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Introduction

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

My research work is aimed at deepening the knowledge gained in class about Archimedean force. Answer the questions that interest me, using life experience, observations of the surrounding reality, conduct my own experiments and explain their results, which will expand my 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 Archimedean force is relevant today.

Hypothesis: I assume that at home you can calculate the magnitude of the buoyancy 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 force in liquids.

Tasks:

Study the history of the discovery of Archimedean force;

Study educational literature on the action of Archimedean force;

Develop skills in conducting independent experiments;

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

Research methods:

Research;

Calculated;

Information search;

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 the story of his discovery that the buoyant force of water is equal in magnitude 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 Archimedes' law.

In the 3rd century BC, there lived Hiero, the king of the ancient Greek city of Syracuse, and he wanted to make himself a new crown from pure gold. I measured it exactly as needed and gave the order to the jeweler. A month later, the master returned the gold in the form of a crown and it weighed as much as the mass of the given gold. But anything can happen, and the master could have cheated by adding silver or, even worse, copper, because you can’t tell the difference by eye, but the mass is what it should be. And the king wants to know: was the work done honestly? And then, he asked the scientist Archimedes to check whether the master made his crown from pure gold. As is known, 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 jewelry-made crown, the volume of which is impossible to determine due to its complexity, but a piece of metal of the same shape that the king gave him, then it would have been immediately clear whether he had mixed another metal into it or not. And while taking a bath, Archimedes noticed that water was pouring out of it. He suspected that it was pouring out in exactly the same volume as the volume occupied by his body parts immersed in water. And it dawned on Archimedes 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 of equal mass. Archimedes immersed the crown in water and measured how the volume of water increased. He also immersed a piece of gold in water, the mass of which was the same as that of the crown. And then he measured how the volume of water increased. The volumes of water displaced in the two cases turned out to be different. Thus, the master was exposed as a deceiver, and science was enriched with 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 was formulated by Archimedes as follows: bodies heavier than the 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.

It is interesting that the Archimedes force is zero when a body immersed in a liquid is tightly pressed to the bottom with its entire base.

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

2. Formulation and explanation of Archimedes' law

Archimedes' law describes the effect 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 body immersed in a liquid (or gas) is acted upon by a buoyant force equal to the weight of the liquid (or gas) in the volume of the immersed part of the body - this force is called by the power of Archimedes:

,

where is the density of the liquid (gas), is the acceleration of gravity, is the volume of the submerged part of the body (or the part of the volume of the body located below the surface).

Consequently, 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 liquid (or intersect with the surface of the liquid). So, for example, Archimedes' law cannot be applied to a cube that lies at the bottom of a tank, hermetically touching the bottom.

3. Definition of Archimedes' force

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

We hang a small bucket and a cylindrical body on a spring fixed to a tripod. We mark the stretch of the spring with an arrow on a tripod, showing the weight of the body in the air. Having lifted the body, we place a glass with a drainage tube under it, filled with liquid to the level of the drainage tube. After which the body is immersed entirely in liquid. In this case, part of the liquid, the volume of which is equal to the volume of the body, is poured from the casting vessel into the glass. The spring pointer rises and the spring contracts, indicating a decrease in body weight in the liquid. In this case, along with the force of gravity, the body is also acted upon by a force that pushes it out of the liquid. If liquid from a glass is poured into the bucket (i.e., the liquid that was displaced by the body), then the spring pointer will return to its initial position.

Based on this experiment, 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. When a body dives, it moves downward under the influence of gravity. The Archimedean force is always directed opposite to the force of gravity, therefore the weight of a body in a liquid or gas is always less than the weight of this body in a vacuum.

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

4. Condition of floating bodies

A body located inside a liquid is acted upon by two forces: the force of gravity, directed vertically downward, and the Archimedean force, directed vertically upward. Let us consider what will happen to the body under the influence 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 goes down, that is, it sinks:

, then the body drowns;

2) If the modulus of gravity is equal to the modulus of Archimedean force, then the body can be in equilibrium inside the liquid 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 a floating body partially protrudes above the surface of the liquid, then the volume of the immersed part of the floating body is such that the weight of the displaced liquid is equal to the weight of the floating body.

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

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

It is these principles of the relationship between gravity and Archimedes’ force that are used in shipping. However, huge river and sea vessels made of steel, the density of which is almost 8 times greater than the density of water, float on the water. This is explained by the fact that only a relatively thin hull of the vessel is made of steel, and most of its volume is occupied by air. The average density of the ship turns out to be significantly less than the density of water; therefore, it not only does not sink, but can also accept a large amount of cargo for transportation. Vessels that navigate 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 fastenings that give ships strength are also made of metals. To build ships, different materials are used, which have both higher and lower density compared to water. The weight of water displaced by the underwater part of the vessel is equal to the weight of the vessel with the cargo in the air or the force of gravity acting on the vessel with the 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 force (buoyancy) acting on the ball be greater than the force of gravity.

