clumsy “mirokolitsa” or “kolozemitsa” - did not take root at all, just as his “skybozem” instead of horizon and other new words did not take root .

Seems like a simple task

The samovar, which holds 30 glasses, is full of water. You place the glass under its tap and, with a watch in your hands, watch the second hand to see how long it takes for the glass to fill to the brim. Let's say half a minute. Now let’s ask the question: how long will it take for the entire samovar to empty if you leave the tap open?
It would seem that this is a childishly simple arithmetic problem: one glass flows out in 0.5 minutes, which means 30 glasses will flow out in 15 minutes.
But do the experiment. It turns out that the samovar empties not in a quarter of an hour, as you expected, but in half an hour.
What's the matter? After all, the calculation is so simple!
Simple, but wrong. You cannot think that the flow rate remains the same from beginning to end. When the first glass flows out of the samovar, the stream flows under less pressure, since the water level in the samovar has decreased; it is clear that the second glass will be filled in more than half a minute; the third will flow out even more lazily, etc.
The rate of flow of any liquid from a hole in an open vessel is directly dependent on the height of the liquid column standing above the hole. The brilliant Toricelli, a student of Galileo, was the first to point out this dependence and expressed it with a simple formula:

Where v is the flow velocity, g is the acceleration of gravity, and h is the height of the liquid level above the hole. From this formula it follows that the speed of the flowing stream is completely independent of the density of the liquid: light alcohol and heavy mercury at the same level flow out of the hole equally quickly (Fig. 56). The formula shows that on the Moon, where gravity is 6 times less than on Earth, it would take about 2.5 times longer to fill a glass than on Earth.
But let's return to our task. If, after 20 glasses have flowed out of the samovar, the water level in it (counting from the tap opening) has dropped four times, then the 21st glass will fill twice as slowly as the 1st. And if in the future the water level drops 9 times, then filling the last glasses will take three times longer than filling the first. Everyone knows how sluggishly water flows from the faucet of a samovar, which is already almost empty. By solving this problem using the methods of higher mathematics, it can be proven that the time required to completely empty the vessel is twice as long as the time during which the same volume of liquid would pour out if the initial level remained unchanged.

Figure 56. Which is more likely to spill out: mercury or alcohol? The liquid level in the vessels is the same.

Pool problem

From what has been said, it is one step to the notorious pool problems, without which not a single arithmetic and algebraic problem book can do. Everyone remembers classically boring, scholastic problems like the following:
“There are two pipes installed into the pool. After one first empty pool can be filled in 5 hours; in one second the full pool can be emptied at 10 o'clock. At what time will the empty pool be filled if both pipes are opened at once?
Problems of this kind have a venerable history - almost 20 centuries, going back to Heron of Alexandria. Here is one of Heron’s problems, although not as intricate as its descendants:

Four fountains are given. There is an extensive reservoir.
Within 24 hours, the first fountain fills it to the brim.
The second one must work on the same thing for two days and two nights.
The third is three times weaker than the first.
At four days the last one can keep up with him.
Tell me if it will be full soon,
What if you open them all at one time?

Pool problems have been solved for two thousand years, and such is the power of routine! – two thousand years have been decided incorrectly. Why it is wrong - you will understand for yourself after what was just said about the flow of water. How are they taught to solve problems about swimming pools? The first problem, for example, is solved like this. At 1 hour, the first pipe pours 0.2 pools, the second pipe pours 0.1 pools; This means that with the action of both pipes, 0.2 – 0.1 = 0.1 enters the pool every hour, which gives the pool filling time 10 hours. This reasoning is incorrect: if the inflow of water can be considered to occur under constant pressure and, therefore, uniform, then its outflow occurs at a changing level and, therefore, unevenly. From the fact that the second pipe empties the pool at 10 o’clock, it does not at all follow that 0.1 of the pool flows out every hour; The school decision method, as we see, is erroneous. It is impossible to solve the problem correctly using elementary mathematics, and therefore problems about a swimming pool (with flowing water) have no place at all in arithmetic problem books.

Figure 57. Pool problem.

Amazing vessel

Is it possible to construct a vessel from which water would flow out all the time in a uniform stream, without slowing down its flow, despite the fact that the liquid level decreases? After what you've learned from previous articles, you're probably prepared to consider this kind of problem insurmountable.
Meanwhile, this is quite feasible. The jar shown in Fig. 58, is just such an amazing vessel. This is an ordinary jar with a narrow neck, through the stopper of which a glass tube is inserted. If you open tap C below the end of the tube, liquid will flow out of it in an unrelenting stream until the water level in the vessel drops to the lower end of the tube. By pushing the tube almost to the level of the tap, you can force all the liquid above the level of the hole to flow out in a uniform, although very weak stream.

Figure 58. Structure of the Mariotte vessel. Water flows uniformly from hole C.
Why is this happening? Mentally observe what happens in the vessel when tap C is opened (Fig. 58). First of all, water is poured out of the glass tube; the level of liquid inside it drops to the end of the tube. With further outflow, the water level in the vessel drops and outside air enters through the glass tube; it seeps through the water in bubbles and collects above it in the upper part of the vessel. Now at all level B the pressure is equal to atmospheric pressure. This means that water flows from tap C only under the pressure of the water layer BC, because the atmospheric pressure from inside and outside the vessel is balanced. And since the thickness of the BC layer remains constant, it is not surprising that the jet flows at the same speed all the time.
Now try to answer the question: how quickly will water flow out if you remove plug B at the level of the end of the tube?
It turns out that it will not flow out at all (of course, if the hole is so small that its width can be neglected; otherwise the water will flow out under the pressure of a thin layer of water, thick as the width of the hole). In fact, here, inside and outside, the pressure is equal to atmospheric pressure, and nothing encourages water to flow out.
And if you were to remove plug A above the lower end of the tube, then not only would water not flow out of the vessel, but outside air would also enter it. Why? For a very simple reason: inside this part of the vessel the air pressure is less than the atmospheric pressure outside.
This vessel with such extraordinary properties was invented by the famous physicist Marriott and was named after the scientist “Mariotte’s vessel.”

Luggage from thin air

In the middle of the 17th century, residents of the city of Rogensburg and the sovereign princes of Germany, led by the emperor, who gathered there, witnessed an amazing sight: 16 horses tried their best to separate two copper hemispheres attached to each other. What connected them? “Nothing” - air. And yet, eight horses pulling in one direction and eight horses pulling in the other were unable to separate them. So burgomaster Otto von Guericke showed everyone with his own eyes that air is not “nothing” at all, that it has weight and presses with considerable force on all earthly objects.
This experiment was carried out on May 8, 1654 in a very solemn atmosphere. The learned burgomaster managed to interest everyone in his scientific research, despite the fact that this happened in the midst of political turmoil and devastating wars.
A description of the famous experiment with the “Magdeburg hemispheres” is available in physics textbooks. Nevertheless, I am sure that the reader will listen with interest to this story from the lips of Guericke himself, this “German Galileo,” as the remarkable physicist is sometimes called. A voluminous book describing a long series of his experiments was published in Latin in Amsterdam in 1672 and, like all books of this era, bore a lengthy title. Here it is:
OTTO von GUERIKE

