Archimedean power in different liquids. Archimedes Act: opening history and essence phenomenon for dummies
One of the first physical laws studied by high school students. At least about this law remembers any adult man, as if far he was from physics. But sometimes it is useful to return to precise definitions and wording - and understand the details of this law that could be forgotten.
What does Archimedia law mean?
There is a legend that its famous law an ancient Greek scientist opened, taking a bath. Immersed in a container filled with water to the edges, Archimeda noticed that the water splashed out to the outside - and experienced an insight, instantly formulating the essence of the opening.
Most likely, in reality, the case was different, and the discovery was preceded by long observations. But this is not so important, because in any case, Archhymedized managed to open the following pattern:
- immersing any liquid, bodies and objects are experiencing several multidirectional, but directed perpendicular to their surface of the forces;
- the final vector of these forces is directed up, so any object or body, being in the liquid at rest, is experiencing pushing out;
- at the same time, the poverty force is exactly equal to the coefficient, which will turn out if you multiply to accelerate the free fall of the volume of the volume and density of the liquid.
So, Archimedes found that the body immersed in the liquid displaces such a volume of fluid, which is equal to the volume of the body itself. If only part of the body is immersed in the liquid, then it will displace the fluid, the volume of which will be equal to the volume of only the part that is immersed.
The same pattern acts for gases - only here the body volume must be correlated with gas density.
It is possible to formulate a physical law and a little simpler - the force that pushes a certain object from liquid or gas, exactly equal to the weight of the liquid or gas, displaced by this item during immersion.
The law is recorded in the form of the following formula:
What is the meaning of Archimedes?
The pattern, open by ancient Greek scientist, is simple and completely obvious. But at the same time its meaning for everyday life is impossible to overestimate.
It is thanks to the knowledge about pushing the bodies with liquids and gases, we can build river and sea vessels, as well as airships and balloons for aeronautics. Heavy metal ships are not drowning due to the fact that their design takes into account the law of Archimedes and numerous consequences of it - they are built so that they can be kept on the surface of the water, and do not go to the bottom. According to the same principle, aeronautics are used - they use the ejecting air abilities, in the process of the flight becoming easier for it.
The body, immersed in liquid or gas, acts the pushing force equal to the weight of the fluid or gas provided by this body.
In integrated form
Archimedean Power It is always directed oppositely by the power of gravity, so body weight in liquid or gas is always less than the weight of this body in vacuo.
If the body floats on the surface or evenly moves up or down, then the ejecting force (called also archimedean power) It is equal to the module (and opposite in direction) the strength of gravity acting on the liquid-out of the body (gas), and is attached to the center of severity of this volume.
As for the bodies that are in Gaza, for example, in the air, it is necessary to replace the density of the fluid to be replaced by the density of the fluid on the gas density. For example, a ball with helium flies up due to the fact that the density of helium is less than the air density.
In the absence of a gravitational field (the force of gravity), that is, in a state of weightlessness, Archimedes Act does not work. Cosmonauts with this phenomenon are familiar enough. In particular, in weightlessness there is no convection phenomenon (natural movement of air in space), therefore, for example, air cooling and ventilation of residential compartments of spacecraft are forcibly produced, fans
In the formula, we used:
Power of Archimedes
Liquid density
Different objects in fluids behave differently. Some sneak, others remain on the surface and swim. Why this happens, explains the law of Archimedes, open with them with very unusual circumstances and has become the main law of hydrostatics.
How Archimedes opened his law
Legend tells us that Archimeda opened his law by chance. And this discovery was preceded by the following event.
Tsar Siracuz Gieron, Rule in 270-215 G. BC, suspected his jeweler that he mixed up a certain amount of silver into his ordered gold crown. To dispel doubt, he asked Archimedes to confirm or refute his suspicions. As a true scientist, Archimedes got involved in this task. To solve it, it was necessary to determine the weight of the crown. After all, if silver is mixed in it, then its weight would be different from how if it was made of pure gold. The proportion of gold was known. But how to calculate the volume of the crown? After all, it had an irregular geometric shape.
