We know that any body in a fluid is subject to two forces directed in opposite directions: the force of gravity and the Archimedean force. The force of gravity is equal to the weight of the body and is directed downwards, while the Archimedean force depends on the density of the liquid and is directed upwards. How physics explains the floating of bodies, and what are the conditions for floating bodies on the surface and in the water column?

Bodies floating condition

According to the law of Archimedes, the condition for the floating of bodies is as follows: if the force of gravity is equal to the Archimedean force, then the body can be in equilibrium anywhere in the liquid, that is, float in its thickness. If gravity is less than the Archimedean force, then the body will rise from the liquid, that is, float. In the case when the weight of the body is greater than the Archimedean force pushing it out, the body will sink to the bottom, that is, sink. The buoyant force depends on the density of the liquid. But whether the body will float or sink depends on the density of the body, since its density will increase its weight. If the density of the body is higher than the density of water, then the body will sink. How to be in such a case?

The density of a dry tree due to cavities filled with air is less than the density of water and the tree can float on the surface. But iron and many other substances are much denser than water. How is it possible to build ships of metal and transport various cargoes by water in this case? And for this man came up with a little trick. The hull of a ship that is submerged in water is made voluminous, and inside this ship has large cavities filled with air, which greatly reduce the overall density of the ship. The volume of water displaced by the ship is thus greatly increased, increasing its pushing force, and the total density of the ship is made less than the density of water, so that the ship can float on the surface. Therefore, each ship has a certain limit on the mass of cargo that it can take away. This is called the ship's displacement.

Distinguish empty displacement is the mass of the ship itself, and total displacement- this is the empty displacement plus the total mass of the crew, all equipment, supplies, fuel and cargo, which this vessel can normally take away without the risk of drowning in relatively calm weather.

The density of the body in organisms inhabiting the aquatic environment is close to the density of water. Thanks to this, they can be in the water column and swim thanks to the devices given to them by nature - flippers, fins, etc. Plays an important role in the movement of fish special body - swim bladder. The fish can change the volume of this bubble and the amount of air in it, due to which its total density can change, and the fish can swim at different depths without experiencing inconvenience.

Density human body slightly more dense than water. However, a person, when he has a certain amount of air in his lungs, can also calmly float on the surface of the water. If, for the sake of experiment, while in the water, you exhale all the air from your lungs, you will slowly begin to sink to the bottom. Therefore, always remember that swimming is not scary, it is dangerous to swallow water and let it into your lungs, which is the most common cause of tragedies on the water.

Swimming is the ability of a body to stay on the surface of a liquid or at a certain level within a liquid.

We know that any body in a fluid is subject to two forces directed in opposite directions: the force of gravity and the Archimedean force.

The force of gravity is equal to the weight of the body and is directed downwards, while the Archimedean force depends on the density of the liquid and is directed upwards. How does physics explain the floating of bodies, and what are the conditions for floating bodies on the surface and in the water column?

Archimedean force is expressed by the formula:

Fvyt \u003d g * m well \u003d g * ρ well * V well \u003d P well,

where m w is the mass of the liquid,

and P W is the weight of the fluid displaced by the body.

And since our mass is equal to: m W = ρ W * V W, then from the formula of the Archimedean force we see that it does not depend on the density of the immersed body, but only on the volume and density of the fluid displaced by the body.

Archimedean force is a vector quantity. The reason for the existence of the buoyancy force is the difference in pressure on the upper and lower part body. The pressure shown in the figure is P 2 > P 1 due to the greater depth. For the emergence of the Archimedes force, it is enough that the body is immersed in a liquid, at least partially.

So, if a body floats on the surface of a liquid, then the buoyant force acting on the part of this body immersed in the liquid is equal to the gravity of the entire body. (Fa = P)

If gravity is less than the Archimedean force (Fa > P), then the body will rise from the liquid, that is, float.

In the case when the weight of the body is greater than the Archimedean force pushing it out (Fa

From the ratio obtained, important conclusions can be drawn:

The buoyant force depends on the density of the liquid. Whether a body will sink or float in a liquid depends on the density of the body.

A body floats completely immersed in a liquid if the density of the body is equal to the density of the liquid

The body floats, partially protruding above the surface of the liquid, if the density of the body is less than the density of the liquid

- if the density of the body is greater than the density of the liquid, swimming is impossible.