The so-called new Magdeburg experiments

over AIRLESS SPACE,

originally described by a mathematics professor
at the University of Würzburg by CASPAR SCHOTT.
Edition by the author himself,
more detailed and enriched with various
new experiences.
Chapter XXIII of this book is devoted to the experience that interests us. We give its literal translation.
“An experiment proving that air pressure connects the two hemispheres so firmly that they cannot be separated by the efforts of 16 horses.
I ordered two copper hemispheres with a diameter of three-quarters of Magdeburg cubits. But in reality, their diameter was only 67/100, since the craftsmen, as usual, could not produce exactly what was required. Both hemispheres fully responded to each other. A tap was attached to one hemisphere; With this tap you can remove air from inside and prevent air from entering from outside. In addition, 4 rings were attached to the hemispheres, through which ropes tied to the horses' harness were threaded. I also ordered a leather ring to be sewn; it was soaked in a mixture of wax and turpentine; sandwiched between the hemispheres, it did not allow air to pass into them. An air pump tube was inserted into the tap and the air inside the balloon was removed. Then it was discovered with what force both hemispheres were pressed against each other through the leather ring. The pressure of the outside air pressed them so tightly that 16 horses (with a jerk) could not separate them at all or only achieved this with difficulty. When the hemispheres, yielding to the tension of all the horses' strength, separated, a roar was heard, as if from a shot.
But as soon as you turned the tap to open free access to air, it was easy to separate the hemispheres with your hands.”
A simple calculation can explain to us why such a significant force (8 horses on each side) is needed to separate the parts of an empty ball. The air presses with a force of about 1 kg per square cm; The area of ​​a circle with a diameter of 0.67 cubits (37 cm) is 1060 cm2. This means that the atmospheric pressure on each hemisphere must exceed 1000 kg (1 ton). Each eight horses therefore had to pull tons of force to counteract the pressure of the outside air.
It would seem that for eight horses (on each side) this is not a very large load. Do not forget, however, that when moving, for example, a load of 1 ton, horses overcome a force not of 1 ton, but much less, namely, the friction of the wheels on the axle and on the pavement. And this force is - on the highway, for example - only five percent, i.e. with a one-ton load - 50 kg. (Not to mention that when combining the efforts of eight horses, as practice shows, 50% of the traction is lost.) Consequently, a traction of 1 ton corresponds to a cart load of 20 tons with eight horses. This is what the air baggage was that the horses of the Magdeburg burgomaster were supposed to carry! It was as if they had to move a small locomotive, which, moreover, was not placed on the rails.
A strong draft horse has been measured to pull a cart with a force of only 80 kg. Consequently, to break the Magdeburg hemispheres, with uniform traction, 1000/80 = 13 horses on each side would be needed.
The reader will probably be amazed to learn that some of the joints of our skeleton do not fall apart for the same reason as the Magdeburg hemispheres. Our hip joint is just such a Magdeburg hemisphere. You can expose this joint from the muscular and cartilaginous connections, and yet the hip does not fall out: it is pressed by atmospheric pressure, since there is no air in the interarticular space.

New Heron fountains

The usual form of the fountain attributed to the ancient mechanician Heron is probably known to my readers. Let me here recall its structure before proceeding to a description of the latest modifications of this curious device. Heron's fountain (Fig. 60) consists of three vessels: the upper open one a and two spherical ones b and c, hermetically sealed. The vessels are connected by three tubes, the location of which is shown in the figure. When there is some water in a, ball b is filled with water, and ball c is filled with air, the fountain begins to operate: water flows through the tube from a to c. displacing air from there into ball b; under the pressure of the incoming air, water from b rushes up the tube and fountains above vessel a. When the ball b is empty, the fountain stops flowing.

Figure 59. The bones of our hip joints are not disintegrated due to atmospheric pressure, just as the Magdeburg hemispheres are held back.

Figure 60. Ancient Heron fountain.

Figure 61. Modern modification of Heron's fountain. Above is a variant of the plate arrangement.
This is the ancient form of Heron's fountain. Already in our time, one school teacher in Italy, prompted to ingenuity by the meager furnishings of his physics classroom, simplified the design of Heron’s fountain and came up with modifications of it that anyone can arrange using the simplest means (Fig. 61). Instead of balls, he used pharmacy bottles; Instead of glass or metal tubes, I took rubber ones. There is no need to make holes in the upper vessel: you can simply insert the ends of the tubes into it, as shown in Fig. 61 above.
In this modification, the device is much more convenient to use: when all the water from jar b has poured through vessel a into jar c, you can simply rearrange jars b and c, and the fountain operates again; Do not forget, of course, to also transfer the tip to another tube.
Another convenience of the modified fountain is that it makes it possible to arbitrarily change the location of the vessels and study how the distance between the levels of the vessels affects the height of the jet.
If you want to increase the height of the jet many times, you can achieve this by replacing water in the lower flasks of the described device with mercury, and air with water (Fig. 62). The operation of the device is clear: mercury, pouring from jar c to jar b, displaces water from it, causing it to flow like a fountain. Knowing that mercury is 13.5 times heavier than water, we can calculate to what height the fountain jet should rise. Let us denote the difference in levels respectively by h1, h2, h3. Now let's figure out under what forces mercury flows from vessel c (Fig. 62) into b. The mercury in the connecting tube is subject to pressure from both sides. On the right it is subject to the pressure of the difference h2 of mercury columns (which is equivalent to the pressure of 13.5 times the higher water column, 13.5 h2) plus the pressure of the water column h1. The water column h3 is pressing on the left. As a result, mercury is carried away by force
13.5h2 + h1 – h3.
But h3 – h1 = h2; Therefore, we replace h1 – h3 with minus h2 and get:
13.5h2 – h2 i.e. 12.5h2.
So, mercury enters vessel b under the pressure of the weight of a water column with a height of 12.5 h2. Theoretically, the fountain should therefore shoot to a height equal to the difference in mercury levels in the bottles, multiplied by 12.5. Friction lowers this theoretical height somewhat.
Nevertheless, the described device provides a convenient opportunity to obtain a jet shooting high upward. To make, for example, a fountain shoot to a height of 10 m, it is enough to raise one can above the other by about one meter. It is curious that, as can be seen from our calculation, the elevation of the plate a above the flasks with mercury does not in the least affect the height of the jet.

Figure 62. Fountain operating under mercury pressure. The jet hits ten times higher than the difference in mercury levels.

Deceptive Vessels

In the old days - in the 17th and 18th centuries - nobles amused themselves with the following instructive toy: they made a mug (or jug), in the upper part of which there were large patterned cutouts (Fig. 63). Such a mug, filled with wine, was offered to an ordinary guest, at whom one could laugh with impunity. How to drink from it? You can’t tilt it: the wine will pour out of many through holes, but not a drop will reach your mouth. It will happen like in a fairy tale:

Figure 63. A deceptive jug from the late 18th century and the secret of its design.
Honey, drank beer,
Yes, he just wet his mustache.
But who knew the secret of the construction of such mugs - the secret that is shown in Fig. 63 on the right - he plugged hole B with his finger, took the spout into his mouth and sucked in the liquid without tilting the vessel: the wine rose through hole E along the channel inside the handle, then along its continuation C inside the upper edge of the mug and reached the spout.
Not so long ago, similar mugs were made by our potters. I happened to see in one house a sample of their work, quite skillfully hiding the secret of the structure of the vessel; There was an inscription on the mug: “Drink, but don’t get wet.”

How much does water weigh in an overturned glass?

“Of course, it doesn’t weigh anything: the water doesn’t hold in such a glass, it spills out,” you say.
– What if it doesn’t pour out? – I’ll ask. – What then?
In fact, it is possible to hold water in an overturned glass so that it does not spill out. This case is shown in Fig. 64. An overturned glass goblet, tied by the bottom to one pan of a scale, is filled with water, which does not spill out, since the edges of the glass are immersed in a vessel with water. An exactly the same empty glass is placed on the other pan of the scale.
Which side of the scale will tip?

Figure 64. Which cup will win?
The one to which the overturned glass of water is tied will win. This glass experiences full atmospheric pressure from above, and atmospheric pressure from below, weakened by the weight of the water contained in the glass. To balance the cups, it would be necessary to fill a glass placed on another cup with water.
Under these conditions, therefore, water in an overturned glass weighs the same as in one placed on the bottom.

Why are ships attracted?

In the fall of 1912, the following incident occurred with the ocean-going steamer Olympic, then one of the greatest ships in the world. The Olympic was sailing in the open sea, and almost parallel to it, at a distance of hundreds of meters, another ship, much smaller, the armored cruiser Gauk, was passing at high speed. When both vessels took the position shown in Fig. 65, something unexpected happened: the smaller ship quickly turned out of the way, as if obeying some invisible force, turned its nose to the large steamer and, not obeying the rudder, moved almost directly towards it. There was a collision. The Gauk crashed nose-first into the side of the Olmpik; the blow was so strong that the Gauk made a large hole in the side of the Olympic.