According to the legend, one day Archimedes, taking a bath, reflected on the task that he had to decide. Suddenly, the scientist drew attention to the fact that the water level in the bath became higher after he plunged into her. When he rose, the water level fell. Archimedes noticed that some kind of water displaces his body from the bath. And the volume of this water was equal to the volume of its own body. And then he understood how to solve the task with the crown. It is enough just to immerse it into the vessel filled with water, and measure the volume of displaced water. It is said that he was so glad that with the cry "Eureka!" ("Found!") Jumped out of the bath, not even dressed.
So it was actually or not, no value. Archimedes found a method for measuring the volume of bodies with a complex geometric shape. He first drew attention to the properties of physical bodies, which are called density, comparing them not with each other, but with water weight. But most importantly, they were opened blooming principle .
Archimedes Act
So, Archimedes found that the body immersed in the liquid displaces such a volume of fluid, which is equal to the volume of the body itself. E if the liquid is immersed only part of the body, it will displace the liquid, the volume of which will be equal to the volume of only the part that is immersed.
And the body itself acts on the body itself, which pushes it to the surface. Its value is equal to the weight of the fluid supplanted to them. This force is called force of Archimedes .
For fluid, the law of Archimedes looks like this: on the body, immersed in the liquid, the ejecting force is acting upward, and equal to the weight of the liquid displaced by this body.
The magnitude of the force of the Archimedes is calculated as follows:
F a \u003d. ρ ɡ V. ,
where ρ - liquid density,
ɡ - acceleration of gravity
V. - Volume of immersed in fluid of the body, or part of the body volume below the liquid surface.
The force of Archimedes is always applied to the center of gravity volume and is directed oppositely by the force of gravity.
It should be said that in order to fulfill this law, one condition should be observed: the body either intersects with the boundary of the fluid, or from all sides is surrounded by this liquid. For the body, which lies at the bottom and hermetically concerned him, the Act Archimedes is not valid. So, if we put on the bottom of the cube, one of the faces of which will be tightly in contact with the bottom, the law of Archimedes for him we can not apply.
The power of Archimedes is also called pushing power .
This force is by its nature - the sum of all pressure forces acting on the side of the liquid to the surface of the body submersible in it. Pulling force arises due to the difference in hydrostatic pressure at different levels of fluid.
Consider this force on the example of a body having a cube form or a parallelogram.
P 2 - P 1 \u003d. ρ ɡ h.
F a \u003d f 2 - f 1 \u003d ρɡhs \u003d ρɡhv
The Archimedes Act is valid for gases. But in this case, the pushing force is called the lifting, and for its calculation, the density of the liquid in the formula is replaced by the gas density.
Body swimming condition
From the ratio of the values \u200b\u200bof the gravity and the forces of the Archimedes, it depends whether the body will swim, sink or pop up.
If the force of the archimedes and the strength of gravity are equal in magnitude, the body in the liquid is in a state of equilibrium when it does not pop up and does not immerse. It is said that it floats in a liquid. In this case F T \u003d. F A. .
If the strength of gravity is greater than the forces of Archimedes, the body is immersed, or sink.
Here F t ˃ F a.
And if the value of gravity is less than the force of the Archimedes, the body pops up. This happens when F t ˂ F A. .
But it floats not infinitely, but only until the moment of gravity and the force of the Archimedes are equal. After that, the body will swim.
Why not all bodies are drown
If we put two of the same in the form and sizes of the bar, one of which is made of plastic, and the other from steel, you can see that the steel bar is drowning, and the plastic will remain afloat. It will also be if you take any other items of the same sizes and forms, but different by weight, for example, plastic and metal balls. The metal ball will go to the bottom, and the plastic will swim.
But why do different plastic and steel bars behave? After all, their volumes are the same.
Yes, the volumes are the same, but the bars themselves are made from different materials that have different density. And if the density of the material is higher than the density of water, then the bar is drowning, and if less - it will be overlooked until it turns out to be on the surface of the water. This is fair not only for water, but also for any other liquid.
