Power of attraction definition. What is gravity for dummies: definition and theory in simple words

Between any material points there is a force of mutual attraction, directly proportional to the product of their masses and inversely proportional to the square of the distance between them, acting along the line connecting these points

Isaac Newton suggested that there are forces of mutual attraction between any bodies in nature. These forces are called by gravitational forces or forces of universal gravity. The force of unnatural 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 by 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 each 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 gravity act between any bodies in nature, but they become noticeable at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is satisfied 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 towards the Earth (or to another planet). This force is called gravity. Under the influence of this force, all bodies acquire free fall acceleration.

In accordance with 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 a 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 geographic latitude of the body's position, the acceleration of gravity takes on different values. On the Earth's surface and in mid-latitudes, the acceleration of gravity is 9.831 m/s 2 .

Body weight

The concept of body weight is widely used in technology and everyday life.

Body weight denoted by \(P\) . The unit of weight is newton (N). Since weight is equal to the force with which the body acts on the support, then, in accordance with Newton’s third law, the largest weight of the body is equal to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the support reaction force is equal to.

In this case, it is assumed that the body is motionless relative to the support or suspension.

The weight of a body and the force of gravity differ in nature: the weight of a body is a manifestation of the action of intermolecular forces, and the force of gravity is of 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 free fall acceleration, 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 gravity acts on the spacecraft. Under the influence of this force, the spaceship and all the bodies in it move with the same acceleration, therefore a state of weightlessness is observed in the ship.

Gravitational interaction manifests itself in the attraction of bodies to each other. This interaction is explained by the presence of a gravitational field around each body.

Modulus of the force of gravitational interaction between two material points of mass m 1 and m 2 located at a distance from each other

(2.49)

where F 1.2, F 2.1 – interaction forces directed along the straight line connecting the material points, G = 6.67
– gravitational constant.

Relationship (2.3) is called law of universal gravitation discovered by Newton.

Gravitational interaction is valid for material points and bodies with a spherically symmetric distribution of masses, the distance between which is measured from their centers.

If we take one of the interacting bodies to be the Earth, and the second is a body with mass m, located near or on its surface, then an attractive force acts between them

, (2.50)

where M 3 ,R 3 – mass and radius of the Earth.

Ratio
- a constant value equal to 9.8 m/s 2, denoted g, has the dimension of acceleration and is called acceleration of free fall.

Product of body mass m and free fall acceleration , called gravity

. (2.51)

Unlike the force of gravitational interaction gravity module
depends on the geographic latitude of the body’s location on Earth. At the poles
, and at the equator it decreases by 0.36%. This difference is due to the fact that the Earth rotates on its axis.

With the body removed relative to the Earth's surface to a height gravity decreases

, (2.52)

Where
– acceleration of free fall at a height h from the Earth.

Mass in formulas (2.3-2.6) is a measure of gravitational interaction.

If you hang a body or place it on a fixed support, it will be at rest relative to the Earth, because the force of gravity is balanced by the reaction force acting on the body from the support or suspension.

Reaction force- the force with which other bodies act on a given body, limiting its movement.

Normal ground reaction forceattached to the body and directed perpendicular to the plane of support.

Thread reaction force(suspension) directed along the thread (suspension)

Body weight –the force with which the body presses on the support or stretches the thread of the suspension and is applied to the support or suspension.

Weight is numerically equal to the force of gravity if the body is on a horizontal surface of a support in a state of rest or uniform linear motion. In other cases, the weight of the body and the force of gravity are not equal in magnitude.

2.6.3.Friction forces

Friction forces arise as a result of the interaction of moving and resting bodies in contact with each other.

There are external (dry) and internal (viscous) friction.

External dry friction divided by:

The listed types of external friction correspond to the forces of friction, rest, sliding, and rolling.

WITH

static friction

If an increasing external force is applied to a body in contact with another body , parallel to the plane of contact (Fig. 2.2.a), then when changing from zero to some value
body movement does not occur. The body begins to move at F F tr. max.

Maximum static friction force

, (2.53)

Where – coefficient of static friction, N – modulus of the normal reaction force of the support.