Figure 65. Position of the ships Olympic and Gauk before the collision.
When this strange case was considered in a maritime court, the captain of the giant “Olympic” was found guilty, since, as the court ruling read, “he did not give any orders to give way to the Hauk going across it.”
The court, therefore, did not see anything unusual here: the captain’s simple lack of management, nothing more. Meanwhile, a completely unforeseen circumstance took place: the case of mutual attraction of ships at sea.
Such cases occurred more than once, probably before, when two ships were moving in parallel. But until very large ships were built, this phenomenon did not manifest itself with such force. When “floating cities” began to plow the waters of the oceans, the phenomenon of attraction of ships became much more noticeable; commanders of military vessels take it into account when maneuvering.
Numerous accidents of small ships sailing in the vicinity of large passenger and military ships probably occurred for the same reason.
What explains this attraction? Of course, there can be no question here of attraction according to Newton’s law of universal gravitation; we have already seen (in Chapter IV) that this attraction is too insignificant. The reason for the phenomenon is of a completely different kind and is explained by the laws of fluid flow in tubes and channels. It can be proven that if a liquid flows through a channel that has narrowings and expansions, then in narrow parts of the channel it flows faster and puts less pressure on the walls of the channel than in wide places where it flows more calmly and puts more pressure on the walls (the so-called “Bernoulli principle”) ").
The same is true for gases. This phenomenon in the study of gases is called the Clément-Desormes effect (named after the physicists who discovered it) and is often called the “aerostatic paradox.” This phenomenon is said to have been discovered for the first time by accident under the following circumstances. In one of the French mines, a worker was ordered to cover with a shield the opening of an external adit through which compressed air was supplied into the mine. The worker struggled with the stream of air for a long time, but suddenly the shield slammed the adit shut on its own with such force that, if the shield had not been large enough, he would have been pulled into the ventilation hatch along with the frightened worker.
By the way, this feature of the flow of gases explains the action of the spray gun. When we blow (Fig. 67) into elbow a, which ends in a narrowing, the air, moving into the narrowing, reduces its pressure. Thus, air with reduced pressure appears above tube b, and therefore atmospheric pressure drives the liquid from the glass up the tube; At the hole, the liquid enters the stream of blown air and is sprayed into it.
Now we will understand what is the reason for the attraction of ships. When two ships sail parallel to one another, it looks like a water channel between their sides. In an ordinary channel, the walls are motionless, but the water moves; here it’s the other way around: the water is motionless, but the walls are moving. But the effect of the forces does not change at all: in the narrow places of the moving dripping water, the pressure on the walls is weaker than in the space around the steamers. In other words, the sides of steamships facing each other experience less pressure from the water than the outer parts of the ships. What should happen as a result of this? The vessels must move towards each other under the pressure of the external water, and it is natural that the smaller vessel moves more noticeably, while the more massive one remains almost motionless. That is why attraction is especially strong when a large ship quickly passes by a small one.

Figure 66. In narrow parts of the canal, water flows faster and puts less pressure on the walls than in wide parts.

Figure 67. Spray bottle.

Figure 68. Water flow between two sailing ships.
So, the attraction of ships is due to the suction effect of flowing water. This also explains the danger of rapids for swimmers and the suction effect of whirlpools. It can be calculated that the flow of water in a river at a moderate speed of 1 m per second draws in a human body with a force of 30 kg! It is not easy to resist such a force, especially in water when our own body weight does not help us maintain stability. Finally, the pulling effect of a fast-moving train is explained by the same Bernoulli principle: a train at a speed of 50 km per hour drags a nearby person with a force of about 8 kg.
Phenomena associated with the “Bernoulli principle,” although very common, are little known among non-specialists. It will therefore be useful to dwell on it in more detail. Below we present an excerpt from an article on this topic published in a popular science magazine.

Bernoulli's principle and its consequences

The principle, first stated by Daniel Bernoulli in 1726, states that in a stream of water or air, the pressure is high if the speed is low, and the pressure is low if the speed is high. There are known limitations to this principle, but we will not dwell on them here.
Rice. 69 illustrates this principle.
Air is blown through tube AB. If the cross-section of the tube is small, as in a, the air speed is high; where the cross section is large, as in b, the air speed is low. Where the speed is high, the pressure is low, and where the speed is low, the pressure is high. Due to the low air pressure in a, the liquid in tube C rises; at the same time, the strong air pressure in b forces the liquid in tube D to descend.

Figure 69. Illustration of Bernoulli's principle. In the narrowed part (a) of the AB tube, the pressure is less than in the wide part (b).
In Fig. 70 tube T is mounted on a copper disk DD; air is blown through tube T and then past the free disk dd. The air between the two disks has a high speed, but this speed quickly decreases as it approaches the edges of the disks, since the cross-section of the air flow quickly increases and the inertia of the air flowing from the space between the disks is overcome. But the pressure of the air surrounding the disk is high, since the speed is low, and the air pressure between the disks is small, since the speed is high. Therefore, the air surrounding the disk has a greater effect on the disks, tending to bring them closer together, than the air flow between the disks, tending to push them apart; As a result, the dd disk sticks to the DD disk the more strongly, the stronger the air current in T.
Rice. 71 is analogous to Fig. 70, but only with water. The fast moving water on the DD disc is at a low level and itself rises to the higher level of calm water in the pool as it wraps around the edges of the disc. Therefore, the calm water under the disk has a higher pressure than the moving water above the disk, causing the disk to rise. Rod P does not allow lateral displacement of the disc.

Figure 70. Experience with disks.

Figure 71. Disc DD is raised on rod P when a stream of water from the tank is poured onto it.
Rice. 72 depicts a light ball floating in a stream of air. The air stream hits the ball and prevents it from falling. When the ball jumps out of the jet, the surrounding air returns it back into the jet, since the pressure of the surrounding air, which has a low speed, is high, and the pressure of the air in the jet, which has a high speed, is small.
Rice. 73 represents two ships moving side by side in calm water, or, what amounts to the same thing, two ships standing side by side and flowing around water. The flow is more confined in the space between the vessels, and the speed of the water in this space is greater than on either side of the vessels. Therefore, the water pressure between the ships is less than on both sides of the ships; the higher water pressure surrounding the ships brings them closer together. Sailors know very well that two ships sailing side by side are strongly attracted to each other.

Figure 72. Ball supported by a stream of air.

Figure 73. Two ships moving in parallel seem to attract each other.

Figure 74. As vessels move forward, vessel B turns its bow toward vessel A.

Figure 75. If air is blown between two light balls, they will come closer together until they touch.
A more serious case may occur when one ship follows another, as shown in Fig. 74. Two forces F and F, which bring the ships together, tend to turn them, and ship B turns towards A with considerable force. A collision in this case is almost inevitable, since the rudder does not have time to change the direction of the ship's movement.
The phenomenon described in connection with Fig. 73 can be demonstrated by blowing air between two light rubber balls suspended as shown in Fig. 75. If you blow air between them, they come closer and hit each other.

