Why do bodies attract each other? All bodies attract each other

Gravitational forces or otherwise gravitational forces acting between two bodies:
- long-range;
- there are no barriers for them;
- directed along a straight line connecting the bodies;
- equal in size;
- opposite in direction.

Gravitational interaction

Proportionality factor G called gravitational constant.

Physical meaning of the gravitational constant:
the gravitational constant is numerically equal to the modulus of the gravitational force acting between two point bodies weighing 1 kg each, located at a distance of 1 m from each other

Condition for the applicability of the law of universal gravitation

1. The sizes of bodies are much smaller than the distances between them;

2. Both bodies are spheres and they are homogeneous;

;

3. One body big ball, and the other is located near it

(planet Earth and bodies near its surface).

Not applicable.

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.
Gravitational interaction is noticeably manifested when bodies of large mass interact.
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. Therefore, the strength universal gravity must be proportional to the product of the masses of interacting bodies.

Examples of gravitational interactions

The attraction from the Moon causes the ebb and flow of water on Earth, huge masses of which rise in the oceans and seas twice a day to a height of several meters. Every 24 hours and 50 minutes, the Moon causes tides not only in the oceans, but also in the Earth's crust and atmosphere. Under the influence of tidal forces, the lithosphere is stretched by about half a meter.

Conclusion

• In astronomy, the law of universal gravitation is fundamental, on the basis of which the parameters of the movement of space objects are calculated and their masses are determined.
• The onset of the ebb and flow of the seas and oceans is predicted.
• The flight trajectories of projectiles and missiles are determined, heavy ore deposits are explored
• One of the manifestations of universal gravitation is the action of gravity

Homework.

1. E.V. Korshak, A.I. Lyashenko, V.F. Savchenko. Physics. Grade 10, “Genesis”, 2010. Read §19 (p.63-66).

2. Solve problems No. 1, 2 exercises 10 (p. 66).

3. Execute test:

1.What force makes the Earth and other planets move around the Sun? Choose the correct statement.

A. Inertial force. B. Centripetal force. B. Gravitational force.

Questions.

1. What was called universal gravity?

Universal gravity was the name given to the mutual attraction of all bodies in the Universe.

2. What is another name for the forces of universal gravity?

The forces of universal gravitation are otherwise called gravitational (from the Latin gravitas - “gravity”).

3. Who discovered the law of universal gravitation and in what century?

The law of universal gravitation was discovered by Isaac Newton in the 17th century.

4. How is the law of universal gravitation read?

Any two bodies attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

5. Write down a formula expressing the law of universal gravitation.

6. In what cases should this formula be used to calculate gravitational forces?

The formula can be used to calculate gravitational forces if the bodies can be taken as material points: 1) if the sizes of the bodies are much smaller than the distances between them; 2) if two bodies are spherical and homogeneous; 3) if one body, spherical in shape, is many times larger in mass and size than the second.

7. Is the Earth attracted to an apple hanging on a branch?

In accordance with the law of universal gravitation, an apple attracts the Earth with the same force as the Earth attracts an apple, only in the opposite direction.

Exercises.

1. Give examples of the manifestation of gravity.

The fall of bodies to the ground under the influence of gravity, the attraction of celestial bodies (Earth, Moon, sun, planets, comets, meteorites) to each other.

2. Space station flies from the Earth to the Moon. How does the modulus of the vector of its force of attraction to the Earth change in this case? to the moon? Is the station attracted to the Earth and the Moon with equal or different magnitude forces when it is in the middle between them? Justify all three answers. (It is known that the mass of the Earth is approximately 81 times the mass of the Moon).

3. It is known that the mass of the Sun is 330,000 times greater than the mass of the Earth. Is it true that the Sun attracts the Earth 330,000 times stronger than the Earth attracts the Sun? Explain your answer.

No, bodies attract each other with equal forces, because... the force of attraction is proportional to the product of their masses.

4. The ball thrown by the boy moved upward for some time. At the same time, its speed decreased all the time until it became equal to zero. Then the ball began to fall down with increasing speed. Explain: a) whether the force of gravity towards the Earth acted on the ball during its upward movement; down; b) what caused the decrease in the speed of the ball as it moved up; increasing its speed when moving down; c) why, when the ball moved up, its speed decreased, and when it moved down, it increased.

a) yes, the force of gravity acted all the way; b) worldwide power gravity (gravity of the Earth); c) when moving up, the speed and acceleration of the body are multidirectional, and when moving down, they are codirectional.

5. Is a person standing on Earth attracted to the Moon? If so, what is it more attracted to: the Moon or the Earth? Is the Moon attracted to this person? Justify your answers.

