The most important phenomenon constantly studied by physicists is motion. Electromagnetic phenomena, laws of mechanics, thermodynamic and quantum processes - all this is a wide range of fragments of the universe studied by physics. And all these processes come down, one way or another, to one thing - to.
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Everything in the universe moves. Gravity is a familiar phenomenon for all people since childhood, we were born in the gravitational field of our planet, this physical phenomenon is perceived by us at the deepest intuitive level and, it would seem, does not even require study.
But, alas, the question is why and How do all bodies attract each other?, remains to this day not fully disclosed, although it has been studied up and down.
In this article, we will consider what Newton's universal attraction is - the classical theory of gravity. However, before moving on to formulas and examples, let's talk about the essence of the problem of attraction and give it a definition.
Perhaps the study of gravity was the beginning of natural philosophy (the science of understanding the essence of things), perhaps natural philosophy gave rise to the question of the essence of gravity, but, one way or another, the question of gravity of bodies interested in ancient Greece.
Movement was understood as the essence of the sensual characteristics of the body, or rather, the body moved while the observer sees it. If we cannot measure, weigh, feel a phenomenon, does this mean that this phenomenon does not exist? Naturally, it doesn't. And since Aristotle understood this, reflections on the essence of gravity began.
As it turned out today, after many tens of centuries, gravity is the basis not only of the earth's attraction and the attraction of our planet to, but also the basis of the origin of the Universe and almost all existing elementary particles.
Movement task
Let's do a thought experiment. Take a small ball in your left hand. Let's take the same one on the right. Let's release the right ball, and it will start to fall down. The left one remains in the hand, it is still motionless.
Let's mentally stop the passage of time. The falling right ball "hangs" in the air, the left one still remains in the hand. The right ball is endowed with the “energy” of movement, the left one is not. But what is the deep, meaningful difference between them?
Where, in what part of the falling ball is it written that it must move? It has the same mass, the same volume. It has the same atoms, and they are no different from the atoms of a ball at rest. Ball has? Yes, this is the correct answer, but how does the ball know that it has potential energy, where is it fixed in it?
This is the task set by Aristotle, Newton and Albert Einstein. And all three brilliant thinkers partly solved this problem for themselves, but today there are a number of issues that need to be resolved.
Newtonian gravity
In 1666, the greatest English physicist and mechanic I. Newton discovered a law capable of quantitatively calculating the force due to which all matter in the universe tends to each other. This phenomenon is called universal gravitation. When asked: "Formulate the law of universal gravitation", your answer should sound like this:
The force of gravitational interaction, which contributes to the attraction of two bodies, is in direct proportion to the masses of these bodies and inversely proportional to the distance between them.
Important! Newton's law of attraction uses the term "distance". This term should be understood not as the distance between the surfaces of bodies, but as the distance between their centers of gravity. For example, if two balls with radii r1 and r2 lie on top of each other, then the distance between their surfaces is zero, but there is an attractive force. The point is that the distance between their centers r1+r2 is nonzero. On a cosmic scale, this refinement is not important, but for a satellite in orbit, this distance is equal to the height above the surface plus the radius of our planet. The distance between the Earth and the Moon is also measured as the distance between their centers, not their surfaces.
For the law of gravity, the formula is as follows:
,
- F is the force of attraction,
- - masses,
- r - distance,
- G is the gravitational constant, equal to 6.67 10−11 m³ / (kg s²).
What is weight, if we have just considered the force of attraction?
Force is a vector quantity, but in the law of universal gravitation it is traditionally written as a scalar. In a vector picture, the law will look like this:
.
But this does not mean that the force is inversely proportional to the cube of the distance between the centers. The ratio should be understood as a unit vector directed from one center to another:
.
