« Physics - 10th grade"

Why does the Moon move around the Earth?
What happens if the moon stops?
Why do planets revolve around the Sun?

Chapter 1 discussed in detail that globe imparts to all bodies near the surface of the Earth the same acceleration - acceleration free fall. But if the globe imparts acceleration to the body, then, according to Newton’s second law, it acts on the body with some force. The force with which the Earth acts on a body is called gravity. First we will find this force, and then we will consider the force universal gravity.

Acceleration in absolute value is determined from Newton's second law:

In general, it depends on the force acting on the body and its mass. Since the acceleration of gravity does not depend on mass, it is clear that the force of gravity must be proportional to mass:

The physical quantity is the acceleration of gravity, it is constant for all bodies.

Based on the formula F = mg, you can specify a simple and practically convenient method for measuring the mass of bodies by comparing the mass of a given body with a standard unit of mass. The ratio of the masses of two bodies is equal to the ratio of the forces of gravity acting on the bodies:

This means that the masses of bodies are the same if the forces of gravity acting on them are the same.

This is the basis for determining masses by weighing on spring or lever scales. By ensuring that the pressure force of the body on the scale pan, equal to the force of gravity applied to the body, is balanced by the pressure force of the weights on the other scale pan, equal strength gravity applied to the weights, we thereby determine the mass of the body.

The force of gravity acting on a given body near the Earth can be considered constant only at a certain latitude near the Earth's surface. If the body is lifted or moved to a place with a different latitude, then the acceleration of gravity, and therefore the force of gravity, will change.

The force of universal gravity.

Newton was the first to strictly prove that the cause of a stone falling to the Earth, the movement of the Moon around the Earth and the planets around the Sun are the same. This force of universal gravity, acting between any bodies in the Universe.

Newton came to the conclusion that if not for air resistance, then the trajectory of a stone thrown from high mountain(Fig. 3.1) with a certain speed, it could become such that it would never reach the surface of the Earth at all, but would move around it in the same way as planets describe their orbits in celestial space.

Newton found this reason and was able to accurately express it in the form of one formula - the law of universal gravitation.

Since the force of universal gravitation imparts the same acceleration to all bodies regardless of their mass, it must be proportional to the mass of the body on which it acts:

“Gravity exists for all bodies in general and is proportional to the mass of each of them... all planets gravitate towards each other...” I. Newton

But since, for example, the Earth acts on the Moon with a force proportional to the mass of the Moon, then the Moon, according to Newton’s third law, must act on the Earth with the same force. Moreover, this force must be proportional to the mass of the Earth. If the force of gravity is truly universal, then from the side of a given body a force must act on any other body proportional to the mass of this other body. Consequently, the force of universal gravity must be proportional to the product of the masses of interacting bodies. From this follows the formulation of the law of universal gravitation.

Law of universal gravitation:

The force of mutual attraction between two bodies is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them:

The proportionality factor G is called gravitational constant.

The gravitational constant is numerically equal to the force of attraction between two material points weighing 1 kg each, if the distance between them is 1 m. Indeed, with masses m 1 = m 2 = 1 kg and distance r = 1 m, we obtain G = F (numerically).

It must be borne in mind that the law of universal gravitation (3.4) as a universal law is valid for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 3.2, a).

It can be shown that homogeneous bodies shaped like a ball (even if they cannot be considered material points, Fig. 3.2, b) also interact with the force determined by formula (3.4). In this case, r is the distance between the centers of the balls. The forces of mutual attraction lie on a straight line passing through the centers of the balls. Such forces are called central. The bodies that we usually consider falling to Earth have dimensions much smaller than the Earth's radius (R ≈ 6400 km).

Such bodies can, regardless of their shape, be considered as material points and determine the force of their attraction to the Earth using the law (3.4), keeping in mind that r is the distance from a given body to the center of the Earth.

A stone thrown to the Earth will deviate under the influence of gravity from a straight path and, having described a curved trajectory, will finally fall to the Earth. If you throw it at a higher speed, it will fall further." I. Newton

Determination of the gravitational constant.

Now let's find out how to find the gravitational constant. First of all, note that G has a specific name. This is due to the fact that the units (and, accordingly, the names) of all quantities included in the law of universal gravitation have already been established earlier. The law of gravitation gives a new connection between known quantities with certain names of units. That is why the coefficient turns out to be a named quantity. Using the formula of the law of universal gravitation, it is easy to find the name of the unit of gravitational constant in SI: N m 2 / kg 2 = m 3 / (kg s 2).

To quantify G, it is necessary to independently determine all the quantities included in the law of universal gravitation: both masses, force and distance between bodies.

