Archimedes' law: definition and formula. Buoyancy force

The reason for the emergence of the Archimedean force is the difference in pressure of the medium at different depths. Therefore, the Archimedes force arises only in the presence of gravity. On the Moon, it will be six times, and on Mars - 2.5 times less than on Earth.

There is no Archimedean force in weightlessness. If we imagine that gravity on Earth suddenly disappeared, then all the ships in the seas, oceans and rivers from the slightest push will go to any depth. But the surface tension of water, which does not depend on gravity, will not let them rise up, so they will not be able to take off, they will all drown.

How is the power of Archimedes manifested?

The magnitude of the Archimedean force depends on the volume of the immersed body and the density of the medium in which it is located. Its exact in the modern view: a body immersed in a liquid or gaseous medium in the field of gravity is affected by a buoyant force exactly equal to the weight of the medium displaced by the body, that is, F = ρgV, where F is the Archimedes force; ρ is the density of the medium; g is the free fall acceleration; V is the volume of the liquid (gas) displaced by the body or part of it immersed.

If in fresh water a buoyancy force of 1 kg (9.81 n) acts on each liter of the volume of an immersed body, then in sea water, the density of which is 1.025 kg * cu. dm, the Archimedes force of 1 kg 25 g will act on the same liter of volume. For a person of average build, the difference in the support force of sea and fresh water will be almost 1.9 kg. Therefore, swimming in the sea is easier: imagine that you need to swim at least a pond without a current with a two-kilogram dumbbell in your belt.

The Archimedean force does not depend on the shape of the immersed body. Take an iron cylinder, measure its strength from the water. Then roll this cylinder into a sheet, immerse in water flat and edgewise. In all three cases, the strength of Archimedes will be the same.

At first glance, it is strange, but if the sheet is immersed flat, then the decrease in the pressure difference for a thin sheet is compensated by an increase in its area perpendicular to the water surface. And when immersed by an edge, on the contrary, the small area of ​​\u200b\u200bthe edge is compensated by the greater height of the sheet.

If the water is very strongly saturated with salts, which is why its density has become higher than the density of the human body, then even a person who cannot swim will not drown in it. In the Dead Sea in Israel, for example, tourists can lie on the water for hours without moving. True, it is still impossible to walk on it - the area of ​​\u200b\u200bsupport turns out to be small, a person falls into the water up to his throat until the weight of the immersed part of the body is equal to the weight of the water displaced by him. However, if you have a certain amount of imagination, you can add up the legend of walking on water. But in kerosene, the density of which is only 0.815 kg * cu. dm, will not be able to stay on the surface and a very experienced swimmer.

Archimedean force in dynamics

The fact that ships float thanks to the power of Archimedes is known to everyone. But fishermen know that Archimedean force can also be used in dynamics. If a large and strong fish (taimen, for example) has caught on, then slowly pulling it up to the net (pulling it out) is not: it will break the line and leave. You need to first pull lightly when she leaves. Feeling the hook at the same time, the fish, trying to get rid of it, will rush towards the fisherman. Then you need to pull very hard and sharply so that the fishing line does not have time to break.

In water, the body of a fish weighs almost nothing, but its mass is preserved with inertia. With this method of fishing, the Archimedean force, as it were, will give the fish a tail, and the prey itself will flop at the feet of the fisherman or into his boat.

Archimedean force in the air

Archimedean force acts not only in liquids, but also in gases. Thanks to her, balloons and airships (zeppelins) fly. 1 cu. m of air under normal conditions (20 degrees Celsius at sea level) weighs 1.29 kg, and 1 kg of helium - 0.21 kg. That is, 1 cubic meter of a filled shell is capable of lifting a load of 1.08 kg. If the shell is 10 m in diameter, then its volume will be 523 cubic meters. m. Having done it from a lightweight synthetic material, we get a lifting force of about half a ton. Aeronauts call the Archimedean force in the air the floating force.