If you designate body density P T. , and the density of the medium in which it is like P S. , if
P T ˃ PS (body density is higher than liquid density) - the body is sinking,
P T \u003d PS (body density is equal to the density of the liquid) - the body floats in the liquid,
P T ˂ PS (body density is less than liquid density) - the body pops up until it turns out on the surface. After that it floats.
Archimedes Act is not performed and in a state of weightlessness. In this case, there is no gravitational field, and, it means, the acceleration of the free fall.
The property of the body immersed in the liquid remains in equilibrium, not popling and does not droking further, called buoyancy .
Often, scientific discoveries become a consequence of a simple chance. But only people with a prepared mind can appreciate the importance of a simple coincidence and make far-reaching conclusions from it. It is thanks to the chain of random events in physics appeared the law of Archimedes, explaining the behavior of the body in water.
Tradition
In Syracuses about Archimedee, legends were made. Once the ruler of this glorious city doubted the honesty of his jeweler. In the crown made for the ruler, a certain amount of gold was supposed to contain. Check this fact was commissioned Archifed.
Archimedes found that in the air and in water body have different weight, the difference is directly proportional to the density of the measured body. Measuring the weight of the crown in the air and in water, and conducting similar experience with a whole piece of gold, Archimedes proved that in the manufactured crown there was an admixture of lighter metal.
According to legend, Archimeda did this opening in the bath, watching the spilled water. What happened next to a dishonest jeweler, the story is silent, but the conclusion of the Syracuse of the scientist has formed the basis of one of the most important laws of physics, which is known to us as the Act of Archimedes.
Formulation
The results of their experiments Archimedes outlined in labor "On floating bodies", which, unfortunately, has reached our days only in the form of passages. Modern physics Act Archimedes describes how cumulative power acting on the body immersed in liquid. The pushing power of the body in the liquid is directed up; Its absolute value is equal to the weight of the displaced fluid.
The effect of liquids and gases on the immersed body
Any item immersed in liquid is experiencing pressure strength. At each point of the surface of the body, these forces are directed perpendicular to the surface of the body. If these were the same, the body would experience only compression. But pressure forces increase in proportion to depth, so the bottom surface of the body is more compressed than the top. You can consider and fold all the forces acting on the body in water. The final vector of their directions will be directed upward, the body is pushed from the liquid. The magnitude of these forces is determined by the Act of Archimedes. Tel swimming is entirely based on this law and various consequences of it. Archimedean forces act in gases. It is thanks to these forces of the poverty in the sky, airs are flying and balloons: due to air-release, they become easier to air.
Physical formula
Visually, the power of Archimedes can be demonstrated by simple weighing. Weighing the training weight in vacuo, in the air and in the water you can see that its weight is significantly changing. In vacuum weight, weights are alone, in the air - just below, and in water - even lower.
If we take body weight in vacuo for p about, then its weight in the air can be described by such a formula: p B \u003d p o - f A;
here p about - weight in vacuum;
As can be seen from the figure, any action with weighing in water greatly facilitate the body, so in such cases the force of the Archimedes must be taken into account.
For air, this difference is insignificant, therefore, usually the weight of the body immersed in the air medium is described by the standard formula.
The density of the medium and the power of Archimedes
Analyzing the simplest experiments with body weight in various media, it can be concluded that the body weight in various media depends on the mass of the object and the density of the immersion environment. And the more denser the environment, the greater the power of Archimedes. The Archimedes Act ringed this dependence and the density of fluid or gas is reflected in its final formula. What else affects this power? In other words, the ARHIMED Act depends on what characteristic?
Formula
Archimedean strength and strength that affect it can be determined using simple logical conclusions. Suppose that the body of a certain volume immersed in the liquid consists of the same fluid itself, in which it is immersed. This assumption does not contradict any other prerequisites. After all, the forces acting on the body in no way depend on the density of this body. In this case, the body will most likely be in equilibrium, and the poverty force will be compensated by the force of gravity.
Thus, the equilibrium of the body in water will be described so.
But the strength of gravity, from the condition, equal to the weight of the fluid, which it displaces: the mass of the liquid is equal to the product of the density on the volume. Substituting the famous values, you can learn body weight in liquid. This parameter is described in the form ρv * g.