Purpose of the fish bladder

The following is usually said and written about the role played by the swim bladder of fish - it would seem quite plausible. In order to emerge from the depths to the surface layers of water, the fish inflates its swim bladder; then the volume of its body increases, the weight of the displaced water becomes greater than its own weight - and, according to the law of swimming, the fish rises upward. To stop rising or going down, she, on the contrary, compresses her swim bladder. The volume of the body, and with it the weight of the displaced water, decreases, and the fish sinks to the bottom according to Archimedes' law.
This simplified idea of ​​the purpose of the swim bladder of fish dates back to the times of scientists of the Florentine Academy (XVII century) and was expressed by Professor Borelli in 1685. For more than 200 years, it was accepted without objection, managed to take root in school textbooks, and only through the works of new researchers (Moreau, Charbonel) the complete inconsistency of this theory was discovered,
The bubble undoubtedly has a very close connection with the swimming of fish, since fish whose bubble was artificially removed during experiments could stay in the water only by working hard with their fins, and when this work stopped, they fell to the bottom. What is his true role? Very limited: it only helps the fish stay at a certain depth, precisely at the one where the weight of the water displaced by the fish is equal to the weight of the fish itself. When the fish, by the action of its fins, falls below this level, its body, experiencing great external pressure from the water, contracts, squeezing the bubble; the weight of the displaced volume of water decreases, the weight of the fish becomes less, and the fish falls uncontrollably. The lower it falls, the stronger the water pressure becomes (by 1 atmosphere for every 10 m lowering), the more the fish’s body is compressed and the more rapidly it continues to descend.
The same thing, only in the opposite direction, happens when the fish, having left the layer where it was in equilibrium, is moved by the action of its fins to higher layers. Its body, freed from part of the external pressure and still being expanded from the inside by the swim bladder (in which the gas pressure was until that moment in equilibrium with the pressure of the surrounding water), increases in volume and, as a result, floats higher. The higher the fish rises, the more its body swells and, consequently, the faster its further rise. The fish is not able to prevent this by “squeezing the bladder”, since the walls of its swim bladder are devoid of muscle fibers that could actively change its volume.
That such a passive expansion of body volume actually occurs in fish is confirmed by the following experiment (Fig. 76). The bleak in the chloroformed state is placed in a closed vessel with water, in which increased pressure is maintained, close to that which prevails at a certain depth in a natural body of water. on the surface of the water the fish lies inactively, belly up. Submerged a little deeper, it floats to the surface again. Placed closer to the bottom, it sinks to the bottom. But in the interval between both levels there is a layer of water in which the fish remains in balance - neither sinks nor floats. All this becomes clear if we remember what was said just now about the passive expansion and contraction of the swim bladder.
So, contrary to popular belief, a fish cannot voluntarily inflate and contract its swim bladder. Changes in its volume occur passively, under the influence of increased or weakened external pressure (according to the Boyle-Mariotte law). These changes in volume are not only not useful for the fish, but, on the contrary, cause harm to it, since they cause either an uncontrollable, ever-accelerating fall to the bottom, or an equally uncontrollable and accelerating rise to the surface. In other words, the bubble helps the fish in a stationary position to maintain balance, but this balance is unstable.
This is the true role of the swim bladder of fish, as far as its relation to swimming is concerned; whether it also performs other functions in the fish’s body and which ones exactly is unknown, so this organ is still mysterious. And only its hydrostatic role can now be considered completely clarified.
Fishermen's observations confirm this.

Figure 76. Experiment with bleak.
When catching fish from great depths, it happens that some fish are released halfway; but, contrary to expectation, it does not sink back into the depths from which it was extracted, but, on the contrary, quickly rises to the surface. In such fish it is sometimes noticed that the bladder protrudes through the mouth.

Waves and vortices

Many of the everyday physical phenomena cannot be explained based on the elementary laws of physics. Even such a frequently observed phenomenon as rough seas on a windy day cannot be fully explained in a school physics course. What causes the waves that spread out in calm water from the bow of a moving steamship? Why do flags wave in windy weather? Why is the sand on the seashore arranged in waves? Why is there smoke billowing out of a factory chimney?

Figure 77. Calm (“laminar”) fluid flow in a pipe.

Figure 78. Vortex (“turbulent”) fluid flow in a pipe.
To explain these and other similar phenomena, you need to know the features of the so-called vortex motion of liquids and gases. We will try to tell here a little about vortex phenomena and note their main features, since vortices are barely mentioned in school textbooks.
Let's imagine a liquid flowing in a pipe. If all the particles of the liquid move along the pipe along parallel lines, then we have the simplest type of liquid movement - a calm, or, as physicists say, “laminar” flow. However, this is not the most common case. On the contrary, much more often liquids flow unsteadily in pipes; vortices go from the walls of the pipe to its axis. This is a vortex-like or turbulent movement. This is how, for example, water flows in the pipes of a water supply network (if you do not mean thin pipes where the flow is laminar). Vortex flow is observed whenever the flow speed of a given liquid in a pipe (of a given diameter) reaches a certain value, the so-called critical speed.
The vortices of a liquid flowing in a pipe can be made visible to the eye by introducing a little light powder, such as lycopodium, into a transparent liquid flowing in a glass tube. Then the vortices coming from the walls of the tube to its axis are clearly visible.
This feature of vortex flow is used in technology for the construction of refrigerators and coolers. A liquid flowing turbulently in a tube with cooled walls brings all its particles into contact with the cold walls much faster than when moving without vortices; It must be remembered that liquids themselves are poor conductors of heat and, in the absence of mixing, cool or warm up very slowly. A lively thermal and material exchange of blood with the tissues it washes is also possible only because its flow in the blood vessels is not laminar, but vortex.
What has been said about pipes applies equally to open canals and river beds: in canals and rivers, water flows turbulently. When accurately measuring the speed of a river flow, the instrument detects pulsations, especially near the bottom: pulsations indicate a constantly changing direction of the flow, i.e. eddies. Particles of river water move not only along the river bed, as is usually imagined, but also from the banks to the middle . That is why it is incorrect to say that in the depths of the river the water has the same temperature all year round, namely +4°C: due to mixing, the temperature of the flowing water near the bottom of the river (but not the lake) is the same as on the surface. The eddies that form at the bottom of the river carry light sand with them and generate sand “waves” here. The same can be seen on the sandy shore of the sea, washed by an incoming wave (Fig. 79). If the water flow near the bottom was calm, the sand at the bottom would have a smooth surface.

Figure 79. Formation of sand waves on the seashore by the action of water vortices.

Figure 80. The wave-like movement of a rope in flowing water is caused by the formation of vortices.
So, vortices are formed near the surface of a body washed by water. Their existence is indicated to us, for example, by a snake-like twisting rope stretched along the flow of water (when one end of the rope is tied and the other is free). What's going on here? The section of the rope near which the vortex has formed is carried away by it; but the next moment this section moves with another vortex in the opposite direction - a serpentine writhing is obtained (Fig. 80).
Let's move from liquids to gases, from water to air.
Who hasn’t seen how air whirlwinds carry away dust, straw, etc. from the ground? This is a manifestation of the vortex flow of air along the surface of the earth. And when air flows along the water surface, then in places where vortices form, due to a decrease in air pressure here, the water rises like a hump - excitement is generated. The same reason generates sand waves in the desert and on the slopes of dunes (Fig. 82).

Figure 81. Flag fluttering in the wind...

Figure 82. Wavy surface of sand in the desert.
It is easy to understand now why the flag ripples in the wind: the same thing happens to it as to a rope in flowing water. The solid plate of the weather vane does not maintain a constant direction in the wind, but, obeying the whirlwinds, oscillates all the time. The clouds of smoke coming out of the factory chimney are of the same vortex origin; flue gases flow through the pipe in a vortex motion, which continues for some time by inertia outside the pipe (Figure 83).
Turbulent air movement is of great importance for aviation. The wings of an aircraft are given such a shape in which the place of rarefaction of air under the wing is filled with the substance of the wing, and the vortex action above the wing, on the contrary, intensifies. As a result, the wing is supported from below and suctioned from above (Fig. 84). Similar phenomena occur when a bird soars with outstretched wings.

Figure 83. Plumes of smoke coming out of a factory chimney.
How does the wind blow across the roof work? The vortices create rarefaction of air above the roof; In an effort to equalize the pressure, the air from under the roof, being carried upward, presses against it. As a result, something happens that, unfortunately, we often have to observe: a light, loosely attached roof is blown away by the wind. For the same reason, large window panes are squeezed out from the inside when the wind blows (rather than being broken by the pressure from the outside). However, these phenomena are more easily explained by a decrease in pressure in moving air (see above “Bernoulli's principle”, p. 125).
When two streams of air of different temperatures and humidity flow along one another, vortices arise in each. The varied shapes of clouds are largely due to this reason.
We see what a wide range of phenomena are associated with vortex flows.