If air is pumped out of the balloon without letting it wrinkle, then each cubic meter of it will pull up all 1.29 kg. An increase of more than 20% in lift is technically very tempting, but helium is expensive, and hydrogen is explosive. Therefore, projects of vacuum airships are born from time to time. But materials capable of withstanding a large (about 1 kg per sq. cm) atmospheric pressure from the outside on the shell, modern technology is not yet able to create.

One of the first physical laws studied by high school students. At least approximately this law is remembered by any adult, no matter how far he may be from physics. But sometimes it is useful to return to the exact definitions and formulations - and understand the details of this law, which could be forgotten.

What does the law of Archimedes say?

There is a legend that the ancient Greek scientist discovered his famous law while taking a bath. Immersed in a container filled with water to the brim, Archimedes noticed that the water splashed out at the same time - and experienced insight, instantly formulating the essence of the discovery.

Most likely, in reality the situation was different, and the discovery was preceded by long observations. But this is not so important, because in any case, Archimedes managed to discover the following pattern:

• immersed in any liquid, bodies and objects experience several multidirectional forces at once, but directed perpendicular to their surface;
• the final vector of these forces is directed upwards, therefore, any object or body, being in a liquid at rest, experiences expulsion;
• in this case, the buoyancy force is exactly equal to the coefficient that will be obtained if the product of the volume of the object and the density of the liquid is multiplied by the acceleration of gravity.

So, Archimedes established that a body immersed in a liquid displaces such a volume of liquid that is equal to the volume of the body itself. If only part of the body is immersed in the liquid, then it will displace the liquid, the volume of which will be equal to the volume of only the part that is immersed.

The same pattern applies to gases - only here the volume of the body must be correlated with the density of the gas.

You can formulate a physical law and a little easier - the force that pushes a certain object out of a liquid or gas is exactly equal to the weight of the liquid or gas displaced by this object when immersed.

The law is written as the following formula:

What is the significance of the law of Archimedes?

The pattern discovered by ancient Greek scientists is simple and completely obvious. But at the same time, its importance for everyday life cannot be overestimated.

It is thanks to the knowledge of the expulsion of bodies by liquids and gases that we can build river and sea vessels, as well as airships and balloons for aeronautics. Heavy metal ships do not sink due to the fact that their design takes into account the law of Archimedes and its numerous consequences - they are built so that they can float on the surface of the water, and do not sink. Aeronautical means operate on a similar principle - they use the buoyancy of the air, becoming, as it were, lighter than it during the flight.

469. Why does a metal ship float in water, while a metal nail sinks?
The weight of the water displaced by the underwater part of the ship is equal to the weight of the ship in the air or the force of gravity acting on the ship.

470. How does the position of the ship's waterline change when it is loaded?
The waterline will move closer to the water as the ship's weight has increased.

471. How will the ship's draft change when moving from the river to the sea?
The waterline will rise above the surface of the water because the density of sea water is higher than that of fresh water.

472. Mercury, water and kerosene are poured into a flask. How will these liquids be located in the flask?
As the density decreases: mercury-water-kerosene.

473. An iron washer was dropped into a jar of mercury. Will the puck sink or float on mercury?
Will not sink, because the density of iron is less than the density of mercury.

474. Figure 64 shows a wooden block floating in two different liquids. When does a liquid have a higher density? Is the force of gravity acting on the block the same? In which case is the Archimedean force greater?

The density of the liquid b) is greater, since the Archimedes force acting on the body is greater.

475. A float with a lead sinker at the bottom is lowered first into water, then into oil. In both cases, the float floats. What liquid does it sink deeper into?
The float will sink deeper into the oil, because its density is less than the density of water.