Yes, all bodies are attracted to each other, but the force of attraction of a person to the Moon is much less than to the Earth, because The moon is much further away.

In the 7th grade physics course, you studied the phenomenon of universal gravitation. It lies in the fact that there are gravitational forces between all bodies in the Universe.

Newton came to the conclusion about the existence of universal gravitational forces (they are also called gravitational forces) as a result of studying the movement of the Moon around the Earth and the planets around the Sun.

Newton's merit lies not only in his brilliant guess about the mutual attraction of bodies, but also in the fact that he was able to find the law of their interaction, i.e. the formula for calculating gravitational force between two bodies.

The law of universal gravitation says:

• any two bodies attract each other with a force directly proportional to the mass of each of them and inversely proportional to the square of the distance between them

where F is the magnitude of the vector of gravitational attraction between bodies of masses m 1 and m 2, g is the distance between the bodies (their centers); G is the coefficient, which is called gravitational constant.

If m 1 = m 2 = 1 kg and g = 1 m, then, as can be seen from the formula, the gravitational constant G is numerically equal to the force F. In other words, the gravitational constant is numerically equal to the force F of attraction of two bodies weighing 1 kg each, located at a distance 1 m apart. Measurements show that

G = 6.67 10 -11 Nm 2 /kg 2.

The formula gives an accurate result when calculating the force of universal gravity in three cases: 1) if the sizes of the bodies are negligible compared to the distance between them (Fig. 32, a); 2) if both bodies are homogeneous and have a spherical shape (Fig. 32, b); 3) if one of the interacting bodies is a ball, the dimensions and mass of which are significantly greater than that of the second body (of any shape) located on the surface of this ball or near it (Fig. 32, c).

Rice. 32. Conditions defining the limits of applicability of the law of universal gravitation

The third of the cases considered is the basis for calculating, using the given formula, the force of attraction to the Earth of any of the bodies located on it. In this case, the radius of the Earth should be taken as the distance between bodies, since the sizes of all bodies located on its surface or near it are negligible compared to the Earth’s radius.

According to Newton's third law, an apple hanging on a branch or falling from it with the acceleration of free fall attracts the Earth to itself with the same absolute force as the Earth attracts it. But the acceleration of the Earth, caused by the force of its attraction to the apple, is close to zero, since the mass of the Earth is incommensurably greater than the mass of the apple.

Questions

1. What was called universal gravity?
2. What is another name for the forces of universal gravity?
3. Who discovered the law of universal gravitation and in what century?
4. Formulate the law of universal gravitation. Write down a formula expressing this law.
5. In what cases should the law of universal gravitation be applied to calculate gravitational forces?
6. Is the Earth attracted to an apple hanging on a branch?

Exercise 15

1. Give examples of the manifestation of gravity.
2. The space station flies from the Earth to the Moon. How does the modulus of the vector of its force of attraction to the Earth change in this case; to the moon? Is the station attracted to the Earth and the Moon with equal or different magnitude forces when it is in the middle between them? If the forces are different, which one is greater and by how many times? Justify all answers. (It is known that the mass of the Earth is about 81 times the mass of the Moon.)
3. It is known that the mass of the Sun is 330,000 times greater than the mass of the Earth. Is it true that the Sun attracts the Earth 330,000 times stronger than the Earth attracts the Sun? Explain your answer.
4. The ball thrown by the boy moved upward for some time. At the same time, its speed decreased all the time until it became equal to zero. Then the ball began to fall down with increasing speed. Explain: a) whether the force of gravity towards the Earth acted on the ball during its upward movement; down; b) what caused the decrease in the speed of the ball as it moved up; increasing its speed when moving down; c) why, when the ball moved up, its speed decreased, and when it moved down, it increased.
5. Is a person standing on Earth attracted to the Moon? If so, what is it more attracted to - the Moon or the Earth? Is the Moon attracted to this person? Justify your answers.

where G=6.67×10 -11 N×m 2 /kg 2 is the universal gravitational constant.

This law is called the law of universal gravitation.

The force with which bodies are attracted to the Earth is called gravity. The main feature of gravity is the experimental fact that this force to all bodies, regardless of their mass, reports the same acceleration directed towards the center of the Earth.

It follows from this that the ancient Greek philosopher Aristotle was wrong when he argued that heavy bodies fall to the Earth faster than light ones. He did not take into account that in addition to gravity, the body is subject to a resistance force against the air, which depends on the shape of the body.

A musket ball and a heavy cannonball thrown by the Italian physicist Galileo Galilei famous tower 54.5 m high, located in the city of Pisa, reached the surface of the Earth almost simultaneously, i.e. fell with the same acceleration (Fig. 4.27).

