Natural science is so human, so true,
that I wish good luck to everyone who gives himself to him ...
Johann Wolfgang von Goethe

We owe Archimedes the foundation of the doctrine of the equilibrium of liquids.
Joseph Louis Lagrange

BOX OF QUALITATIVE TASKS IN PHYSICS
ARCHIMEDE'S FORCE

Didactic materials on physics for students and their parents ;-) and, of course, for creative teachers.
For those who love to learn!

I bring to your attention 55 quality tasks in physics on the topic: "Archimedean force". Let's give credit to the integration: in the first lines... biophysical material; according to the tradition of green pages, we will not disregard fiction And illustrative material;-) and also accompany the tasks with informative notes and comments - for the curious, we will give detailed answers to some problems.
And more ;-) legendary tale of Archimedes' challenge with the golden crown.

Task #1
Most algae (for example, spirogyra, kelp, etc.) have thin, flexible stems. Why don't algae need strong, hard stems? What happens to algae if you release water from the reservoir in which they are located?

For the curious: Many aquatic plants remain upright, despite the extreme flexibility of their stems, because large air bubbles are enclosed at the ends of their branches, playing the role of floats.
water chestnut chilim. Curious aquatic plant chilim (water chestnut) grows in the backwaters of the Volga, in lakes and estuaries. Its fruits (water nuts) reach a diameter of 3 cm and have a shape similar to a sea anchor with or without a few sharp horns. This "anchor" serves to keep the young germinating plant in a suitable place. When the chilim fades, heavy fruits begin to form under water. They could drown the plant, but just at that time on the petioles of the leaves swellings are formed - a kind of "rescue belts". Thus, the volume of the underwater part of the plants increases, and, consequently, the buoyancy force increases. This achieves a balance between the weight of the fruit and the buoyancy force generated by the swelling.

Otto Wilhelm Thome(Otto Wilhelm Thome; 1840–1925) was a German botanist and illustrator. Author of a collection of botanical illustrations "Flora of Germany, Austria and Switzerland (Flora von Deutschland, Österreich und der Schweiz)", 1885

§ For flower growers, I suggest that you admire the flower portraits on the green page "Reinagle George Philip (botanical illustrations)".

Task #2
In mammals living on land, strong limbs are adapted for movement, but in marine mammals (whales, dolphins), fins and a tail are sufficient for movement. Explain why.

Answer: Archimedean force is an important natural factor that determines the structure of the skeleton of marine mammals. Since a buoyant (Archimedean force) acts on a creature living in water, its weight in liquid is less than in air by the value of this force. Thus, a “light” whale in the water, a dolphin, does not need strong limbs for movement, for this purpose they have enough fins and a tail.

Task #3
What role does the swim bladder play in fish?

For the curious: The density of living organisms inhabiting the aquatic environment differs very little from the density of water, so their weight is almost completely balanced by the Archimedean force. Thanks to this, aquatic animals do not need such massive skeletons as terrestrial ones. The role of the swim bladder in fish is interesting. This is the only body part of the fish that has noticeable compressibility; By squeezing the bubble with the efforts of the pectoral and abdominal muscles, the fish changes the volume of its body and, thereby, the average density, due to which it can regulate the depth of its diving within certain limits.

Task #4
How does a whale regulate its diving depth?

Answer: Whales regulate their diving depth by increasing and decreasing their lung capacity.

Archibald Thorburn(Archibald Thorburn; 05/31/1860 - 10/09/1935) - Scottish illustrator.

§ For lovers of animalistics, I recommend to look at the green page “Mystery Paintings by Artist Stephen Gardner” and count the tails of whales ;-)

Task #5
Although the whale lives in water, it breathes with lungs. Despite the presence of lungs, the whale will not live even an hour if it accidentally finds itself aground or on land. Why?

For the curious: The largest representatives of the order of cetaceans - blue whales. The mass of the blue whale reaches 130 tons; largest land animal elephant has a mass of 3 to 6 tons(like the language of some whales ;-) At the same time, the whale is able to develop a very decent speed in the water up to 20 knots. The force of gravity acting on the whale is estimated at millions of newtons, but in the water it is supported by the Archimedean force and the whale in the water is weightless. On land, the enormous force of gravity will press the whale to the ground. The whale's skeleton is not adapted to withstand this weight, the whale will not even be able to breathe, since in order to inhale it must expand the lungs, that is, raise the muscles surrounding the chest. Under the influence of such a huge force, breathing significantly worsens, blood vessels are pinched, and the whale dies.

Knot - unit of speed equal to one nautical mile per hour. It is used in nautical and aviation practice. By international definition, one knot is equal to 1,852 km/h.

Task #6
How to adjust diving depth cephalopod nautilus pompilius(lat. Nautilus pompilius)?

Answer: Cephalopods from the nautilus genus live in shells separated by partitions into separate chambers, the animal itself occupies the last chamber, while the rest are filled with gas. When the nautilus wants to sink to the bottom, it fills the shell with water, it becomes heavy and sinks easily. To float to the surface, the nautilus pumps gas into its hydrostatic "balloons", it displaces the water, and the shell floats. Liquid and gas are under pressure in the shell, so the mother-of-pearl house does not burst even at a depth of seven hundred meters, where nautiluses sometimes swim. The steel tube would flatten here, and the glass would turn into a snow-white powder. Nautilus manages to avoid death only thanks to the internal pressure that is maintained in its tissues, and to keep its house intact by filling it with an incompressible liquid. Everything happens, as in a modern deep-sea boat - a bathyscaphe, for which nature received a patent five hundred million years ago ;-)

Nautilus pompilius(lat. Nautilus pompilius) is a species of cephalopod molluscs of the genus Nautilus. It usually lives at a depth of up to 400 meters. It lives off the coast of Indonesia, the Philippines, New Guinea and Melanesia, in the South China Sea, the northern coast of Australia, western Micronesia and western Polynesia. Nautiluses lead a benthic lifestyle, collecting dead animals and large organic remains - that is, nautiluses are marine scavengers.

Kondakov Nikolai Nikolaevich(1908-1999) - Soviet biologist, candidate of biological sciences, animal painter. His main contribution to biological science was his drawings of various representatives of the fauna. These illustrations have been included in many publications, such as TSB (Great Soviet Encyclopedia), Red Book of the USSR, in animal atlases and teaching aids.

