Why can we lie on the surface of the sea without sinking to the bottom? Why do heavy ships float on the surface of the water?
There is probably some kind of force that pushes people and boats, that is, all bodies out of the water and allows them to float on the surface.
The dependence of pressure in a liquid or gas on the depth of immersion of a body leads to the appearance of a buoyancy force, or otherwise the Archimedes force, acting on any body immersed in a liquid or gas. Let's take a closer look at the Archimedes force using an example.
We all launched boats through puddles. What's a boat without a captain? What did we observe? The ship sinks deeper under the weight of the captain. What if we placed five or eight captains on our boat? Our boat sank to the bottom.
What can we learn useful from this experience? When the weight of the boat increased, we saw that the boat sank lower into the water. That is, the body weight increased the pressure on the water, but the buoyancy force remained the same.
When the weight of the body exceeded the magnitude of the buoyancy force, the boat, under the influence of this force, sank to the bottom. That is, there is a buoyancy force that is the same for a particular body, but different for different bodies.
The buoyant force, also known as the Archimedes force, acting on a body immersed in a liquid is equal to the weight of the liquid displaced by this body.
A brick, as everyone knows, will sink to the bottom in any case, but a wooden door will not only float on the surface, but can also hold a couple of passengers. This power is called Archimedean force and is expressed by the formula:
Fout = g*m f = g* ρ f * V f = P f,
where m is the mass of the liquid,
and Pf is the weight of the fluid displaced by the body.
And since our mass is equal to: m f = ρ f * V f, then from the formula 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 vector quantity. The reason for the existence of the buoyant force is the difference in pressure on the upper and lower parts of the body. The pressure indicated in the figure is P 2 > P 1 due to the greater depth. For the Archimedes force to arise, it is enough that the body is at least partially immersed in the liquid.
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 gravitational force of the entire body. If the body density more density liquid, then the body sinks, if less, then it floats.
A body immersed in a liquid loses exactly as much weight as the water it displaces. Therefore, it is natural to assume that if body weight less weight water of the same volume, then it will float on the surface, and if it is more, it will sink.
If the weight of the body and the water is equal, then the body can swim remarkably well in the water, as all aquatic inhabitants do. The density of organisms living in water is almost no different from the density of water, so they don’t need strong skeletons!
Fish regulate their diving depth by changing the average density of their body. To do this, they only need to change the volume of the swim bladder by contracting or relaxing the muscles.
Off the coast of Egypt, there is an amazing fagak fish. The approach of danger forces the fagak to quickly swallow water. At the same time, rapid decomposition of food products occurs in the fish esophagus with the release of significant amount gases Gases fill not only the active cavity of the esophagus, but also the blind outgrowth attached to it. As a result, the phagak's body swells greatly, and, in accordance with Archimedes' law, it quickly floats to the surface of the reservoir. Here he swims, hanging upside down, until the gases released in his body disappear. After this, gravity lowers it to the bottom of the reservoir, where it takes refuge among the bottom algae.
Archimedes' law is the law of statics of liquids and gases, according to which a buoyant force acts on a body immersed in a liquid (or gas), equal to weight fluids in the body volume.
Background
"Eureka!" (“Found!”) - this is the exclamation, according to legend, made by the ancient Greek scientist and philosopher Archimedes, who discovered the principle of repression. Legend has it that the Syracusan king Heron II asked the thinker to determine whether his crown was made of pure gold without harming the royal crown itself. It was not difficult to weigh the crown of Archimedes, but this was not enough - it was necessary to determine the volume of the crown in order to calculate the density of the metal from which it was cast and determine whether it was pure gold. Then, according to legend, Archimedes, preoccupied with thoughts about how to determine the volume of the crown, plunged into the bath - and suddenly noticed that the water level in the bath had risen. And then the scientist realized that the volume of his body displaced an equal volume of water, therefore, the crown, if lowered into a basin filled to the brim, would displace a volume of water equal to its volume. A solution to the problem was found and, according to the most common version of the legend, the scientist ran to report his victory to the royal palace, without even bothering to get dressed.
However, what is true is true: it was Archimedes who discovered the principle of buoyancy. If a solid body is immersed in a liquid, it will displace a volume of liquid equal to the volume of the part of the body immersed in the liquid. The pressure that previously acted on the displaced liquid will now act on the solid body that displaced it. And, if the buoyant force acting vertically upward turns out to be more power gravity pulling the body vertically downwards, the body will float up; otherwise it will sink (drown). Speaking modern language, the body floats if it average density less density the liquid in which it is immersed.
Archimedes' Law and Molecular Kinetic Theory
In a fluid at rest, pressure is produced by the impacts of moving molecules. When a certain volume of liquid is displaced solid body, the upward impulse of the collisions of molecules will fall not on the liquid molecules displaced by the body, but on the body itself, which explains the pressure exerted on it from below and pushing it towards the surface of the liquid. If the body is completely immersed in the liquid, the buoyant force will continue to act on it, since the pressure increases with increasing depth, and the lower part of the body is subjected to more pressure than the upper, which is where the buoyant force arises. This is the explanation of buoyant force at the molecular level.
This pushing pattern explains why a ship made of steel, which is much denser than water, remains afloat. The fact is that the volume of water displaced by a ship is equal to the volume of steel submerged in water plus the volume of air contained inside the ship's hull below the waterline. If we average the density of the hull shell and the air inside it, it turns out that the density of the ship (as physical body) is less than the density of water, therefore the buoyant force acting on it as a result of upward impulses of impact of water molecules is higher gravitational force the gravity of the Earth pulling the ship to the bottom - and the ship floats.
Formulation and explanations
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 sea, you can easily lift and move very heavy stones along the bottom - ones that cannot be lifted on land. 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.
Existence hydrostatic pressure leads to the fact that any body located in a liquid or gas is subject to a buoyant force. Archimedes was the first to determine the value of this force in liquids experimentally. Archimedes' law is formulated as follows: a body immersed in a liquid or gas is subject to a buoyancy force equal to the weight of the amount of liquid or gas that is displaced by the immersed part of the body.
Formula
The Archimedes force acting on a body immersed in a liquid can be calculated by the formula: F A = ρ f gV Fri,
where ρl is the density of the liquid,
g – free fall acceleration,
Vpt is the volume of the body part immersed in the liquid.
The behavior of a body located in a liquid or gas depends on the relationship between the modules of gravity Ft and the Archimedean force FA, which act on this body. The following three cases are possible:
1) Ft > FA – the body sinks;
2) Ft = FA – the body floats in liquid or gas;
3) Ft< FA – тело всплывает до тех пор, пока не начнет плавать.
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 turns out to be washed up on the shore - out aquatic environment the animal cannot move - 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 opposite side faces, equal and opposite directions - they try to compress the cube, but cannot influence its balance or movement. There remain forces 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 bottom edge, naturally, is located below the top 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 times the weight of one cubic centimeter 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 the body free form(Fig. 2) occupies 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 full immersion Archimedes' force will be less than the weight of the body, then it will drown. Archimedes introduced the concept " 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
