It is known that all bodies left to themselves fall to the Earth. Bodies thrown up return to Earth. We say that this fall is due to the gravity of the Earth.

This is a general phenomenon, and for this reason the study of laws free fall bodies only under the influence of the Earth's gravity is of particular interest. However, everyday observations show that under normal conditions, bodies fall differently. A heavy ball falls quickly, a light sheet of paper falls slowly and along a complex trajectory.

The nature of the motion, speed and acceleration of falling bodies under normal conditions turn out to depend on the gravity of the bodies, their size and shape.

Experiments show that these differences are due to the action of air on moving bodies. This air resistance is also used in practice, for example when skydiving. The fall of a skydiver before and after the opening of the parachute is of a different nature. The opening of the parachute changes the nature of the movement, the speed and acceleration of the parachutist change.

It goes without saying that such movements of bodies cannot be called free fall under the influence of gravity alone. If we want to study the free fall of bodies, then we must either completely free ourselves from the action of air, or at least somehow equalize the influence of the shape and size of bodies on their movement.

The great Italian scientist Galileo Galilei was the first to come up with this idea. In 1583, in Pisa, he made the first observations on the features of the free fall of heavy balls of the same diameter, studied the laws of motion of bodies according to inclined plane and movement of bodies thrown at an angle to the horizon.

The results of these observations allowed Galileo to discover one of the most important laws of modern mechanics, which is called Galileo's law: all bodies under the influence of earth's gravity fall to the Earth with the same acceleration.

The validity of Galileo's law can be clearly seen from simple experience. Let us place several heavy pellets, light feathers and pieces of paper into a long glass tube. If you put this tube vertically, then all these objects will fall in it in different ways. If the air is pumped out of the tube, then when the experiment is repeated, the same bodies will fall in exactly the same way.

In free fall, all bodies near the Earth's surface move with uniform acceleration. If, for example, a series of snapshots of a falling ball are taken at regular intervals, then by the distances between successive positions of the ball, it can be determined that the motion was indeed uniformly accelerated. By measuring these distances, it is also easy to calculate the numerical value of the gravitational acceleration, which is usually denoted by the letter

At different points on the globe, the numerical value of the acceleration of free fall is not the same. It varies roughly from at the pole to at the equator. Conventionally, the value is taken as the "normal" value of the free fall acceleration. We will use this value in solving practical problems. For rough calculations, we will sometimes take a value, specifically stipulating this at the beginning of solving the problem.

The significance of Galileo's law is very great. It expresses one of the most important properties of matter, allows us to understand and explain many features of the structure of our Universe.

Galileo's law, called the principle of equivalence, entered the foundation of the general theory gravity(gravity), which was created by A. Einstein at the beginning of our century. Einstein called this theory the general theory of relativity.

The importance of Galileo's law is also evidenced by the fact that the equality of accelerations in the fall of bodies has been checked continuously and with ever-increasing accuracy for almost four hundred years. The last most famous measurements belong to the Hungarian scientist Eötvös and the Soviet physicist V. B. Braginsky. Eötvös in 1912 checked the equality of free fall accelerations to the eighth decimal place. V. B. Braginsky in 1970-1971, using modern electronic equipment, checked the validity of Galileo's law with an accuracy of up to the twelfth decimal place when determining the numerical value

Theory

Free fall of bodies is called the fall of bodies to the Earth in the absence of air resistance (in a void). At the end of the 16th century, the famous Italian scientist G. Galileo experimentally established with the accuracy available for that time that in the absence of air resistance, all bodies fall to the Earth with uniform acceleration, and that at a given point on the Earth, the acceleration of all bodies during the fall is the same. Prior to this, for almost two thousand years, starting with Aristotle, it was generally accepted in science that heavy bodies fall to Earth faster than light ones.

The acceleration with which bodies fall to the Earth is called free fall acceleration. The gravitational acceleration vector is indicated by the symbol, it is directed vertically down. in different parts of the world, depending on geographical latitude and height above sea level, the numerical value of g turns out to be unequal, varying from approximately 9.83 m/s 2 at the poles to 9.78 m/s 2 at the equator. At the latitude of Moscow, g \u003d 9.81523 m / s 2. Usually, if high accuracy is not required in the calculations, then the numerical value of g at the Earth's surface is taken equal to 9.8 m/s 2 or even 10 m/s 2.

EXPERIMENTS OF GALILEO WITH FALLING BODIES

Galileo first figured out that heavy objects fall down just as fast as light ones. To test this assumption, Galileo Galilei dropped from the Leaning Tower of Pisa at the same moment a cannonball weighing 80 kg and a much lighter musket bullet weighing 200 g. Both bodies had approximately the same streamlined shape and reached the ground at the same time. Before him, the point of view of Aristotle dominated, who argued that light bodies fall from a height more slowly than heavy ones.