5. Conducting the experiment

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

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

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

The water is clean;

Water saturated with salt;

Sunflower oil.

First, I lowered the raw egg into clean water - the egg sank - “sank 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 less the force of gravity.

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

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

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

First, I measured my body weight using a scale. 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 immersed myself in the water, I was completely submerged (except for my head). Next, using a centimeter tape, I marked the distance from the top edge of the bath to the water level ℓ 1, and then when immersed in water ℓ 2. After that, using a pre-graduated three-liter jar, I began to pour water into the bath from level ℓ 1 to level ℓ 2 - this is how I measured the volume of water I displaced (Appendix 5). I calculated the density using the formula:

The force of gravity acting on a body in the air was calculated using the formula: , where is the acceleration of gravity ≈ 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 it drowns 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 buoyant force is greater.

Conclusion

In the process of working on this topic, we learned a lot of new and interesting things. The range of our knowledge has increased not only in the field of action of Archimedes’ power, but also in its application in life. Before starting work, we had a far from detailed idea about it. During the experiments, we experimentally confirmed the validity of Archimedes' law and found out that the buoyancy force depends on the volume of the body and the density of the liquid; the higher the density of the liquid, the greater the Archimedean force. The resulting force, which determines the behavior of a body in a liquid, depends on the mass, volume of the body and the density of the liquid.

In addition to the experiments performed, additional literature was studied about the discovery of Archimedes' force, about the floating 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. We just need to look a little more carefully at the world around us, be a little more independent in our judgments, and discoveries will not keep you waiting. The reluctance of most people to explore the world around them leaves a lot of scope for the curious in the most unexpected places.

Bibliography

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

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

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

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

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

Annex 1

Appendix 2

Appendix 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 for a liquid the situation is different. 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 on the part of the fluid per unit area $S$.

$ρ = \frac(\Delta P)(\Delta S)$.

Note 1

Pressure is measured in pascals. One Pa is equal to a force of 1 N acting per unit area of ​​1 square. 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 a liquid produced by external forces is transmitted by the liquid equally in all directions.

In mechanical equilibrium, the horizontal fluid pressure is always the same; therefore, the free surface of a static liquid 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 medium under consideration does not depend on pressure.

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

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

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

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

Formulation of Archimedes' law

Archimedes' law, one of the basic laws of hydrostatics and aerostatics, states: a body immersed in a liquid or gas is acted upon by 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.

Note 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; in this case the body is pushed out of the medium.

Hence the second name for this phenomenon - 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 Archimedean force is due to the difference in environmental pressure at different depths. For example, the pressure on the lower layers of water is always greater than on the upper layers.

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

The emergence of Archimedes' Force

Let's imagine any liquid medium, for example, ordinary water. Let us mentally select an arbitrary volume of water by a closed surface $S$. Since all liquid is in mechanical equilibrium, the volume we have allocated is also static. This means that the resultant and moment of external forces acting on this limited volume take 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 $S$. 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 limited by the surface $S$. In order for the total moment of external forces to vanish, the resultant $F$ must be directed upward and pass through the center of mass of the selected volume of liquid.

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

Note 3

If a body immersed in a liquid is in mechanical equilibrium, then the buoyant force of hydrostatic pressure acts on it from the environment surrounding it, which is 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 Archimedes’ law, the buoyancy force holds:

$F_A = ρgV$, where:

• $V_A$ - buoyancy force, H;
• $ρ$ - density of liquid or gas, $kg/m^3$;
• $V$ - volume of a 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 gravity moduli $F_T$ and the Archimedean force $F_A$. There are three possible cases here:

1. $F_T$ > $F_A$. The force of gravity exceeds the buoyant force, therefore the body sinks/falls;
2. $F_T$ = $F_A$. The force of gravity is equalized with the buoyant force, so the body “hangs” in the liquid;
3. $F_T$

ARCHIMEDES' LAW– the law of statics of liquids and gases, according to which a body immersed in a liquid (or gas) is acted upon by a buoyant force equal to the weight of the liquid in the volume of the body.