Fishermen's boats are made of dry wood, the density of which is less than that of water.

Why do ships float?

The hull of a ship that is submerged in water is made voluminous, and inside this ship has large cavities filled with air, which greatly reduce the overall density of the ship. The volume of water displaced by the ship is thus greatly increased, increasing its pushing force, and the total density of the ship is made less than the density of water, so that the ship can float on the surface. Therefore, each ship has a certain limit on the mass of cargo that it can take away. This is called the ship's displacement.

Lesson type: study

Used technologies: Traditional, group, innovative.

The purpose of the lesson: Find out the conditions for floating bodies depending on the density of the liquid and the body, assimilate them at the level of understanding and application, using the logic of scientific knowledge.

Tasks:

1. establish theoretically and experimentally the relationship between the density of the body and the liquid, necessary to ensure the conditions for the floating of bodies;
2. continue to form the ability of students to conduct experiments and draw conclusions from them;
3. development of skills to observe, analyze, compare, generalize;
4. fostering interest in the subject;
5. education of culture in the organization of educational work.

Expected results:

Know: Sailing conditions tel.

Be able to: Experimentally find out the conditions for floating bodies.

Equipment: Multimedia, screen, individual task cards, density table, test materials.

During the classes

Activation of knowledge:

Teacher:

– In previous lessons, we considered the effect of liquid and gas on a body immersed in them, studied the law of Archimedes, the conditions for floating bodies. We will learn the topic of today's lesson by solving a crossword puzzle.

Horizontally: 1. Division unit. 2. Unit of mass. 3. Multiple unit of mass. 4. Unit of area. 5. Unit of time. 6. Unit of force. 7. Unit of volume. 8. Unit of length.

Answers: 1. Pascal. 2. Kilogram. 3. Ton. 4. Square meter. 5. Hour. 6. Newton. 7. Liter. 8. Meter.

(The topic of the lesson is written in a notebook)

Teacher: But now, before proceeding with the solution of experimental problems, we will answer a few questions. What force is generated when a body is immersed in a liquid?

Students: Archimedean strength.

Teacher: Where is this force directed?

Students: It is directed vertically upwards.

Teacher: What does the Archimedean force depend on?

Students: Archimedean force depends on the volume of the body and on the density of the liquid.

Teacher: And if the body is not completely immersed in a liquid, then how is the Archimedean force determined?

Students: Then, to calculate the Archimedean force, it is necessary to use the formula F A = ​​ρ x gV, where V is the volume of that part of the body that is immersed in the liquid.

Teacher: How can one determine the Archimedean force experimentally?

Students: You can weigh the liquid displaced by the body, and its weight will be equal to the Archimedean force. You can find the difference in the readings of the dynamometer when weighing a body in air and in a liquid, this difference is also equal to the Archimedean force. You can determine the volume of the body using a ruler or beaker. Knowing the density of the liquid, the volume of the body, you can calculate the Archimedean force.

Teacher: So, we know that any body immersed in a liquid is affected by the Archimedean force. And also, what force acts on any body immersed in a liquid?

Students: Gravity.

Teacher: Can you give examples of bodies that float on the surface of water? What bodies sink in water? How else can a body behave in water? What are these bodies? Try to guess which floating body we are talking about now.

Over the sea today
Great heat;
And floats in the sea
Ice mountain.
Floating and probably
Considers:
She won't melt in the heat either.

Students: Iceberg.

Teacher: Would anything change if we instantly changed the water in the ocean to kerosene?

(Students get confused)

You cannot accurately answer this question. But you already have ideas, hypotheses. Let's solve the problem together today in the lesson: Find out: What are the conditions for floating bodies in a liquid.

Solving research problems:

Write the topic of the lesson in your notebook – "Conditions for floating bodies".

Teacher: Guys, do you know which scientist studied the swimming of bodies?

Students: Archimedes.

Teacher: Let's try to check all the information about the conditions of floating of bodies experimentally by doing research. We have already done this when studying the force of friction. Each group will receive their own assignment. After completing the tasks, we will discuss the results obtained and find out the conditions for the floating of bodies.

Record all results in a notebook. Raise your hand if you have any questions.

