On a body, ______ into a liquid or gas ____________ vertically _________________ a force equal to ____________ liquid or gas in _________ of the body (or its immersed part). The force is applied at the point of contact of the object with the support. Theme “Buoyant force. Law of Archimedes. Force is denoted as, measured in Newtons. Body weight may not be equal to gravity. Force types. Balanced forces and resultant.

The calculator was written at the request of the user, which sounded like this: "calculation of the weight of a cylinder in a liquid." The part of the volume remaining under water will be determined by the ratio of densities - if the density of the body is half the density of the liquid, only half of the volume will sink.

Now with weight - the weight will decrease by the value of the Archimedes force. In the absence of a gravitational field, that is, in a state of weightlessness, Archimedes' law does not work. Here, is the Archimedes force, is the density of the liquid, is the free fall acceleration (m/s), is the volume of the displaced liquid. The unit of force is N (newton). The pressure indicated in the figure is due to the greater depth. For the emergence of the Archimedes force, it is enough that the body is at least partially immersed in the liquid.

The law of Archimedes was first mentioned by him in the treatise "On Floating Bodies". As a result, the body of the fagaka swells strongly, and, in accordance with the law of Archimedes, it quickly floats to the surface of the reservoir. After that, gravity lowers it to the bottom of the reservoir, where it takes refuge among the bottom algae. Determine body weight in air and in liquid. Calculate the density of the body in two ways (1st method - by mass and volume, 2nd - by the force of Archimedes).

Physics grade 7, topic 03. Forces around us (13 + 2 hours) Force and dynamometer. The 150-page color hardback textbook was out of print in July 2015 in its fourth edition. It is necessary to know the point of application and the direction of each force. It is important to be able to determine exactly what forces act on the body and in what direction. Below are the main forces acting in nature. It is impossible to invent non-existent forces when solving problems!

Other forces are also mentioned, which will be discussed in other sections. Let's get acquainted with the force of friction. This force arises when bodies move and two surfaces come into contact. The force arises as a result of the fact that the surfaces, when viewed under a microscope, are not smooth as they seem.

This force arises as a result of deformation (changes in the initial state of matter). In all these examples, a force arises that prevents deformation - the elastic force. The elastic force is directed opposite to the deformation. Body weight is the force with which an object acts on a support. You say it's gravity! Gravity is the force that results from interaction with the Earth.

The support reaction force or elastic force arises in response to the impact of an object on a suspension or support, therefore the body weight is always numerically the same as the elastic force, but has the opposite direction. The reaction force of the support and the weight are forces of the same nature, according to Newton's 3rd law they are equal and oppositely directed.

In order to correctly designate the forces, it is necessary to list all the bodies with which the body under study interacts. Determine the type of force, correctly indicate the direction. Attention! The number of forces will coincide with the number of bodies with which the interaction takes place.

What you need to know about strength

This is the fluid pressure force acting on the surface of the body at a certain depth. In this case, the formula can be written as follows: FA = ρghS. Thus emphasizing that we are talking about the power of Archimedes. This is the law of Archimedes. This body is also affected by gravity, which is equal to Fg = mg or Fg = pvg. But, if an object is immersed in a liquid, then the Archimedes force begins to compensate for this gravity.

Archimedes... Who is this person who left a bright mark on science? (There is a portrait of Archimedes on the screen. Archimedes spent the last years of his life in Syracuse. And the scientist, sparing no effort, organized engineering defense. Do not step on my circles! ”Archimedes exclaimed. After Archimedes, a lot of work remained.

Today we have to get acquainted with this problem, make sure that the buoyancy force exists, find out the reasons for its occurrence and derive rules for its calculation. Teacher. That's right, power, she pushed the ball out of the water. This same force pushes your friend's body out of the water when learning to swim, so what shall we call it?

electrical forces

Now think about how to find the magnitude of this force? What do I need to do? Thus, we made sure that all bodies immersed in a liquid are subject to a buoyant force: both those that sink and those that float (photo illustrations are shown on the screen). As the aeronauts say, they are lifted and kept in the air by the gift of nature - the power of Archimedes. Teacher. That's right, therefore, the forces with which the liquid acts on the side surfaces of the bar are equal. They are directed towards each other and compress the bar.

So, under the action of the Archimedean force, the spring contracted, and under the influence of the weight of the displaced water, it returned to its original position. Teacher. We have considered the third way to find the Archimedean force. To find the Archimedes force acting on a body, you need to determine the weight of the fluid that this body displaces.

Support reaction force

Upon completion of task 4). And now let's take a close look at this figure and find out what the strength of Archimedes does not depend on. Teacher (on task 5). A first grader and an eleventh grader dived into the water. Who is affected by the largest buoyant force? Why? One of them says: "Both the water and the earth here are cursed by God."

However, despite the legends, swimming in this sea is very fun and exciting. What happens to the buoyant force acting on the fish when the volume of the swim bladder decreases?

In the air, we neglect the force of Archimedes. The magnitude of the Archimedean force is determined by the law of Archimedes. The Archimedes force is approximately 392 newtons. And in life you will have to meet more than once with the power of Archimedes. Force is a vector quantity. Task 8. How well do you know the power of Archimedes? And if the body is immersed in gas, will the force of Archimedes act on it in this case?

A body immersed in a liquid or gas is subjected to a buoyant force equal to the weight of the liquid or gas displaced by this body.

In integral form

Archimedean force 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.

If a body floats on a surface or moves up or down uniformly, then the buoyant force (also called 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.

As for bodies that are in a gas, for example, in air, to find the lifting force (Archimedes Force), you need 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.

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

In the formula we used:

Strength of Archimedes

Liquid Density

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) displaced by this body. The force is called the power of Archimedes:

where is the density of the liquid (gas), is the acceleration of free fall, and is the volume of the submerged body (or part of the volume of the body below the surface). If the body floats on the surface or 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.