476. Depict the forces acting on the body when it floats on the surface of a liquid (Fig. 65).

477. What forces act on a body when it floats to the surface of a liquid (Fig. 66)? Show them with arrows to scale.

478. Depict with arrows the forces acting on the body when it sinks (Fig. 67).

479. A lead scroll was hung on one side of the balance beam, and a piece of glass of equal weight was hung on the other. Will the balance be maintained if both lead and glass are completely immersed in water? If not, which shoulder will pull?
The balance will not be maintained. Shoulder with a body of smaller volume, i.e. with lead will pull, tk. the force of Archimedes acting on it will be less.

480. Two identical brass weights of 2 g each were suspended from the balance beam from both sides and one weight was lowered into water, and the other into alcohol. What weight will pull?
A weight lowered into a liquid with a lower density (i.e. alcohol) will pull.

481. A jar of water and a wooden block were placed next to an electronic scale. Will the reading of the scales change if the bar is placed in a jar of water, where it will float?
The scale readings will decrease as the force of Archimedes will act on the block.

482. Due to what physical law can fish, by squeezing their swim bladder, rise and fall in the water?
Thanks to the law of Archimedes.

483. Heavy lead plates are placed on the chest and back of the diver, the soles of the shoes are also made of lead. What is it for?
So that the weight of the diver is greater than the force of Archimedes acting on him.

484. An empty, tightly closed metal can, almost completely immersed in water, floats in cold water, and if the water is heated, it sinks. What explains this interesting phenomenon?
The density of the heated water decreases, therefore, the Archimedes force acting on the jar also decreases.

485. A marble ball with a volume of 20 cm3 was dropped into a river. With what force is it pushed out of the water?

486. With what force is a piece of glass with a volume of 10 cm3 pushed out by kerosene?

487. What is the volume of an immersed body if it is pushed out by water with a force of 50 N?

488. What volume of water displaces a ship if a buoyant force of 200,000 kN acts on it?

489. With what force will a person be pushed out of sea water if a buoyant force equal to 686 N acts on him in fresh water?

490. Determine the weight of 1 cm3 of copper in fresh water.

491. What is the weight of iron with a volume of 1 cm3 in pure water?

492. Determine how much a 1 cm3 glass cube weighs in water.

493. An empty metal ball weighing 3 N (in air) and with a volume of 1200 cm3 is held under water. Will the ball stay underwater if it is released? How much force is required to keep it under water?

494. A piece of granite with a volume of 5.5 dm3 and a mass of 15 kg is completely immersed in a pond. What force must be applied to keep it in the water?

495. A block of marble with a volume of 1 m3 lies at the bottom of a river. What force must be applied to lift it in the water? What is its weight in air?

496. What is the weight in river water of a marble slab whose weight in air is 260 N?

497. What tension does the cable experience when lifting a granite slab with a volume of 2 m3 from the bottom of a lake?

498. A well iron bucket weighing 1.56 kg and a volume of 12 liters is lowered into the well. What force must be applied to lift a full bucket of water? Above the water? Friction is ignored.

499. What is the density of an object if its weight in air is 100 N, and in fresh water 60 N?

500. A glass stopper weighs 0.5 N in air, 0.32 N in water, and 0.35 N in alcohol. What is the density of glass? What is the density of alcohol?

501. The weight of a marble figurine in air is 0.686 N, and in fresh water 0.372 N. Determine the density of the figurine.

502. A weight of 100 g weighs 0.588 N in fresh water, and 0.666 N in an unknown liquid. What is the density of the unknown liquid? What is this liquid?

503. Find the density of alcohol if a piece of glass weighs 0.25 N in alcohol, 0.36 N in air, and 0.22 N in water.

504. A glass plate, when immersed in pure water, became lighter by 49 mN, and when immersed in kerosene, by 39 mN. What is the density of kerosene?

505. A raft with an area of ​​600 m2, after being loaded, sank by 30 cm. Find the mass of the load placed on the raft.

506. A truck drove into a ferry 5 m long and 4 m wide, as a result of which the ferry sank 5 cm into the water. What is the mass of the truck?