Figure 84. What forces is an airplane wing subject to?
Distribution of pressure (+) and rarefaction (-) of air along the wing based on experiments. As a result of all the applied efforts, propping and sucking, the wing is pulled upward. (Solid lines show pressure distribution; dotted line – the same with a sharp increase in flight speed)

Journey into the bowels of the Earth

Not a single person has ever descended deeper into the Earth than 3.3 km - and yet the radius of the globe is 6400 km. There is still a very long way to go to the center of the Earth. Nevertheless, the inventive Jules Verne lowered his heroes - the eccentric professor Lidenbrock and his nephew Axel - deep into the bowels of the Earth. In the novel “Journey to the Center of the Earth,” he described the amazing adventures of these underground travelers. Among the surprises they encountered underground was, by the way, an increase in air density. As the air rises, it becomes rarefied very quickly: its density decreases in geometric progression, while the height of the rise increases in arithmetic progression. On the contrary, when lowering down, below ocean level, the air under the pressure of the overlying layers should become increasingly dense. Underground travelers, of course, could not help but notice this.
This is the conversation that took place between the scientist uncle and his nephew at a depth of 12 leagues (48 km) in the bowels of the Earth.
“Look what the pressure gauge shows? - asked my uncle.
- Very strong pressure.
“Now you see that, as we descend little by little, we gradually get used to the condensed air and do not suffer from it at all.”
- Except for the pain in the ears.
- Nonsense!
“Okay,” I answered, deciding not to contradict my uncle. – It’s even pleasant to be in condensed air. Have you noticed how loud the sounds are in it?
- Certainly. In this atmosphere, even the deaf could hear.
– But the air will become more and more dense. Will it eventually acquire the density of water?
– Of course: under a pressure of 770 atmospheres.
- And even lower?
– The density will increase even more.
- How are we going to get down then?
- Let's fill our pockets with stones.
- Well, uncle, you have an answer to everything!
I did not go further into the realm of guesswork, because, perhaps, I would again come up with some kind of obstacle that would anger my uncle. It was, however, obvious that under a pressure of several thousand atmospheres the air could turn into a solid state, and then, even assuming that we could withstand such pressure, we would still have to stop. No amount of arguing will help here.”

Fantasy and mathematics

This is how the novelist narrates; but this will turn out to be the case if we check the facts mentioned in this passage. We will not have to go down into the bowels of the Earth for this; For a small excursion into the field of physics, it is enough to stock up on pencil and paper.
First of all, we will try to determine to what depth we need to descend so that the atmospheric pressure increases by a 1000th part. Normal atmospheric pressure is equal to the weight of a 760 mm column of mercury. If we were immersed not in air, but in mercury, we would only need to descend by 760/1000 = 0.76 mm for the pressure to increase by a 1000th part. In the air, of course, we must descend much deeper for this, and exactly as many times as air is lighter than mercury - 10,500 times. This means that in order for the pressure to increase by 1000th of normal, we will have to drop not by 0.76 mm, as in mercury, but by 0.76x10500, i.e. almost 8 m. When we drop another 8 m, then the increased pressure will increase by another 1000 of its value, etc... At whatever level we are - at the very “ceiling of the world” (22 km), at the top of Mount Everest (9 km) or near the surface of the ocean - we need to drop 8 m for the atmospheric pressure to increase by 1000th of its original value. Therefore, we get the following table of air pressure increasing with depth:
At ground level pressure
760 mm = normal
"depth 8 m" = 1.001 normal
"depth 2x8" =(1.001)2
"depth 3x8" =(1.001)3
"depth 4x8" =(1.001)4
And in general, at a depth of nx8 m, the atmospheric pressure is (1.001)n times greater than normal; and while the pressure is not very high, the density of the air will increase by the same amount (Mariotte's law).
Note that in this case we are talking, as can be seen from the novel, about deepening into the Earth by only 48 km, and therefore the weakening of gravity and the associated decrease in the weight of air can not be taken into account.
Now you can calculate how big it was, approximately. the pressure that Jules Verne's underground travelers experienced at a depth of 48 km (48,000 m). In our formula, n equals 48000/8 = 6000. We have to calculate 1.0016000. Since multiplying 1.001 by itself 6000 times is quite boring and would take a lot of time, we will turn to the help of logarithms. about which Laplace rightly said that, by reducing labor, they double the life of calculators. Taking logarithms, we have: the logarithm of the unknown is equal to
6000 * lg 1.001 = 6000 * 0.00043 = 2.6.
Using the logarithm of 2.6 we find the required number; it is equal to 400.
So, at a depth of 48 km, the atmospheric pressure is 400 times stronger than normal; The density of air under such pressure will increase, as experiments have shown, by 315 times. It is therefore doubtful that our underground travelers would not suffer at all, experiencing only “pain in the ears”... The novel by Jules Werp speaks, however, of people reaching even greater underground depths, namely 120 and even 325 km. The air pressure must have reached monstrous levels there; a person is able to tolerate air pressure of no more than three or four atmospheres harmlessly.
If, using the same formula, we began to calculate at what depth air becomes as dense as water, that is, it becomes 770 times denser, we would get the figure: 53 km. But this result is incorrect, since at high pressures the density of the gas is no longer proportional to the pressure. Mariotte's law is quite true only for not too significant pressures, not exceeding hundreds of atmospheres. Here are the data on air density obtained experimentally:
Pressure Density
200 atmospheres... 190
400" ............... 315
600" ............... 387
1500" ............... 513
1800" ............... 540
2100" ............... 564
The increase in density, as we see, noticeably lags behind the increase in pressure. In vain did the Jules Verne scientist expect that he would reach a depth where the air is denser than water - he would not have had to wait for this, since the air reaches the density of water only under a pressure of 3000 atmospheres, and then hardly compresses. There can be no talk of turning air into a solid state with one pressure, without extreme cooling (below minus 146°).
Fairness requires noting, however, that the aforementioned novel by Jules Verne was published long before the facts presented now became known. This justifies the author, although it does not correct the narrative.
Let's use the formula given earlier to calculate the greatest depth of the mine at the bottom of which a person can remain without harm to his health. The highest air pressure that our body can still tolerate is 3 atmospheres. Denoting the desired depth of the shaft through x, we have the equation (1.001)x/8 = 3, from which (using logarithms) we calculate x. We get x = 8.9 km.
So, a person could be at a depth of almost 9 km without harm. If the Pacific Ocean suddenly dried up, people could live on its bottom almost everywhere.

In a deep mine

Who has moved closest to the center of the Earth - not in the fantasy of a novelist, but in reality? Of course, miners. We already know (see Chapter IV) that the deepest mine in the world is dug in South Africa. It goes deeper than 3 km. What is meant here is not the depth of penetration of the drill bit, which reaches 7.5 km, but the deepening of the people themselves. Here is what, for example, the French writer Dr. Luc Durten, who personally visited it, says about the mine at the Morro Velho mine (depth about 2300 m):
“The famous gold mines of Morro Veljo are located 400 km from Rio de Janeiro. After 16 hours of rail travel in rocky terrain, you descend into a deep valley surrounded by jungle. Here, an English company is developing gold-bearing veins at a depth to which man has never descended before.
The vein goes into the depths obliquely. The mine follows it with six ledges. Vertical shafts are wells, horizontal shafts are tunnels. It is extremely characteristic of modern society that the deepest mine dug in the crust of the globe - man's most daring attempt to penetrate the bowels of the planet - was made in search of gold.
Wear canvas overalls and a leather jacket. Be careful: the slightest pebble falling into the well can injure you. We will be accompanied by one of the “captains” of the mine. You enter the first tunnel, well lit. You shudder from the chilling wind of 4°: this is ventilation to cool the depths of the mine.
After passing through the first well, 700 m deep, in a narrow metal cage, you find yourself in the second tunnel. Go down into the second well; the air becomes warmer. You are already below sea level.
Starting from the next well, the air burns your face. Dripping with sweat, bent under the low arch, you move towards the roar of drilling machines. Naked people work in thick dust; They are dripping with sweat, their hands are constantly passing the water bottle. Do not touch the fragments of ore that have now been broken off: their temperature is 57°.
What is the outcome of this terrible, disgusting reality? “About 10 kilograms of gold a day...”
Describing the physical conditions at the bottom of the mine and the extent of extreme exploitation of the workers, the French writer notes the high temperature, but does not mention the increased air pressure. Let's calculate what it is like at a depth of 2300 m. If the temperature remained the same as on the surface of the Earth, then, according to the formula already familiar to us, the air density would increase by

Raza.
In reality, the temperature does not remain constant, but increases. Therefore, the air density does not increase as significantly, but less. Ultimately, the air at the bottom of the mine differs in density from the air on the surface of the Earth little more than the air on a hot summer day differs from the frosty air of winter. It is now clear why this circumstance did not attract the attention of the mine visitor.
But the significant air humidity in such deep mines is of great importance, making staying in them unbearable at high temperatures. In one of the South African mines (Johansburg), 2553 m deep, the humidity at 50° heat reaches 100%; a so-called “artificial climate” is now installed here, and the cooling effect of the installation is equivalent to 2000 tons of ice.

