Newton, like Galileo, began research mechanical movement from studying law of falling bodies, but his task was already somewhat easier. Newton had at his disposal an air pump that Galileo could only dream of.
Galileo conducted his experiments by throwing iron cores from the Leaning Tower of Pisa (more details:). Newton took a long glass tube, sealed at one end, put a small piece of cork and a shot into it, and connected the tube to an air pump. The pump has pumped out most of the air.
The scientist soldered the other end of the tube. And the pellet with a piece of cork remained in a very rarefied air space. Newton turned the tube with one end up, then with the other - a piece of cork and a shot fell down with equal speed. So it was possible to prove that in the void objects of different weights fall at the same speed. Now these simple devices - " Newton tubes» - are available in every school. 
Falling speed is independent of weight
Falling speed is independent of weight. Falling objects have no weight, (more:), Galileo said. So, Newton concluded, weight is not a fundamental property of all objects or substances. Any objects have weight only as long as they lie or hang on something, and when they fall, they lose weight.
What is weight
One of Newton's predecessors, the French mathematician René Descartes, argued that weight is the pressure exerted by things on the ground or on the stand on which they lie. Newton remembered Galileo's experiments with buckets. While the water was pouring from one bucket to another, their total weight was less than before - the falling water moved freely, nothing stopped it, it really weighed nothing during the fall.
As soon as all the water was in the lower bucket, the balance of the scales was restored. And this did not surprise Newton either. Since all the water has collected in the lower bucket, then its pressure on the bottom must be exactly equal to the sum of the water pressures in the two buckets. The water seemed to have regained its weight.
Why do bodies press on the stand
But why do bodies press on the stand? Descartes did not know this. Take a weight and hang it on a spring. The spring will stretch. Now let's remove this weight and grab the hook of the spring with our hand. We can, by applying force, stretch the spring as much as the weight stretched it with its weight. The weight of the weight and the force of the hand have the same effect on the spring. This means that the reason for the pressure of the bodies on the stand - their weight - is some kind of force. Newton defined it.
Law of gravity
It is the globe that attracts the weight and other bodies to itself, holding them near it. We observe this phenomenon everywhere and everywhere and call it gravitation. Galileo also studied. All bodies, both large and small, are attracted to each other, obeying law of gravity, discovered by Newton. So, weight is the force with which objects attracted by the Earth put pressure on the supports holding them. Weight is a manifestation of universal gravity. Newton was able to bring to its logical conclusion the law of falling bodies, which was initiated by Galileo Galilei.
IN Ancient Greece mechanical movements were classified into natural and violent. The fall of the body to the Earth was considered a natural movement, some kind of striving inherent in the body "to its place",
According to the idea of the greatest ancient Greek philosopher Aristotle (384-322 BC), the body falls to the Earth the faster, the greater its mass. This representation was the result of a primitive life experience: observations have shown, for example, that apples and apple leaves fall at different speeds. The concept of acceleration in ancient Greek physics was absent.
Galileo was born in Pisa in 1564. His father was a talented musician and a good teacher. Until the age of 11, Galileo attended school, then, according to the custom of that time, his upbringing and education took place in a monastery. Here he became acquainted with the works of Latin and Greek writers.
Under the pretext of a severe eye disease, his father managed to rescue Galileo from the walls of the monastery and give him a good education at home, introduce musicians, writers, and artists into society.
At the age of 17, Galileo entered the University of Pisa, where he studied medicine. Here he first became acquainted with the physics of ancient Greece, primarily with the works of Aristotle, Euclid and Archimedes. Under the influence of the works of Archimedes, Galileo is fond of geometry and mechanics and leaves medicine. He leaves the University of Pisa and studies mathematics in Florence for four years. Here his first scientific works appeared, and in 1589 Galileo received the chair of mathematics, first in Pisa, then in Padua. In the Padua period of Galileo's life (1592-1610) there was the highest flowering of the scientist's activity. At this time, the laws of free fall of bodies, the principle of relativity were formulated, the isochronism of pendulum oscillations was discovered, a telescope was created and a number of sensational astronomical discoveries were made (the relief of the Moon, the satellites of Jupiter, the structure milky way, phases of Venus, sunspots).
In 1611 Galileo was invited to Rome. Here he began a particularly active struggle against the church worldview for the approval of a new experimental method for studying nature. Galileo propagates the Copernican system, thereby antagonizing the church (in 1616, a special congregation of Dominicans and Jesuits declared the teachings of Copernicus heretical and included his book on the banned list).
Galileo had to mask his ideas. In 1632 he published a remarkable book, Dialogue Concerning the Two Systems of the World, in which he developed materialist ideas in the form of a discussion between three interlocutors. However, "Dialogue" was banned by the church, and the author was brought to trial and for 9 years was considered a "prisoner of the Inquisition."
In 1638, Galileo managed to publish in Holland the book "Conversations and Mathematical Proofs Concerning Two New Branches of Science", which summed up his many years of fruitful work.
