When preparing a salt solution of a certain density, the housewives immerse a raw egg in it: if the density of the solution is insufficient, the egg sinks, if it is sufficient, it floats. Similarly, determine the density of sugar syrup during conservation. from the material in this paragraph you will learn when a body floats in a liquid or gas, when it floats and when it sinks.

We substantiate the conditions for floating bodies

You can certainly give many examples of the floating of bodies. Ships and boats, wooden toys and balloons float, fish, dolphins and other creatures swim. And what determines the ability of the body to swim?

Let's do an experiment. Let's take a small vessel with water and several balls made of different materials. We will alternately immerse the bodies in water, and then let them go without initial velocity. Further, depending on the density of the body, different options are possible (see table).

Option 1. Dive. The body begins to sink and eventually sinks to the bottom of the vessel. Let's find out why this happens. There are two forces acting on the body:

The body is sinking, which means that the downward force is greater:

a body sinks in a liquid or gas if the density of the body is greater than the density of the liquid or gas.

Option 2. Swimming inside the liquid. The body does not sink and does not float, but remains floating inside the liquid.

Try to prove that in this case the density of the body is equal to the density of the liquid:

a body floats inside a liquid or gas if the density of the body is equal to the density of the liquid or gas.

Option 3. Ascent. The body begins to float and eventually stops on the surface of the liquid, partially immersed in the liquid.

While the body floats, the Archimedean force is greater than the force of gravity:

Stopping the body on the surface of the liquid means that the Archimedean force and the force of gravity are balanced: ^ str = F arch.

a body floats in a liquid or gas or floats on the surface of the liquid if the density of the body is less than the density of the liquid or gas.

We observe the swimming of bodies in wildlife

The bodies of the inhabitants of the seas and rivers contain a lot of water in their composition, so their average density is close to the density of water. In order to move freely in the liquid, they must "control" the average density of their body. Let's give examples.

In fish with a swim bladder, this control occurs due to a change in the volume of the bladder (Fig. 28.1).

The nautilus mollusk (Fig. 28.2), which lives in tropical seas, can quickly float up and again sink to the bottom due to the fact that it can change the volume of internal cavities in the body (the mollusk lives in a shell twisted in a spiral).

The water spider common in Europe (Fig. 28.3) carries with it an air shell on the abdomen with it - it is she who gives him a reserve of buoyancy and helps him return to the surface.

Learning to solve problems

A task. A copper ball weighing 445 g has a cavity with a volume of 450 cm 3 inside. Will this ball float in water?

Analysis of a physical problem. To answer the question of how a ball will behave in water, you need to compare the density of the ball (ball) with the density

in °dy (water).

To calculate the density of a sphere, its volume and mass must be determined. The mass of air in the ball is negligible compared to the mass of copper, so t of the ball = t of copper. The volume of the ball is the volume of the copper shell Y copper and the volume of the cavity V - . The volume of the copper shell can be determined by knowing

mass and density of copper.

We learn about the densities of copper and water from the tables of densities (p. 249).

It is advisable to solve the problem in the presented units.

2. Knowing the volume and mass of the ball, we determine its density:

Analysis of the result: the density of the ball is less than the density of water, so the ball will float on the surface of the water.

Answer: Yes, the ball will float on the surface of the water.

Summing up

The body sinks in a liquid or gas if the density of the body is greater than the density of the liquid or gas (p t > p f) The body floats inside the liquid or gas if the density of the body is equal to the density of the liquid or gas (t = p f). A body floats in a liquid or gas or floats on the surface of the liquid if the density of the body is less than the density of the liquid or gas

test questions

1. Under what condition will the body sink in a liquid or gas? Give examples. 2. What condition must be met for a body to float inside a liquid or gas? Give examples. 3. Formulate the condition under which a body in a liquid or gas floats. Give examples. 4. Under what condition will the body float on the surface of the liquid? 5. Why and how do the inhabitants of the seas and rivers change their density?