507. Find the mass of water displaced by a ship with a displacement of 50,000 tons.
The mass of water is equal to the displacement, i.e. 50,000 tons

508. Rectangular ferry 10 m long and 4 m wide when loaded, the donkey 75 cm. Find the mass of the load.

509. The mass of an amphibious tank is about 2 tons. What should be the volume of the part of the tank submerged in water so that the tank can float in water?

510. A block of cork, the density of which is 25 g/cm3, floats in fresh water. What part of the block is submerged in water?

511. A log floats along the river. What part of it is immersed in water if the density of the tree is 0.5 g/cm3?

512. What is more: the underwater or surface part of the ice floe, if the ice density is 0.9 g/cm3?

513. The depth of a puddle is 2 cm. Will a pine cube with a side of 7 cm float in this water? Will a plank with a mass equal to a cube and a thickness of 2 cm float in this puddle?

514. What mass of cargo will be held in river water by a cork lifebuoy weighing 12 kg?

515. Why does a child weighing 30 kg float freely on the water in inflatable sleeves, the volume of which is only 1.5 dm3?

516. A round iron pellet weighing 11.7 g is connected to a foam plastic cube weighing 1.2 g. The entire system is completely immersed in water. Total weight in water 6.4 10-2 N. What is the density of the foam?

517. A piece of wax weighs 882 mN in air. The ball was covered with wax and immersed in water. The weight of the entire system in water is 98 mN. Determine the density of the wax if the weight of the ball in water is 196 mN.

518. A puck was tied to a piece of paraffin candle weighing 4.9 g, which weighs 98 nM in water. The total weight of the system immersed in water is 78.4 mN. Find the density of the wax.

519. With what buoyant force does air act on a body with a volume of 1 m3 at 0°C and normal atmospheric pressure?

523. In 1933, the airship B-3 was built, with a volume of 6800 m3. What is the lift force of this airship if it was filled with hydrogen?

524. One of the first designers of a controlled balloon, Santos Dumont, built a balloon with a volume of 113 m3 and a weight with all equipment of 27.5 kg. The balloon was filled with hydrogen. Could Santos Dumont rise on such a ball if his mass was 52 kg?

525. Can a balloon filled with hydrogen with a volume of 1500 m3 lift three passengers weighing 60 kg each, if the shell of the balloon and the gondola together have a mass of 250 kg?

526. In 1931, Professor Picard on a specially built balloon rose to a height of 16 km. At this altitude, the barometer showed a pressure of 76 mm. rt. Art. The gondola of the balloon, where Picard was placed, was made of duralumin and tightly closed. The pressure inside the gondola remained at 1 atmosphere all the time (1 atm=760 mm Hg=1013 hPa.) Calculate the pressure per 1 cm2 of the gondola wall from inside and outside.

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Introduction

Relevance: If you look closely at the world around you, you can discover many events taking place around. Since ancient times, man has been surrounded by water. When we swim in it, our body pushes some forces to the surface. I have been asking myself the question for a long time: “Why do bodies float or sink? Does water push things out?

My research work is aimed at deepening the knowledge gained in the lesson about the Archimedean force. Answers to my questions, using life experience, observations of the surrounding reality, conduct my own experiments and explain their results, which will expand knowledge on this topic. All sciences are interconnected. And the common object of study of all sciences is man "plus" nature. I am sure that the study of the action of the Archimedean force is relevant today.

Hypothesis: I suppose that at home it is possible to calculate the magnitude of the buoyant force acting on a body immersed in a liquid and determine whether it depends on the properties of the liquid, the volume and shape of the body.

Object of study: Buoyancy in liquids.

Tasks:

To study the history of the discovery of Archimedean force;

To study the educational literature on the action of the Archimedean force;

Develop skills for conducting an independent experiment;

Prove that the value of the buoyant force depends on the density of the liquid.