Law of gravitational interaction
Weight and gravity
Having considered the law of gravity, one can understand that there is nothing surprising in the fact that we personally we feel the attraction of the sun is much weaker than the earth's. The massive Sun, although it has a large mass, is very far from us. also far from the Sun, but it is attracted to it, as it has a large mass. How to find the force of attraction of two bodies, namely, how to calculate the gravitational force of the Sun, the Earth and you and me - we will deal with this issue a little later.
As far as we know, the force of gravity is:
where m is our mass, and g is the free fall acceleration of the Earth (9.81 m/s 2).
Important! There are no two, three, ten kinds of forces of attraction. Gravity is the only force that quantifies attraction. Weight (P = mg) and gravitational force are one and the same.
If m is our mass, M is the mass of the globe, R is its radius, then the gravitational force acting on us is:
Thus, since F = mg:
.
The masses m cancel out, leaving the expression for the free fall acceleration:
As you can see, the acceleration of free fall is indeed a constant value, since its formula includes constant values - the radius, the mass of the Earth and the gravitational constant. Substituting the values of these constants, we will make sure that the acceleration of free fall is equal to 9.81 m / s 2.
At different latitudes, the radius of the planet is somewhat different, since the Earth is still not a perfect sphere. Because of this, the acceleration of free fall at different points on the globe is different.
Let's return to the attraction of the Earth and the Sun. Let's try to prove by example that the globe attracts us stronger than the Sun.
For convenience, let's take the mass of a person: m = 100 kg. Then:
- The distance between a person and the globe is equal to the radius of the planet: R = 6.4∙10 6 m.
- The mass of the Earth is: M ≈ 6∙10 24 kg.
- The mass of the Sun is: Mc ≈ 2∙10 30 kg.
- Distance between our planet and the Sun (between the Sun and man): r=15∙10 10 m.
Gravitational attraction between man and the Earth:
This result is fairly obvious from a simpler expression for the weight (P = mg).
The force of gravitational attraction between man and the Sun:
As you can see, our planet attracts us almost 2000 times stronger.
How to find the force of attraction between the Earth and the Sun? In the following way:
Now we see that the Sun pulls on our planet more than a billion billion times stronger than the planet pulls you and me.
first cosmic speed
After Isaac Newton discovered the law of universal gravitation, he became interested in how fast a body should be thrown so that it, having overcome the gravitational field, left the globe forever.
True, he imagined it a little differently, in his understanding there was not a vertically standing rocket directed into the sky, but a body that horizontally makes a jump from the top of a mountain. It was a logical illustration, since at the top of the mountain, the force of gravity is slightly less.
So, at the top of Everest, the acceleration of gravity will not be the usual 9.8 m / s 2, but almost m / s 2. It is for this reason that there is so rarefied, the air particles are no longer as attached to gravity as those that "fell" to the surface.
Let's try to find out what cosmic speed is.
The first cosmic velocity v1 is the velocity at which the body leaves the surface of the Earth (or another planet) and enters a circular orbit.
Let's try to find out the numerical value of this quantity for our planet.
Let's write Newton's second law for a body that revolves around the planet in a circular orbit:
,
where h is the height of the body above the surface, R is the radius of the Earth.
In orbit, centrifugal acceleration acts on the body, thus:
.
The masses are reduced, we get:
,
This speed is called the first cosmic speed:
As you can see, the space velocity is absolutely independent of the mass of the body. Thus, any object accelerated to a speed of 7.9 km / s will leave our planet and enter its orbit.
first cosmic speed
Second space velocity
However, even having accelerated the body to the first cosmic speed, we will not be able to completely break its gravitational connection with the Earth. For this, the second cosmic velocity is needed. Upon reaching this speed, the body leaves the gravitational field of the planet and all possible closed orbits.
Important! By mistake, it is often believed that in order to get to the moon, astronauts had to reach the second cosmic velocity, because they first had to "disconnect" from the gravitational field of the planet. This is not so: the Earth-Moon pair are in the Earth's gravitational field. Their common center of gravity is inside the globe.
