Hooke's law. Formula

The life processes of all organisms living on our planet are based on chemical reactions.

In mammals, oxygen is certainly involved in these reactions, which enters the body through the lungs from the surrounding gaseous environment.

What is the function of respiration?

It is customary to distinguish three of its most essential elements.

The first is external respiration - the entry of atmospheric air into the lungs and gas exchange between the blood flowing to the lungs and the air filling the pulmonary alveoli.

The second is the transport of oxygen captured by the blood in the lungs to various tissues of the body and the removal of excess carbon dioxide through the lungs.

The third is cellular respiration, during which biological oxidation is carried out organic matter: proteins, fats and carbohydrates; oxygen is consumed and carbon dioxide, water and other metabolic products are formed.

The basis of the structure of the lungs is made up of air tubes - the bronchi and the alveoli directly adjacent to them - thin-walled microscopic bubbles. The structure of the lungs is such that large bronchi consistently branch into smaller and smaller ones, the smallest bronchioles lose their cartilaginous tissue, their walls become thin, hemispherical protrusions appear on them, and the bronchioles turn into alveolar passages ending in alveoli.

The final branching of the bronchus - the bronchiole with a group of alveoli adjacent to it - is called Lobule: pulmonary lobule. Each alveolus is surrounded by a network of capillaries. Gas exchange in the lungs is carried out as a result of the diffusion process, since the walls of the alveoli and capillaries are semi-permeable membranes, that is, partitions that allow molecules of only certain substances to pass through.

In this regard, gas exchange depends on the size of the area through which the diffusion of gases takes place, and the difference in the partial pressures of the diffusing gases: oxygen and carbon dioxide.

What is this area? The surface of the alveoli of the lungs during inhalation reaches 90-100 m2, during exhalation it decreases to 25-30 m2.

What are the oxygen and carbon dioxide pressure gradients between blood and alveolar air? The partial pressure of oxygen in the blood flowing to the lungs is on average 60 mm Hg. Art., and in the alveolar air - 100-105 mm Hg, the oxygen gradient is 40-45 mm Hg.

The partial pressure of carbon dioxide in the blood is 47 mm Hg. Art., and in the alveolar air - 40 mm Hg. Art. The carbon dioxide gradient is 7 mm Hg.

One liter of air contains 210 cm3 of oxygen. In a state of relative rest, about six liters of air pass through the lungs of an adult per minute. The tissues consume about 300 cm3 of oxygen per minute. It must be taken into account that the exhaled air contains an average of 16% oxygen, that is, from the air entering the lungs, the body uses only 25% oxygen.

In highly qualified athletes, when performing intensive muscular work, oxygen consumption increases to 5-6 liters. Pulmonary ventilation also accordingly increases to 100-120 liters per minute.

If a person were to breathe water in which oxygen would be dissolved under normal pressure (in optimal conditions a liter of water contains 10 cm3 of oxygen), then for a normal supply of oxygen to the body at rest, it would be necessary to supply 126 liters of water per minute to the lungs. And when doing hard work up to 2100 liters!

Increasing oxygen and removing carbon dioxide

However, such a large amount of breathing fluid may not be needed if the content of dissolved oxygen in it is significantly increased. This is what scientists do, whose work is described in the article by D.A. Kilstra.

In the case of using liquid for breathing, much greater difficulties arise due to the need to remove carbon dioxide from the blood. It is known that even a slight increase in the content of carbon dioxide in the blood leads to profound violations of the physiological state.

What to do? The oxygen gradient can be increased artificially. Carbon dioxide gradient - 7 mm Hg. Art.- is determined by "internal" reasons, and there is no way to change it. Of course, you can not pass through light alkaline liquids, greedily absorbing carbon dioxide!

It is necessary to look for such substances, to develop such chemical composition liquid, which would not be toxic and at the same time had a high ability to bind carbon dioxide.

More recently, a group of physiologists has specifically considered physical conditions in which the lungs are ventilated. They concluded that, given the surface tension of the alveoli, the resistance to breathing must be so great that it's a miracle how we breathe.

It turned out that in the lung tissue is produced Chemical substance called surfactan. It in the form of a thin monomolecular film covers the inner surface of the alveoli. Possessing small surface tension, surfactan prevents the alveoli from sticking together.

The close contact of the walls of the alveoli with the capillaries ensures the diffusion of gases in the lungs.