Static friction coefficient can be determined experimentally by finding the tangent of the angle of inclination to the horizon of the surface from which the body begins to roll under the influence of its gravity.

When F>
bodies slide relative to each other at a certain speed (Fig. 2.11 b).

The sliding friction force is directed against the speed . The modulus of the sliding friction force at low speeds is calculated in accordance with Amonton's law

, (2.54)

Where – dimensionless coefficient of sliding friction, depending on the material and state of the surface of the contacting bodies, and is always less .

The rolling friction force occurs when a body in the shape of a cylinder or ball of radius R rolls along the surface of a support. The numerical value of the rolling friction force is determined in accordance with Coulomb's law

, (2.55)

where k[m] – rolling friction coefficient.

Gravity, also known as attraction or gravitation, is a universal property of matter that all objects and bodies in the Universe possess. The essence of gravity is that all material bodies attract all other bodies around them.

Earth gravity

If gravity is a general concept and quality that all objects in the Universe possess, then gravity is a special case of this comprehensive phenomenon. The earth attracts to itself all material objects located on it. Thanks to this, people and animals can safely move across the earth, rivers, seas and oceans can remain within their shores, and the air can not fly across the vast expanses of space, but form the atmosphere of our planet.

A fair question arises: if all objects have gravity, why does the Earth attract people and animals to itself, and not vice versa? Firstly, we also attract the Earth to us, it’s just that, compared to its force of attraction, our gravity is negligible. Secondly, the force of gravity depends directly on the mass of the body: the smaller the mass of the body, the lower its gravitational forces.

The second indicator on which the force of attraction depends is the distance between objects: the greater the distance, the less the effect of gravity. Thanks also to this, the planets move in their orbits and do not fall on each other.

It is noteworthy that the Earth, Moon, Sun and other planets owe their spherical shape precisely to the force of gravity. It acts in the direction of the center, pulling towards it the substance that makes up the “body” of the planet.

Earth's gravitational field

The Earth's gravitational field is a force energy field that is formed around our planet due to the action of two forces:

• gravity;
• centrifugal force, which owes its appearance to the rotation of the Earth around its axis (diurnal rotation).

Since both gravity and centrifugal force act constantly, the gravitational field is a constant phenomenon.

The field is slightly affected by the gravitational forces of the Sun, Moon and some other celestial bodies, as well as the atmospheric masses of the Earth.

The law of universal gravitation and Sir Isaac Newton

The English physicist, Sir Isaac Newton, according to a well-known legend, one day while walking in the garden during the day, he saw the Moon in the sky. At the same time, an apple fell from the branch. Newton was then studying the law of motion and knew that an apple falls under the influence of a gravitational field, and the Moon rotates in orbit around the Earth.

And then the brilliant scientist, illuminated by insight, came up with the idea that perhaps the apple falls to the ground, obeying the same force thanks to which the Moon is in its orbit, and not rushing randomly throughout the galaxy. This is how the law of universal gravitation, also known as Newton’s Third Law, was discovered.

In the language of mathematical formulas, this law looks like this:

F=GMm/D 2 ,

Where F- the force of mutual gravity between two bodies;

M- mass of the first body;

m- mass of the second body;

D 2- the distance between two bodies;

G- gravitational constant equal to 6.67x10 -11.

To the question “What is force?” physics answers this way: “Force is a measure of the interaction of material bodies with each other or between bodies and other material objects - physical fields.” All forces in nature can be classified into four fundamental types of interactions: strong, weak, electromagnetic and gravitational. Our article talks about what gravitational forces are - a measure of the last and, perhaps, most widespread type of these interactions in nature.

Let's start with the gravity of the earth

Everyone alive knows that there is a force that attracts objects to the earth. It is commonly referred to as gravity, gravity, or gravity. Thanks to its presence, humans have the concepts of “up” and “down,” which determine the direction of movement or location of something relative to the earth’s surface. So in a particular case, on the surface of the earth or near it, gravitational forces manifest themselves, which attract objects with mass to each other, manifesting their effect at any distance, both small and very large, even by cosmic standards.