In order to find this speed, we set the problem a little differently. Suppose a body flies from infinity to a planet. Question: what speed will be achieved on the surface upon landing (without taking into account the atmosphere, of course)? It is this speed and it will take the body to leave the planet.
The law of universal gravitation. Physics Grade 9
The law of universal gravitation.
Conclusion
We have learned that although gravity is the main force in the universe, many of the reasons for this phenomenon are still a mystery. We learned what Newton's universal gravitational force is, learned how to calculate it for various bodies, and also studied some useful consequences that follow from such a phenomenon as the universal law of gravitation.
Gravity is the most powerful force in the Universe, one of the four fundamental foundations of the universe, which determines its structure. Once, thanks to her, planets, stars and entire galaxies arose. Today, it keeps the Earth in orbit in its never-ending journey around the Sun.
Attraction is of great importance for everyday life of a person. Thanks to this invisible force, the oceans of our world pulsate, rivers flow, raindrops fall to the ground. Since childhood, we feel the weight of our body and surrounding objects. The influence of gravity on our economic activity is also enormous.
The first theory of gravity was created by Isaac Newton at the end of the 17th century. His law of universal gravitation describes this interaction within the framework of classical mechanics. This phenomenon was described more widely by Einstein in his general theory of relativity, which was published at the beginning of the last century. The processes occurring with the force of gravity at the level of elementary particles should be explained by the quantum theory of gravity, but it has yet to be created.
Today we know much more about the nature of gravity than in Newton's time, but despite centuries of study, it still remains a real stumbling block in modern physics. There are many white spots in the existing theory of gravity, and we still do not understand exactly what generates it, and how this interaction is transferred. And, of course, we are very far from being able to control the force of gravity, so that antigravity or levitation will exist only on the pages of science fiction novels for a long time to come.
What fell on Newton's head?
People have thought about the nature of the force that attracts objects to the earth at all times, but it was only in the 17th century that Isaac Newton managed to lift the veil of secrecy. The basis for his breakthrough was laid by the works of Kepler and Galileo, brilliant scientists who studied the movements of celestial bodies.
A century and a half before Newton's Law of universal gravitation, the Polish astronomer Copernicus believed that attraction is "... nothing more than a natural desire that the father of the Universe bestowed on all particles, namely, to unite into one common whole, forming spherical bodies." Descartes, on the other hand, considered attraction to be the result of perturbations in the world ether. The Greek philosopher and scientist Aristotle was sure that mass affects the speed of falling bodies. And only Galileo Galilei at the end of the 16th century proved that this is not true: if there is no air resistance, all objects accelerate equally.
Contrary to the popular legend about the head and the apple, Newton went to understand the nature of gravity for more than twenty years. His law of gravity is one of the most significant scientific discoveries of all time. It is universal and allows you to calculate the trajectories of celestial bodies and accurately describes the behavior of objects around us. The classical theory of gravitation laid the foundations of celestial mechanics. Newton's three laws gave scientists the opportunity to discover new planets literally "on the tip of a pen", in the end, thanks to them, a person was able to overcome the earth's gravity and fly into space. They brought a strict scientific basis under the philosophical concept of the material unity of the universe, in which all natural phenomena are interconnected and controlled by common physical rules.
Newton not only published a formula that allows you to calculate what the force that attracts bodies to each other is, he created a holistic model, which also included mathematical analysis. These theoretical conclusions have been repeatedly confirmed in practice, including with the help of the most modern methods.
In Newtonian theory, any material object generates an attraction field, which is called gravitational. Moreover, the force is proportional to the mass of both bodies and inversely proportional to the distance between them:
F = (G m1 m2)/r2
G is the gravitational constant, which is equal to 6.67 × 10−11 m³ / (kg s²). Henry Cavendish was the first to calculate it in 1798.
In everyday life and applied disciplines, the force with which the earth pulls on a body is spoken of as its weight. The attraction between any two material objects in the universe is what gravity is in simple terms.