The difficulty is that the gravitational forces between bodies of small masses are extremely small. It is for this reason that we do not notice the attraction of our body to surrounding objects and the mutual attraction of objects to each other, although gravitational forces are the most universal of all forces in nature. Two people with masses of 60 kg at a distance of 1 m from each other are attracted with a force of only about 10 -9 N. Therefore, to measure the gravitational constant, fairly subtle experiments are needed.

The gravitational constant was first measured by the English physicist G. Cavendish in 1798 using an instrument called a torsion balance. The diagram of the torsion balance is shown in Figure 3.3. A light rocker with two identical weights at the ends is suspended from a thin elastic thread. Two heavy balls are fixed nearby. Gravitational forces act between the weights and the stationary balls. Under the influence of these forces, the rocker turns and twists the thread until the resulting elastic force becomes equal to the gravitational force. By the angle of twist you can determine the force of attraction. To do this, you only need to know the elastic properties of the thread. The masses of the bodies are known, and the distance between the centers of interacting bodies can be directly measured.

From these experiments the following value for the gravitational constant was obtained:

G = 6.67 10 -11 N m 2 / kg 2.

Only in the case when bodies of enormous mass interact (or at least the mass of one of the bodies is very large) does the gravitational force reach of great importance. For example, the Earth and the Moon are attracted to each other with a force F ≈ 2 10 20 N.

Dependence of the acceleration of free fall of bodies on geographic latitude.

One of the reasons for the increase in the acceleration of gravity when the point where the body is located moves from the equator to the poles is that the globe is somewhat flattened at the poles and the distance from the center of the Earth to its surface at the poles is less than at the equator. Another reason is the rotation of the Earth.

Equality of inertial and gravitational masses.

The most striking property of gravitational forces is that they impart the same acceleration to all bodies, regardless of their masses. What would you say about a football player whose kick would be equally accelerated by an ordinary leather ball and a two-pound weight? Everyone will say that this is impossible. But the Earth is just such an “extraordinary football player” with the only difference that its effect on bodies is not of the nature of a short-term blow, but continues continuously for billions of years.

In Newton's theory, mass is the source of the gravitational field. We are in the Earth's gravitational field. At the same time, we are also sources of the gravitational field, but due to the fact that our mass is significantly less than the mass of the Earth, our field is much weaker and surrounding objects do not react to it.

The extraordinary property of gravitational forces, as we have already said, is explained by the fact that these forces are proportional to the masses of both interacting bodies. The mass of a body, which is included in Newton’s second law, determines the inertial properties of the body, i.e. its ability to acquire a certain acceleration under the influence of a given force. This inert mass m and.

It would seem, what relation can it have to the ability of bodies to attract each other? The mass that determines the ability of bodies to attract each other is the gravitational mass m r.

It does not at all follow from Newtonian mechanics that the inertial and gravitational masses are the same, i.e. that

m and = m r . (3.5)

Equality (3.5) is a direct consequence of experiment. It means that we can simply talk about the mass of a body as a quantitative measure of both its inertial and gravitational properties.

In nature there are various forces, which characterize the interaction of bodies. Let us consider the forces that occur in mechanics.

Gravitational forces. Probably the very first force whose existence man realized was the force of gravity acting on bodies from 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 planets (Kepler's laws), he came to the conclusion that the observed laws of motion of planets can be fulfilled only if there is an attractive force between them, directly proportional to their masses and inversely proportional to the square of the distance between them.

Newton formulated law of universal gravitation. Any two bodies attract 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 as bodies whose dimensions are many times smaller than the distance between them.

The forces of universal gravity are called gravitational forces. The proportionality coefficient 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 acceleration of gravity (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 some weight is placed on horizontal plane(support). At the first moment after the load is lowered, it begins to move downward under the influence of gravity (Fig. 8).

The plane bends and an elastic force (support reaction) directed upward appears. After the elastic force (Fу) 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 ground reaction force and is directed in the opposite direction.

P = - Fу = Fheavy.

Body weight is called the force P with which a body acts on a horizontal support that is motionless relative to it.

Since the force of gravity (weight) is applied to the support, it is deformed and, due to its elasticity, counteracts the force of gravity. The forces developed in this case from the side of the support are called support reaction forces, and the very phenomenon of the development of counteraction is called the support reaction. According to Newton's third law, the support reaction force is equal in magnitude to the force of gravity of the body and opposite in direction.

If a person on a support moves with the acceleration of the parts of his body directed from the support, then the reaction force of the support increases by the amount ma, where m is the mass of the person, and is the acceleration with which the parts of his body move. These dynamic effects can be recorded using strain gauge devices (dynamograms).

Weight should not be confused with body weight. The mass of a body characterizes its inert properties and does not depend either on the force of gravity or on the acceleration with which it moves.