For the curious: At cuttlefish- an animal from the class cephalopods(the closest relative of squids and octopuses), vestigial internal calcareous shell contains numerous cavities. To regulate buoyancy, the cuttlefish pumps water out of its skeleton and allows gas to fill the emptied cavities, that is, it acts on the principle of water tanks in a submarine. The main way of movement of cuttlefish, octopuses, squids is jet, but this is a topic for another box of quality problems in physics ;-)
Microscopic radiolarians they have droplets of oil in their protoplasm, with the help of which they regulate their weight and thanks to which they rise and fall into the sea.
Siphonophores zoologists call a special group of intestinal animals. Like jellyfish, they are free-swimming marine animals. However, unlike the former, they form complex colonies with a very pronounced polymorphism. At the very top of the colony there is usually a bubble containing gas, with the help of which the entire colony is kept in the water column and moved. The gas is produced by special glands. This bubble sometimes reaches a length of 30 cm.

Rudimentary organs, rudiments(from Latin rudimentum - germ, fundamental principle) - organs that have lost their main significance in the process of evolutionary development of the organism.
Polymorphism - multiplicity, the presence in the same species of organisms of several different forms.

Illustrations from Ernst Haeckel's book
"Art Forms of Nature (Kunstformen der Natur)", 1904

cephalopods Gamochonia		Siphonophores Siphonophorae		deep sea radiolarians Phaeodaria

Ernst Heinrich Philipp August Haeckel(Ernst Heinrich Philipp August Haeckel; 1834–1919) was a German naturalist and philosopher.
"Art Forms of Nature (Kunstformen der Natur)"- lithographic book Ernst Haeckel originally published between 1899 and 1904 in sets of 10 prints, a full version of 100 prints appeared in 1904.

Task #7
Why do ducks and other waterfowl submerge little when swimming?

Answer: An important factor in the life of waterfowl is the presence of a thick, impermeable layer of feathers and down, which contains a significant amount of air; due to this peculiar air bubble surrounding the entire body of the bird, its average density is very low. This explains the fact that ducks and other waterfowl do not submerge much when swimming.

Task #8
"Meshchorskaya side", 1939

“... Water rats live in deep holes on the banks of these rivers. There are rats completely gray with old age. If you quietly follow the hole, you can see how the rat is catching fish. She crawls out of the hole, dives very deep and swims out with a terrible noise ... To make it easier to swim, water rats gnaw off a long stalk of the kugi and swim holding it in their teeth. The stalk of the coogee is full of air cells. He perfectly holds on the water not even such a weight as a rat ... "
Explain the measure taken by water rats to facilitate swimming.

Answer: Body buoyancy- its ability to float at a given load, having a predetermined immersion. Buoyancy margin - additional load, which corresponds to the weight of the liquid in the volume of the surface part of the floating body. The buoyancy of the body is determined by the law of Archimedes.
Law of Archimedes is formulated as follows: a buoyant force acts on a body immersed in a liquid or gas, equal to the weight of the amount of liquid or gas that is displaced by the immersed part of the body. Based on the law of Archimedes, it can be concluded that for a body to float, it is necessary that the weight of the liquid displaced by this body be equal to or exceed the weight of the body itself.
The enterprising water rat, unfamiliar with the law of Archimedes, successfully used it for its unselfish, but beneficial purposes ...

Kuga- the popular name of some aquatic plants of the sedge family, mainly lake reeds. The stems of the lake reed, like many other aquatic plants, are very loose, porous - they are densely penetrated by a network of air channels and therefore have excellent buoyancy.

Task #9
"Steppe. History of one trip", 1888. Anton Pavlovich Chekhov
“... Egorushka also undressed, but did not go down the bank, but ran up and flew from a height of one and a half sazhens. Describing an arc in the air, he fell into the water, sank deep, but did not reach the bottom; some force, cold and pleasant to the touch, picked him up and carried him back upstairs.
What kind of force "cold and pleasant to the touch" are we talking about?

For the curious: Sazhen - old Russian measure of length, first mentioned in Russian sources at the beginning of the 11th century. In the XI-XVII centuries, there was a sazhen of 152 and 176 cm. This was the so-called fly fathom, determined by the span of a person’s hands from the end of the fingers of one hand to the end of the fingers of the other.
So-called oblique sazhen- measuring 216 and 248 cm - was determined by the distance from the fingers of the outstretched hand to the foot of the opposite leg. Under Peter I, Russian measures of length were equalized with English ones. The size of a sazhen was determined to be 7 English feet, or 84 inches. This corresponded to 3 arshins, or 48 inches, which equaled 213.35 cm.

1 fathom= 1/500 versts = 3 arshins = 12 spans = 48 versts = 2.1336 meters

It is interesting that the the word "sazhen" comes from the Old Slavonic verb "squeeze" (walk wide). In Ancient Russia, not one, but many different fathoms were used. We have already met with the flywheel and oblique fathom, the turn has come for some other fathoms:

1 fathom ≈ 1.83 meters
1 Greek fathom ≈ 2.304 meters
1 masonry sazhen ≈ 1.597 meters
1 pipe fathom ≈ 1.87 meters (this fathom was used to measure the length of pipes in salt mines)
1 church fathom ≈ 1.864 meters
1 royal sazhen ≈ 1.974 meters

However, there are also square and cubic fathoms. The amount of something measured by such a measure: fathom of earth(sazhen square); fathom of firewood(sazhen cubic).

Task #10
"Grandfather Mazai and hares", 1870. Nikolay Alekseevich Nekrasov
“A knotty log floated past,
Sitting, and standing, and lying in a layer,
A dozen hares were saved on it
"I would take you - but sink the boat!"
It’s a pity for them, however, but it’s a pity for the find -
I got hooked on a knot
And he dragged a log behind him ... "
Explain why the hares could sink the boat. What is meant by displacement and carrying capacity of a ship? What is a waterline?