Substituting the known values, we get:
This is the law of Archimedes.
The formula derived by us describes the density as the density of the body under study. But in the initial conditions it was stated that the density of the body is identical to the density of its surrounding fluid. Thus, this formula can safely substitute the fluid density value. Visual observation, according to which, in a more dense medium, the poverty force is greater, received theoretical justification.
Application of the law of Archimedes
The first experiments, demonstrating the law of Archimedes, are known since school bench. The metal plate is sinking in water, but, folded in the form of a box, can not only be kept afloat, but also to carry a certain cargo. This rule is the most important conclusion from the Archimedian rule, it determines the possibility of building river and maritime courts, taking into account their maximum capacity (displacement). After all, the density of sea and fresh water is different and ships, and submarines must take into account the differences of this parameter when entering the mouth of the rivers. Wrong calculation can lead to a catastrophe - the vessel will be stranded, and considerable efforts will be required for its lifting.
The Act of Archimedes is necessary and submariners. The fact is that the density of seawater changes its value depending on the depth of the dive. The correct calculation of the density will allow the submarinations to correctly calculate the air pressure inside the square, which will affect the maneuverability of the diver and will provide its safe immersion and ascent. The Archimedes Act should also be taken into account with deep-sea drilling, huge drilling rigs lose up to 50% of their weight, which makes them transport and exploitation of a less costly event.
The dependence of the pressure in the liquid or gas from the depth of the body immersion leads to the appearance of the pushing force / or otherwise the forces of the Archimedes / acting on any body, immersed in liquid or gas.
Archimedean strength is always directed oppositely by the power of gravity, so body weight in liquid or gas is always less than the weight of this body in vacuo.
The magnitude of the archimedes is determined by the law of Archimedes.
The law is named after an ancient Greek scientist Archimedes living in the 3rd century BC.
The discovery of the basic law of hydrostatics is the largest conquest of antique science. Most likely, you already know the legend about how Archimeda opened his law: "He called him the Syracuse of King Gieron once .... And what happened next? ...
The law of Archimedes, for the first time, was mentioned in the treatise "On floating bodies". Archimedes wrote: "The bodies are heavier than the liquid lowered into this liquid will be descended until they reach the nose itself, and the liquid will be easier to the amount of fluid weight in the amount equal to the volume of the immersion body."
Another formula for the definition of archimedean power:
Interestingly, the force of Archimedes is zero, when the body immersed in the liquid is tight, all the base is pressed to the bottom.
Body weight immersed in liquid (or gas)
Body weight in vacuum Po \u003d Mg..
If the body is immersed in liquid or gas,
that P \u003d Po - FA \u003d RO - PZ
The weight of the body immersed in liquid or gas decreases by the magnitude of the pushing force acting on the body.
Or otherwise:
The body, immersed in liquid or gas, loses in its weight as much as weighs fluid supplied to them.
BOOKSHELF
It turns out
The density of the densities living in water is almost no different from the density of water, so they do not need durable skeletons!
Pisces regulate the depth of dive, changing the average density of its body. To do this, they only need to change the volume of the swimming bubble, reducing or relaxing the muscles.
The shores of Egypt, there is an amazing Fugak fish. The danger approximation makes the Fagak quickly collect water. At the same time, in the fish esophagus there is a rapid decomposition of food with the allocation of a significant amount of gases. Gases are filled not only by the active cavity of the esophagus, but also the blind grown with it. As a result, the Fagak's body is very inflated, and, in accordance with the Archimedes law, it quickly pops up to the surface of the reservoir. Here he floats, hanging up the belly until the gases distinguished in his body will not destroy. After that, the strength of gravity lowers it on the bottom of the reservoir, where it is covered among the bottom algae.
Chile (water walnut) after flowering gives heavy fruits under water. These fruits are so heavy that it may well get into the bottom of the whole plant. However, at this time, a chilim, growing in deep water, a bloating appear on the leaves of leaves, giving it the necessary lifting force, and it does not sink.