Calculations carried out by G. Galilei showed that the acceleration acquired by bodies under the influence of the Earth's gravity is equal to 9.8 m/s 2 .

Further more accurate experiments were carried out by I. Newton. He took a long glass tube into which he placed a lead ball, a stopper and a feather (Fig. 4.28).

This tube is now called a "Newton tube". Turning the tube over, he saw that the ball fell first, then the cork, and only then the feather. If the air is first pumped out of the tube using a pump, then after turning the tube over, all the bodies will fall to the bottom of the tube simultaneously. And this means that in the second case all bodies increased their speed equally, i.e. received the same acceleration. And this acceleration was imparted to them by a single force - the force of attraction of bodies to the Earth, i.e. gravity. The calculations made by Newton confirmed the correctness of the calculations of G. Galileo, since he also obtained the value of the acceleration acquired by freely falling bodies in the “Newton tube”, equal to 9.8 m/s 2. This constant acceleration is called acceleration of free fall on Earth and is designated by the letter g(from Latin word“gravitas” - heaviness), i.e. g = 9.8 m/s 2.

Free fall is understood as the movement of a body that occurs under the influence of one single force - gravity (air resistance forces are not taken into account).

On other planets or stars, the value of this acceleration is different, as it depends on the masses and radii of the planets and stars.

We present the values ​​of the acceleration of free fall on some planets solar system and on the Moon:

1. Sun g = 274 N/kg

2. Venus g = 8.69N/kg

3. Mars g = 3.86 N/kg

4. Jupiter g = 23 N/kg

5. Saturn g = 9.44 N/kg

6. Moon (Earth satellite) g = 1.623 N/kg

How can we explain the fact that the acceleration of all bodies freely falling to the Earth is the same? After all, the greater the body weight, the great strength gravity affects him. You and I know that 1 N is the force that imparts an acceleration of 1 m/s 2 to a body weighing 1 kg. At the same time, the experiments of G. Galileo and I. Newton showed that the force of gravity changes the speed of any body 9.8 times more. Consequently, a force of 9.8 N acts on a body weighing 1 kg, and a force of gravity equal to 19.6 N will act on a body weighing 2 kg, etc. That is, the greater the mass of the body, the greater the force of gravity will act on it, and the proportionality coefficient will be equal to 9.8 N/kg. Then the formula for calculating gravity will look like or in general view:

Accurate measurements showed that the acceleration of gravity decreases with height and changes slightly with changes in latitude due to the fact that the Earth is not a strictly spherical body (it is slightly flattened at the poles). In addition, it may depend on geographical location on the planet, since the density of the rocks that make up the surface layer of the Earth is different. Last fact allows you to detect mineral deposits.

Here are some values ​​of the acceleration of gravity on Earth:

1. At the North Pole g = 9.832 N/kg

2. At the equator g = 9.780 N/kg

3. At latitude 45 o g = 9.806 N/kg

4. At sea level g = 9.8066 N/kg

5. At the peak of Khan Tengri, 7 km high, g = 9.78 N/kg

6. At a depth of 12 km g = 9.82 N/kg

7. At a depth of 3000 km g = 10.20 N/kg

8. At a depth of 4500 km g = 6.9 N/kg

9. At the center of the Earth g = 0 N/kg

The attraction of the Moon leads to the formation of ebbs and flows in the seas and oceans on Earth. Tide magnitude in open ocean about 1 m, and off the coast of the Bay of Fundy in Atlantic Ocean reaches 18 meters.

The distance from the Earth to the Moon is enormous: about 384,000 km. But the gravitational force between the Earth and the Moon is large and amounts to 2 × 10 20 N. this is due to the fact that the masses of the Earth and the Moon are large.

When solving problems, unless there are special reservations, the value of 9.8 N/kg can be rounded to 10 N/kg.

The lag of the pendulums of clocks synchronized on the first floor of a high-rise building is associated with a change in the quantity g. Since the value g decreases with increasing altitude, then the clock on top floor will begin to lag behind.

Example. Determine the force with which a steel bucket weighing 500 g, volume 12 liters, completely filled with water, presses on the support.

The force of gravity is equal to the sum of the force of gravity of the bucket itself, equal to F gravity1 = m 1 g, and the force of gravity of water poured into a bucket, equal to F heavy1 = m 2 g= ρ 2 V 2 g, i.e.

F cord = m 1 g+ρ 2 V 2 g

Substituting numerical values, we get:

F strand = 0.5 kg 10 N/kg + 10 3 kg/m 3 12 10 -3 m 3 10 N/kg = = 125 N.