(Children receive cards with tasks and equipment for their implementation – 7 options. Task options are not the same in terms of difficulty: the first ones are the simplest, 6 and 7 are more difficult. They are given according to the level of training.)

Tasks:

Task for group 1:

1. Observe which of the proposed bodies sink and which float in the water.
2. Find the density of the corresponding substances in the textbook table and compare with the density of water.
3. Present the results in the form of a table.

Equipment: a vessel with water and a set of bodies: a steel nail, a porcelain roller, pieces of lead, a pine bar.

Equipment: a vessel with water and a set of bodies: pieces of aluminum, organic glass, foam plastic, cork, paraffin.

Task for group 2:

1. Compare the depth of immersion in water of wooden and foam cubes of the same size.
2. Find out if the depth of immersion of a wooden cube in liquids of different densities differs. Show the result of the experiment in the figure.

Equipment: two vessels (with water and oil), wooden and foam cubes.

Task for group 3:

1. Compare the Archimedean force acting on each of the tubes with the force of gravity on each tube.
2. Draw conclusions based on the results of the experiments.

Equipment: a beaker, a dynamometer, two test tubes with sand (test tubes with sand should float in water, immersed to different depths).

Task for group 4:

1. "Can you 'make' a potato float in water? Make the potato float in the water.
2. Explain the results of the experiment. Arrange them in the form of drawings.

Equipment: a vessel with water, a test tube with table salt, a spoon, a medium-sized potato.

Task group 5:

1. Get the piece of plasticine to float in the water.
2. Get the piece of foil to float in the water.
3. Explain the results of the experiment.

Equipment: a vessel with water; a piece of plasticine and a piece of foil.

Teacher: We talked about the condition of floating solids in a liquid. Can one liquid float on top of another?

Task group 6: Observation of an oil slick rising up due to the buoyancy of water.

Objective: To observe the ascent of oil immersed in water, to discover by experiment the buoyant effect of water, to indicate the direction of the buoyant force.

Equipment: vessels with oil, water, pipette.

The sequence of the experiment:

1. Take a few drops of oil with a pipette.
2. Lower the pipette to a depth of 3-4 cm into a glass of water.
3. Release the oil and observe the formation of an oil stain on the surface of the water.
4. Make a conclusion based on your experience.

After the experiment, the results of the work are discussed, the results are summed up.

While the students complete the tasks, I observe their work, provide the necessary assistance.

Teacher: We finish the work, move the appliances to the edge of the table. Let's move on to discussing the results. First, let's find out which bodies float in a liquid, and which ones sink. (Group 1)

Students: One of them names those bodies that sink in water, the other - bodies that float, the third compares the densities of the bodies of each group with the density of water. After that, they all draw a conclusion together.

Conclusions:

1. If the density of the substance from which the body is made is greater than the density of the liquid, then the body sinks.
2. If the density of the substance is less than the density of the liquid, then the body floats.

(Conclusions are written in notebooks.)

Teacher: What will happen to the body if the densities of the liquid and the substance are equal?

Students: give an answer.

Let's see how the bodies floating on the surface of the liquid behave. Guys group 2 considered how bodies made of wood and foam behave in the same liquid. What did they notice?

Students: The depth of immersion of bodies is different. The styrofoam floats almost on the surface, and the tree is slightly submerged in water.

Teacher: What can be said about the depth of immersion of a wooden block floating on the surface of water, oil?

Students: In oil, the bar sank deeper than in water.

Conclusion: Thus, the depth of immersion of a body in a liquid depends on the density of the liquid and the body itself.

Let's write this conclusion.

Teacher: Now let's find out whether it is possible to make bodies float that normally sink in water, such as a potato or plasticine or foil. (Group 4; Group 5)

What are you observing?

Students: They drown in water. To make the potato float, we added more salt to the water.

Teacher: What's the matter? What happened?

Students: Salt water has increased density and it has become stronger to push the potato. The density of water has increased and the Archimedean force has become greater.

Teacher: Correctly. And the guys who performed the task with plasticine did not have salt. How did you manage to make plasticine float in water?

Students: We made a boat out of plasticine. It has a larger volume and therefore floats. You can make a box out of plasticine, it also floats. She also has more volume than a piece of plasticine.