The weight of a body characterizes the force with which it acts on the support and depends on both the force of gravity and the acceleration of movement.

For example, on the Moon the weight of a body is approximately 6 times less than the weight of a body on Earth. The mass in both cases is the same and is determined by the amount of matter in the body.

In everyday life, technology, and 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 gravity of this body. When the support and the body move with some acceleration, then, depending on its direction, the body can 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, therefore a state of weightlessness arises (ISS, high-speed elevator when lowering down). When the acceleration of the support movement is opposite to the acceleration of free fall, the person experiences an overload (the launch of a manned spacecraft from the surface of the Earth, a high-speed elevator rising upward).

Definition

Between any bodies that have masses, forces act that attract the above-mentioned bodies to each other. Such forces are called forces of mutual attraction.

Let's consider two material points (Fig. 1). They attract with forces directly proportional to the product of the masses of these material points and inversely proportional to the distance between them. So, the gravitational force () will be equal to:

where a material point of mass m 2 acts on a material point of mass m 1 with an attractive force - radius - a vector drawn from point 2 to point 1, the modulus of this vector is equal to the distance between material points (r); G=6.67 10 -11 m 3 kg -1 s -2 (in the SI system) – gravitational constant (gravity constant).

In accordance with Newton's third law, the force with which material point 2 is attracted to material point 1 () is equal to:

Gravity between bodies is carried out through a gravitational field (gravitational field). Gravitational forces are potential. This makes it possible to introduce such an energy characteristic of the gravitational field as potential, which is equal to the ratio of the potential energy of a material point located at the field point under study to the mass of this point.

Formula for the force of attraction of bodies of arbitrary shape

In two bodies of arbitrary shape and size, we identify elementary masses that can be considered material points, and:

where are the matter 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:

Consequently, the force of attraction of the first body by the second can be found by the formula:

where integration must be carried out 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 obtained:

Formula for the force of attraction of spherical solids

If the attractive forces are considered for two solids spherical shape (or close to balls), 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. Thus, formula (7) can be used to calculate the forces of attraction of bodies to the Earth.

Units of gravity

The basic unit of measurement for the force of attraction (like any other force) in the SI system is: =H.

In GHS: =din.

Examples of problem solving

Example

Exercise. What is the force of attraction between two identical homogeneous spheres of mass equal to 1 kg? The distance between their centers is 1 m.

Solution. 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 carry out the calculations:

Answer.

Example

Exercise. With what force (in absolute value) 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 substance of the rod is equal to tau

Every person in his life has come across this concept more than once, because gravity is the basis not only of modern physics, but also of a number of other related sciences.

Many scientists have been studying the attraction of bodies since ancient times, but the main discovery is attributed to Newton and is described as the well-known story of a fruit falling on one’s head.

What is gravity in simple words

Gravity is the attraction between several objects throughout the universe. The nature of the phenomenon varies, as it is determined by the mass of each of them and the extent between them, that is, the distance.

Newton's theory was based on the fact that both the falling fruit and the satellite of our planet are affected by the same force - gravity towards the Earth. But the satellite did not fall into earthly space precisely because of its mass and distance.

Gravity field

The gravitational field is the space within which the interaction of bodies occurs according to the laws of attraction.

Einstein's theory of relativity describes the field as a certain property of time and space, characteristically manifested when physical objects appear.

Gravity wave

These are certain types of field changes that are formed as a result of radiation from moving objects. They come off the object and spread in a wave effect.

Theories of gravity

The classical theory is Newtonian. However, it was imperfect and subsequently alternative options appeared.

These include:

• metric theories;
• non-metric;
• vector;
• Le Sage, who first described the phases;
• quantum gravity.

Today there are several dozen different theories, all of them either complement each other or look at phenomena from a different perspective.

Worth noting: ideal option does not yet exist, but ongoing developments are opening up more possible answers regarding the attraction of bodies.

The force of gravitational attraction

The basic calculation is as follows - the force of gravity is proportional to the multiplication of the mass of the body by another, between which it is determined. This formula is expressed this way: force is inversely proportional to the distance between objects squared.

The gravitational field is potential, which means it is conserved kinetic energy. This fact simplifies the solution of problems in which the force of attraction is measured.

Gravity in space

Despite the misconception of many, there is gravity in space. It is lower than on Earth, but still present.

As for the astronauts, who at first glance seem to be flying, they are actually in a state of slow decline. Visually, it seems that nothing attracts them, but in practice they experience gravity.

The strength of attraction depends on the distance, but no matter how large the distance between objects is, they will continue to be attracted to each other. Mutual attraction will never be zero.

Gravity in the Solar System

IN solar system It's not just the Earth that has gravity. Planets, as well as the Sun, attract objects to themselves.

