Many rightly call the 16th-17th centuries one of the most glorious periods in history. It was at this time that the foundations were largely laid, without which the further development of this science would be simply unthinkable. Copernicus, Galileo, Kepler have done a great job to declare physics as a science that can answer almost any question. Standing apart in a whole series of discoveries is the law of universal gravitation, the final formulation of which belongs to the outstanding English scientist Isaac Newton.
The main significance of the work of this scientist was not in his discovery of the force of universal gravitation - both Galileo and Kepler spoke about the presence of this quantity even before Newton, but in the fact that he was the first to prove that the same forces act both on Earth and in outer space. same forces of interaction between bodies.
Newton in practice confirmed and theoretically substantiated the fact that absolutely all bodies in the Universe, including those located on the Earth, interact with each other. This interaction is called gravitational, while the process of universal gravitation itself is called gravity.
This interaction occurs between bodies because there is a special type of matter, unlike others, which in science is called the gravitational field. This field exists and acts around absolutely any object, while there is no protection against it, since it has an unparalleled ability to penetrate any materials.
The force of universal gravitation, the definition and formulation of which he gave, is directly dependent on the product of the masses of interacting bodies, and inversely on the square of the distance between these objects. According to Newton, irrefutably confirmed by practical research, the force of universal gravitation is found by the following formula:
In it, of particular importance belongs to the gravitational constant G, which is approximately equal to 6.67 * 10-11 (N * m2) / kg2.
The gravitational force with which bodies are attracted to the Earth is a special case of Newton's law and is called gravity. In this case, the gravitational constant and the mass of the Earth itself can be neglected, so the formula for finding the force of gravity will look like this:
Here g is nothing more than an acceleration whose numerical value is approximately equal to 9.8 m/s2.
Newton's law explains not only the processes occurring directly on the Earth, it gives an answer to many questions related to the structure of the entire solar system. In particular, the force of universal gravitation between has a decisive influence on the motion of the planets in their orbits. The theoretical description of this movement was given by Kepler, but its justification became possible only after Newton formulated his famous law.
Newton himself connected the phenomena of terrestrial and extraterrestrial gravitation using a simple example: when fired from it, it does not fly straight, but along an arcuate trajectory. At the same time, with an increase in the charge of gunpowder and the mass of the nucleus, the latter will fly farther and farther. Finally, if we assume that it is possible to obtain so much gunpowder and construct such a cannon that the cannonball will fly around the globe, then, having made this movement, it will not stop, but will continue its circular (ellipsoidal) movement, turning into an artificial one. As a result, the force of the universal gravity is the same in nature both on Earth and in outer space.
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 that 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 gravity, 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).
Gravitational force is the force with which objects of a certain mass are attracted to each other, located at a certain distance from each other.
The English scientist Isaac Newton in 1867 discovered the law of universal gravitation. This is one of the fundamental laws of mechanics. The essence of this law is as follows:any two material particles are attracted to each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The force of attraction is the first force that a person felt. This is the force with which the Earth acts on all bodies located on its surface. And any person feels this force as his own weight.
Law of gravity
There is a legend that Newton discovered the law of universal gravitation quite by accident, walking in the evening in the garden of his parents. Creative people are constantly on the lookout for scientific discoveries- this is not an instant insight, but the fruit of a long mental work. Sitting under an apple tree, Newton was thinking about another idea, and suddenly an apple fell on his head. It was clear to Newton that the apple fell as a result of the Earth's gravity. “But why doesn’t the moon fall to the Earth? he thought. “It means that some other force is acting on it, keeping it in orbit.” This is how the famous law of gravity.
Scientists who had previously studied the rotation of celestial bodies believed that celestial bodies obey some completely different laws. That is, it was assumed that there are completely different laws of attraction on the surface of the Earth and in space.
Newton combined these supposed kinds of gravity. Analyzing Kepler's laws describing the motion of the planets, he came to the conclusion that the force of attraction arises between any bodies. That is, both the apple that fell in the garden and the planets in space are affected by forces that obey the same law - the law of universal gravitation.
Newton found that Kepler's laws only work if there is an attractive force between the planets. And this force is directly proportional to the masses of the planets and inversely proportional to the square of the distance between them.
The force of attraction is calculated by the formula F=G m 1 m 2 / r 2
m 1 is the mass of the first body;
m2is the mass of the second body;
r is the distance between the bodies;
G is the coefficient of proportionality, which is called gravitational constant or gravitational constant.