The force of attraction is the weakest of the four fundamental interactions of physics, but due to its features, it is able to regulate the movement of star systems and galaxies:
- Attraction works at any distance, this is the main difference between gravity and strong and weak nuclear interaction. With increasing distance, its effect decreases, but it never becomes equal to zero, so we can say that even two atoms located at different ends of the galaxy exert mutual influence. It's just very small;
- Gravity is universal. The field of attraction is inherent in any material body. Scientists have not yet discovered an object on our planet or in space that would not participate in this type of interaction, so the role of gravity in the life of the Universe is enormous. This gravitation differs from the electromagnetic interaction, the influence of which on space processes is minimal, since in nature most bodies are electrically neutral. Gravitational forces cannot be limited or shielded;
- Gravity acts not only on matter, but also on energy. For him, the chemical composition of objects does not matter, only their mass plays a role.
Using the Newtonian formula, the force of attraction can be easily calculated. For example, gravity on the Moon is several times less than on Earth, because our satellite has a relatively small mass. But it is enough for the formation of regular tides in the World Ocean. On Earth, the free fall acceleration is about 9.81 m/s2. Moreover, at the poles it is somewhat larger than at the equator.
Despite their great importance for the further development of science, Newton's laws had a number of weaknesses that haunted researchers. It was not clear how gravity works through absolutely empty space over vast distances, and at an incomprehensible speed. In addition, data gradually began to accumulate that contradicted Newton's laws: for example, the gravitational paradox or the shift of Mercury's perihelion. It became obvious that the theory of universal gravitation needs to be improved. This honor fell to the brilliant German physicist Albert Einstein.
Attraction and relativity
Newton's refusal to discuss the nature of gravity ("I make no hypotheses") was an obvious weakness in his concept. Not surprisingly, many theories of gravity emerged in the years that followed.
Most of them belonged to the so-called hydrodynamic models, which tried to justify the emergence of gravity by the mechanical interaction of material objects with some intermediate substance that has certain properties. Researchers called it differently: "vacuum", "ether", "flow of gravitons", etc. In this case, the force of attraction between bodies arose as a result of a change in this substance, when it was absorbed by objects or screened flows. In reality, all such theories had one serious drawback: quite accurately predicting the dependence of the gravitational force on distance, they should have led to the deceleration of bodies that moved relative to the “ether” or “graviton flow”.
Einstein approached this issue from a different angle. In his general theory of relativity (GR), gravity is seen not as an interaction of forces, but as a property of space-time itself. Any object that has mass causes it to bend, which causes attraction. In this case, gravity is a geometric effect, which is considered within the framework of non-Euclidean geometry.
Simply put, the space-time continuum affects matter, causing its movement. And that, in turn, affects the space, “indicating” to it how to bend.
The forces of attraction also act in the microcosm, but at the level of elementary particles their influence, in comparison with the electrostatic interaction, is negligible. Physicists believe that the gravitational interaction was not inferior to the rest in the first moments (10 -43 seconds) after the Big Bang.
At present, the concept of gravity, proposed in the general theory of relativity, is the main working hypothesis accepted by the majority of the scientific community and confirmed by the results of numerous experiments.
Einstein in his work foresaw the amazing effects of gravitational forces, most of which have already been confirmed. For example, the ability of massive bodies to bend light rays and even slow down the passage of time. The latter phenomenon is necessarily taken into account in the operation of global satellite navigation systems such as GLONASS and GPS, otherwise after a few days their error would be tens of kilometers.
In addition, a consequence of Einstein's theory are the so-called subtle effects of gravity, such as the gravimagnetic field and drag of inertial frames of reference (aka the Lense-Thirring effect). These manifestations of gravity are so weak that for a long time they could not be detected. Only in 2005, thanks to NASA's unique Gravity Probe B mission, the Lense-Thirring effect was confirmed.