Interestingly, Miguel Servet, who described the pulmonary circulation in 1546, and the English physician William Harvey, who discovered the systemic circulation in 1628, did not know about the existence of capillaries. They could not see them, since they used only the "naked" eye in the studies.

They only guessed that the circulatory system is closed - the veins somehow communicate with the arteries. At the same time, Harvey mistakenly assumed that the connection between the arterial system and the venous system is due to the porous structure of the tissues themselves.

Malpighi opens the capillaries

In 1661, Marcello Malpighi discovered the capillaries. It is noteworthy that the object of his study were light frogs, that is, the tissue richest in capillaries.

This is how Malpighi described his discovery: “Slightly noticeable, but quite numerous traces of blood appeared before my eyes ...

Looking at them with a magnifying glass, I saw not just scattered spots, but vessels connected like rings.

These vessels, branching off on one side from the vein, and on the other side from the artery, do not penetrate the tissue in a straight line, but twist, forming a whole network in the space between the veins and arteries.

It is also significant that Malpighi understood the significance of his discovery. He rightfully asserted: “I was lucky to see such that I, perhaps, not without reason, can now repeat the saying of Homer: “I see with my eyes a great creation.” Later, Malpighi and his students, naturally, had a desire to discover capillaries in the body of warm-blooded animals, but they did not succeed.

Now this seems amazing. After all, as soon as they point the microscope lens at their own nail bed, they could see the capillaries. Apparently, the imperfection of research methods did not allow this.

Surprising but true! The discovery of capillaries in warm-blooded animals was made only 110 years after Malpighi's research by his compatriot Lazzaro Spallanzani, a physiologist. The object of his research was a chicken embryo, he observed the capillaries connecting the umbilical arteries and veins.

Refutation of dogma

Dogmatic science, referring to the authority of Aristotle, and then Galen, has argued for many centuries that the function of breathing is associated only with thermoregulation. The movement of the lungs and the flow of air into them are necessary for cooling the body. At the same time, the very movement of the lungs was given paramount importance.

The famous English naturalist and architect Robert Hooke experimentally refuted this dogma. He opened the dog's chest, inserted a tube connected to bellows into the trachea, and made small holes in the lungs.

Then he began to evenly pass fresh air through the lungs, keeping the lungs motionless. At the same time, the animal kept alive. Based on this experiment, Hooke came to the conclusion that only fresh air is needed for the function of breathing.

Subsequently, he conducted an experiment, which once again confirmed the correctness of this conclusion. This time, the remarkable scientist's subjects were members of the royal society. To everyone who wanted this, Guk offered to breathe air from the bag, while the exhaled air entered the bag again, there was no influx of fresh air.

The venerable academicians after 20-30 breaths stopped testing, as they felt a "lack" of air.

The chemical composition of the air was unknown in those years. This did not allow R. Hooke to make a correct conclusion about the role of air in respiration.

Anti-overload effect

As is known, the idea that it is expedient to immerse cosmonauts in a liquid during the period of exposure to large overloads was first expressed by K. E. Tsiolkovsky at the end of the last century.

So, for example, in the famous story "On the Moon", describing the flight of astronauts to the Moon, Tsiolkovsky places them in special tanks with liquid.

True, they breathed air through special tubes. But interestingly, Tsiolkovsky understood that filling the lungs with air would reduce the anti-G effect of immersion in liquid.

The fact is that the lungs filled with air, on the one hand, and such tissue structures as, for example, bones, on the other, due to the large difference in their specific density, will shift during the action of accelerations. This will lead to a certain tension of the tissues and to their damage.

This point of view was further confirmed by the experiments of researchers, both Soviet and foreign. About the experiments of Italian physiologists, in particular, the author of the article D. A. Kilstra reports.

Doctor of Medical Sciences V. Malkin

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How to understand the complex laws of physics. 100 simple and exciting experiences for children and their parents Dmitriev Alexander Stanislavovich

73 Force in centimeters, or Clearly Hooke's law

Force in centimeters, or Clearly Hooke's law

For experience we need: balloon, marker.

Hooke's law is passed at school. There lived such a famous scientist who studied the compressibility of objects and substances and deduced his own law. This law is very simple: the more we stretch or compress an object, the more its dimensions change. Or scientifically: the change in the length of an object is directly proportional to the tension or compression force applied to it.

It is clear that different objects are compressed and stretched in different ways. Rubber stretches easily, but marble or brick almost does not shrink, burst.