Its value was determined experimentally. G\u003d 6.67 10 -11 Nm 2 / kg 2
If two material points with a mass equal to a unit of mass are at a distance equal to a unit of distance, then they are attracted with a force equal to G.
The forces of attraction are the gravitational forces. They are also called gravity. They are subject to the law of universal gravitation and appear everywhere, since all bodies have mass.
Gravity
The gravitational force near the surface of the Earth is the force with which all bodies are attracted to the Earth. They call her gravity. It is considered constant if the distance of the body from the Earth's surface is small compared to the radius of the Earth.
Since gravity, which is the gravitational force, depends on the mass and radius of the planet, it will be different on different planets. Since the radius of the Moon is less than the radius of the Earth, then the force of attraction on the Moon is less than on the Earth by 6 times. And on Jupiter, on the contrary, gravity is 2.4 times greater than gravity on Earth. But body weight remains constant, no matter where it is measured.
Many people confuse the meaning of weight and gravity, believing that gravity is always equal to weight. But it's not.
The force with which the body presses on the support or stretches the suspension, this is the weight. If the support or suspension is removed, the body will begin to fall with the acceleration of free fall under the action of gravity. The force of gravity is proportional to the mass of the body. It is calculated according to the formulaF= m g , Where m- body mass, g- acceleration of gravity.
Body weight can change, and sometimes disappear altogether. Imagine that we are in an elevator on the top floor. The elevator is worth it. At this moment, our weight P and the force of gravity F, with which the Earth pulls us, are equal. But as soon as the elevator began to move down with acceleration A , weight and gravity are no longer equal. According to Newton's second lawmg+ P = ma . P \u003d m g -ma.
It can be seen from the formula that our weight decreased as we moved down.
At the moment when the elevator picked up speed and began to move without acceleration, our weight is again equal to gravity. And when the elevator began to slow down its movement, acceleration A became negative and the weight increased. There is an overload.
And if the body moves down with the acceleration of free fall, then the weight will completely become equal to zero.
At a=g R=mg-ma= mg - mg=0
This is a state of weightlessness.
So, without exception, all material bodies in the Universe obey the law of universal gravitation. And the planets around the Sun, and all the bodies that are near the surface of the Earth.
The interaction inherent in all bodies of the Universe and manifested in their mutual attraction to each other is called gravitational, and the very phenomenon of universal gravitation gravity .
Gravitational interaction carried out by means of a special type of matter called gravitational field.
Gravitational forces (gravitational forces) due to the mutual attraction of the bodies and directed along the line connecting the interacting points.
The expression for the force of gravity was given to Newton in 1666 when he was only 24 years old.
Law of gravity: two bodies are attracted to each other with forces that are directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them:
The law is valid provided that the dimensions of the bodies are negligibly small compared to the distances between them. Also, the formula can be used to calculate the forces of universal gravitation, for spherical bodies, for two bodies, one of which is a ball, the other is a material point.
The coefficient of proportionality G = 6.68 10 -11 is called gravitational constant.
physical meaning The gravitational constant is that it is numerically equal to the force with which two bodies weighing 1 kg each are attracted, located at a distance of 1 m from each other.
Gravity
The force with which the Earth attracts nearby bodies is called gravity , and the gravitational field of the Earth - gravity field .
The force of gravity is directed downward towards the center of the Earth. In the body, it passes through a point called center of gravity. The center of gravity of a homogeneous body with a center of symmetry (ball, rectangular or round plate, cylinder, etc.) is located at this center. Moreover, it may not coincide with any of the points of the given body (for example, near the ring).
In the general case, when it is required to find the center of gravity of any body of irregular shape, one should proceed from the following regularity: if the body is suspended on a thread attached sequentially to different points of the body, then the directions marked by the thread will intersect at one point, which is precisely the center the gravity of this body.
The modulus of gravity is found using the law of universal gravitation and is determined by the formula:
F t \u003d mg, (2.7)
where g is the free fall acceleration of the body (g=9.8 m/s 2 ≈10m/s 2).
Since the direction of free fall acceleration g coincides with the direction of gravity F t, the last equality can be rewritten as
It follows from (2.7) that, i.e., the ratio of the force acting on a body of mass m at any point in the field to the mass of the body determines the free fall acceleration at a given point in the field.