For the curious: Waterline- this is the line along which the calm surface of the water comes into contact with the hull of a ship or other floating vessel. The waterline can be of different types (constructive, calculated, operating, cargo).
Load waterline is of great practical importance. Before this mark became mandatory, many ships were lost in the fleets of the whole world. The main reason for the loss of ships is overload, due to the desire to obtain additional profit from transportation, which was exacerbated by the difference in water density (depending on its temperature and salinity, the ship's sediment can vary significantly). The first precedent in modern history is the British Load Line (Load Line) Act of 1890, under which the minimum allowable freeboard was set not by the shipowner, but by a government agency.

Illustrations by Alexei Nikanorovich Komarov
to Nikolai Alekseevich Nekrasov's poem "Grandfather Mazai and Hares"

... I see one small island - Hares on it gathered in a crowd ...		Instantly my team fled, Only two couples left on the boat ...

Komarov Alexey Nikanorovich(1879–1977) is considered the founder of the Russian animalistic school. Aleksey Nikanorovich Komarov illustrated scientific and children's books, created drawings for stamps, postcards, and visual aids. Several generations of children grew up learning from textbooks with his wonderful drawings.

Task #11
Where is the carrying capacity of the same barge greater - in river or sea water?

Answer: The density of river water is less than sea water, since the density of ordinary water is 1000 kg / m 3, and salt water is 1030 kg / m 3. So the strength of Archimedes in sea water will be greater. That is, in sea water, a barge can lift a load with greater gravity and not sink. This means that the carrying capacity of the same barge in sea water is greater.

Task #12
Submarines sailing in the northern seas are often covered with a thick layer of ice while on the surface of the water. Is it easier or more difficult to submerge the boat in the presence of such an additional ice load?

Task #13
For submarines, a depth is set below which they must not sink. What explains the existence of such a limit?

Answer: The deeper the submarine sinks, the more pressure will be experienced by its walls. Since there is a limit to the strength of the boat structure, there is also a limit to the depth of its immersion.

For the curious:
What design features do submarines have?
Submarines play an important role in all navies - warships capable of diving to a considerable depth (over 100 meters) and moving there hidden from the enemy.
Submarines must be able to float and submerge, as well as sail below the surface of the water. Since the volume of the boat remains unchanged in all cases, in order to perform these maneuvers, the boat must have a device for changing its weight. This device consists of a number of ballast compartments in the hull of the boat, which, using special devices, can be filled with outboard water (in this case, the weight of the boat increases and it sinks) or freed from water (in this case, the weight of the boat decreases and it floats).
Note that a small excess or lack of water in the ballast compartments is enough for the boat to sink to the very bottom of the sea or float to the surface of the water. It often happens that in a certain layer under water, the density of water changes rapidly with depth, increasing from top to bottom. Near the level of such a layer, the equilibrium of the boat is stable. Indeed, if the boat, being at this level, for any reason, sinks a little deeper, then it falls into an area of ​​\u200b\u200bhigher water density. The supporting force increases and the boat will begin to float, returning to its original depth. If the boat rises for any reason, then it will fall into an area of ​​​​lower density of water, the supporting force will decrease, and the boat will return to its original level. Therefore, submariners call such layers " liquid soil": the boat can “lie” on it, maintaining balance indefinitely, while in a homogeneous environment this is not possible and in order to maintain a given depth, the boat must constantly change the amount of ballast, taking or displacing water from the ballast compartments, or must all the time move by maneuvering the depth rudders.

Raising the State Flag of the USSR at the North Pole the crew of the submarine "Leninsky Komsomol", 1962 Pen Sergey Varlenovich, 1985 Central Naval Museum, St. Petersburg

For the curious: "Lenin Komsomol", originally K-3 - the first Soviet nuclear submarine, project 627. The name "Leninsky Komsomol" was inherited by the submarine from the diesel submarine of the same name "M-106" of the Northern Fleet, which died in one of the military campaigns in 1943.
In July 1962, for the first time in the history of the Soviet Navy, she made a long trip under the ice of the Arctic Ocean, during which she twice passed the North Pole. Under command Lev Mikhailovich Zhiltsov July 17, 1962 for the first time in the history of the Soviet submarine fleet surfaced near the North Pole. The crew of the ship hoisted the State Flag of the USSR near the Pole in the ice of the Central Arctic.
In 1991, she was withdrawn from the Northern Fleet. After a series of dark days and a still incomplete reconstruction, it was decided to convert the Leninsky Komsomol submarine into a museum. They say that on the Neva they are already looking for a place for her eternal parking. Perhaps it will be next to the legendary Aurora ...

Task #14
"Amphibian Man", 1927. Alexander Romanovich Belyaev
“Dolphins are much heavier on land than in water. In general, everything is more difficult for you here. Even your own body. It's easier to live in water... ...And you'll sink to the bottom... It's like you're swimming in thick, blue air. Quiet. You don't feel your body. It becomes free, light, obedient to your every movement ... "
Is the author of the novel right? Explain the answer.

Alexander Romanovich Belyaev(03/16/1884 - 01/06/1942) - Soviet science fiction writer, one of the founders of Soviet science fiction literature. Among his most famous novels: "Professor Dowell's Head", "Amphibian Man", "Ariel" ...
If you haven't read it yet, I highly recommend it ;-)

§ I recommend to readers of the green pages a very entertaining and informative biophysical material that lifts the veil of secrecy over some features of the organization of dolphins: the anti-turbulent properties of the skin and an unsurpassed sonar ... on the green page of "Secrets of the Dolphin".

Task #15
In what water and why is it easier to swim: sea or river?

Answer: It is easier to swim in sea water, since a large buoyant force will act on a body immersed in sea water due to the fact that the density of sea water is greater than the density of river water.

Task #16
Why can we easily pick up our friend or a rather heavy stone in the water?

Task #17
A piece of marble weighs as much as a copper weight. Which of these bodies is easier to keep in water?

Answer: The density of marble is less than the density of copper, therefore, with the same mass, marble has a larger volume, which means that a large buoyant force will act on it and it is easier to keep it in water than a copper weight.

Task #18
Walking along the shore strewn with sea pebbles hurts with bare feet. And in the water, plunging deeper than the belt, walking on small stones does not hurt. Why?