Is it possible to somehow visually "see" the operation of Hooke's law? I will give a very simple experiment in which we can immediately see how a force acts on an object.

Take an ordinary balloon and inflate it. On the surface, draw a cage with a felt-tip pen. (I tried to draw with a ballpoint pen, and the ball burst, pretty much frightening me.) It turned out like in the photo.

A ball with a painted cage.

Deflated balloon with a slogan.

Now let's "deflate" the balloon, and we get a rubber rag with a small cage painted on it. Even the inscription is visible on the photo - "Physics is interesting!".

The ball is stretched - the cell is deformed. "Hookometer" in action.

If we now stretch the ball, applying a stretching force to it, we will see how our cell changes its dimensions, deforms. It is clearly seen that where the force is applied, the geometric dimensions of the ball change there. You can stretch the ball in different directions stronger or weaker, and our drawn coordinate system will immediately show where and how the force is applied! You can take an ordinary ruler and measure the dimensions of the cell in centimeters, and then - how much these dimensions have changed, the applied force changes exactly to the same extent. We got a device from a balloon, let's call it a "gookometer". A device for demonstrating Hooke's law "live"!

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The law of proportionality of the lengthening of a spring to the applied force was discovered by the English physicist Robert Hooke (1635-1703).

Scientific interests Hooke's ideas were so broad that he often did not have time to complete his research. This gave rise to the most acute disputes about the priority in the discovery of certain laws with leading scientists (Huygens, Newton, etc.). However, Hooke's law has been so convincingly substantiated by numerous experiments that Hooke's priority here has never been disputed.

Robert Hooke's spring theory:

This is Hooke's Law!


PROBLEM SOLVING

Determine the stiffness of the spring, which, under the action of a force of 10 N, lengthened by 5 cm.

Given:
g = 10 H/kg
F=10H
X=5cm=0.05m
Find:
k = ?

The load is in balance.

Answer: spring stiffness k = 200H/m.


TASK FOR "5"

(we hand over on a piece of paper).

Explain why it is safe for an acrobat to jump onto a trampoline net from a great height? (we call on the help of Robert Hooke)
Looking forward to an answer!


LITTLE EXPERIENCE

Place the rubber tube vertically, on which the metal ring is first tightly put on, and stretch the tube. What will happen to the ring?



Dynamics - Cool physics

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Hooke's law is formulated as follows: the elastic force that occurs when a body is deformed due to the application of external forces is proportional to its elongation. Deformation, in turn, is a change in the interatomic or intermolecular distance of a substance under the action of external forces. The elastic force is the force that tends to return these atoms or molecules to a state of equilibrium.


Formula 1 - Hooke's Law.

F - Force of elasticity.

k - rigidity of the body (Proportionality factor, which depends on the material of the body and its shape).

x - Deformation of the body (lengthening or compression of the body).

This law was discovered by Robert Hooke in 1660. He conducted an experiment which consisted in the fact that. A thin steel string was fixed at one end, and a different force was applied to the other end. Simply put, the string was suspended from the ceiling, and a load of various masses was applied to it.

Figure 1 - Stretching of a string under the action of gravity.

As a result of the experiment, Hooke found out that in small aisles, the dependence of the stretching of the body is linear with respect to the force of elasticity. That is, when a unit of force is applied, the body lengthens by one unit of length.

Figure 2 - Graph of the dependence of the elastic force on the elongation of the body.

Zero on the graph is the original length of the body. Everything on the right is an increase in body length. The force of elasticity in this case has a negative value. That is, she strives to return the body to its original state. Accordingly, it is directed opposite to the deforming force. Everything on the left is body compression. The force of elasticity is positive.

The stretching of the string of envy is not only from an external force, but also from the section of the string. A thin string will still somehow stretch from a small weight. But if you take a string of the same length, but let's say 1 m in diameter, it's hard to imagine how much weight it will take to stretch it.

To assess how a force acts on a body of a certain section, the concept of normal mechanical stress is introduced.

Formula 2 - normal mechanical stress.

S-Cross-sectional area.

This stress is ultimately proportional to the relative elongation of the body. Relative elongation is the ratio of the increment in the length of the body to its total length. And the coefficient of proportionality is called Young's modulus. Module because the value of body elongation is taken modulo, without taking into account the sign. It is not taken into account whether the body is shortened or lengthened. It is important to change its length.

Formula 3 - Young's modulus.

|e|- Relative elongation of the body.

s is the normal tension of the body.

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