What is the force of gravity in physics. Gravitational forces

According to Newton's laws, the movement of a body with acceleration is possible only under the action of a force. Because falling bodies move with an acceleration directed downward, then they are acted upon by the force of gravity to the earth. But not only the Earth has the property to act on all bodies by the force of gravity. Isaac Newton suggested that forces of attraction act between all bodies. These forces are called forces of gravity or gravitational forces.

Having spread the established regularities - the dependence of the force of attraction of bodies to the Earth on the distances between bodies and on the masses of interacting bodies, obtained as a result of observations - Newton discovered in 1682. the law of universal gravitation:All bodies are attracted to each other, the force of universal gravity is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them:

The vectors of the forces of universal gravitation are directed along the straight line connecting the bodies. The proportionality coefficient G is called gravitational constant (constant of universal gravitation) and is equal

.

By gravity is called the force of gravity acting from the Earth on all bodies:

.

Let be
Is the mass of the Earth, and
Is the radius of the Earth. Consider the dependence of the acceleration of gravity on the rise above the Earth's surface:

Body weight. Weightlessness

Body weight - the force with which a body presses on a support or suspension due to the attraction of this body to the ground. The body weight is applied to the support (suspension). The amount of body weight depends on how the body moves with the support (suspension).

Body weight, i.e. the force with which the body acts on the support, and the elastic force with which the support acts on the body, in accordance with Newton's third law, are equal in absolute value and opposite in direction.

If the body is at rest on a horizontal support or evenly moves, only gravity and the elastic force from the support act on it, therefore the body weight is equal to gravity (but these forces are applied to different bodies):

.

With accelerated movement, the weight of the body will not be equal to the force of gravity. Let us consider the motion of a body with mass m under the action of gravity and elastic forces with acceleration. According to Newton's 2nd law:

If the acceleration of the body is directed downward, then the weight of the body is less than the force of gravity; if the acceleration of the body is directed upward, then all bodies are greater than the force of gravity.

The increase in body weight caused by accelerated movement of the support or suspension is called overload.

If the body falls freely, then from the formula * it follows that the body's weight is zero. The disappearance of weight when the support moves with the acceleration of gravity is called weightlessness.

The state of weightlessness is observed in an airplane or spacecraft when they move with the acceleration of gravity, regardless of their speed of movement. Outside the earth's atmosphere, when the jet engines are turned off, only the force of universal gravity acts on the spacecraft. Under the action of this force, the spaceship and all the bodies in it move with the same acceleration; therefore, the phenomenon of weightlessness is observed in the ship.

The movement of the body under the influence of gravity. The movement of artificial satellites. First space speed

If the modulus of movement of the body is much less than the distance to the center of the Earth, then the force of universal gravitation during the movement can be considered constant, and the movement of the body is uniformly accelerated. The simplest case of a body moving under the action of gravity is a free fall with zero initial velocity. In this case, the body moves with the acceleration of gravity towards the center of the Earth. If there is an initial velocity not directed vertically, then the body moves along a curvilinear trajectory (a parabola, if the air resistance is not taken into account).

At a certain initial velocity, a body thrown tangentially to the Earth's surface, under the action of gravity, in the absence of an atmosphere, can move in a circle around the Earth without falling on it and not moving away from it. This speed is called first space speed, and a body moving in this way - artificial Earth satellite (AES).

Let's define the first space velocity for the Earth. If a body under the action of gravity moves around the Earth uniformly around the circumference, then the acceleration of gravity is its centripetal acceleration:

.

Hence, the first cosmic speed is

.

The first cosmic velocity for any celestial body is determined in the same way. Free fall acceleration at a distance R from the center of a celestial body can be found using Newton's second law and the law of universal gravitation:

.

Consequently, the first cosmic velocity at a distance R from the center of a celestial body with mass M is

.