Task #19
Swimming in a river with a muddy bottom, you can see that the legs get stuck more in the mud in a shallow place than in a deep one. Explain why.

Answer: As we dive deeper, we displace more water. According to the law of Archimedes, a large buoyant force will act on us in this case.

Task #20
Why are diving shoes equipped with heavy lead soles?

Answer: To increase the weight of the diver and give him more stability while working in the water. Heavy lead soles help the diver overcome the buoyancy of the water.

Task #21
Why does an empty glass bottle float on the surface of water, while a filled one sinks?

Answer: An empty glass bottle is immersed in water to such a depth at which the volume of displaced water is equal in gravity to the gravity of the bottle, which corresponds to the condition of bodies floating on the surface of the water. If the bottle is filled with water, the volume displaced will decrease and the bottle will sink.

Task #22
A brick sinks in water, while a dry pine log floats up. Does this mean that a large buoyant force acts on the log?

Task #23
"Dead Head", 1928. Alexander Romanovich Belyaev
“Morel rose, but the water soon reached the ankles of the legs and was constantly rising. His raft definitely didn't float. Maybe he got caught on something? At least one of its edges must rise! ... the raft was still resting on the bottom ...
"But what the hell is the matter?" Morel yelled angrily. He took a piece of iron wood lying on the shore, from which the raft was made, threw it into the water and immediately exclaimed:
“Is there another donkey like me in the world?” The stump sank like a stone. The iron tree was too heavy and could not float on the water.
Tough lesson! Lowering his head, Morel looked at the boiling river, in the waters of which so much effort and labor had been buried.
Can there be stones that float in water like wood and trees whose wood sinks in water like stone? Where can you find floating rocks, and where is sinking wood? What are both used for?

For the curious: When milk boils, foam rises. During volcanic eruptions, foam is also formed in boiling lava, but only stone. Freezing, this stone foam forms pumice. It is so light that it does not sink in water. As an abrasive pumice is applied for grinding metal and wood, polishing stone products, and is also used for hygienic removal of rough skin of the feet. Pumice deposits have been known since ancient times in the Aeolian Islands in the Tyrrhenian Sea north of Sicily. Significant pumice deposits are located in Kamchatka and in Transcaucasia (in Armenia near Yerevan). Wood birch Schmidt, temir-agacha, saxaul so thick and heavy drowning in water. Saxaul grows in semi-deserts and deserts of Asia; it is not suitable for construction, but it is an excellent fuel: in terms of its calorie content, saxaul approaches coal.
The hero of Alexander Belyaev's story, Professor Joseph Morel, received a scientific mission to Brazil, and ... it may very well be that he used trunks to build a raft caesalpinia ironwood (Brazilian ironwood), or maybe ... trunks guaiac (backout) tree- the wood of which sinking in water.

"Meshchorskaya side", 1939
Konstantin Georgievich Paustovsky
“There are a lot of lakes in the meadows. Their names are strange and varied: Quiet, Bull, Hotets, Ramoina, Kanava, Staritsa, Muzga, Bobrovka, Selyanskoye Lake and, finally, Langobardskoe.
At the bottom of Hotz lie black bog oaks.
What is bog oak and what is its density?

For the curious: In ancient times, majestic oak forests grew on the shores of Lake Hottsa. From year to year, water eroded and washed away the shores of the lake, and mighty oaks full of strength sank into the water (the density of wood of a live (or freshly cut) oak is 1020-1070 kg / m 3, and the density of water is 1000 kg / m 3). Oaks went under water, time passed, sand and silt washed the trunks of mighty oaks with a multi-meter layer. If the majority of trees in such conditions are doomed to fleeting and complete destruction, then the oak is just starting its second life. After a few hundred years, it reaches a delightful maturity and is awarded the honorary title - stained!
Such durability, as well as the inimitable color of bog oak, are caused by the reactions of tannin (tannic acid) with water containing metal salts (for example, iron). Depending on the amount of metal salts contained in lake or river water and the amount of tannins contained in wood, for a long time (from 200 to 2000 years or more ...) a specific coloration of bog oak wood took place - in colors from outrageous - ash- silvery with a pinkish-gray tint ... to a mystical blue-black with purple streaks. Real bog or peat oak is usually found during excavations of drained lakes and swamps. This is a very rare and expensive wood, which is sometimes not inferior to iron in terms of strength.
In historical descriptions, you can find the name of bog oak as "ebony" And "iron tree". It is characteristic that in Russia there was no concept of "cabinet maker" - craftsmen working with elite wood were called "blackwoods".
The wood of dried, prepared for processing, bog oak has a fairly high density (750-850 kg / m 3) compared to ordinary oak (650-760 kg / m 3).

Oaks in Old Peterhof Shishkin Ivan Ivanovich, 1891

Shishkin Ivan Ivanovich(01/25/1832–03/20/1898) - Russian landscape painter, academician, professor, head of the landscape workshop of the Imperial Academy of Arts, one of the founding members of the Association of Traveling Art Exhibitions.

Task #24
Why do air bubbles rise quickly in water?

Answer: The buoyant force acting on an air bubble in water is many times greater than the weight of the bubble itself (the gas compressed in the bubble). Rising up, the bubble enters the layers of water with less pressure, the bubble expands, the supporting force increases, and the speed of its ascent increases.

Task #25
In what gases could a soap bubble filled with helium rise?

Task #26
If a soap bubble with air inside it is placed in an open vessel filled with carbon dioxide, the bubble does not sink to the bottom of the vessel. Explain the phenomenon.

Answer: A soap bubble filled with air will float for some time on an invisible surface of carbon dioxide in a vessel.

Problem #27
The flask filled with hydrogen was turned upside down. Will hydrogen come out of the flask?

Task #28
Explain why the volume of hydrogen contained in the shell of a balloon increases as it rises.

Carnicero Antonio(Antonio Carnicero; 1748–1814) was a Spanish neoclassical painter.
Hot air balloon(fr. Montgolfiere) - a balloon with a shell filled with hot air. Named after surname the inventors of the Mongolf brothers e - Joseph-Michel and Jacques-Etienne. The first flight was made in France in the city of Annonay on June 5, 1783.
November 21, 1783 - a significant date in the history of aeronautics(in 2013 it is also round - 230 years ;-) On this day, two brave Frenchmen: Pilatre de Rozier and the Marquis d'Arlande, for the first time in history, flew in a balloon of the Montgolfier brothers.