Such is the legend. There is no evidence in the archives that such an experiment was actually carried out. Moreover, a cannonball and a bullet have a different radius, they will be affected by different air resistance forces and, therefore, they cannot reach the ground at the same time. Galileo understood this too. However, he wrote that "... the difference in the speed of movement in the air of balls of gold, lead, copper, porphyry and other heavy materials is so insignificant that a ball of gold, in free fall at a distance of one hundred cubits, would certainly outstrip a ball of copper no more than four fingers. Having made this observation, I came to the conclusion that in a medium completely devoid of any resistance, all bodies would fall with the same speed. " Assuming what would happen in the case of a free fall of bodies in a vacuum, Galileo derived the following laws for the fall of bodies for the ideal case:
1. When falling, all bodies move in the same way: having started falling at the same time, they move at the same speed
2. Movement occurs with constant acceleration.

Shortly after Galileo, air pumps were created that made it possible to experiment with free fall in a vacuum. To this end, Newton deflated the air from a long glass tube and dropped a bird's feather and a gold coin from above at the same time. Even bodies that differed so much in their density fell at the same speed.

We know from everyday life that gravity causes bodies released from bonds to fall to the surface of the Earth. For example, a load suspended on a thread hangs motionless, and as soon as the thread is cut, it begins to fall vertically downward, gradually increasing its speed. A ball thrown vertically upwards, under the influence of the Earth's gravity, first reduces its speed, stops for a moment and begins to fall down, gradually increasing its speed. A stone thrown vertically down, under the influence of gravity, also gradually increases its speed. The body can also be thrown at an angle to the horizon or horizontally...

Usually bodies fall in the air, therefore, in addition to the attraction of the Earth, they are also affected by air resistance. And it can be significant. Take, for example, two identical sheets of paper and, having crumpled one of them, we drop both sheets simultaneously from the same height. Although the earth's gravity is the same for both sheets, we will see that the crumpled sheet reaches the ground faster. This happens because the air resistance for it is less than for an uncreased sheet. Air resistance distorts the laws of falling bodies, so to study these laws, you must first study the fall of bodies in the absence of air resistance. This is possible if the fall of bodies occurs in a vacuum.

To make sure that in the absence of air, both light and heavy bodies fall equally, you can use Newton's tube. This is a thick-walled tube about a meter long, one end of which is sealed and the other is equipped with a tap. There are three bodies in the tube: a pellet, a piece of foam sponge and a light feather. If the tube is quickly turned over, then the pellet will fall the fastest, then the sponge, and the last to reach the bottom of the tube is the feather. This is how bodies fall when there is air in the tube. Now we pump out the air from the tube with a pump and, closing the valve after pumping out, turn the tube over again, we will see that all bodies fall with the same instantaneous speed and reach the bottom of the tube almost simultaneously.

The fall of bodies in airless space under the influence of gravity alone is called free fall.

If the force of air resistance is negligible compared to the force of gravity, then the motion of the body is very close to free (for example, when a small heavy smooth ball falls).

Since the force of gravity acting on each body near the surface of the Earth is constant, a freely falling body must move with constant acceleration, that is, uniformly accelerated (this follows from Newton's second law). This acceleration is called free fall acceleration and is marked with a letter. It is directed vertically down to the center of the Earth. The value of the gravitational acceleration near the Earth's surface can be calculated by the formula

(the formula is obtained from the law of universal gravitation), g\u003d 9.81 m / s 2.

The free fall acceleration, like gravity, depends on the height above the Earth's surface (

), from the shape of the Earth (the Earth is flattened at the poles, so the polar radius is less than the equatorial one, and the free fall acceleration at the pole is greater than at the equator: g P =9.832 m/s 2 ,g uh =9.780 m/s 2 ) and from deposits of dense terrestrial rocks. In places of deposits, for example, iron ore, the density of the earth's crust is greater and the acceleration of free fall is also greater. And where there are oil deposits, g less. This is used by geologists in the search for minerals.

Table 1. Acceleration of free fall at different heights above the Earth.

Table 2. Acceleration of free fall for some cities.

Since the acceleration of free fall near the surface of the Earth is the same, the free fall of bodies is a uniformly accelerated motion. So it can be described by the following expressions:

and

. At the same time, it is taken into account that when moving upward, the velocity vector of the body and the acceleration vector of free fall are directed in opposite directions, therefore their projections have different signs. When moving down, the velocity vector of the body and the free-fall acceleration vector are directed in the same direction, so their projections have the same signs.

If a body is thrown at an angle to the horizon or horizontally, then its motion can be decomposed into two: uniformly accelerated vertically and uniformly horizontally. Then, to describe the motion of the body, two more equations must be added: v x = v 0 x and s x = v 0 x t.

Substituting into the formula

instead of the mass and radius of the Earth, respectively, the mass and radius of some other planet or its satellite, one can determine the approximate value of the acceleration of free fall on the surface of any of these celestial bodies.

Table 3 Acceleration of free fall on the surface of some

celestial bodies (for the equator), m / s 2.