To launch an artificial satellite into a near-earth orbit, it is first necessary to launch it outside the atmosphere. Therefore, spaceships start vertically. At an altitude of 200 - 300 km from the Earth's surface, where the atmosphere is rarefied and has almost no effect on the movement of the satellite, the rocket makes a turn and imparts the first space velocity to the satellite in the direction perpendicular to the vertical.

DEFINITION

The law of universal gravitation was discovered by I. Newton:

Two bodies are attracted to each other with, directly proportional to their product and inversely proportional to the square of the distance between them:

Description of the law of universal gravitation

The coefficient is the gravitational constant. In the SI system, the gravitational constant matters:

This constant, as can be seen, is very small, therefore the forces of gravity between bodies with small masses are also small and practically not felt. However, the motion of cosmic bodies is completely determined by gravity. The presence of universal gravitation or, in other words, gravitational interaction explains what the Earth and the planets are "held on", and why they move around the Sun along certain trajectories, and do not fly away from it. The law of gravitation makes it possible to determine many characteristics of celestial bodies - the masses of planets, stars, galaxies and even black holes. This law makes it possible to calculate the orbits of the planets with great accuracy and create a mathematical model of the Universe.

Using the law of universal gravitation, it is also possible to calculate cosmic velocities. For example, the minimum speed at which a body moving horizontally above the surface of the Earth will not fall on it, but will move in a circular orbit - 7.9 km / s (the first cosmic speed). In order to leave the Earth, i.e. overcome its gravitational attraction, the body must have a speed of 11.2 km / s, (the second cosmic speed).

Gravity is one of the most amazing natural phenomena. In the absence of gravitational forces, the existence of the Universe would be impossible, the Universe could not even arise. Gravity is responsible for many processes in the Universe - its birth, the existence of order instead of chaos. The nature of gravity is still completely unsolved. Until now, no one has been able to develop a decent mechanism and model of gravitational interaction.

Gravity

A special case of the manifestation of gravitational forces is the force of gravity.

Gravity is always directed vertically downward (toward the center of the earth).

If gravity acts on the body, then the body commits. The type of movement depends on the direction and module of the initial speed.

We are faced with the action of gravity every day. , after a while appears on the ground. The book, released from the hands, falls down. Having jumped, a person does not fly away into open space, but sinks down to the ground.

Considering the free fall of a body near the Earth's surface as a result of the gravitational interaction of this body with the Earth, we can write:

where is the acceleration of gravity:

Free fall acceleration does not depend on body weight, but depends on the body's height above the Earth. The globe will flatten slightly at the poles, so the bodies near the poles are located a little closer to the center of the Earth. In this regard, the acceleration of gravity depends on the latitude of the terrain: at the pole it is slightly higher than at the equator and other latitudes (at the equator m / s, at the North Pole equator m / s.

The same formula allows you to find the acceleration of gravity on the surface of any planet by mass and radius.

Examples of problem solving

EXAMPLE 1 (the problem of "weighing" the Earth)

EXAMPLE 2

Gravitational force is the force with which bodies of a certain mass, located at a certain distance from each other, are attracted to each other.

The English scientist Isaac Newton discovered the law of universal gravitation in 1867. 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 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 on its surface. And any person feels this force as his own weight.

The law of universal gravitation

There is a legend that Newton discovered the law of universal gravitation by accident, walking in the evening in the garden of his parents. Creative people are constantly in search, and scientific discoveries are not instant insights, but the fruit of long-term mental work. Sitting under an apple tree, Newton was comprehending 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. “So there’s some other force acting on it, keeping it in orbit.” This is how the famous the law of universal gravitation.

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 forms 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 has fallen in the garden and the planets in space are acted upon by forces that obey the same law - the law of gravity.

Newton established that Kepler's laws are valid only if there is a force of gravity 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 - the mass of the first body;

m 2- the mass of the second body;

r - distance between bodies;

G - coefficient of proportionality, which is called gravitational constant or constant universal gravitation.