Exercise number 28

1. Will a uniform lead bar float in mercury? in water? in sunflower oil?

2. Arrange the balls shown in fig. 1, in order of increasing density.

3. Will a bar with a mass of 120 g and a volume of 150 cm 3 float in water?

4. According to fig. 2 Explain how a submarine dives and resurfaces.

5. The body floats in kerosene, completely immersed in it. Determine the mass of a body if its volume is 250 cm 3.

6. Three liquids were poured into the vessel, which do not mix - mercury, water, kerosene (Fig. 3). Then three balls were lowered into the vessel: steel, foam plastic and oak.

How are the layers of liquids arranged in a vessel? Determine which ball is which. Explain answers.

7. Determine the volume of the part of the amphibious machine submerged in water if the machine is affected by the Archimedean force of 140 kN. What is the mass of the amphibious vehicle?

8. Make up a problem inverse to the problem considered in § 28, and solve it.

9. Establish a correspondence between the density of a body floating in water and the part of this body above the surface of the water.

A r t \u003d 400 kg / m 3 1 0

B r t \u003d 600 kg / m 3 2 ° D

V p t \u003d 900 kg / m 3 3 0, 4

G p t \u003d 1000 kg / m 3 4 0, 6

10. A device for measuring the density of liquids is called a hydrometer. Using additional sources of information, learn about the structure of the hydrometer and the principle of its operation. Write instructions on how to use the hydrometer.

11. Fill in the table. Consider that in each case the body is completely immersed in the liquid.

Experimental task

"Carthusian diver". Make a physics toy inspired by the French scientist René Descartes. Pour water into a plastic jar with a tight-fitting lid and place a small beaker (or small medicine bottle) partly filled with water upside down (see picture). There should be enough water in the beaker so that the beaker protrudes slightly above the surface of the water in the jar. Close the jar tightly and squeeze the sides of the jar. Follow the behavior of the beaker. Explain the operation of this device.

LAB #10

Topic. Determination of sailing conditions tel.

Purpose: to determine experimentally under what condition: the body floats on the surface of the liquid; the body floats inside the liquid; the body sinks into the liquid.

Equipment: a test tube (or a small medicine bottle) with a stopper; thread (or wire) 20-25 cm long; container with dry sand; measuring cylinder half filled with water; scales with weights; paper napkins.

instructions for work

Preparation for the experiment

1. Before starting work, make sure you know the answers to the following questions.

1) What forces act on a body immersed in a liquid?

2) What is the formula for finding the force of gravity?

3) What is the formula for finding the Archimedean force?

4) By what formula is the average density of a body found?

2. Determine the scale interval of the measuring cylinder.

3. Attach the test tube to the thread so that, holding the thread, you can immerse the test tube into the measuring cylinder and then remove it.

4. Remember the rules for working with scales and prepare the scales for work. Experiment

Strictly follow the safety instructions (see flyleaf). Record the measurement results immediately in the table.

Experiment 1. Determination of the condition under which the body sinks in a liquid.

1) Measure the water volume V 1 in the measuring cylinder.

2) Fill the test tube with sand. Close the cork.

3) Lower the tube into the measuring cylinder. As a result, the test tube should be at the bottom of the cylinder.

4) Measure the volume V 2 of water and test tubes; determine the volume of the test tube:

5) Remove the test tube, wipe it with a napkin.

6) Put the test tube on the balance and measure its mass to the nearest 0.5 g. Experiment 2. Determination of the condition under which the body floats inside the liquid.

1) When pouring sand from the test tube, ensure that the test tube floats freely inside the liquid.

Experience 3. Determination of the condition under which the body emerges and floats on the surface of the liquid.

1) Pour some more sand out of the test tube. Make sure that after being fully immersed in the liquid, the tube floats to the surface of the liquid.

2) Repeat the steps described in paragraphs 5-6 of experiment 1.

Processing the results of the experiment

1. For each experience:

1) make a schematic drawing showing the forces acting on the test tube;

2) Calculate the average density of the test tube with sand.