Answer: F strand = 125 N

Questions for self-control:

1. What force is called gravitational? What is the reason for this power?

2. What does the law of universal gravitation say?

3. What force is called gravity? What does it consist of main feature?

4. Does gravity exist on other planets? Justify your answer.

5. For what purpose did G. Galileo conduct experiments on the Leaning Tower of Pisa?

6. What do the experiments that Newton conducted with the “Newton tube” prove to us?

7. What acceleration is called the acceleration of gravity?

8. You have two identical sheets of paper. Why does a crumpled leaf fall to the ground faster, even though each leaf has the same force of gravity?

9. What is the fundamental difference in the explanation of free fall by Aristotle and Newton?

10. Give a report on how Aristotle, Galileo and Newton studied free fall.

Sir Isaac Newton, having been hit on the head with an apple, deduced the law of universal gravitation, which states:

Any two bodies are attracted to each other with a force directly proportional to the product of the masses of the body and inversely proportional to the square of the distance between them:

F = (Gm 1 m 2)/R 2, where

m1, m2- body masses
R- distance between the centers of bodies
G = 6.67 10 -11 Nm 2 /kg- constant

Let us determine the acceleration of free fall on the Earth's surface:

F g = m body g = (Gm body m Earth)/R 2

R (radius of the Earth) = 6.38 10 6 m
m Earth = 5.97 10 24 kg

m body g = (Gm body m Earth)/R 2 or g = (Gm Earth)/R 2

Please note that the acceleration due to gravity does not depend on the mass of the body!

g = 6.67 10 -11 5.97 10 24 /(6.38 10 6) = 398.2/40.7 = 9.8 m/s 2

We said earlier that the force of gravity (gravitational attraction) is called weight.

On the surface of the Earth, the weight and mass of a body have the same meaning. But as you move away from the Earth, the weight of the body will decrease (since the distance between the center of the Earth and the body will increase), and the mass will remain constant (since mass is an expression of the inertia of the body). Mass is measured in kilograms, weight - in newtons.

Thanks to the force of gravity, celestial bodies rotate relative to each other: the Moon around the Earth; Earth around the Sun; The Sun around the center of our Galaxy, etc. In this case, the bodies are held by centrifugal force, which is provided by the force of gravity.

The same applies to artificial bodies (satellites) revolving around the Earth. The circle around which the satellite rotates is called the orbit.

In this case, a centrifugal force acts on the satellite:

F c = (m satellite V 2)/R

Gravity force:

F g = (Gm satellite m Earth)/R 2

F c = F g = (m satellite V 2)/R = (Gm satellite m Earth)/R 2

V2 = (Gm Earth)/R; V = √(Gm Earth)/R

Using this formula, you can calculate the speed of any body rotating in an orbit with a radius R around the Earth.

The Earth's natural satellite is the Moon. Let us determine its linear speed in orbit:

Earth mass = 5.97 10 24 kg

R is the distance between the center of the Earth and the center of the Moon. To determine this distance, we need to add three quantities: the radius of the Earth; radius of the Moon; distance from the Earth to the Moon.

R moon = 1738 km = 1.74 10 6 m
R earth = 6371 km = 6.37 10 6 m
R zł = 384400 km = 384.4 10 6 m

Total distance between the centers of the planets: R = 392.5·10 6 m

Linear speed of the Moon:

V = √(Gm Earth)/R = √6.67 10 -11 5.98 10 24 /392.5 10 6 = 1000 m/s = 3600 km/h

The Moon moves in a circular orbit around the Earth with a linear speed of 3600 km/h!

Let us now determine the period of revolution of the Moon around the Earth. During its orbital period, the Moon covers a distance equal to the length of its orbit - 2πR. Moon orbital speed: V = 2πR/T; on the other side: V = √(Gm Earth)/R:

2πR/T = √(Gm Earth)/R hence T = 2π√R 3 /Gm Earth

T = 6.28 √(60.7 10 24)/6.67 10 -11 5.98 10 24 = 3.9 10 5 s

The Moon's orbital period around the Earth is 2,449,200 seconds, or 40,820 minutes, or 680 hours, or 28.3 days.

1. Vertical rotation

Previously, a very popular trick in circuses was in which a cyclist (motorcyclist) made a full turn inside a vertical circle.

What minimum speed should a stuntman have to avoid falling down at the top?

To pass the top point without falling, the body must have a speed that creates a centrifugal force that would compensate for the force of gravity.

Centrifugal force: F c = mV 2 / R

Gravity: F g = mg

F c = F g ; mV 2 /R = mg; V = √Rg

Again, note that body weight is not included in the calculations! Please note that this is the speed that the body should have at the top!

Let's say that there is a circle with a radius of 10 meters in the circus arena. Let's calculate the safe speed for the trick:

V = √Rg = √10 9.8 = 10 m/s = 36 km/h