Research methods:

Research;

Estimated;

Information retrieval;

Observations

1. Discovery of the power of Archimedes

There is a famous legend about how Archimedes ran down the street and shouted "Eureka!" This just tells about his discovery that the buoyant force of water is equal in absolute value to the weight of the water displaced by it, the volume of which is equal to the volume of the body immersed in it. This discovery is called the law of Archimedes.

In the III century BC, Hieron lived - the king of the ancient Greek city of Syracuse, and he wanted to make himself a new crown of pure gold. He measured it strictly as needed, and gave the jeweler an order. A month later, the master returned the gold in the form of a crown and it weighed as much as the mass of this gold. But after all, anything can happen and the master could cheat by adding silver or even worse - copper, because you can’t tell by eye, and the mass is as it should be. And the king wants to know: is the work done honestly? And then, he asked the scientist Archimedes, to check whether the master made his crown from pure gold. As you know, the mass of a body is equal to the product of the density of the substance from which the body is made and its volume:. If different bodies have the same mass, but they are made of different substances, then they will have different volumes. If the master had returned to the king not a jewel-made crown, the volume of which cannot be determined because of its complexity, but a piece of metal of the same shape that the king had given him, then it would immediately be clear whether he mixed another metal there or not. And while taking a bath, Archimedes noticed that water was pouring out of it. He suspected that it poured out exactly in the volume that his body parts immersed in water occupy. And Archimedes realized that the volume of the crown can be determined by the volume of water displaced by it. Well, if you can measure the volume of the crown, then it can be compared with the volume of a piece of gold, equal in mass. Archimedes immersed the crown in water and measured how the volume of water increased. He also immersed in water a piece of gold, whose mass was the same as that of the crown. And then he measured how the volume of water had increased. The volumes of water displaced in the two cases were different. Thus, the master was convicted of deceit, and science was enriched by a remarkable discovery.

It is known from history that the problem of the golden crown prompted Archimedes to study the question of the floating of bodies. The experiments carried out by Archimedes were described in the essay "On Floating Bodies", which has come down to us. The seventh sentence (theorem) of this work is formulated by Archimedes as follows: bodies heavier than a liquid, immersed in this liquid, will sink until they reach the very bottom, and in the liquid they will become lighter by the weight of the liquid in a volume equal to the volume of the immersed body.

Interestingly, the Archimedes force is zero when a body immersed in a liquid is dense, with its entire base pressed to the bottom.

The discovery of the basic law of hydrostatics is the greatest achievement of ancient science.

2. Formulation and explanation of the law of Archimedes

Archimedes' law describes the action of liquids and gases on a body immersed in them, and is one of the main laws of hydrostatics and gas statics.

Archimedes' law is formulated as follows: a buoyant force acts on a body immersed in a liquid (or gas), equal to the weight of the liquid (or gas) in the volume of the immersed part of the body - this force is called the power of Archimedes:

,

where is the density of the liquid (gas), is the acceleration of free fall, is the volume of the immersed part of the body (or the part of the volume of the body below the surface).

Therefore, the Archimedean force depends only on the density of the liquid in which the body is immersed, and on the volume of this body. But it does not depend, for example, on the density of the substance of a body immersed in a liquid, since this quantity is not included in the resulting formula.

It should be noted that the body must be completely surrounded by the liquid (or intersect with the surface of the liquid). So, for example, the law of Archimedes cannot be applied to a cube that lies at the bottom of the tank, hermetically touching the bottom.