2. Enter the results of the calculations in the table; finish filling it out.

Analysis of the experiment and its results

After analyzing the results, draw a conclusion in which indicate the condition under which: 1) the body sinks in a liquid; 2) the body floats inside the liquid; 3) the body floats on the surface of the liquid.

Creative task

Suggest two ways to determine the average density of an egg. Write down the plan for each experiment.

This is textbook material.

The tearing force of the liquid pressure is counteracted by the resistance force of the wall material M:

М=2σ р δ L,

where σr is the rupture stress of the material, δ is the wall thickness, L is the length of the pipe, 2 is the resistance force acting on both sides.

Provided that the system is in equilibrium, we equate the pressure forces of the liquid, and the resistance of the wall material P x = M we get:

P Ld=2σ р δ L

P δ=2σр δ, hence

P=2σ р δ/ d.

Rice. 3.15. Fluid pressure on the inner walls of the pipe

3.8. Archimedes' law and the conditions for floating bodies

A body completely or partially immersed in a liquid experiences a total pressure from the side of the liquid directed upwards and equal to the weight of the liquid in the volume of the immersed part of the body:

P = ρgWt.

In other words, a buoyant force equal to the weight of the liquid in the volume of this body acts on a body immersed in a liquid. Such a force is called Archimedean force, and its definition is Archimedes' law.

Rice. 3.17. Center of gravity C and center of displacement d of the vessel

For a homogeneous body floating on the surface, the relation is true:

Wzh /Wt = ρm / ρ,

where W t is the volume of the floating body; ρm is the density of the body. The ratio of the density of a floating body and liquid is inversely proportional to the ratio of the volume of the body and the volume of the liquid displaced by it.

In the theory of floating bodies, two concepts are used: buoyancy and stability.

Buoyancy is the ability of a body to float in a semi-submerged state.

Stability - the ability of a floating body to restore its disturbed balance after the removal of external forces (for example, wind or a sharp turn) that cause a roll.

The weight of the liquid, the vessel taken in the volume of the submerged part of the vessel is called displacement, and the point of application of the resultant pressure (i.e. the center of pressure) -

displacement center.

The theory of floating of bodies is based on the law of Archimedes. The center of displacement does not always coincide with the center of gravity of the body C. If it is higher than the center of gravity, then the ship does not capsize. In the normal position of the vessel, the center of gravity C and the center of displacement d lie on the same vertical line O "-O", representing the axis of symmetry of the vessel and called the axis of navigation (Fig. 3.17).

Let, under the influence of external forces, the vessel tilted at a certain angle α, part of the vessel KLM left the liquid, and part K "L" M", on the contrary, sank into it. In this case, we obtain a new position of the center of displacement - d" . We apply a lifting force P to the point d "and continue its line of action until it intersects with the axis of symmetry O"-O". The resulting point m is called metacenter, and the segment mC \u003d h

called metacentric height. We will consider h

positive if the point m lies above the point C , and negative otherwise.

Now let's consider the ship's equilibrium conditions: if h > 0, then the ship returns to its original position; if h = 0, then this is the case

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 parts of the body. The pressure shown in the figure is P 2 > P 1 due to 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.

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. A special organ, the swim bladder, plays an important role in the movement of fish. 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.

The density of the human body is slightly greater than the density of 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.

And gas statics.

Encyclopedic YouTube

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  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. The force is called the power of Archimedes:

  F A = ​​ρ g V , (\displaystyle (F)_(A)=\rho (g)V,)

  where ρ (\displaystyle \rho ) is the density of the liquid (gas), g(\displaystyle(g))- acceleration free fall , and V (\displaystyle V)- the volume of the submerged part of the body (or the part of the volume of the body below the surface). If the body floats on the surface (moves uniformly up or down), then the buoyant force (also called the Archimedean force) is equal in absolute value (and opposite in direction) to the force of gravity acting on the volume of liquid (gas) displaced by the body, and is applied to the center of gravity of this volume.

  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.

  As for a body that is in a gas, for example, in air, to find the lifting force, it is necessary to replace the density of the liquid with the density of the gas. For example, a balloon with helium flies upwards due to the fact that the density of helium is less than the density of air.