Gravitational radiation or the most fundamental discovery of recent years
Gravitational waves are fluctuations in the geometric space-time structure that propagate at the speed of light. The existence of this phenomenon was also predicted by Einstein in general relativity, but due to the weakness of the gravitational force, its magnitude is very small, so it could not be detected for a long time. Only indirect evidence spoke in favor of the existence of radiation.
Such waves generate any material objects moving with asymmetric acceleration. Scientists describe them as "ripples of space-time." The most powerful sources of such radiation are colliding galaxies and collapsing systems consisting of two objects. A typical example of the latter case is the merger of black holes or neutron stars. In such processes, gravitational radiation can pass more than 50% of the total mass of the system.
Gravitational waves were first detected in 2015 by two LIGO observatories. Almost immediately, this event received the status of the largest discovery in physics in recent decades. In 2017, he was awarded the Nobel Prize. After that, scientists managed to detect gravitational radiation several more times.
Back in the 70s of the last century - long before experimental confirmation - scientists proposed using gravitational radiation for long-distance communication. Its undoubted advantage is its high ability to pass through any substance without being absorbed. But at present this is hardly possible, because there are huge difficulties in generating and receiving these waves. Yes, and we still do not have enough real knowledge about the nature of gravity.
Today, several installations similar to LIGO are operating in different countries of the world, and new ones are being built. It is likely that we will learn more about gravitational radiation in the near future.
Alternative theories of universal gravitation and the reasons for their creation
Currently, the dominant concept of gravity is general relativity. The entire existing array of experimental data and observations is consistent with it. At the same time, it has a large number of frankly weak points and controversial points, so attempts to create new models that explain the nature of gravity do not stop.
All theories of universal gravitation developed so far can be divided into several main groups:
- standard;
- alternative;
- quantum;
- unified field theory.
Attempts to create a new concept of universal gravitation were made as early as the 19th century. Various authors included in it the ether or the corpuscular theory of light. But the emergence of general relativity put an end to these researches. After its publication, the goal of scientists changed - now their efforts were aimed at improving the Einstein model, including new natural phenomena in it: the spin of particles, the expansion of the Universe, etc.
By the early 1980s, physicists had experimentally rejected all concepts except those that included general relativity as an integral part. At this time, "string theories" came into fashion, looking very promising. But experimental confirmation of these hypotheses has not been found. Over the past decades, science has reached significant heights and has accumulated a huge array of empirical data. Today, attempts to create alternative theories of gravity are inspired mainly by cosmological studies related to such concepts as "dark matter", "inflation", "dark energy".
One of the main tasks of modern physics is the unification of two fundamental directions: quantum theory and general relativity. Scientists seek to connect attraction with other types of interactions, thus creating a "theory of everything." This is exactly what quantum gravity does, the branch of physics that attempts to give a quantum description of the gravitational interaction. An offshoot of this direction is the theory of loop gravity.
Despite active and long-term efforts, this goal has not yet been achieved. And it's not even the complexity of this problem: it's just that quantum theory and general relativity are based on completely different paradigms. Quantum mechanics deals with physical systems operating against the background of ordinary space-time. And in the theory of relativity, space-time itself is a dynamic component that depends on the parameters of the classical systems that are in it.
Along with the scientific hypotheses of universal gravitation, there are theories that are very far from modern physics. Unfortunately, in recent years, such "opuses" have simply flooded the Internet and the shelves of bookstores. Some authors of such works generally inform the reader that gravity does not exist, and the laws of Newton and Einstein are fictions and hoaxes.
An example is the work of the "scientist" Nikolai Levashov, who claims that Newton did not discover the law of universal gravitation, and only the planets and our satellite the Moon have gravitational force in the solar system. The evidence given by this "Russian scientist" is rather strange. One of them is the flight of the American probe NEAR Shoemaker to the asteroid Eros, which took place in 2000. Levashov considers the lack of attraction between the probe and the celestial body to be evidence of the falsity of Newton's works and the conspiracy of physicists who hide the truth about gravity from people.