Its value was determined experimentally. G= 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 gravitational forces. They are also called forces of gravity... They are subject to the law of universal gravitation and are manifested 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 by gravity... It is considered constant if the distance of the body from the surface of the Earth is small in comparison with the radius of the Earth.

Since the force of 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 gravity on the Moon is 6 times less than on Earth. And on Jupiter, on the contrary, the force of gravity is 2.4 times greater than the force of 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 this is not the case.

The force with which the body presses on the support or stretches the suspension, this is the weight. If you remove the support or suspension, the body will begin to fall with the acceleration of free fall under the force of gravity. Gravity is proportional to body weight. It is calculated by the formulaF= m g , where m- body mass, g - acceleration of gravity.

Body weight can change and sometimes disappear altogether. Let's imagine that we are in the elevator on the top floor. The elevator is standing. At this moment, our weight P and the force of gravity F, with which the Earth attracts us, are equal. But as soon as the elevator started to move down with acceleration a , weight and gravity are no longer equal. According to Newton's second lawmg+ P = ma. P = m g -ma.

It can be seen from the formula that our weight decreased as we moved down.

The moment the elevator picks up speed and begins to move without acceleration, our weight is again equal to the force of gravity. And when the elevator began to slow down, the acceleration a became negative and the weight increased. An overload sets in.

And if the body moves downward with the acceleration of free fall, then the weight will become completely 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 bodies located at 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 through a special type of matter called gravitational field.

Gravitational forces (gravitational forces) due to the mutual attraction of bodies and are directed along the line connecting the interacting points.

The expression for the force of gravity in 1666 was received by Newton when he was only 24 years old.

The law of universal gravitation: two bodies are attracted to each other with forces 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 negligible in comparison with 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 a material point.

The proportionality coefficient G = 6.68 10 -11 is called gravitational constant.

Physical sense the gravitational constant is that it is numerically equal to the force with which two bodies weighing 1 kg each, located at a distance of 1 m from each other, are attracted.

Gravity

The force with which the Earth attracts those near the body is called by gravity , and the gravitational field of the Earth - by the field of gravity .

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 in this center. Moreover, it may not coincide with any of the points of the given body (for example, at 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 pattern: if the body is suspended on a thread attached sequentially to different points of the body, then the directions marked with a thread will intersect at one point, which is precisely the center the weight of this body.

The gravity modulus is found using the law of universal gravitation and is determined by the formula:

F т = mg, (2.7)

where g is the free fall acceleration of the body (g = 9.8 m / s 2 ≈10 m / s 2).

Since the direction of the acceleration of gravity g coincides with the direction of the force of gravity F t, then the last equality can be rewritten in the form

From (2.7) it follows 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 acceleration of gravity at a given point of the field.

For points located at a height h from the Earth's surface, the free fall acceleration of a body is equal to:

(2.8)

where R З is the radius of the Earth; M Z is the mass of the Earth; h is the distance from the center of gravity of the body to the surface of the Earth.

This formula implies that,

At first, the acceleration of gravity does not depend on the mass and size of the body and,

Secondly, with increasing altitude above the Earth, the acceleration of gravity decreases. For example, at an altitude of 297 km it turns out to be equal not to 9.8 m / s 2, but 9 m / s 2.

A decrease in the acceleration of gravity means that the force of gravity also decreases with an increase in height above the Earth. The further the body is from the Earth, the weaker it attracts it.

From the formula (1.73) it can be seen that g depends on the radius of the Earth R s.

But due to the flattening of the Earth, it has different meanings in different places: it decreases as it moves from the equator to the pole. At the equator, for example, it is equal to 9.780 m / s 2, and at the pole - 9.832 m / s 2. In addition, local g values ​​may differ from their average g avg 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, while negative Δg<0– о залежах лёгких полезных ископаемых, например нефти и газа.

The method for determining mineral deposits by accurately measuring the acceleration of gravity 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-pervading ability. If you can protect yourself from electric and magnetic fields with the help of special metal screens, then nothing can be protected from the gravitational field: it penetrates through any materials.