3. Determination of the strength of Archimedes

The force with which a body in a liquid is pushed out by it can be determined experimentally using this device:

We hang a small bucket and a cylindrical body on a spring fixed in a tripod. We mark the stretching of the spring with an arrow on a tripod, showing the weight of the body in the air. Raising the body, we substitute a glass with a drain tube under it, filled with liquid to the level of the drain tube. Then the whole body is immersed in the liquid. In this case, a part of the liquid, the volume of which is equal to the volume of the body, is poured from the pouring vessel into a glass. The spring pointer rises, the spring contracts, indicating a decrease in the weight of the body in the liquid. In this case, along with the force of gravity, the body is also affected by a force that pushes it out of the fluid. If you pour liquid from the glass into the bucket (that is, the one that was displaced by the body), then the spring pointer will return to its initial position.

Based on this experience, we can conclude that the force pushing out a body completely immersed in a liquid is equal to the weight of the liquid in the volume of this body. The dependence of pressure in a liquid (gas) on the depth of immersion of a body leads to the appearance of a buoyant force (Archimedes force) acting on any body immersed in a liquid or gas. The body moves downward under the influence of gravity. The Archimedean force is always directed opposite to gravity, so the weight of a body in a liquid or gas is always less than the weight of this body in a vacuum.

This experience confirms that the Archimedean force is equal to the weight of the liquid in the volume of the body.

4. Condition of floating bodies

Two forces act on a body inside a liquid: gravity, directed vertically downwards, and the Archimedean force, directed vertically upwards. Consider what will happen to the body under the action of these forces, if at first it was motionless.

In this case, three cases are possible:

1) If the force of gravity is greater than the Archimedean force, then the body sinks down, that is, it sinks:

, then the body sinks;

2) If the modulus of gravity is equal to the modulus of the Archimedean force, then the body can be in equilibrium inside the fluid at any depth:

, then the body floats;

3) If the Archimedean force is greater than the force of gravity, then the body will rise from the liquid - float:

, then the body floats.

If the floating body partially protrudes above the liquid surface, then the volume of the submerged part of the floating body is such that the weight of the displaced liquid is equal to the weight of the floating body.

The Archimedean force is greater than the force of gravity if the density of the liquid is greater than the density of the body immersed in the liquid, if

1) \u003d - the body floats in a liquid or gas, 2) >body sinks 3) < — тело всплывает до тех пор, пока не начнет плавать.

It is these principles of the relationship between gravity and the force of Archimedes that are used in shipbuilding. However, huge river and sea vessels made of steel, the density of which is almost 8 times greater than the density of water, keep on the water. This is explained by the fact that only a relatively thin ship hull is made of steel, and most of its volume is occupied by air. In this case, the average value of the ship's density turns out to be much less than the density of water; therefore, it not only does not sink, but can also take a large amount of cargo for transportation. Ships that sail on rivers, lakes, seas and oceans are built from different materials with different densities. The hull of ships is usually made of steel sheets. All internal fasteners that give ships strength are also made of metals. For the construction of ships, different materials are used, having both higher and lower density compared to water. The weight of water displaced by the underwater part of the ship is equal to the weight of the ship with cargo in the air or the force of gravity acting on the ship with cargo.

For aeronautics, balloons were first used, which were previously filled with heated air, now with hydrogen or helium. In order for the ball to rise into the air, it is necessary that the Archimedean (buoyant) force acting on the ball be greater than the force of gravity.

5. Conducting an experiment

Investigate the behavior of a raw egg in liquids of various kinds.

Task: prove that the value of the buoyant force depends on the density of the liquid.

I took one raw egg and liquids of various kinds (Appendix 1):

The water is clean;

Water saturated with salt;

Sunflower oil.

First, I lowered the raw egg into clean water - the egg drowned - "went to the bottom" (Appendix 2). Then I added a tablespoon of table salt to a glass of clean water, as a result, the egg floats (Appendix 3). And finally, I lowered the egg into a glass with sunflower oil - the egg sank to the bottom (Appendix 4).

Conclusion: in the first case, the density of the egg is greater than the density of water, and therefore the egg sank. In the second case, the density of salt water is greater than the density of the egg, so the egg floats in the liquid. In the third case, the density of the egg is also greater than the density of sunflower oil, so the egg sank. Therefore, the greater the density of the liquid, the lower the force of gravity.