In fact, the spacecraft successfully completed its mission: first, it entered the asteroid's orbit, and then made a soft landing on its surface.
Artificial gravity and what it is for
There are two concepts associated with gravity that, despite their current theoretical status, are well known to the general public. These are anti-gravity and artificial gravity.
Antigravity is the process of countering the force of attraction, which can significantly reduce it or even replace it with repulsion. The mastery of such technology would lead to a real revolution in transportation, aviation, space exploration and radically change our whole life. But at present, the possibility of antigravity does not even have theoretical confirmation. Moreover, proceeding from general relativity, such a phenomenon is not feasible at all, since there can be no negative mass in our Universe. It is possible that in the future we will learn more about gravity and learn how to build aircraft based on this principle.
Artificial gravity is a man-made change in the existing force of gravity. Today, we do not really need such technology, but the situation will definitely change after the start of long-term space travel. And it has to do with our physiology. The human body, “accustomed” by millions of years of evolution to the constant gravity of the Earth, perceives the impact of reduced gravity extremely negatively. A long stay even in the conditions of lunar gravity (six times weaker than the earth) can lead to sad consequences. The illusion of attraction can be created using other physical forces, such as inertia. However, these options are complex and expensive. At the moment, artificial gravity does not even have theoretical justifications, it is obvious that its possible practical implementation is a matter of a very distant future.
Gravity is a concept known to everyone since school. It would seem that scientists should have thoroughly investigated this phenomenon! But gravity remains the deepest mystery to modern science. And this can be called an excellent example of how limited human knowledge about our vast and wonderful world is.
If you have any questions - leave them in the comments below the article. We or our visitors will be happy to answer them.
First, imagine the Earth as a non-moving ball (Fig. 3.1, a). The gravitational force F between the Earth (mass M) and an object (mass m) is determined by the formula: F=Gmm/r2
where r is the radius of the Earth. The constant G is known as universal gravitational constant and extremely small. When r is constant, the force F is const. m. The attraction of a body of mass m by the Earth determines the weight of this body: W = mg comparison of the equations gives: g = const = GM/r 2 .
The attraction of a body of mass m by the Earth causes it to fall "down" with an acceleration g, which is constant at all points A, B, C and everywhere on the earth's surface (Fig. 3.1.6).
The free body force diagram also shows that there is a force acting on the Earth from the side of a body of mass m, which is directed opposite to the force acting on the body from the Earth. However, the mass M of the Earth is so large that the "upward" acceleration a "of the Earth, calculated by the formula F \u003d Ma", is insignificant and can be neglected. The earth has a shape other than spherical: the radius at the pole r p is less than the radius at the equator r e. This means that the force of attraction of a body with mass m at the pole F p \u003d GMm / r 2 p is greater than at the equator F e = GMm/r e . Therefore, the acceleration of free fall g p at the pole is greater than the acceleration of free fall g e at the equator. The acceleration g changes with latitude in accordance with the change in the radius of the Earth.
As you know, the Earth is in constant motion. It rotates around its axis, making one revolution every day, and moves in orbit around the Sun with a revolution of one year. Taking for simplicity the Earth as a homogeneous ball, let's consider the motion of bodies of mass m on the pole A and on the equator C (Fig. 3.2). In one day, the body at point A rotates 360 °, remaining in place, while the body located at point C covers a distance of 2lg. In order for the body located at point C to move in a circular orbit, some kind of force is needed. This is a centripetal force, which is determined by the formula mv 2 /r, where v is the speed of the body in orbit. The force of gravitational attraction acting on a body located at point C, F = GMm/r must:
a) ensure the movement of the body in a circle;
b) attract the body to the Earth.
Thus, F = (mv 2 /r) + mg at the equator, and F = mg at the pole. This means that g changes with latitude as the radius of the orbit changes from r at C to zero at A.