  Archimedes' law can be explained using the difference in hydrostatic pressure using the example of a rectangular body.

  P B − P A = ρ g h (\displaystyle P_(B)-P_(A)=\rho gh) F B − F A = ​​ρ g h S = ρ g V , (\displaystyle F_(B)-F_(A)=\rho ghS=\rho gV,)

  where P A , P B- pressure points A and B, ρ - liquid density, h- level difference between points A and B, S is the area of ​​the horizontal cross section of the body, V- the volume of the immersed part of the body.

  In theoretical physics, Archimedes' law is also used in integral form:

  F A = ​​∬ S p d S (\displaystyle (F)_(A)=\iint \limits _(S)(p(dS))),

  where S (\displaystyle S)- surface area, p (\displaystyle p)- pressure at an arbitrary point, integration is performed over the entire surface of the body.

  In the absence of a gravitational field, that is, in a state of weightlessness, Archimedes' law does not work. Astronauts are familiar with this phenomenon quite well. In particular, in weightlessness there is no phenomenon of (natural) convection, therefore, for example, air cooling and ventilation of the living compartments of spacecraft are carried out forcibly, by fans.

  Generalizations

  A certain analogue of Archimedes' law is also valid in any field of forces that act differently on a body and on a liquid (gas), or in an inhomogeneous field. For example, this refers to the field of forces inertia (for example, centrifugal force) - centrifugation is based on this. An example for a field of non-mechanical nature: a diamagnet in vacuum is displaced from a region of a magnetic field of greater intensity to a region of lesser intensity.

  Derivation of the law of Archimedes for a body of arbitrary shape

  Hydrostatic pressure of a liquid at depth h (\displaystyle h) there is p = ρ g h (\displaystyle p=\rho gh). At the same time, we consider ρ (\displaystyle \rho ) liquid and the strength of the gravitational field are constant values, and h (\displaystyle h)- parameter. Let's take an arbitrary-shaped body with a non-zero volume. Let us introduce a right orthonormal coordinate system O x y z (\displaystyle Oxyz), and choose the direction of the z axis coinciding with the direction of the vector g → (\displaystyle (\vec (g))). Zero along the z axis is set on the surface of the liquid. Let us single out an elementary area on the surface of the body d S (\displaystyle dS). It will be acted upon by the fluid pressure force directed inside the body, d F → A = − p d S → (\displaystyle d(\vec (F))_(A)=-pd(\vec (S))). To get the force that will act on the body, we take the integral over the surface:

  F → A = − ∫ S p d S → = − ∫ S ρ g h d S → = − ρ g ∫ S h d S → = ∗ − ρ g ∫ V g r a d (h) d V = ∗ ∗ − ρ g ∫ V e → z d V = − ρ g e → z ∫ V d V = (ρ g V) (− e → z) (\displaystyle (\vec (F))_(A)=-\int \limits _(S)(p \,d(\vec (S)))=-\int \limits _(S)(\rho gh\,d(\vec (S)))=-\rho g\int \limits _(S)( h\,d(\vec (S)))=^(*)-\rho g\int \limits _(V)(grad(h)\,dV)=^(**)-\rho g\int \limits _(V)((\vec (e))_(z)dV)=-\rho g(\vec (e))_(z)\int \limits _(V)(dV)=(\ rho gV)(-(\vec (e))_(z)))

  When passing from the integral over the surface to the integral over the volume, we use the generalized Ostrogradsky-Gauss theorem.

  ∗ h (x, y, z) = z; ∗ ∗ g r a d (h) = ∇ h = e → z (\displaystyle ()^(*)h(x,y,z)=z;\quad ^(**)grad(h)=\nabla h=( \vec (e))_(z))

  We get that the modulus of the Archimedes force is equal to ρ g V (\displaystyle \rho gV), and it is directed in the direction opposite to the direction of the gravitational field strength vector.

  Another wording (where ρ t (\displaystyle \rho _(t))- body density, ρ s (\displaystyle \rho _(s)) is the density of the medium in which it is immersed).