Conclusion: So, in order to make normally sinking bodies float, you can change the density of the liquid or the volume of the submerged part of the body. In this case, the Archimedean force acting on the body also changes. Do you think there is any connection between the force of gravity and the Archimedean force for floating bodies?

Teacher:(Group 6) Let's go back to the density table of substances. Explain why an oil film forms on water.

So the problem is solved, so liquids, like solids, are subject to the conditions of floating of bodies.

Let's talk about liquids.

One shallow vessel invited three immiscible liquids of different densities to visit at once and invited them to settle down with all conveniences. How the liquids were located in the hospitable vessel, if they were: engine oil, honey and gasoline.

Specify the order of the liquids.

Students:(Group 3) We submerged two tubes of sand, one lighter and one heavier, into the water, and both of them floated in the water. We have determined that the Archimedean force in both cases is approximately equal to the force of gravity.

Teacher: Well done. So, if the body floats, then F A \u003d F heavy. (write on the board). And if the body sinks in liquid?

Students: Then the force of gravity is greater than the Archimedean force.

Teacher: What if the body floats?

Students: Hence, the Archimedean force is greater than the force of gravity.

Teacher: So, we got the condition of floating bodies. But it is not connected with the density of the body or with the density of the liquid itself. (This dependence was considered by the guys of the 1st group). This means that the conditions of bodies can be formulated in two ways: by comparing the Archimedean force and the force of gravity, or by comparing the densities of the liquid and the substance in it. Where in engineering are these conditions taken into account?

Students: When building ships. They used to make wooden ships and boats. The density of wood is less than the density of water, and the ships floated in the water.

Teacher: Metal ships also float, but pieces of steel sink in water.

Students: They are treated like we did with plasticine: they increase the volume, the Archimedean force becomes greater, and they float. They also make pontoons and submarines.

Teacher: So, in shipbuilding, the fact is used that by changing the volume it is possible to impart buoyancy to almost any body. Is there any way to take into account the connection between the conditions of floating of bodies and the change in the density of the liquid?

Students: Yes, when moving from the sea to the river, the draft depth of ships changes.

Teacher: Give examples of using the conditions of floating of bodies in engineering.

Students: Pontoons are used for river crossings. Submarines float in the seas and oceans. For scuba diving, part of their tank is filled with water, and for surface diving, water is pumped out.

(I show drawings of modern ships.)

Teacher: Look carefully at the nuclear icebreaker. Several such icebreakers operate in our country. They are the most powerful in the world and can sail without entering ports for more than a year. But we will talk more about this in the next lesson.

Board layout: Homework § 48.

Lesson topic: Sailing conditions tel.

Lesson Summary:

We make a conclusion with the guys about the research. Once again, we summarize the conditions for floating bodies using the table presented on the board.

Reflection:

• I enjoyed my lesson today...
• I want to …
• I found out …
• I am myself today...

A body immersed in a liquid, in addition to gravity, is affected by a buoyant force - the Archimedes force. The fluid presses on all faces of the body, but the pressure is not the same. After all, the lower face of the body is immersed in the liquid more than the upper, and the pressure increases with depth. That is, the force acting on the lower face of the body will be greater than the force acting on the upper face. Therefore, a force arises that tries to push the body out of the liquid.

The value of the Archimedean force depends on the density of the liquid and the volume of that part of the body that is directly in the liquid. The Archimedes force acts not only in liquids, but also in gases.

Law of Archimedes: a body immersed in a liquid or gas is subjected to a buoyant force equal to the weight of the liquid or gas in the volume of the body. In order to calculate the Archimedes force, it is necessary to multiply the density of the liquid, the volume of the part of the body immersed in the liquid, and the constant value g.

Two forces act on a body that is inside a liquid: the force of gravity and the force of Archimedes. Under the influence of these forces, the body can move. There are three conditions for floating bodies:

If gravity is greater than the Archimedean force, the body will sink, sink to the bottom.

If gravity is equal to the Archimedes force, then the body can be in equilibrium at any point in the fluid, the body floats inside the fluid.

If the force of gravity is less than the Archimedean force, the body will float, rise up.