For points located at a height h from the Earth's surface, the free fall acceleration of a body is:
(2.8)
where R З is the radius of the Earth; MZ is the mass of the Earth; h is the distance from the center of gravity of the body to the surface of the Earth.
From this formula it follows that,
Firstly, the free fall acceleration does not depend on the mass and dimensions of the body and,
Secondly, with increasing height above the Earth, the acceleration of free fall decreases. For example, at an altitude of 297 km, it turns out to be not 9.8 m/s 2 , but 9 m/s 2 .
The decrease in the acceleration of free fall means that the force of gravity also decreases as the height above the Earth increases. The farther the body is from the Earth, the weaker it attracts it.
From formula (1.73) it can be seen that g depends on the radius of the Earth R z.
But due to the oblateness of the Earth, it has a different meaning in different places: it decreases as you move from the equator to the pole. At the equator, for example, it is equal to 9.780m/s 2 , and at the pole - 9.832m/s 2 . In addition, local g values may differ from their average g cf values due to the heterogeneous structure of the earth's crust and subsoil, mountain ranges and depressions, as well as mineral deposits. The difference between the values of g and g cf is called gravitational anomalies:
Positive anomalies Δg >0 often indicate deposits of metal ores, and negative Δg<0– о залежах лёгких полезных ископаемых, например нефти и газа.
The method of determining mineral deposits by accurately measuring the acceleration of free fall is widely used in practice and is called gravimetric exploration.
An interesting feature of the gravitational field, which electromagnetic fields do not have, is its all-penetrating ability. If you can protect yourself from electric and magnetic fields with the help of special metal screens, then nothing can protect you from the gravitational field: it penetrates through any materials.
Isaac Newton suggested that between any bodies in nature there are forces of mutual attraction. These forces are called gravity forces or forces of gravity. The force of irrepressible gravity manifests itself in space, the solar system and on Earth.
Law of gravity
Newton generalized the laws of motion of celestial bodies and found out that the force \ (F \) is equal to:
\[ F = G \dfrac(m_1 m_2)(R^2) \]
where \(m_1 \) and \(m_2 \) are the masses of interacting bodies, \(R \) is the distance between them, \(G \) is the proportionality coefficient, which is called gravitational constant. The numerical value of the gravitational constant was experimentally determined by Cavendish, measuring the force of interaction between lead balls.
The physical meaning of the gravitational constant follows from the law of universal gravitation. If \(m_1 = m_2 = 1 \text(kg) \), \(R = 1 \text(m) \) , then \(G = F \) , i.e. the gravitational constant is equal to the force with which two bodies of 1 kg are attracted at a distance of 1 m.
Numerical value:
\(G = 6.67 \cdot() 10^(-11) N \cdot() m^2/ kg^2 \) .
The forces of universal gravitation act between any bodies in nature, but they become tangible at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is fulfilled only for material points and balls (in this case, the distance between the centers of the balls is taken as the distance).
Gravity
A special type of universal gravitational force is the force of attraction of bodies to the Earth (or to another planet). This force is called gravity. Under the action of this force, all bodies acquire free fall acceleration.
According to Newton's second law \(g = F_T /m \) , therefore \(F_T = mg \) .
If M is the mass of the Earth, R is its radius, m is the mass of the given body, then the force of gravity is equal to
\(F = G \dfrac(M)(R^2)m = mg \) .
The force of gravity is always directed towards the center of the Earth. Depending on the height \ (h \) above the Earth's surface and the geographical latitude of the position of the body, the free fall acceleration acquires different values. On the surface of the Earth and in middle latitudes, the free fall acceleration is 9.831 m/s 2 .
Body weight
In technology and everyday life, the concept of body weight is widely used.
Body weight denoted by \(P \) . The unit of weight is newton (N). Since the weight is equal to the force with which the body acts on the support, then, in accordance with Newton's third law, the weight of the body is equal in magnitude to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the reaction force of the support is equal to.
It is assumed that the body is motionless relative to the support or suspension.
Body weight and gravity differ in nature: body weight is a manifestation of the action of intermolecular forces, and gravity has a gravitational nature.
The state of a body in which its weight is zero is called weightlessness. The state of weightlessness is observed in an airplane or spacecraft when moving with the acceleration of free fall, regardless of the direction and value of the speed of their movement. Outside the earth's atmosphere, when the jet engines are turned off, only the force of universal gravitation acts on the spacecraft. Under the action of this force, the spaceship and all the bodies in it move with the same acceleration, so the state of weightlessness is observed in the ship.
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