It is interesting to imagine what would happen if the speed of the Earth's rotation increased so much that the centripetal force acting on the body at the equator would become equal to the force of attraction, i.e. mv 2 / r = F = GMm / r 2 . The total gravitational force would be used solely to keep the body at point C in a circular orbit, and there would be no force left on the surface of the Earth. Any further increase in the speed of the Earth's rotation would allow the body to "float away" into space. At the same time, if a spacecraft with astronauts on board is launched to a height R above the center of the Earth with a speed v, such that the equality mv*/R=F = GMm/R 2 is satisfied, then this spacecraft will rotate around the Earth in conditions of weightlessness.
Precise measurements of the free fall acceleration g show that g varies with latitude, as shown in Table 3.1. It follows from this that the weight of a certain body changes over the surface of the Earth from a maximum at a latitude of 90 ° to a minimum at a latitude of 0 °.
At this level of training, small changes in acceleration g are usually neglected and an average value of 9.81 m-s 2 is used. To simplify calculations, acceleration g is often taken as the nearest integer, i.e. 10 ms - 2, and, thus, the force of attraction acting from the Earth on a body of mass 1 kg, i.e. weight, taken as 10 N. Most examination boards for examinees suggest using g \u003d 10 m-s - 2 or 10 N-kg -1 in order to simplify calculations.
In nature, there are various forces that characterize the interaction of bodies. Consider those forces that occur in mechanics.
gravitational forces. Probably, the very first force, the existence of which was realized by a person, was the force of attraction acting on bodies from the side of the Earth.
And it took many centuries for people to understand that the force of gravity acts between any bodies. And it took many centuries for people to understand that the force of gravity acts between any bodies. The English physicist Newton was the first to understand this fact. Analyzing the laws that govern the motion of the planets (Kepler's laws), he came to the conclusion that the observed laws of planetary motion can only be fulfilled if there is an attractive force between them, which is directly proportional to their masses and inversely proportional to the square of the distance between them.
Newton formulated law of gravity. Any two bodies are attracted to each other. The force of attraction between point bodies is directed along the straight line connecting them, is directly proportional to the masses of both and inversely proportional to the square of the distance between them:
In this case, point bodies are understood to mean bodies whose dimensions are many times smaller than the distance between them.
The forces of gravity are called gravitational forces. The coefficient of proportionality G is called the gravitational constant. Its value was determined experimentally: G = 6.7 10¯¹¹ N m² / kg².
gravity acting near the surface of the Earth, is directed towards its center and is calculated by the formula:
where g is the free fall acceleration (g = 9.8 m/s²).
The role of gravity in living nature is very significant, since the size, shape and proportions of living beings largely depend on its magnitude.
Body weight. Consider what happens when a load is placed on a horizontal plane (support). At the first moment after the load is lowered, it begins to move downward under the action of gravity (Fig. 8).
The plane bends and there is an elastic force (reaction of the support), directed upwards. After the elastic force (Fy) balances the force of gravity, the lowering of the body and the deflection of the support will stop.
The deflection of the support arose under the action of the body, therefore, a certain force (P) acts on the support from the side of the body, which is called the weight of the body (Fig. 8, b). According to Newton's third law, the weight of a body is equal in magnitude to the support reaction force and is directed in the opposite direction.
P \u003d - Fu \u003d F heavy.
body weight called the force P, with which the body acts on a horizontal support that is stationary relative to it.
Since gravity (weight) is applied to the support, it deforms and, due to elasticity, counteracts the force of gravity. The forces developed in this case from the side of the support are called the forces of the reaction of the support, and the very phenomenon of the development of counteraction is called the reaction of the support. According to Newton's third law, the reaction force of the support is equal in magnitude to the force of gravity of the body and opposite to it in direction.
If a person on a support moves with the acceleration of the links of his body directed away from the support, then the reaction force of the support increases by the value ma, where m is the mass of the person, and are the accelerations with which the links of his body move. These dynamic effects can be recorded using strain gauge devices (dynamograms).