Floating bodies on the surface of a liquid

In the surface position, two forces act on the floating body along the OZ axis (Fig. 1.1). This is the force of gravity of the body G and buoyant Archimedean force P z .

swimming, i.e. submerged . The main concepts of the theory of navigation include the following:

- sailing plane(I-I) - the plane of the free surface of the liquid intersecting the body;

- waterline - the line of intersection of the body surface and the swimming plane;

- draft (y)- the depth of immersion of the lowest point of the body. The greatest allowable draft of the vessel is marked on it with a red waterline;

- displacement - the weight of water displaced by the ship. The ship's displacement at full load is its main technical specification;

The center of displacement (point D, Fig. 1.1) is the center of gravity of the displacement through which the line of action of the buoyant Archimedean force passes;

Axis of navigation (О О ") - a line passing through the center of gravity C and the center of displacement D when the body is in balance.

To maintain balance, the melting axis must be vertical. If an external force acts on a floating vessel in the transverse direction, for example, the force of wind pressure, then the vessel will roll, the navigation axis will rotate relative to point C and a torque M k will appear, rotating the vessel relative to the longitudinal axis counterclockwise (Fig. 1.2)

The stability of a floating body depends on the relative position of points C and D. If the center of gravity C is below the center of displacement D, then during surface navigation the body is always stable, since the torque M k that occurs during a roll is always directed in the direction opposite to the roll.

If point C is above point D (Fig. 1.3), then the floating body can be stable and unstable. Let's consider these cases in more detail.

With a roll, the center of displacement D shifts horizontally towards the roll, since one side of the ship displaces a larger volume of water than the other.

Then the line of action of the buoyant Archimedean force P z will pass through the new center of displacement D "and intersect with the navigation axis OO" at the point M, called metacenter. To formulate the stability condition, we denote the segment

M D 1 = b,aCD 1 =∆ , where b - metacentric radius; ∆- eccentricity.

Stability condition: the body is stable if its metacentric radius is greater than the eccentricity, i.e. b > ∆.

Graphical interpretation of the stability condition is shown in fig. 1.3, which shows that in case a) b > ∆ and the resulting torque is directed in the direction opposite to the roll, and in case b) we have: b< ∆ and moment M to rotates the body in the direction of roll, i.e. the body is unstable.

Displacement ship (vessel) - the amount of water displaced by the underwater part of the ship (vessel) hull. The weight of this amount of liquid is equal to the weight of the entire ship, regardless of its size, material and shape.

Distinguish volumetric and massive standard, normal, complete, greatest, empty displacement.

Displacement Waterline(dutch. water line) - the line of contact of a calm water surface with the hull of a floating vessel. Also - in the theory of the ship, an element of the theoretical drawing: a section of the hull by a horizontal plane.

Mass displacement

Standard displacement

Normal displacement

Full displacement

Maximum displacement

Light displacement

Underwater displacement

surface displacement

Stability of floating bodies

Stability floating bodies is called their ability to return to starting position after they were brought out of this position due to the influence of any external forces.

To give a floating body stability, it is necessary that when it deviates from the equilibrium position, a pair of forces is created, which will return the body to its original position. Such a pair of forces can only be created by forces G and P n. There are three possible various options the relative position of these forces (Fig. 5.3).

Rice. 5.3. Stability of semi-submerged bodies with mutual arrangement of the center of gravity and the center of displacement a and b- stable balance

The center of mass is located below the center of displacement.When heeling, the center of displacement moves both due to a change in the position of the body, and due to a change in the shape of the displaced volume. In this case, a couple of forces arise, striving to return the body to its original position. Therefore, the body has positive stability.

The center of mass coincides with the center of displacement- the body will also have positive stability due to the displacement of the center of displacement due to a change in the shape of the displaced volume.

The center of mass is above the center of displacement.Here there are two main options (Fig. 5.4):

1) the point of intersection of the lifting force with the axis of navigation M (metacenter) lies below the center of mass - the balance will be unstable (Fig. 5.4, a);

2) the metacenter lies above the center of mass - the balance will be stable (Fig. 5.4, b). The distance from the metacenter to the center of mass is called metacentric height. Metacenter - the point of intersection of the lift force with the axis of navigation. If point M lies above the point FROM, then the metacentric height is considered positive if it lies below the point FROM- then it is considered negative.