High with stratospheric balloons

In previous articles, we mentally traveled into the bowels of the earth, and the formula for the dependence of air pressure on depth helped us. Let us now venture up and, using the same formula, see how air pressure changes at high altitudes. The formula for this case takes the following form:
p = 0.999h/8,
where p is pressure in atmospheres, h is altitude in meters. The fraction 0.999 replaced the number 1.001 here, because when moving up 8 m, the pressure does not increase by 0.001, but decreases by 0.001.
Let's first solve the problem: how high do you need to rise so that the air pressure is halved?
To do this, let us equate the pressure p = 0.5 in our formula and begin to look for the height h. We get the equation 0.5 = 0.999h/8, which will not be difficult to solve for readers who know how to handle logarithms. The answer h = 5.6 km determines the height at which the air pressure should be halved.
Let us now head even higher, following the brave Soviet balloonists who reached altitudes of 19 and 22 km. These high regions of the atmosphere are already in the so-called “stratosphere”. Therefore, the balloons on which such ascents are made are given the name not balloons, but “stratostats”. I don’t think that among the older generation there is at least one who has not heard the names of the Soviet stratospheric balloons “USSR” and “OAKh-1”, which set world altitude records in 1933 and 1934: the first - 19 km, the second - 22 km.
Let's try to calculate what the atmospheric pressure is at these altitudes.
For an altitude of 19 km we find that the air pressure should be
0.99919000/8 = 0.095 atm = 72 mm.
For an altitude of 22 km
0.99922000/8 = 0.066 atm = 50 mm.
However, looking at the records of the stratonauts, we find that at the indicated altitudes other pressures were noted: at an altitude of 19 km - 50 mm, at an altitude of 22 km - 45 mm.
Why is the calculation not confirmed? What is our mistake?
Mariotte's law for gases at such low pressure is completely applicable, but this time we made another omission: we considered the air temperature to be the same throughout the entire 20-kilometer thickness, while it noticeably drops with height. On average they accept; that the temperature drops by 6.5° for every kilometer rise; This happens up to an altitude of 11 km, where the temperature is minus 56° and then remains unchanged for a considerable distance. If we take this circumstance into account (for which the means of elementary mathematics are no longer sufficient), we will obtain results that are much more consistent with reality. For the same reason, the results of our previous calculations relating to air pressure in the depths must also be viewed as approximate.

In school physics lessons, teachers always say that physical phenomena are everywhere in our lives. Only we often forget about this. Meanwhile, amazing things are nearby! Don't think that you need anything extravagant to organize physical experiments at home. And here's some proof for you ;)

Magnetic pencil

What needs to be prepared?

• Battery.
• Thick pencil.
• Insulated copper wire with a diameter of 0.2–0.3 mm and a length of several meters (the longer, the better).
• Scotch.

Conducting the experiment

Wind the wire tightly, turn to turn, around the pencil, 1 cm short of its edges. When one row ends, wind another on top in the opposite direction. And so on until all the wire runs out. Don’t forget to leave two ends of the wire, 8–10 cm each, free. To prevent the turns from unwinding after winding, secure them with tape. Strip the free ends of the wire and connect them to the battery contacts.

What happened?

It turned out to be a magnet! Try bringing small iron objects to it - a paper clip, a hairpin. They are attracted!

Lord of Water

What needs to be prepared?

• A plexiglass stick (for example, a student’s ruler or a regular plastic comb).
• A dry cloth made of silk or wool (for example, a wool sweater).

Conducting the experiment

Open the tap so that a thin stream of water flows. Rub the stick or comb vigorously on the prepared cloth. Quickly bring the stick closer to the stream of water without touching it.

What will happen?

The stream of water will bend in an arc, being attracted to the stick. Try the same thing with two sticks and see what happens.

Top

What needs to be prepared?

• Paper, needle and eraser.
• A stick and a dry woolen cloth from previous experience.

Conducting the experiment

You can control more than just water! Cut a strip of paper 1–2 cm wide and 10–15 cm long, bend it along the edges and in the middle, as shown in the picture. Insert the sharp end of the needle into the eraser. Balance the top workpiece on the needle. Prepare a “magic wand”, rub it on a dry cloth and bring it to one of the ends of the paper strip from the side or top without touching it.

What will happen?

The strip will swing up and down like a swing, or spin like a carousel. And if you can cut a butterfly out of thin paper, the experience will be even more interesting.

Ice and fire

(the experiment is carried out on a sunny day)

What needs to be prepared?

• A small cup with a round bottom.
• A piece of dry paper.

Conducting the experiment

Pour water into a cup and place it in the freezer. When the water turns to ice, remove the cup and place it in a container of hot water. After some time, the ice will separate from the cup. Now go out onto the balcony, place a piece of paper on the stone floor of the balcony. Use a piece of ice to focus the sun on a piece of paper.

What will happen?

The paper should be charred, because it’s not just ice in your hands anymore... Did you guess that you made a magnifying glass?

Wrong mirror

What needs to be prepared?

• A transparent jar with a tight-fitting lid.
• Mirror.

Conducting the experiment

Fill the jar with excess water and close the lid to prevent air bubbles from getting inside. Place the jar with the lid facing up against the mirror. Now you can look in the “mirror”.

Bring your face closer and look inside. There will be a thumbnail image. Now start tilting the jar to the side without lifting it from the mirror.

What will happen?

The reflection of your head in the jar, of course, will also tilt until it turns upside down, and your legs will still not be visible. Lift the can and the reflection will turn over again.

Cocktail with bubbles

What needs to be prepared?

• A glass with a strong solution of table salt.
• A battery from a flashlight.
• Two pieces of copper wire approximately 10 cm long.
• Fine sandpaper.

Conducting the experiment

Clean the ends of the wire with fine sandpaper. Connect one end of the wire to each pole of the battery. Dip the free ends of the wires into a glass with the solution.

What happened?

Bubbles will rise near the lowered ends of the wire.

Lemon battery

What needs to be prepared?

• Lemon, thoroughly washed and wiped dry.
• Two pieces of insulated copper wire approximately 0.2–0.5 mm thick and 10 cm long.
• Steel paper clip.
• A light bulb from a flashlight.

Conducting the experiment

Strip the opposite ends of both wires at a distance of 2–3 cm. Insert a paper clip into the lemon and screw the end of one of the wires to it. Insert the end of the second wire into the lemon, 1–1.5 cm from the paperclip. To do this, first pierce the lemon in this place with a needle. Take the two free ends of the wires and apply them to the contacts of the light bulb.

What will happen?

The light will light up!

Publishing house "RIMIS" is a laureate of the Literary Prize named after. Alexandra Belyaev 2008.

The text and drawings are restored from the book by Ya. I. Perelman “Entertaining Physics”, published by P. P. Soykin (St. Petersburg) in 1913.

© RIMIS Publishing House, edition, design, 2009

* * *

Outstanding popularizer of science

The singer of mathematics, the bard of physics, the poet of astronomy, the herald of astronautics - this was and remains in the memory of Yakov Isidorovich Perelman, whose books were sold all over the world in millions of copies.

The name of this remarkable person is associated with the emergence and development of a special – entertaining – genre of scientific popularization of the fundamentals of knowledge. The author of more than a hundred books and brochures, he had the rare gift of talking about dry scientific truths in an exciting and interesting way, arousing burning curiosity and inquisitiveness - these are the first stages of the independent work of the mind.

It is enough to even briefly familiarize yourself with his popular science books and essays to see the special direction of their author’s creative thinking. Perelman's goal was to show ordinary phenomena in an unusual, paradoxical perspective, while at the same time maintaining the scientific impeccability of their interpretation. The main feature of his creative method was his exceptional ability to surprise the reader and capture his attention from the very first word. “We early cease to be surprised,” Perelman wrote in his article “What is Entertaining Science,” “we early lose the ability that prompts us to be interested in things that do not directly affect our existence... Water would be, without a doubt, the most amazing substance in nature, and the Moon - the most amazing sight in the sky, if both did not come into view too often.”