Gravity and Newton's third law

As is known, any force, if it is considered as a measure of the interaction of physical bodies, is always applied to one of them. So in the gravitational interaction of bodies with each other, each of them experiences such types of gravitational forces that are caused by the influence of each of them. If there are only two bodies (it is assumed that the action of all others can be neglected), then each of them, according to Newton’s third law, will attract the other body with the same force. So the Moon and the Earth attract each other, resulting in the ebb and flow of the Earth's seas.

Each planet in the solar system experiences several gravitational forces from the Sun and other planets. Of course, it is the gravitational force of the Sun that determines the shape and size of its orbit, but astronomers also take into account the influence of other celestial bodies in their calculations of the trajectories of their movement.

Which will fall to the ground faster from a height?

The main feature of this force is that all objects fall to the ground at the same speed, regardless of their mass. Once upon a time, right up to the 16th century, it was believed that everything was the other way around - heavier bodies should fall faster than lighter ones. To dispel this misconception, Galileo Galilei had to perform his famous experiment of simultaneously dropping two cannonballs of different weights from the leaning Tower of Pisa. Contrary to the expectations of witnesses to the experiment, both nuclei reached the surface at the same time. Today, every schoolchild knows that this happened due to the fact that gravity imparts to any body the same acceleration of free fall g = 9.81 m/s 2 regardless of the mass m of this body, and its value according to Newton’s second law is equal to F = mg.

Gravitational forces on the Moon and on other planets have different values ​​of this acceleration. However, the nature of the action of gravity on them is the same.

Gravity and body weight

If the first force is applied directly to the body itself, then the second to its support or suspension. In this situation, elastic forces always act on the bodies from the supports and suspensions. Gravitational forces applied to the same bodies act towards them.

Imagine a weight suspended above the ground by a spring. Two forces are applied to it: the elastic force of the stretched spring and the force of gravity. According to Newton's third law, the load acts on the spring with a force equal and opposite to the elastic force. This force will be its weight. A load weighing 1 kg has a weight equal to P = 1 kg ∙ 9.81 m/s 2 = 9.81 N (newton).

Gravitational forces: definition

The first quantitative theory of gravity, based on observations of planetary motion, was formulated by Isaac Newton in 1687 in his famous “Principles of Natural Philosophy.” He wrote that the gravitational forces that act on the Sun and planets depend on the amount of matter they contain. They spread over long distances and always decrease as the reciprocal of the square of the distance. How can we calculate these gravitational forces? The formula for the force F between two objects with masses m 1 and m 2 located at a distance r is:

• F=Gm 1 m 2 /r 2 ,
  where G is a constant of proportionality, a gravitational constant.

Physical mechanism of gravity

Newton was not completely satisfied with his theory, since it assumed interaction between attracting bodies at a distance. The great Englishman himself was sure that there must be some physical agent responsible for transferring the action of one body to another, which he quite clearly stated in one of his letters. But the time when the concept of a gravitational field that permeates all space was introduced came only four centuries later. Today, speaking about gravity, we can talk about the interaction of any (cosmic) body with the gravitational field of other bodies, the measure of which is the gravitational forces arising between each pair of bodies. The law of universal gravitation, formulated by Newton in the above form, remains true and is confirmed by many facts.

Gravity theory and astronomy

It was very successfully applied to solving problems of celestial mechanics during the 18th and early 19th centuries. For example, mathematicians D. Adams and W. Le Verrier, analyzing disturbances in the orbit of Uranus, suggested that it is subject to gravitational forces of interaction with an as yet unknown planet. They indicated its expected position, and soon Neptune was discovered there by astronomer I. Galle.

There was still one problem though. Le Verrier in 1845 calculated that the orbit of Mercury precesses by 35" per century, in contrast to the zero value of this precession obtained from Newton's theory. Subsequent measurements gave a more accurate value of 43". (The observed precession is actually 570"/century, but a careful calculation to subtract the influence from all other planets gives a value of 43".)