Thus, the following conclusions can be drawn:

the stability of a body in a semi-submerged state depends on the relative position of the points M and FROM(from metacentric height);

the body will be stable if the metacentric height is positive, i.e. the metacenter is located above the center of gravity. Almost all military floating vehicles are built with a metacentric height of 0.3-1.5m.

Rice. 5.4. Stability of semi-submerged bodies with the relative position of the center of gravity and the metacenter:

a- unstable balance; b- stable balance

Displacement ship (vessel) - the amount of water displaced by the underwater part of the ship (vessel) hull. The mass of this amount of liquid is equal to the mass of the entire ship, regardless of its size, material and shape.

Distinguish volumetric and massive displacement. According to the state of the load of the ship, they distinguish standard, normal, complete, greatest, empty displacement.

For submarines, there are underwater displacement and surface displacement.

Displacement

displacement equal to the volume of the underwater part of the ship (vessel) to the waterline.

Mass displacement

displacement equal to the mass of the ship (vessel).

Standard displacement

displacement of a fully equipped ship (vessel) with a crew, but without fuel, lubricants and drinking water in tanks.

Normal displacement

a displacement equal to the standard displacement plus half the fuel, lubricants and potable water in the tanks.

Full displacement

displacement equal to the standard displacement plus full reserves of fuel, lubricants, drinking water in tanks, cargo.

Maximum displacement

displacement equal to standard displacement plus maximum reserves fuel, lubricants, drinking water in tanks, cargo.

Light displacement)

displacement of an empty ship (vessel), that is, a ship (vessel) without a crew, fuel, supplies, etc.

Underwater displacement

displacement of a submarine (batyscaphe) and other underwater vessels in a submerged position. Exceeds the surface displacement by the mass of water taken when immersed in the main ballast tanks.

surface displacement

displacement of a submarine (bathyscaphe) and other underwater vessels in a position on the water surface before immersion or after surfacing.

Swimming bodies- the state of equilibrium of a solid body partially or completely immersed in a liquid (or gas).

The main task of the theory of swimming of bodies is to determine the equilibrium of a body immersed in a liquid, to determine the conditions for the stability of equilibrium. The simplest conditions for floating bodies are indicated by the law of Archimedes. Let's consider these conditions.

As you know, all bodies immersed in a liquid are affected by the Archimedes force F A(extrusive force) directed vertically upwards, however, not all of them emerge. To understand why some bodies float and others sink, it is necessary to take into account one more force acting on all bodies - the force of gravity. Ft which is directed vertically downward, i.e. opposite F A. If the body is left inside the liquid at rest, then it will begin to move in the direction in which the largest of the forces is directed. In this case, the following cases are possible:

1. if the Archimedean force is less than the force of gravity ( F A< F т ), then the body will sink to the bottom, i.e., it will sink (Fig. a);
2. if the Archimedean force is greater than the force of gravity ( F A > F t), then the body will float (Fig. b);

If this force is greater than the force of gravity acting on the body, then the body will take off. Aeronautics is based on this.

Aircraft used in aeronautics are called balloons(from Greek. air- air, status- standing). Unmanaged free-flight balloons with a shell shaped like a ball are called balloons. Not so long ago, huge balloons were used to study the upper layers of the atmosphere (stratosphere) - stratostats. Controlled balloons (having an engine and propellers) are called airships.

The balloon not only rises by itself, but can also lift some cargo: cabins, people, instruments. In order to determine what kind of cargo an air container can lift, its lifting force should be known. The lifting force of a balloon is equal to the difference between the Archimedean force and the force of gravity acting on the balloon:

F \u003d F A - F t.

The lower the density of the gas filling a balloon of a given volume, the lower the force of gravity acting on it and the greater the resulting lifting force. Balloons can be filled with helium, hydrogen or heated air. Although hydrogen has a lower density than helium, helium is still used more often for safety reasons (hydrogen is a combustible gas).

It is much easier to raise and lower a balloon filled with hot air. To do this, a burner is placed under the hole located in the lower part of the ball. It allows you to regulate the air temperature, and hence its density and lift.

You can choose such a temperature of the ball at which the weight of the ball and the cabin will be equal to the buoyant force. Then the ball will hang in the air, and it will be easy to make observations from it.