2. The action of the Archimedean force on the human body in water.

Determine by experience the density of the human body, compare it with the density of fresh and sea water and draw a conclusion about the fundamental possibility of a person to swim;

Calculate the weight of a person in the air, the Archimedean force acting on a person in water.

First, I used a scale to measure my body weight. Then he measured the volume of the body (without the volume of the head). To do this, I poured enough water into the bath so that when I was immersed in water, I was completely in the water (except for the head). Then, with the help of a centimeter tape, I marked from the upper edge of the bath the distance to the water level ℓ 1, and then - when immersed in water ℓ 2. After that, using a pre-calibrated three-liter jar, I began to pour water into the bath from the level ℓ 1 to the level ℓ 2 - so I measured the volume of water displaced by me (Appendix 5). I calculated the density using the formula:

The force of gravity acting on a body in air was calculated by the formula: , where is the free fall acceleration ≈ 10 . The value of the buoyancy force was calculated using the formula described in paragraph 2.

Conclusion: The human body is denser than fresh water, which means that it sinks in it. It is easier for a person to swim in the sea than in a river, since the density of sea water is greater, and therefore the value of the buoyancy force is greater.

Conclusion

In the process of working on this topic, we learned a lot of new and interesting things for ourselves. The circle of our knowledge has increased not only in the field of action of the force of Archimedes, but also in its application in life. Before starting work, we had a far from detailed idea of ​​\u200b\u200bit. During the experiments, we experimentally confirmed the validity of the law of Archimedes and found out that the buoyant force depends on the volume of the body and the density of the liquid, the greater the density of the liquid, the greater the Archimedean force. The resulting force, which determines the behavior of a body in a fluid, depends on the mass, volume of the body, and the density of the fluid.

In addition to the experiments performed, additional literature was studied on the discovery of Archimedes' force, on the navigation of bodies, and aeronautics.

Each of you can make amazing discoveries, and for this you do not need to have any special knowledge or powerful equipment. You just need to take a closer look at the world around us, be a little more independent in your judgments, and discoveries will not keep you waiting. The unwillingness of most people to learn about the world around them leaves a lot of space for the inquisitive in the most unexpected places.

Bibliography

1. Big book of experiments for schoolchildren - M.: Rosmen, 2009. - 264 p.

2. Wikipedia: https://ru.wikipedia.org/wiki/Law_Archimedes.

3. Perelman Ya.I. Entertaining physics. - book 1. - Yekaterinburg .: Thesis, 1994.

4. Perelman Ya.I. Entertaining physics. - book 2. - Ekaterinburg .: Thesis, 1994.

5. Peryshkin A.V. Physics: grade 7: a textbook for educational institutions / A.V. Peryshkin. - 16th ed., stereotype. - M.: Bustard, 2013. - 192 p.: ill.

Annex 1

Appendix 2

Annex 3

Appendix 4

Despite the obvious differences in the properties of liquids and gases, in many cases their behavior is determined by the same parameters and equations, which makes it possible to use a unified approach to studying the properties of these substances.

In mechanics, gases and liquids are considered as continuous media. It is assumed that the molecules of a substance are distributed continuously in the part of space they occupy. In this case, the density of a gas depends significantly on pressure, while the situation is different for a liquid. Usually, when solving problems, this fact is neglected, using the generalized concept of an incompressible fluid, the density of which is uniform and constant.

Definition 1

Pressure is defined as the normal force $F$ acting from the side of the fluid per unit area $S$.

$ρ = \frac(\Delta P)(\Delta S)$.

Remark 1

Pressure is measured in pascals. One Pa is equal to a force of 1 N acting on a unit area of ​​1 sq. m.

In a state of equilibrium, the pressure of a liquid or gas is described by Pascal's law, according to which the pressure on the surface of the liquid, produced by external forces, is transferred by the liquid equally in all directions.