It was not until 1915 that Albert Einstein was able to explain this discrepancy within the framework of his theory of gravity. It turned out that the massive Sun, like any other massive body, bends space-time in its vicinity. These effects cause deviations in the orbits of planets, but on Mercury, as the smallest and closest planet to our star, they are most pronounced.

Inertial and gravitational masses

As noted above, Galileo was the first to observe that objects fall to the ground at the same speed, regardless of their mass. In Newton's formulas, the concept of mass comes from two different equations. His second law says that a force F applied to a body with mass m gives acceleration according to the equation F = ma.

However, the force of gravity F applied to a body satisfies the formula F = mg, where g depends on the other body interacting with the one in question (the earth usually when we talk about gravity). In both equations m is a coefficient of proportionality, but in the first case it is inertial mass, and in the second it is gravitational mass, and there is no obvious reason that they should be the same for any physical object.

However, all experiments show that this is indeed the case.

Einstein's theory of gravity

He took the fact of equality of inertial and gravitational masses as a starting point for his theory. He managed to construct the gravitational field equations, the famous Einstein equations, and with their help calculate the correct value for the precession of the orbit of Mercury. They also give a measured value for the deflection of light rays that pass near the Sun, and there is no doubt that they give the correct results for macroscopic gravity. Einstein's theory of gravity, or general theory of relativity (GR) as he called it, is one of the greatest triumphs of modern science.

Are gravitational forces acceleration?

If you cannot distinguish inertial mass from gravitational mass, then you cannot distinguish gravity from acceleration. The gravitational field experiment can instead be performed in an accelerating elevator in the absence of gravity. When an astronaut in a rocket accelerates away from the earth, he experiences a force of gravity that is several times greater than Earth's, with the vast majority of it coming from acceleration.

If no one can distinguish gravity from acceleration, then the former can always be reproduced by acceleration. A system in which acceleration replaces gravity is called inertial. Therefore, the Moon in near-Earth orbit can also be considered as an inertial system. However, this system will differ from point to point as the gravitational field changes. (In the example of the Moon, the gravitational field changes direction from one point to another.) The principle that one can always find an inertial system at any point in space and time at which physics obeys the laws in the absence of gravity is called the equivalence principle.

Gravity as a manifestation of the geometric properties of space-time

The fact that gravitational forces can be thought of as accelerations in inertial coordinate systems that differ from point to point means that gravity is a geometric concept.

We say that spacetime is curved. Consider a ball on a flat surface. It will rest or, if there is no friction, move uniformly in the absence of any forces acting on it. If the surface is curved, the ball will accelerate and move to the lowest point, taking the shortest path. Similarly, Einstein's theory states that four-dimensional space-time is curved, and a body moves in this curved space along a geodesic line that corresponds to the shortest path. Therefore, the gravitational field and the gravitational forces acting in it on physical bodies are geometric quantities that depend on the properties of space-time, which change most strongly near massive bodies.

DEFINITION

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

Two bodies attract 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 has the meaning:

This constant, as can be seen, is very small, therefore the gravitational forces between bodies with small masses are also small and practically not felt. However, the movement of cosmic bodies is completely determined by gravity. The presence of universal gravitation or, in other words, gravitational interaction explains what the Earth and planets are “supported” by, and why they move around the Sun along certain trajectories, and do not fly away from it. The law of universal gravitation allows us 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 planets with great accuracy and create a mathematical model of the Universe.

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

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 not fully understood. 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 the force of gravity acts on a body, then the body does . The type of movement depends on the direction and magnitude of the initial speed.

We face the effects of gravity every day. , after a while he finds himself on the ground. The book, released from the hands, falls down. Having jumped, a person does not fly into outer space, but falls 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 does the acceleration of gravity come from:

The acceleration of gravity does not depend on the mass of the body, but depends on the height of the body above the Earth. The globe is slightly flattened at the poles, so bodies located 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 area: at the pole it is slightly greater 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 with mass and radius.

Examples of problem solving

EXAMPLE 1 (problem about “weighing” the Earth)

EXAMPLE 2