Weight should not be confused with body mass. The mass of a body characterizes its inertial properties and does not depend on either the gravitational force or the acceleration with which it moves.
The weight of the body characterizes the force with which it acts on the support and depends both on the force of gravity and on the acceleration of movement.
For example, on the Moon, the weight of a body is about 6 times less than the weight of a body on Earth. The mass is the same in both cases and is determined by the amount of matter in the body.
In everyday life, technology, sports, weight is often indicated not in newtons (N), but in kilograms of force (kgf). The transition from one unit to another is carried out according to the formula: 1 kgf = 9.8 N.
When the support and the body are motionless, then the mass of the body is equal to the force of gravity of this body. When the support and the body move with some acceleration, then, depending on its direction, the body may experience either weightlessness or overload. When the acceleration coincides in direction and is equal to the acceleration of free fall, the weight of the body will be zero, so a state of weightlessness occurs (ISS, high-speed elevator when lowering down). When the acceleration of the movement of the support is opposite to the acceleration of free fall, the person experiences an overload (start from the surface of the Earth of a manned spacecraft, a high-speed elevator going up).
Definition
Between any bodies that have masses, there are forces that attract the above bodies to each other. Such forces are called forces of mutual attraction.
Consider two material points (Fig. 1). They are attracted with forces directly proportional to the product of the masses of these material points and inversely proportional to the distance between them. So, the force of gravity () will be equal to:
where a material point of mass m 2 acts on a material point of mass m 1 with an attraction force - radius - a vector drawn from point 2 to point 1, the module of this vector is equal to the distance between material points (r); G \u003d 6.67 10 -11 m 3 kg -1 s -2 (in the SI system) - gravitational constant (gravitational constant).
In accordance with Newton's third law, the force with which the material point 2 is attracted to the material point 1 () is equal to:
Gravitation between bodies is carried out by means of a gravitational field (field of gravity). Gravitational forces are potential. This makes it possible to introduce such an energy characteristic of the gravitational field as a potential, which is equal to the ratio of the potential energy of a material point, located in the studied point of the field, to the mass of this point.
The formula for the force of attraction of bodies of arbitrary shape
In two bodies of arbitrary shape and size, we single out elementary masses, which can be considered material points, and:
where are the substance densities of the material points of the first and second bodies, dV 1 ,dV 2 are the elementary volumes of the selected material points. In this case, the force of attraction (), with which the element dm 2 acts on the element dm 1, is equal to:
Therefore, the force of attraction of the first body by the second can be found by the formula:
where integration must be performed over the entire volume of the first (V 1) and second (V 2) bodies. If the bodies are homogeneous, then the expression can be slightly transformed and get:
The formula for the attractive force of solid spherical bodies
If the forces of attraction are considered for two solid bodies of a spherical shape (or close to spheres), the density of which depends only on the distances to their centers, formula (6) will take the form:
where m 1 ,m 2 are the masses of the balls, is the radius - the vector connecting the centers of the balls,
Expression (7) can be used if one of the bodies has a shape other than spherical, but its dimensions are much smaller than the dimensions of the second body - a ball. So, formula (7) can be used to calculate the forces of attraction of bodies to the Earth.
Units of gravity force
The basic unit of measurement of the attractive force (as well as any other force) in the SI system is: \u003d H.
In GHS: =dyn.
Examples of problem solving
Example
Exercise. What is the force of attraction of two identical homogeneous balls, the mass of which is equal to 1 kg each? The distance between their centers is 1 m.
Decision. The basis for solving the problem is the formula:
To calculate the modulus of the attractive force, formula (1.1) is transformed to the form:
Let's do the calculations:
Answer.
Example
Exercise. With what force (in modulus) does an infinitely long and thin and straight rod attract a material particle of mass m. The particle is located at a distance a from the rod. The linear mass density of the rod substance is equal to tau