Problem #29
In which case does a homemade paper balloon filled with hot air have more lift: when the guys launched it in the school building or in the school yard, where it was pretty cool?

Answer: The lift force of a balloon is equal to the difference between the weight of the air in the balloon and the weight of the gas filling the balloon. The greater the difference in the densities of air and gas filling the balloon, the greater the lifting force. Therefore, the lifting force of the ball is greater on the street, where the air is less heated.

Task #30
What explains the maximum height ("ceiling") for the balloon, which he is not able to overcome?

Answer: The decrease in air density with the height of the balloon.

Jacob Alt(Jacob Alt; 09/27/1798–09/30/1872) was an Austrian landscape painter, graphic artist and lithographer.

Task #31
A saucepan upside down floats in a vessel of water. Will the water level in the vessel change with the temperature of the air surrounding the pan? (Ignore the thermal expansion of the water, pot, and vessel.)

Answer: The water level in the vessel will not change. Since the weight of the contents in the vessel will not change with a change in the temperature of the air surrounding the pan, the force of water pressure on the bottom of the vessel will not change either.

Task #32
Why is it impossible to extinguish burning kerosene by pouring water on it? How should you stew?

Answer: The water will sink down and will not close the access of air (oxygen necessary for combustion) to the kerosene.

Task #33
One bottle contains vegetable oil and vinegar. How can any of these liquids be poured from a bottle?

Answer: The oil floats on top of the vinegar. To pour the oil, you just need to tilt the bottle. To pour vinegar, you need to close the bottle with a cork, turn it upside down, then open the cork just enough to pour out the right amount of vinegar.

Problem #34
Lactometer - a device for determining the fat content of milk - is a sealed glass tube floating in a liquid in a vertical position due to the load placed in its lower part. The markings on the tube show the fat content of the milk. In which milk - whole or skimmed (less fat) - should the lactometer sink deeper? Why?

Answer: The lactometer sinks deeper in whole milk. The density of higher fat milk is lower.

Problem #35
Half a liter of vegetable oil floats on the surface of the water in a bucket. How to collect most of the oil in a bottle without any tools and without touching the bucket?

Answer: The bottle is filled with water, closed with a finger, turned upside down and lowered with its neck into a layer of oil. If you remove your finger, the water will flow out of the bottle, and oil will enter the bottle in its place. You can also lower the empty bottle into the water in a vertical position so that the edge of the neck is at the level of the oil.

Problem #36
To clean rye seeds from poisonous horns, ergot seeds are immersed in a twenty percent aqueous solution of table salt. The ergot horns float up, but the rye remains at the bottom. What does this indicate?

Answer: The density of poisonous ergot horns is less, and the grain density is greater than the density of the solution.

Problem #37
A strong solution of table salt was poured into the vessel, and clean water was carefully poured on top. If a raw chicken egg is placed in a vessel, it will stay on the border between the solution and pure water. Explain the phenomenon.

Answer: The density of pure water is less than the average density of the egg, so it sinks in it. The density of the salt solution is greater than the density of the egg, so it floats in it.

Problem #38
Take a saucer and lower it edgewise into the water, it will sink. If the saucer is carefully lowered upside down into the water, it floats on the surface. Why?

Answer: Porcelain or faience has a higher density than water, so when the saucer is lowered with an edge, it sinks. When the bottom of the saucer is lowered into the water, it is immersed in water to such a depth at which the volume of displaced water in terms of gravity is equal to the gravity of the saucer, which corresponds to the condition of bodies floating on the surface of the water.

Problem #39
On the cups of equal-armed scales are two identical glasses, filled to the brim with water. A wooden block floats in one glass. What position are the scales in?

Answer: In balance.

Task #40
Two identical weights are suspended from the ends of an equal-arm lever. What happens if one weight is placed in water and the other in kerosene?

Answer: The balance will be broken.

Task #41
Brass and glass balls are balanced on the beam of equal-arm balances. Will the equilibrium be disturbed if the device is placed in an airless space (in carbon dioxide, in water)?

Answer: A glass ball will descend in the void, a brass ball in carbon dioxide and water.

Task #42
What material should the weights be made of so that when weighing accurately, it would be possible not to correct for weight loss in air?

Answer: The weights must be made from the same material as the body to be weighed.

Task #43
Will the water in the communicating vessels be at the same level if a wooden spoon floats on its surface in one of the vessels?

Answer: Since a wooden spoon is in equilibrium on the surface of the water, its weight is equal to the weight of the water displaced by it. Therefore, if the spoon were replaced with water, then it would occupy a volume equal to the volume of the immersed part of the spoon, and the water level would not change. Therefore, the water in the communicating vessels will be at the same level.

Task #44
A massive ball of ice is frozen to the bottom of a vessel with water. How will the level of water in the vessel change when the ice melts? Will the force of water pressure on the bottom of the vessel change?

Answer: will go down; decrease. The density of ice is less than the density of water, so the volume of an ice ball is greater than the volume of water formed from this ball. It follows that the level of water in the vessel will decrease.

Problem #45
A piece of ice floats in a glass filled to the brim with water. Will the water overflow when the ice melts? What happens if the glass contains not water, but: 1) a denser liquid (for example, very salty water), 2) a less dense liquid (for example, kerosene)?

Answer: According to the law of Archimedes, the weight of floating ice is equal to the weight of the water displaced by it. Therefore, the volume of water formed when the ice melts will be exactly equal to the volume of water displaced by it, and the level of water in the glass will not change. If there is a liquid in the glass that is denser than water, then the volume of water formed after the ice melts will be greater than the volume of liquid displaced by the ice, and the water will overflow. Conversely, in the case of a less dense liquid, after the ice melts, the level will drop.

Task #46
A piece of ice floats in a vessel filled with water with a steel ball frozen into it. Will the water level in the vessel change when the ice melts? Make a detailed explanation.