The fact that a certain force acts on a body immersed in water is well known to everyone: heavy bodies seem to become lighter - for example, our own body when immersed in a bath. When swimming in a river or in the sea, you can easily lift and move very heavy stones along the bottom - ones that we cannot lift on land; the same phenomenon is observed when, for some reason, a whale is washed up on the shore - the animal cannot move outside the aquatic environment - its weight exceeds the capabilities of its muscular system. At the same time, lightweight bodies resist immersion in water: sinking a ball the size of a small watermelon requires both strength and dexterity; It will most likely not be possible to immerse a ball with a diameter of half a meter. It is intuitively clear that the answer to the question - why a body floats (and another sinks) is closely related to the effect of the liquid on the body immersed in it; one cannot be satisfied with the answer that light bodies float and heavy ones sink: a steel plate, of course, will sink in water, but if you make a box out of it, then it can float; however, her weight did not change. To understand the nature of the force acting on a submerged body from the side of a liquid, it is enough to consider a simple example (Fig. 1).

Cube with an edge a immersed in water, and both the water and the cube are motionless. It is known that the pressure in a heavy liquid increases in proportion to depth - it is obvious that a higher column of liquid presses more strongly on the base. It is much less obvious (or not at all obvious) that this pressure acts not only downwards, but also sideways and upwards with the same intensity - this is Pascal's law.

If we consider the forces acting on the cube (Fig. 1), then due to the obvious symmetry, the forces acting on the opposite side faces are equal and oppositely directed - they try to compress the cube, but cannot affect its balance or movement. The forces remaining are acting on the upper and lower faces. Let h– depth of immersion of the upper face, r– fluid density, g– acceleration of gravity; then the pressure on the upper face is equal to

r· g · h = p 1

and on the bottom

r· g(h+a)= p 2

The pressure force is equal to the pressure multiplied by the area, i.e.

F 1 = p 1 · a\up122, F 2 = p 2 · a\up122 , where a– cube edge,

and strength F 1 is directed downwards and the force F 2 – up. Thus, the action of the liquid on the cube is reduced to two forces - F 1 and F 2 and is determined by their difference, which is the buoyancy force:

F 2 – F 1 =r· g· ( h+a)a\up122 – r gha· a 2 = pga 2

The force is buoyant, since the lower edge is naturally located below the upper one and the force acting upward is greater than the force acting downward. Magnitude F 2 – F 1 = pga 3 is equal to the volume of the body (cube) a 3 multiplied by the weight of one cubic centimeter of liquid (if we take 1 cm as a unit of length). In other words, the buoyant force, which is often called the Archimedean force, is equal to the weight of the liquid in the volume of the body and is directed upward. This law was established by the ancient Greek scientist Archimedes, one of the greatest scientists on Earth.

If a body of arbitrary shape (Fig. 2) occupies a volume inside the liquid V, then the effect of a liquid on a body is completely determined by the pressure distributed over the surface of the body, and we note that this pressure is completely independent of the material of the body - (“the liquid doesn’t care what to press on”).

To determine the resulting pressure force on the surface of the body, you need to mentally remove from the volume V given body and fill (mentally) this volume with the same liquid. On the one hand, there is a vessel with a liquid at rest, on the other hand, inside the volume V– a body consisting of a given liquid, and this body is in equilibrium under the influence of its own weight (the liquid is heavy) and the pressure of the liquid on the surface of the volume V. Since the weight of liquid in the volume of a body is equal to pgV and is balanced by the resultant pressure forces, then its value is equal to the weight of the liquid in the volume V, i.e. pgV.

Having mentally made the reverse replacement - placing it in volume V given body and noting that this replacement will not affect the distribution of pressure forces on the surface of the volume V, we can conclude: a body immersed in a heavy liquid at rest is acted upon by an upward force (Archimedean force), equal to the weight of the liquid in the volume of the given body.

Similarly, it can be shown that if a body is partially immersed in a liquid, then the Archimedean force is equal to the weight of the liquid in the volume of the immersed part of the body. If in this case the Archimedean force is equal to the weight, then the body floats on the surface of the liquid. Obviously, if, during complete immersion, the Archimedean force is less than the weight of the body, then it will drown. Archimedes introduced the concept of "specific gravity" g, i.e. weight per unit volume of a substance: g = pg; if we assume that for water g= 1, then a solid body of matter for which g> 1 will drown, and when g < 1 будет плавать на поверхности; при g= 1 a body can float (hover) inside a liquid. In conclusion, we note that Archimedes' law describes the behavior of balloons in the air (at rest at low speeds).

Vladimir Kuznetsov

One of the first physical laws studied by high school students. Any adult remembers at least approximately this law, no matter how far he is from physics. But sometimes it is useful to return to the exact definitions and formulations - and understand the details of this law that may have been forgotten.

What does Archimedes' law say?

There is a legend that the ancient Greek scientist discovered his famous law while taking a bath. Having plunged into a container filled to the brim with water, Archimedes noticed that the water splashed out - and experienced an epiphany, 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:

• plunging into 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 upward, so any object or body, finding itself in a liquid at rest, experiences pushing;
• in this case, the buoyancy force is exactly equal to the coefficient that is obtained if the product of the volume of the object and the density of the liquid is multiplied by the acceleration of free fall.