To show the ordinary in an unusual light, Perelman brilliantly used the method of unexpected comparison. Sharp scientific thinking, a huge general and physical and mathematical culture, the skillful use of numerous literary, scientific and everyday facts and plots, their amazingly witty, completely unexpected interpretation led to the appearance of fascinating scientific and artistic short stories and essays that are read with unflagging attention and interest. However, entertaining presentation is by no means an end in itself. On the contrary, it is not to turn science into fun and entertainment, but to put the liveliness and artistry of presentation at the service of understanding scientific truths - this is the essence of Yakov Isidorovich’s literary and popularization method. “So that there is no superficiality, so that the facts are known...” - Perelman strictly followed this thought throughout his 43-year creative career. It is in the combination of strict scientific reliability and an entertaining, non-trivial form of presentation of material that the secret of the continued success of Perelman’s books lies.

Perelman was not an armchair writer, divorced from living reality. He responded promptly to the practical needs of his country in a journalistic manner. When in 1918 the Council of People's Commissars of the RSFSR issued a decree on the introduction of the metric system of weights and measures, Yakov Isidorovich was the first to publish several popular brochures on this topic. He often gave lectures in work, school and military audiences (he gave about two thousand lectures). At the suggestion of Perelman, supported by N.K. Krupskaya, in 1919 the first Soviet popular science magazine “In the Workshop of Nature” began to be published (under his own editorship). Yakov Isidorovich did not remain aloof from the secondary school reform.

It must be emphasized that Perelman’s teaching activities were also marked by genuine talent. For a number of years he taught courses in mathematics and physics at higher and secondary educational institutions. In addition, he wrote 18 textbooks and teaching aids for the Soviet Unified Labor School. Two of them - “Physical Reader”, issue 2, and “New Problem Book on Geometry” (1923) received the very high honor of taking places on the shelf of Vladimir Ilyich Lenin’s Kremlin Library.

The image of Perelman is preserved in my memory - a widely educated, extremely modest, somewhat shy, extremely correct and charming person, always ready to provide the necessary help to his colleagues. He was a true worker of science.

On October 15, 1935, the House of Entertaining Science began to function in Leningrad - a visible, embodied exhibition of Perelman’s books. Hundreds of thousands of visitors walked through the halls of this unique cultural and educational institution. Among them was Leningrad schoolboy Georgy Grechko, now a pilot-cosmonaut of the USSR, twice Hero of the Soviet Union, Doctor of Physical and Mathematical Sciences. The fate of two other cosmonauts - Heroes of the Soviet Union K. P. Feoktistov and B. B. Egorov - is also connected with Perelman: in childhood they became acquainted with the book “Interplanetary Travel” and became interested in it.

When the Great Patriotic War began, Ya. I. Perelman’s patriotism and his high consciousness of civic duty to the Motherland clearly manifested themselves. Remaining in besieged Leningrad, he, no longer a young man (he was 60 years old), steadfastly endured, along with all the Leningraders, the inhuman torments and difficulties of the blockade. Despite enemy artillery shelling and aerial bombardment of the city, Yakov Isidorovich found the strength to overcome hunger and cold and walk from end to end of Leningrad to attend lectures in military units. He lectured army and naval reconnaissance officers, as well as partisans, on what was extremely important at that time - the ability to navigate the terrain and determine distances to targets without any instruments. Yes, and entertaining science served the purpose of defeating the enemy!

To our great chagrin, on March 16, 1942, Yakov Isidorovich passed away - he died during the siege from hunger...

The books of Ya. I. Perelman continue to serve the people to this day - they are constantly republished in our country, they enjoy constant success among readers. Perelman's books are widely known abroad. They have been translated into Hungarian, Bulgarian, English, French, German and many other foreign languages.

At my suggestion, one of the craters on the far side of the Moon was given the name “Perelman”.

Academician V. P. Glushko

Excerpts from the preface to the book “Doctor of Entertaining Sciences” (G. I. Mishkevich, M.: “Znanie”, 1986).

Preface

The proposed book, in terms of the nature of the material collected in it, is somewhat different from other collections of this type. Physical experiments, in the strict sense of the word, are given a secondary place in it; entertaining tasks, intricate questions and paradoxes from the field of elementary physics, which can serve the purposes of mental entertainment, are brought to the fore. By the way, some works of fiction (Jules Verne, C. Flammarion, E. Poe, etc.) are used as similar material; issues of physics are touched upon. The collection also includes articles on some interesting issues of elementary physics, usually not discussed in textbooks.

Of the experiments, the book includes mainly those that are not only instructive, but also entertaining, and, moreover, can be performed using objects that are always at hand. Experiments and illustrations for them were borrowed from Tom Titus, Tisandier, Beuys and others.

I consider it a pleasant duty to express my gratitude to the learned forester I.I. Polferov, who provided me with irreplaceable services in reading the latest proofs.

St. Petersburg, 1912

Ya. Perelman

Stevin's drawing on the title page of his book ("Miracle and Not a Miracle").

Chapter I
Addition and decomposition of movements and forces

When do we move faster around the Sun - during the day or at night?

Weird question! The speed of the Earth's movement around the Sun cannot, it would seem, be connected in any way with the change of day and night. In addition, on Earth it is always day in one half and night in the other, so the question itself is apparently meaningless.

However, it is not. It's not about when Earth moves faster, but about when We, people, we are moving rather in global space. And this changes things. Don't forget that we make two movements: we rush around the Sun and at the same time we rotate around the earth's axis. Both of these movements fold up– and the result is different, depending on whether we are on the day or night half of the Earth. Take a look at the drawing - and you will immediately see that at night the rotation speed is added to the forward speed of the Earth, and during the day, on the contrary, is taken away from her.

Rice. 1. People on the night half of the globe move around the Sun faster than on the day half.

This means that at night we move faster in world space than during the day.

Since each point of the equator runs about half a mile per second, for the equatorial strip the difference between midday and midnight speeds reaches a whole mile per second. For St. Petersburg (located at the 60th parallel) this difference is exactly half as much.

The Cartwheel Mystery

Attach a white wafer to the side of the rim of a cart wheel (or to a bicycle tire) and observe it as the cart (or bicycle) moves. You will notice a strange phenomenon: while the wafer is at the bottom of the rolling wheel, it is visible quite clearly; on the contrary, in the upper part of the wheel the same wafer flashes so quickly that you do not have time to see it. What is it? Is it possible that the top of the wheel moves faster than the bottom?

Your bewilderment will further increase if you compare the upper and lower spokes of a rolling wheel: it turns out that while the upper spokes merge into one continuous whole, the lower ones remain visible quite clearly. Again, it is as if the top of the wheel is rolling faster than the bottom. But meanwhile, we are firmly convinced that the wheel moves evenly in all its parts.

What is the answer to this strange phenomenon? Yes, simply that the upper parts of every rolling wheel really move faster than the ones below. This seems completely incredible at first glance, and yet it is so.

Simple reasoning will convince us of this. Let us remember that each point of a rolling wheel makes two movements at once: it revolves around an axis and at the same time moves forward along with this axis. Happening addition of two movements- and the result of this addition is not at all the same for the upper and lower parts of the wheel. Namely, at the top of the wheel there is a rotational movement is added to translational, since both movements are directed in the same direction. In the lower part of the wheel, the rotational movement is directed in the opposite direction and is taken away from progressive. The first result, of course, is greater than the second - and that is why the upper parts of the wheel move faster than the lower ones.

The top of a rolling wheel moves faster than the bottom. Compare the movements of AA" and BB".

That this is indeed the case can be easily verified by a simple experiment, which we recommend doing at the first favorable opportunity. Stick a stick into the ground next to the wheel of a standing cart so that the stick is against the axis (see Fig. 2). On the wheel rim, at the very top and at the very bottom, make a mark with chalk; these marks are dots A And B in the picture - they will have to fight against the stick. Now roll the cart forward a little (see Figure 3) until the axle is about 1 foot away from the stick - and notice how your marks move. It turns out that the top mark is A– has moved significantly more than the lower one – B, which only slightly moved away from the stick at an upward angle.

In a word, both reasoning and experience confirm the idea, strange at first glance, that the upper part of any rolling wheel moves faster than the lower.

Which part of the bicycle moves slowest than all the others?

You already know that not all points of a moving cart or bicycle move equally quickly, and that those points of the wheels that are currently in contact with the ground move the slowest.

Of course, all this only takes place for rolling wheels, and not for one that rotates on a fixed axis. In a flywheel, for example, both the top and bottom points of the rim move at the same speed.