Answer: Will go down. A piece of ice with a steel ball weighs more than a piece of ice of the same volume, therefore, it is immersed in water deeper than a pure piece of ice, and displaces a larger volume of water than that which will be taken up by the water formed when the ice melts. When the ice melts, the water level will drop. The ball will then fall to the bottom, but its volume will remain the same, and it does not directly change the water level.

Problem #47
A piece of ice floats in a vessel filled with water, containing an air bubble. Will the water level in the vessel change when the ice melts?

Answer: In the presence of an air bubble, ice weighs less than a solid piece of ice of the same volume and, therefore, is immersed in water to a lesser depth. However, since the weight of the air can be neglected, the water level in the vessel will not change.

Problem #48
A block of ice floats in a vessel filled with water. How will the depth of immersion of the bar in water change if kerosene is poured over the water?

Answer: will decrease. With the addition of kerosene on top of the water, the pressure on the lower edge of the bar increases.

Problem #49
A block of ice floats in a vessel filled with water, on which lies a wooden ball. The density of the substance of the ball is less than the density of water. Will the water level in the vessel change when the ice melts?

Answer: Will not change. A block of ice and a ball float in the ode. This means that they displace as much water as they weigh. Since after the ice melts, the weight of the contents in the vessel will not change, since the force of water pressure on the bottom of the vessel will not change either. This means that the water level in the vessel will remain the same.

Problem #50
The density of a body is determined by weighing it in air and water. When a small body is immersed in water, air bubbles are retained on its surface, due to which an error is obtained in determining the density. Is the density value more or less obtained in this case?

Answer: Adhering air bubbles slightly increase body weight, but significantly increase its volume. Therefore, the density value is smaller.

Problem #51
Explain the essence of the work of water sedimentation tanks. Why does the settling of water lead to the purification of water from substances insoluble in it? But what about soluble impurities?

Answer: Every particle in water is affected by gravity and the Archimedean force. If the first of them is greater than the second, then under the action of their resultant particle sinks to the bottom, then the water after settling becomes drinkable.

Problem #52
Ancient Greek scientist Aristotle to prove the weightlessness of air, he weighed an empty leather bag and the same bag filled with air. In both cases, the readings of the scales were the same. Why is Aristotle's conclusion that air has no weight wrong?

Answer: Because the weight of the air bag increased by as much as the buoyant force of the air acting on the inflated bag increased. To prove the gravity of air, it would be enough to pump air out of some vessel or pump it into a strong vessel.

Aristotle(384 BC–322 BC) – Ancient Greek philosopher. Student Plato. From 343 BC e. - mentor Alexander the Great. The most influential of the dialecticians of antiquity; founder of formal logic. Aristotle developed many physical theories and hypotheses based on the knowledge of the time. Actually myself the term "physics" was introduced by Aristotle.
Rembrandt Harmenszoon van Rijn(Rembrandt Harmenszoon van Rijn; 1606-1669) - Dutch artist, draftsman and engraver, great master of chiaroscuro, the largest representative of the golden age of Dutch painting.

Problem #53
Under terrestrial conditions, various methods are used to train and test astronauts in a state of weightlessness. One of them is as follows: a person in a special spacesuit is immersed in a pool of water in which he does not sink and does not float. Under what condition is this possible?

Answer: This is possible provided that the force of gravity acting on a person in a space suit will be balanced by the Archimedean force.

Problem #54
What conclusion can be drawn about the magnitude of the Archimedean force by conducting appropriate experiments on the Moon, where the force of gravity is six times less than on Earth?

Answer: The same as on Earth: a body immersed in a liquid (or gas) is affected by a buoyant force (Archimedean force) equal to the weight of the liquid (or gas) displaced by this body.

Problem #55
Will a steel key sink in water under weightless conditions, for example, on board an orbital station, inside which normal atmospheric air pressure is maintained?

Answer: The key can be located at any point in the liquid, since neither gravity nor the Archimedean force acts on the key under weightlessness.

The legendary tale of Archimedes' challenge with the golden crown

Archimedes(287 BC–212 BC) was an ancient Greek mathematician, physicist and engineer from Syracuse. He made many discoveries in geometry. He laid the foundations of mechanics, hydrostatics, the author of a number of important inventions.

Thinking Archimedes Domenico Fetti 1620

Domenico Fetti(c. 1589-1623) - Italian painter of the Baroque era.

The legendary tale of Archimedes' challenge with the golden crown transmitted in various forms. The Roman architect Vitruvius, reporting on the discoveries of various scientists that struck him, gives the following story:

“As for Archimedes, of all his numerous and varied discoveries, the discovery that I will tell about seems to me made with boundless wit.
During his reign in Syracuse, Hiero, after the successful completion of all his activities, made a vow to donate a golden crown to the immortal gods in some temple. He agreed with the master on a high price for the work and gave him the amount of gold he needed by weight. On the appointed day, the master brought his work to the king, who found it perfectly executed; after weighing, the crown was found to correspond to the given weight of gold.
After that, a denunciation was made that part of the gold was taken from the crown and the same amount of silver was mixed in instead. Hiero was angry that he had been tricked, and, not finding a way to convict this theft, asked Archimedes to think carefully about it. He, immersed in thoughts on this issue, somehow accidentally came to the bathhouse and there, sinking into the bathtub, noticed that such an amount of water was flowing out of it, what was the volume of his body immersed in the bathtub. Finding out for himself the value of this fact, he, without hesitation, jumped out of the bath with joy, ran home naked and in a loud voice informed everyone that he had found what he was looking for. He ran and shouted the same thing in Greek: "Eureka, Eureka" (Found, found!).
Then, based on his discovery, but, they say, he made two ingots, each of the same weight as the crown, one of gold, the other of silver. Having done this, he filled the vessel to the very brim and lowered a silver ingot into it, and ... an appropriate amount of water flowed out. Taking out the ingot, he poured the same amount of water into the vessel ..., measuring the poured water sextarium so that, as before, the vessel was filled with water to the very brim. So he found what weight of silver corresponds to what specific volume of water.
Having made such a study, he lowered the gold ingot in the same way ..., and, adding the same measure of the spilled amount of water, found on the basis of a smaller amount sextants water, how much less volume the ingot occupies.

Then the same method was used to determine the volume of the crown. She displaced more water than a gold bar, and the theft was proven.