In mechanical equilibrium, the horizontal pressure of a fluid is always the same; consequently, the free surface of a static fluid is always horizontal (except in cases of contact with the walls of the vessel). If we take into account the condition of incompressibility of the liquid, then the density of the considered medium does not depend on pressure.

Imagine a certain volume of fluid bounded by a vertical cylinder. We denote the cross section of the liquid column $S$, its height $h$, the liquid density $ρ$, and the weight $P=ρgSh$. Then the following is true:

$p = \frac(P)(S) = \frac(ρgSh)(S) = ρgh$,

where $p$ is the pressure on the bottom of the vessel.

It follows that the pressure varies linearly with altitude. In this case, $ρgh$ is the hydrostatic pressure, the change of which explains the emergence of the Archimedes force.

Formulation of the Law of Archimedes

The law of Archimedes, one of the basic laws of hydrostatics and aerostatics, states: a body immersed in a liquid or gas is subjected to a buoyant or lifting force equal to the weight of the volume of liquid or gas displaced by the part of the body immersed in the liquid or gas.

Remark 2

The emergence of the Archimedean force is due to the fact that the medium - liquid or gas - tends to occupy the space taken away by the body immersed in it; while the body is pushed out of the medium.

Hence the second name for this phenomenon is buoyancy or hydrostatic lift.

The buoyancy force does not depend on the shape of the body, as well as on the composition of the body and its other characteristics.

The emergence of the Archimedean force is due to the difference in pressure of the medium at different depths. For example, the pressure on the lower layers of water is always greater than on the upper layers.

The manifestation of the Archimedes force is possible only in the presence of gravity. So, for example, on the Moon the buoyancy force will be six times less than on Earth for bodies of equal volumes.

The Emergence of the Force of Archimedes

Imagine any liquid medium, for example, ordinary water. Mentally select an arbitrary volume of water by a closed surface $S$. Since the entire liquid is in mechanical equilibrium by condition, the volume allocated by us is also static. This means that the resultant and the moment of external forces acting on this limited volume take on zero values. External forces in this case are the weight of a limited volume of water and the pressure of the surrounding fluid on the outer surface $S$. In this case, it turns out that the resultant $F$ of the forces of hydrostatic pressure experienced by the surface $S$ is equal to the weight of the volume of liquid that was bounded by the surface $S$. In order for the total moment of the external forces to vanish, the resultant $F$ must be directed upwards and pass through the center of mass of the selected liquid volume.

Now we denote that instead of this conditional limited liquid, any solid body of the corresponding volume was placed in the medium. If the condition of mechanical equilibrium is observed, then no changes will occur from the side of the environment, including the pressure acting on the surface $S$ will remain the same. Thus, we can give a more precise formulation of the law of Archimedes:

Remark 3

If a body immersed in a liquid is in mechanical equilibrium, then from the side of the environment surrounding it, the buoyant force of hydrostatic pressure acts on it, numerically equal to the weight of the medium in the volume displaced by the body.

The buoyant force is directed upward and passes through the center of mass of the body. So, according to the law of Archimedes for the buoyant force, the following is true:

$F_A = ρgV$, where:

• $V_A$ - buoyancy force, H;
• $ρ$ - liquid or gas density, $kg/m^3$;
• $V$ - volume of the body immersed in the medium, $m^3$;
• $g$ - free fall acceleration, $m/s^2$.

The buoyant force acting on the body is opposite in direction to the force of gravity, therefore the behavior of the immersed body in the medium depends on the ratio of the modules of gravity $F_T$ and Archimedean force $F_A$. There are three possible cases here:

1. $F_T$ > $F_A$. The force of gravity exceeds the buoyant force, hence the body sinks/falls;
2. $F_T$ = $F_A$. The force of gravity equalizes with the buoyant force, so the body "hangs" in the fluid;
3. $F_T$