The mystery of the railway wheel

An even more unexpected phenomenon occurs in a railway wheel. You know, of course, that these wheels have a protruding edge on the rim. And so, the lowest point of such a rim when the train moves does not move forward at all, but backward! This is easy to verify by reasoning similar to the previous one - and we leave it to the reader to reach the unexpected, but quite correct conclusion that in a fast moving train there are points that move not forward, but backward. True, this reverse movement lasts only an insignificant fraction of a second, but this does not change the matter: reverse movement (and quite fast at that - twice as fast as a pedestrian) still exists, contrary to our usual ideas.

Rice. 4. When the railway wheel rolls along the rail to the right, the point R his rim moves back to the left.

Where is the boat coming from?

Imagine that a steamboat is sailing on a lake, and let the arrow a in Fig. 5 depicts the speed and direction of its movement. A boat is sailing across him, and the arrow b depicts its speed and direction. If you are asked where this boat departed from, you will immediately indicate the point A on the shore. But if you ask the passengers of a sailing ship with the same question, they will indicate a completely different point.

This happens because the passengers of the ship see the boat moving not at all at right angles to its movement. It should not be forgotten that they do not feel their own movement. It seems to them that they themselves are standing still, and the boat is rushing at their speed in the opposite direction (remember what we see when we travel in a railway carriage). That's why for them the boat does not move only in the direction of the arrow b, but also in the direction of the arrow c, – which is equal a, but directed in the opposite direction (see Fig. 6). Both of these movements - real and apparent - add up, and as a result, it seems to the passengers of the ship that the boat is moving diagonally along a parallelogram built on b And c. This diagonal, indicated in Fig. 6 with a dotted line expresses the magnitude and direction of apparent movement.

Rice. 5. Boat ( b) is sailing across the steamer ( a).

This is why passengers will claim that the boat set sail at B, not in A.

When we, rushing along with the Earth in its orbit, meet the rays of some star, then we judge the place of origin of these rays as incorrectly as the above-mentioned passengers make a mistake in determining the place of departure of the second boat. Therefore, all the stars appear to us to be slightly moved forward along the path of the Earth's movement. But since the speed of the Earth’s movement is negligible compared to the speed of light (10,000 times less), this movement is extremely insignificant and can be detected only with the help of the most precise astronomical instruments. This phenomenon is called “light aberration”.

Rice. 6. Passengers of the ship ( a) seems like a boat ( b) floats from a point B.

But let's return to the problem about the steamship and the boat discussed above.

If you are interested in such phenomena, try, without changing the conditions of the previous problem, to answer the questions: in what direction is the ship moving? for boat passengers? To what point on the shore is the ship heading, according to its passengers? To answer these questions you need to be on line a construct, as before, a parallelogram of velocities. Its diagonal will show that for the passengers of the boat the steamer seems to be sailing in an oblique direction, as if about to moor at some point on the shore lying (in Fig. 6) to the right B.

Is it possible to lift a person on seven fingers?

Anyone who has never tried this experiment will probably say that lifting an adult on your fingers is impossible. Meanwhile, this is done very easily and simply. Five people should participate in the experiment: two put their index fingers (of both hands) under the feet of the person being lifted; the other two support his elbows with the index fingers of his right hand; finally, the fifth one places his index finger under the chin of the person being lifted. Then, on command: “One, two, three!” – all five of them unanimously lift their comrade, without noticeable tension.

Rice. 7. You can lift an adult with seven fingers.

If you are doing this experiment for the first time, you will be amazed at the unexpected ease with which it is performed. The secret of this ease lies in the law decomposition strength The average adult weight is 170 pounds; these 170 pounds put pressure on seven fingers at once, so each finger only bears about 25 pounds. It is relatively easy for an adult to lift such a load with one finger.

Raise a carafe of water with a straw

This experience also seems completely impossible at first glance. But we have just seen how careless it is to trust “first glance.”

Take a long, solid, strong straw, bend it and insert it into a carafe of water as shown in Fig. 8: its end should rest against the wall of the decanter. Now you can lift it - the straw will hold the decanter.

Rice. 8. A decanter of water hangs on a straw.

When introducing a straw, you must ensure that the part of it that rests against the wall of the decanter is completely straight; otherwise the straw will bend and the whole system will collapse. The whole point here is that the force (the weight of the decanter) acts strictly in length Straws: In the longitudinal direction, straw has great strength, although it breaks easily in the transverse direction.

It is best to first learn how to perform this experiment with a bottle and only then try to repeat it with a decanter. We recommend that inexperienced experimenters place something soft on the floor, just in case. Physics is a great science, but there is no need to break decanters...

The following experiment is very similar to the one described and is based on the same principle.

Pierce a coin with a needle

Steel is harder than copper, and therefore, under a certain pressure, a steel needle should pierce a copper coin. The only trouble is that when a hammer hits the needle, it will bend and break it. It is necessary, therefore, to arrange the experiment in such a way as to prevent the needle from bending. This is achieved very simply: stick the needle into the cork along its axis - and you can get down to business. Place a coin (kopeck) on two wooden blocks, as shown in Fig. 9, and place a plug with a needle on it. A few careful blows and the coin is broken. The cork for the experiment must be dense and high enough.

Rice. 9. The needle pierces the copper coin.

Why are pointed objects prickly?

Have you ever thought about the question: why does a needle penetrate different objects so easily? Why is it easy to pierce cloth or cardboard with a thin needle and so difficult to pierce with a thick rod? Indeed, in both cases, it would seem that the same force acts.

The fact of the matter is that the strength is not the same. In the first case, all the pressure is concentrated on the tip of the needle, while in the second case the same force is distributed over a much larger area of ​​the end of the rod. The area of ​​the needle tip is thousands of times less than the area of ​​the end of the rod, and therefore, the pressure of the needle will be thousands of times greater than the pressure of the rod - with the same force of our muscles.

In general, when we talk about pressure, it is always necessary, in addition to force, to also take into account the size of the area on which this force acts. When we are told that someone receives 600 rubles. salary, then we do not yet know whether it is a lot or a little: we need to know - per year or per month? In the same way, the effect of a force depends on whether the force is distributed per square inch or concentrated on 1/100 square inch. millimeter.

For exactly the same reason, a sharp knife cuts better than a dull one.

So, sharpened objects are prickly, and sharpened knives cut well because enormous power is concentrated on their points and blades.

Chapter II
Gravity. Lever arm. Scales

Up the slope

We are so accustomed to seeing weighty bodies rolling down an inclined plane that the example of a body freely rolling upward along it seems at first glance almost a miracle. However, there is nothing easier than to arrange such an imaginary miracle. Take a strip of flexible cardboard, bend it into a circle and glue the ends together - you will get a cardboard ring. Glue a heavy coin, such as a fifty-kopeck piece, to the inside of this ring with wax. Now place this ring at the base of the inclined board so that the coin is in front of the fulcrum, at the top. Release the ring and it will roll up the slope on its own (see Fig. 10).

Rice. 10. The ring rolls up on its own.

The reason is clear: the coin, due to its weight, tends to occupy the lowest position in the ring, but, moving with the ring, it thereby forces it to roll upward.

If you want to turn the experience into a focal point and wow your guests, you need to stage it a little differently. Attach a heavy object to the inside side of an empty round hat box; then, having closed the box and placed it properly in the middle of the inclined board, ask the guests: where will the box roll if it is not held - up or down? Of course, everyone will unanimously say that it’s down, and they will be quite amazed when the box rolls up before their eyes. The tilt of the board should, of course, not be too great for this.

Versta is a Russian unit of distance measurement equal to five hundred fathoms or 1,066.781 meters. – Approx. ed.

Foot – (English foot – foot) – British, American and Old Russian unit of distance measurement, equal to 30.48 centimeters. Not included in the SI system. – Approx. ed.

Inch - (from Dutch duim - thumb) - the Russian name for a unit of distance in some European non-metric systems, usually equal to 1/12 or 1/10 ("decimal inch") of a foot of the corresponding country. The word inch was introduced into the Russian language by Peter I at the very beginning of the 18th century. Today, an inch is most often understood as an English inch, equal to 2.54 cm exactly. – Approx. ed.