Sextarius (sextarius)- Roman measure of volume, equal to 0.547 l
Sextant (sextans)- Roman measure of mass, equal to 54.6 g(1 sextant = 2 ounces; weight of 1 sextant = 0.53508 N)

And now, attention, question: Is it possible to calculate the amount of gold replaced by silver in the crown using the method of Archimedes?

Answer: According to the data that Archimedes had, he was only entitled to assert that the crown was not pure gold. But to establish exactly how much gold was concealed by the master and replaced by silver, Archimedes could not. This would be possible if the volume of an alloy of gold and silver were strictly equal to the sum of the volumes of its constituent parts. In fact, only a few alloys have this property. As for the volume of an alloy of gold and silver, it is less than the sum of the volumes of the metals included in it. In other words, the density of such an alloy is greater than the density obtained as a result of the calculation according to the rules of simple mixing. Another thing is if gold were replaced not by silver, but by copper: the volume of an alloy of gold and copper is exactly equal to the sum of the volumes of its constituent parts. In this case, the method of Archimedes, described in the above story, gives an unmistakable result.

Quite often this story is associated with the discovery of the law of Archimedes, although it concerns the method determining the volume of bodies of irregular shape and methods determining the specific gravity of bodies by measuring their volume by immersion in a liquid.

I wish you success in your decision
quality problems in physics!

Literature:
§ Katz Ts.B. Biophysics at physics lessons
Moscow: Enlightenment publishing house, 1988
§ Zhytomyr S.V. Archimedes
Moscow: Enlightenment publishing house, 1981
§ Gorev L.A. Entertaining experiments in physics
Moscow: Enlightenment publishing house, 1977
§ Lukashik V.I. Physics Olympiad
Moscow: Enlightenment publishing house, 1987
§ Perelman Ya.I. Do you know physics?
Domodedovo: VAP publishing house, 1994
§ Tulchinsky M.E. Qualitative problems in physics
Moscow: Enlightenment publishing house, 1972
§ Erdavletov S.R., Rutkovsky O.O. Interesting geography of Kazakhstan
Alma-Ata: Mektep publishing house, 1989.

In the fourth task of the exam in physics, we test our knowledge of communicating vessels, the forces of Archimedes, Pascal's law, moments of forces.

Theory for assignment No. 4 USE in physics

Moment of power

Moment of force is a quantity that characterizes the rotational action of a force on a rigid body. The moment of force is equal to the product of the force F at a distance h from the axis (or center) to the point of application of this force and is one of the main concepts of dynamics: M 0 = Fh.

Distanceh commonly referred to as the shoulder of strength.

In many problems of this section of mechanics, the rule of moments of forces that are applied to a body, conventionally considered a lever, is applied. The equilibrium condition of the lever F 1 / F 2 \u003d l 2 / l 1 can be used even if more than two forces are applied to the lever. In this case, the sum of all moments of forces is determined.

Law of communicating vessels

According to the law of communicating vessels in open communicating vessels of any type, the fluid pressure at each level is the same.

At the same time, the pressures of the columns above the liquid level in each vessel are compared. The pressure is determined by the formula: p=ρgh. If we equate the pressures of the columns of liquids, we get the equality: ρ 1 gh 1 = ρ 2 gh 2. From this follows the relation: ρ 1 h 1 = ρ 2 h 2, or ρ 1 / ρ 2 \u003d h 2 / h 1. This means that the heights of the liquid columns are inversely proportional to the density of the substances.

Strength of Archimedes

Archimedean or buoyant force occurs when some solid body is immersed in a liquid or gas. A liquid or gas tends to occupy the place “taken away” from them, therefore they push it out. The Archimedes force only works when the force of gravity acts on the body mg

The Archimedes force is traditionally referred to as F A.

Analysis of typical options for tasks No. 4 USE in physics

Demo version 2018

Solution algorithm:

1. Remember the rule of moments.
2. Find the moment of force created by load 1.
3. We find the shoulder of the force that will create load 2 when it is suspended. We find its moment of force.
4. We equate the moments of forces and determine the desired value of the mass.
5. We write down the answer.

Solution:

The first version of the task (Demidova, No. 1)

The moment of force acting on the lever on the left is 75 N∙m. What force must be applied to the lever on the right to keep it in balance if its arm is 0.5 m?

Solution algorithm:

1. We introduce the notation for the quantities that are given in the condition.
2. We write out the rule of moments of force.
3. We express force through the moment and shoulder. Calculate.
4. We write down the answer.

Solution:

1. To bring the lever into balance, moments of forces M 1 and M 2 applied to the left and right are applied to it. The moment of force on the left is conditionally equal to M 1 = 75 N∙m. The arm of the force on the right is equal to l= 0.5 m
2. Since it is required that the lever be in equilibrium, then by the rule of moments M 1 = M 2. Insofar as M 1 =F· l, then we have: M 2 =F∙ l.
3. From the resulting equality, we express the force: F\u003d M 2 /l= 75/0.5=150 N.

The second version of the task (Demidova, No. 4)

Archimedean or buoyant force occurs when some solid body is immersed in a liquid or gas. A liquid or gas tends to occupy the place “taken away” from them, therefore they push it out. The Archimedes force only works when gravity acts on the body mg. In weightlessness, this force does not arise.

Thread tension force T occurs when the thread is trying to stretch. It does not depend on whether gravity is present.

If several forces act on a body, then when studying its motion or state of equilibrium, the resultant of these forces is considered.

Solution algorithm:

1. We translate the data from the condition into SI. We enter the tabular value of water density necessary for solving.
2. We analyze the condition of the problem, determine the pressure of liquids in each vessel.
3. We write down the equation of the law of communicating vessels.
4. We write down the answer.

Solution:

The third version of the task (Demidova, No. 20)

Solution algorithm:

1. We analyze the condition of the problem, determine the pressure of liquids in each vessel.
2. We write down the equality of the law of communicating vessels.
3. We substitute the numerical values ​​of the quantities and calculate the desired density.
4. We write down the answer.

During this lesson, it is experimentally established what determines and does not depend on the magnitude of the buoyancy force that occurs when a body is immersed in a liquid.