So, Archimedes established that a body immersed in a liquid displaces a volume of liquid that is equal to the volume of the body itself. If only part of a body is immersed in a 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 principle 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 a little more simply - the force that pushes an object out of a liquid or gas is exactly equal to the weight of the liquid or gas displaced by this object during immersion.

The law is written in the form of the following formula:

What is the significance of Archimedes' law?

The pattern discovered by the ancient Greek scientist 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 pushing 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 Archimedes' law and numerous consequences from it - they are built so that they can float on the surface of the water, and do not sink. Aeronautics operate on a similar principle - they use the buoyancy of air, becoming, as it were, lighter in the process of flight.

Liquids and gases, according to which any body immersed in a liquid (or gas) is acted upon by this liquid (or gas) by a buoyant force equal to the weight of the liquid (gas) displaced by the body and directed vertically upward.

This law was discovered by the ancient Greek scientist Archimedes in the 3rd century. BC e. Archimedes described his research in his treatise “On Floating Bodies,” which is considered one of his last scientific works.

Below are the conclusions drawn from Archimedes' law.

The action of liquid and gas on a body immersed in them.

If you immerse a ball filled with air in water and release it, it will float up. The same thing will happen with a piece of wood, with a cork and many other bodies. What force makes them float?

A body immersed in water is affected by water pressure forces from all sides (Fig. A). At every point of the body these forces are directed perpendicular to its surface. If all these forces were equal, the body would experience only all-round compression. But at different depths the hydrostatic pressure is different: it increases with increasing depth. Therefore, the pressure forces applied to the lower parts of the body are greater than the pressure forces acting on the body from above.

If we replace all the pressure forces applied to a body immersed in water by one (resultant or resultant) force that has the same effect on the body as all these individual forces together, then the resultant force will be directed upward. This is what makes the body float. This force is called buoyant force, or Archimedean force (named after Archimedes, who first pointed out its existence and established what it depends on). On the image b it is designated as F A.

The Archimedean (buoyant) force acts on a body not only in water, but also in any other liquid, since in any liquid there is hydrostatic pressure, different at different depths. This force also acts in gases, which is why balloons and airships fly.

Thanks to the buoyant force, the weight of any body located in water (or any other liquid) turns out to be less than in air, and in air less than in airless space. This can be easily verified by weighing a weight using a training spring dynamometer, first in the air, and then lowering it into a vessel with water.

A decrease in weight also occurs when a body is transferred from a vacuum to air (or some other gas).

If the weight of a body in a vacuum (for example, in a vessel from which air has been pumped out) is equal to P0, then its weight in the air is:

,

Where F´A- Archimedean force acting on a given body in the air. For most bodies this force is negligible and can be neglected, i.e. we can assume that P air =P 0 =mg.

The weight of a body in liquid decreases much more than in air. If the body's weight is in the air P air =P 0, then the weight of the body in the liquid is equal to P liquid = P 0 - F A. Here F A- Archimedean force acting in a liquid. It follows that

Therefore, in order to find the Archimedean force acting on a body in any liquid, you need to weigh this body in air and in liquid. The difference between the obtained values ​​will be the Archimedean (buoyant) force.

In other words, taking into account formula (1.32), we can say:

The buoyant force acting on a body immersed in a liquid is equal to the weight of the liquid displaced by this body.

The Archimedean force can also be determined theoretically. To do this, assume that a body immersed in a liquid consists of the same liquid in which it is immersed. We have the right to assume this, since the pressure forces acting on a body immersed in a liquid do not depend on the substance from which it is made. Then the Archimedean force applied to such a body F A will be balanced by the downward force of gravity mandg(Where m- mass of liquid in the volume of a given body):

But gravity is equal to the weight of the displaced fluid R. Thus.

Considering that the mass of a liquid is equal to the product of its density ρ on volume, formula (1.33) can be written as:

Where Vand— volume of displaced liquid. This volume is equal to the volume of that part of the body that is immersed in the liquid. If the body is completely immersed in liquid, then it coincides with the volume V of the whole body; if the body is partially immersed in liquid, then the volume Vand the displaced liquid is less than the volume V bodies (Fig. 1.39).

Formula (1.33) is also valid for the Archimedean force acting in a gas. Only in this case should the density of the gas and the volume of the displaced gas, and not the liquid, be substituted into it.

Taking into account the above, Archimedes' law can be formulated as follows:

Any body immersed in a liquid (or gas) at rest is acted upon by a buoyant force from this liquid (or gas) equal to the product of the density of the liquid (or gas), the acceleration of gravity and the volume of that part of the body that is immersed in the liquid ( or gas).