The body floats if the force of Archimedes balances the force of gravity of the body.

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 pressures using the example of a rectangular body.

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.

18. Equilibrium of a body in a fluid at rest

A body immersed (completely or partially) 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 you are t = ρ and gV burial

For a homogeneous body floating on the surface, the relation

Where: V- the volume of the floating body; p m is the density of the body.

The existing theory of a floating body is quite extensive, so we will confine ourselves to considering only the hydraulic essence of this theory.

The ability of a floating body, taken out of equilibrium, to return to this state again is called stability. The weight of the liquid taken in the volume of the submerged part of the ship is called displacement, and the point of application of the resultant pressure (i.e. the center of pressure) - displacement center. In the normal position of the vessel, the center of gravity WITH and displacement center d lie on the same vertical line O"-O", representing the axis of symmetry of the vessel and called the axis of navigation (Fig. 2.5).

Let, under the influence of external forces, the ship tilted at a certain angle α, part of the ship KLM came out of the liquid, and part K"L"M" on the contrary, plunged into it. At the same time, a new position of the center of displacement was obtained d". Apply to a point d" lifting force R and continue its line of action until it intersects with the axis of symmetry O"-O". Received point m called metacenter, and the segment mC = h called metacentric height. We assume h positive if the point m lies above the point C, and negative otherwise.

Rice. 2.5. Vessel transverse profile

Now consider the conditions for the equilibrium of the vessel:

1) if h> 0, then the ship returns to its original position; 2) if h= 0, then this is a case of indifferent equilibrium; 3) if h<0, то это случай неостойчивого равновесия, при котором продолжается дальнейшее опрокидывание судна.

Therefore, the lower the center of gravity and the greater the metacentric height, the greater the stability of the vessel.

It would seem that there is nothing simpler than the law of Archimedes. But once Archimedes himself broke his head over his discovery. How it was?

An interesting story is connected with the discovery of the basic law of hydrostatics.

Interesting facts and legends from the life and death of Archimedes

In addition to such a gigantic breakthrough as the discovery of the actual law of Archimedes, the scientist also has a whole list of merits and achievements. In general, he was a genius who worked in the fields of mechanics, astronomy, and mathematics. He wrote such works as a treatise "on floating bodies", "on a ball and a cylinder", "on spirals", "on conoids and spheroids" and even "on grains of sand". In the latest work, an attempt was made to measure the number of grains of sand needed to fill the universe.

The role of Archimedes in the siege of Syracuse

In 212 BC, Syracuse was besieged by the Romans. The 75-year-old Archimedes designed powerful catapults and short-range light throwing machines, as well as the so-called "Archimedes' claws". With their help, it was possible to literally turn over enemy ships. Faced with such powerful and technological resistance, the Romans could not take the city by storm and were forced to begin a siege. According to another legend, Archimedes, with the help of mirrors, managed to set fire to the Roman fleet by focusing the sun's rays on the ships. The veracity of this legend seems doubtful, because. none of the historians of that time mentions this.

Death of Archimedes

According to many testimonies, Archimedes was killed by the Romans when they did take Syracuse. Here is one of the possible versions of the death of the great engineer.

On the porch of his house, the scientist pondered the diagrams that he drew with his hand right on the sand. A passing soldier stepped on the drawing, and Archimedes, immersed in thought, shouted: "Get away from my drawings." In response to this, a soldier hurrying somewhere simply pierced the old man with a sword.

Well, now about the sore point: about the law and the power of Archimedes ...

How was the law of Archimedes discovered and the origin of the famous "Eureka!"

Antiquity. Third century BC. Sicily, where there is still no mafia, but there are ancient Greeks.

Inventor, engineer and theoretical scientist from Syracuse (Greek colony in Sicily) Archimedes served under King Hieron II. Once jewelers made a golden crown for the king. The king, as a suspicious person, called the scientist to him and instructed him to find out if the crown contained silver impurities. Here it must be said that at that distant time no one solved such issues and the case was unprecedented.

Archimedes thought for a long time, did not come up with anything, and one day decided to go to the bathhouse. There, sitting in a bowl of water, the scientist found a solution to the problem. Archimedes drew attention to a completely obvious thing: the body, plunging into water, displaces a volume of water equal to its own volume of the body. Just then, without even bothering to get dressed, Archimedes jumped out of the bath and shouted his famous "Eureka", which means "found." Appearing to the king, Archimedes asked to give him ingots of silver and gold, equal in weight to the crown. By measuring and comparing the volume of water forced out by the crown and the ingots, Archimedes discovered that the crown was not made of pure gold, but had silver impurities. This is the story of the discovery of the law of Archimedes.

The essence of the law of Archimedes

If you are asking yourself how to understand Archimedes' principle, we will answer. Just sit down, think, and understanding will come. In fact, this law says:

A body immersed in a gas or liquid is acted upon by a buoyant force equal to the weight of the liquid (gas) in the volume of the immersed part of the body. This force is called the Archimedes force.

As you can see, the Archimedes force acts not only on bodies immersed in water, but also on bodies in the atmosphere. The force that makes the balloon rise up is the same force of Archimedes. The Archimedean force is calculated using the formula:

Here the first term is the density of the liquid (gas), the second is the acceleration of free fall, the third is the volume of the body. If the force of gravity is equal to the force of Archimedes, the body floats, if it is greater, it sinks, and if it is less, it floats until it starts to float.

In this article, we examined the law of Archimedes for dummies. If you want to know how to solve problems where there is Archimedes' law, please contact. The best authors will gladly share their knowledge and break down the solution to the most difficult task “on the shelves”.

And gas statics.

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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).