The ancient Greek scientist Archimedes (Fig. 1) became famous for his numerous discoveries.

Rice. 1. Archimedes (287-212 BC)

It was he who first discovered, explained and managed to calculate the buoyancy force. In the last lesson, we found out that this force acts on any body immersed in a liquid or gas (Fig. 2).

Rice. 2. Strength of Archimedes

In honor of Archimedes, this force is also called the Archimedean force. By calculation, we have obtained a formula for calculating this force. In this lesson, we will use an experimental method to find out if what factors does the buoyancy force depend on, and what factors does it not depend on.

For the experiment, we will use bodies of various volumes, a vessel with liquid and a dynamometer.

Attach a weight of a smaller volume to a dynamometer and measure the weight of this weight first in air: , and then lowering the weight into liquid: . In this case, it can be seen that the value of the deformation of the spring after lowering the load into the liquid practically did not change. This suggests that the buoyant force acting on the load is small.

Fig 3. Experiment with a small volume load

Now we attach a larger weight to the dynamometer spring and immerse it in the liquid. We will see that the deformation of the spring has decreased more significantly.

This happened due to the fact that the magnitude of the buoyant force became greater.

Fig 4. Experiment with a load of a larger volume

Based on the results of this experiment, an intermediate conclusion can be drawn.

The larger the volume of the part of the body immersed in the liquid, the greater the buoyant force acting on the body.

Let's take two bodies of the same volume, but made of different materials. This means that they have different densities. We first hang one weight from the dynamometer and lower it into the liquid. By changing the readings of the dynamometer, we find the buoyancy force.

Rice. 5 Experiment with the first weight

Then we will carry out the same operation with the second load.

Rice. 6 Experiment with the second weight

Although the weight of the first and second weights are different, but when immersed in liquid, the dynamometer readings will decrease by the same amount.

This means that in both cases the value of the buoyancy force is the same, although the weights are made of different materials.

Thus, one more intermediate conclusion can be drawn.

The magnitude of the buoyancy force does not depend on the density of the bodies immersed in the liquid.

We attach the weight to the spring of the dynamometer and lower it into the water so that it is completely immersed in the liquid. Note the dynamometer readings. Now we will slowly pour the liquid into the vessel. We will notice that the dynamometer readings practically do not change . This means that the buoyancy force does not change.

Rice. 7 Experiment #3

Third intermediate conclusion.

The magnitude of the buoyancy force does not depend on the height of the liquid column above the body immersed in the liquid.

Attach the weight to the dynamometer spring. Noticing the readings of the dynamometer when the body is in the air: , let's immerse the body first in water: and then in oil: . By changing the dynamometer readings, it can be judged that the buoyancy force acting on a body in water is greater than the buoyancy force acting on the same body in oil.

Rice. 8 Experiment #4

Note that the density of water is , and the density of oil is less and is only . This leads to the following conclusion.

The greater the density of the fluid in which the body is immersed, the greater the buoyancy force acting on the body from the given fluid.

So, summarizing the results of the experiments performed, we can conclude that the magnitude of the buoyancy force

depends:

1) on the density of the liquid;

2) on the volume of the submerged part of the body;

does not depend:

1) on the density of the body;

2) on the shape of the body;

3) on the height of the liquid column above the body;

The results obtained are in full accordance with the formula for the magnitude of the buoyancy force obtained in the previous lesson:

This formula, in addition to the free fall acceleration, includes only two quantities that describe the conditions of the experiments: the density of the liquid and the volume of the immersed part of the body.

Bibliography

1. Peryshkin A.V. Physics. 7 cells - 14th ed., stereotype. - M.: Bustard, 2010.
2. A.V. Peryshkin Physics Grade 7: textbook. for general education institutions. - 2nd ed., stereotype. - M.: Bustard, 2013. - 221 p.
3. Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7-9 of educational institutions. - 17th ed. - M.: Enlightenment, 2004.

1. Internet portal "eduspb.com" ()
2. Internet portal "class-fizika.narod.ru" ()
3. Internet portal "krugosvet.ru" ()

Homework

1. What is buoyant force? Write down the formula for it.
2. A cube of a certain volume was placed in water. How will the buoyant force that acts on the cube change if its volume is doubled?
3. Identical bodies were placed in different liquids: one was placed in oil, and the second in water. In which case will the buoyant force acting on the body be greater?

What do you need to pass the exam in physics with a high score? Solve more problems and listen to the advice of an experienced teacher. We will help you with both the first and the second. Andrei Alekseevich consider a problem in mechanics.

Task #28

The task:

A wooden block floats on the surface of water in a container. The container rests on the surface of the earth. What will happen to the depth of the block in the water if the bowl is on the floor of an elevator that is accelerating vertically upwards? Explain your answer using physical laws.

Solution:

Let's consider several aspects of this task.

1) If the bar floats on the surface of the water, it means that a force acts on it, which is called the power of Archimedes. In our case, the bar just floats, and does not sink, which means that in our case, the Archimedes force is so great that it supports the bar on the surface of the water. Numerically, this force modulo will be equal to the weight of the water displaced by the bar. This follows from the definition of Archimedean force.

2) According to the condition of the problem, at first the bar, water and container are at rest relative to the Earth. This means that the Archimedes force balances the force of gravity acting on the floating block. In this case, the mass of the bar and the mass of water displaced by it are equal.

3) Further, according to the condition, the bar, water and container are at rest relative to each other and together move upwards in the elevator with acceleration relative to the Earth. It turns out that the same force of Archimedes, together with the force of gravity, imparts the same acceleration to both the floating bar and the water in the volume displaced by the bar, which leads to the relation:

It turns out that the summing acceleration is the same for both the bar and the water displaced by it. From this we conclude that when moving relative to the Earth with acceleration, the mass of the bar and the mass of water displaced by it are the same. Since the mass of the bar under the first condition (rest relative to the Earth) and under the second condition (accelerated upward movement) is the same, the mass of water displaced by it in both cases will be the same.

4) One more addition. Water under normal conditions is practically incompressible, so we take the density of water in both cases to be the same.

On the basis of our reasoning, we conclude that when moving up, the volume of displaced water does not change, and the depth of immersion of the bar into the water in the elevator will remain unchanged.

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