Since the force is determined by the mass of the object, then highest indicator at the Sun. For example, if our planet has an indicator of one, then the luminary’s indicator will be almost twenty-eight.

Next in gravity after the Sun is Jupiter, so its gravitational force is three times higher than that of the Earth. Pluto has the smallest parameter.

For clarity, let’s denote this: in theory, on the Sun, the average person would weigh about two tons, but on the smallest planet of our system - only four kilograms.

What does the planet's gravity depend on?

Gravitational pull, as mentioned above, is the power with which the planet pulls toward itself objects located on its surface.

The force of gravity depends on the gravity of the object, the planet itself and the distance between them. If there are many kilometers, gravity is low, but it still keeps objects connected.

Several important and fascinating aspects related to gravity and its properties that are worth explaining to your child:

1. The phenomenon attracts everything, but never repels - this distinguishes it from other physical phenomena.
2. There is no such thing as zero. It is impossible to simulate a situation in which pressure does not apply, that is, gravity does not work.
3. The earth is falling from average speed 11.2 kilometers per second, having reached this speed you can leave the attracting well of the planet.
4. The existence of gravitational waves has not been scientifically proven, it is just a guess. If they ever become visible, then many mysteries of the cosmos related to the interaction of bodies will be revealed to humanity.

According to the theory of basic relativity of a scientist like Einstein, gravity is a curvature of the basic parameters of existence material world, which represents the basis of the Universe.

Gravity is the mutual attraction of two objects. The strength of interaction depends on the gravity of the bodies and the distance between them. Not all the secrets of the phenomenon have been revealed yet, but today there are several dozen theories describing the concept and its properties.

The complexity of the objects being studied affects the research time. In most cases, the relationship between mass and distance is simply taken.

Gravitational force is the foundation on which the Universe rests. Thanks to gravity, the Sun does not explode, the atmosphere does not escape into space, people and animals move freely on the surface, and plants bear fruit.

Celestial mechanics and theory of relativity

The law of universal gravitation is studied in grades 8-9 high school. Diligent students They know about the famous apple that fell on the head of the great Isaac Newton and about the discoveries that followed. In fact, giving a clear definition of gravity is much more difficult. Modern scientists continue discussions on how bodies interact in outer space and whether antigravity exists. It is extremely difficult to study this phenomenon in earthly laboratories, so several basic theories of gravity are distinguished:

Newtonian gravity

In 1687, Newton laid the foundations of celestial mechanics, which studies the motion of bodies in empty space. He calculated the force of gravity of the Moon on the Earth. According to the formula, this force directly depends on their mass and the distance between objects.

F = (G m1 m2)/r2
Gravitational constant G=6.67*10-11

The equation is not entirely relevant when analyzing a strong gravitational field or the attraction of more than two objects.

Einstein's theory of gravity

In the course of various experiments, scientists came to the conclusion that there are some errors in Newton's formula. The basis of celestial mechanics is a long-range force that operates instantly regardless of distance, which does not correspond to the theory of relativity.

According to A. Einstein’s theory developed at the beginning of the 20th century, information is not disseminated faster speed light in a vacuum, so gravitational effects arise as a result of the deformation of space-time. The greater the mass of the object, the greater the curvature into which lighter objects roll.

Quantum gravity

A very controversial and not fully formed theory that explains the interaction of bodies as the exchange of special particles - gravitons.

At the beginning of the 21st century, scientists managed to conduct several significant experiments, including using the Hadron Collider, and develop the theory of loop quantum gravity and string theory.

Universe without gravity

Science fiction novels often describe various gravitational distortions, anti-gravity chambers and spaceships with an artificial gravitational field. Readers sometimes don’t even think about how unrealistic the plots of books are and what will happen if gravity decreases/increases or completely disappears.

1. Man is adapted to earth's gravity, so in other conditions it will have to change dramatically. Weightlessness leads to muscle atrophy, a reduction in the number of red blood cells and disruption of all vital functions. important systems body, and with an increase in the gravitational field, people simply will not be able to move.
2. Air and water, plants and animals, houses and cars will fly away into open space. Even if people manage to stay, they will quickly die without oxygen and food. Low gravity on the Moon is the main reason for the absence of an atmosphere and, accordingly, life.
3. Our planet will fall apart as the pressure in the very center of the Earth disappears, all existing volcanoes will erupt and tectonic plates will diverge.
4. Stars will explode due to intense pressure and chaotic collisions of particles in the core.
5. The universe will become a formless stew of atoms and molecules that are unable to combine to create anything greater.

Fortunately for humanity, the shutdown of gravity and the terrible events that follow will never happen. The dark scenario simply demonstrates how important gravity is. She is much weaker than electromagnetism, strong or weak interaction, but in fact, without it, our world will cease to exist.