In 1637 he became blind, but continued intensive scientific work together with his students Viviani and Torricelli. Galileo died in 1642 and was buried in Florence in the church of Santa Croce next to Michelangelo.
Galileo rejected the ancient Greek classification of mechanical motions. He first introduced the concepts of uniform and accelerated motion and began the study of mechanical motion by measuring distances and time of motion. Galileo's experiments with uniformly accelerated motion body by inclined plane are still repeated in all schools of the world.
Galileo paid special attention pilot study free fall bodies. His experiments on the Leaning Tower in Pisa gained worldwide fame. According to Viviani, Galileo threw a half-pound ball and a hundred-pound bomb at the same time from the tower. Contrary to opinion. Aristotle, they reached the surface of the Earth almost simultaneously: the bomb was ahead of the ball by only a few inches. Galileo explained this difference by the presence of air resistance. This explanation was then fundamentally new. The fact is that since the time of Ancient Greece, the following idea of the mechanism for moving bodies has been established: when moving, the body leaves a void; nature is afraid of emptiness (there was a false principle of fear of emptiness). Air rushes into the void and pushes the body. Thus, it was believed that air does not slow down, but, on the contrary, accelerates bodies.
Next, Galileo eliminated another centuries-old misconception. It was believed that if the movement is not supported by any force, then it should stop, even if there are no obstacles. Galileo first formulated the law of inertia. He argued that if a force acts on a body, then the result of its action does not depend on whether the body is at rest or moving. In the case of free fall, the force of attraction constantly acts on the body, and the results of this action are continuously summed up, because according to the law of inertia, the action caused by the time is preserved. This representation is the basis of his logical construction, which led to the laws of free fall.
Galileo determined the free fall acceleration with a big error. In the "Dialogue" he states that the ball fell from a height of 60 m within 5 s. This corresponds to a g value that is almost half the true value.
Galileo, of course, could not accurately determine g, since he did not have a stopwatch. An hourglass, a water clock, or the pendulum clock invented by him did not contribute to an accurate reading of time. The acceleration due to gravity was only accurately determined by Huygens in 1660.
To achieve greater measurement accuracy, Galileo looked for ways to reduce the rate of fall. This led him to experiments with an inclined plane.
Methodical note. Talking about the works of Galileo, it is important to explain to students the essence of the method that he used in establishing the laws of nature. First, he carried out a logical construction, from which the laws of free fall followed. But the results of logical construction must be verified by experience. Only the coincidence of theory with experience leads to conviction in the justice of the law. To do this, you need to measure. Galileo harmoniously combined power theoretical thinking with experimental art. How to check the laws of free fall, if the movement is so fast and there are no instruments for counting short periods of time?
Galileo reduces the rate of fall by using an inclined plane. A groove was made in the board, lined with parchment to reduce friction. A polished brass ball was launched down the chute. To accurately measure the time of movement, Galileo came up with the following. A hole was made in the bottom of a large vessel with water, through which a thin stream flowed. She went to a small vessel, which was preliminarily weighed. The time interval was measured by the increment in the weight of the vessel! Launching a ball from a half, a quarter, etc. e. the length of the inclined plane, Galileo found that the paths traveled were related as the squares of the time of movement.
The repetition of these experiments by Galileo can serve as the subject of useful work in a school physics circle.
Back in school, at one of the physics lessons, I was puzzled by the conclusion of the teacher, confirmed in the text of the textbook, that all bodies falling from the same height will reach the Earth's surface in the same time, regardless of the mass of the falling bodies. Of course, in the absence of air resistance. 
It is clear that if the accelerations of the bodies are the same, then the speeds of their fall at any time are equal when the bodies are allowed to fall from the same height with the same initial speed.
v = v0 + gt
And I remember the description of the following experiment, supposedly carried out by Newton. Air was pumped out of a long glass tube and at the same time a lead weight and a feather were allowed to fall. And both objects, both bodies simultaneously touched the bottom of the tube. Hence the conclusion formulated above was drawn.
Then, at school, I thought: after all, at that time there were no photocells. How did the scientist manage to fix the time when the bodies touched the surface? After all, on Earth, bodies fall from a height of two meters in less than a second, and a person's reaction is about one second. But what if the bodies still do not reach the bottom of the tube at the same time, but the difference is very difficult to fix?
Let's try to figure it out. If someone notices an error in reasoning - I will be grateful for any constructive remark.
Before proceeding, it is necessary to recall how the speed of approach of two bodies is calculated. Let's say there are 600 km between cities, and two cars drove towards them at a constant speed. One travels 80 km per hour, the other 120 km per hour. In 3 hours, the first one will travel 240 km, the second - 360 km, in total - 600 km. Those. the cars will meet, which means that in this case the speed must be added up, and in order to find out the moment of the meeting of the bodies, simply divide the distance between them by the total speed of approach.
Now let's do a thought experiment. There is a planet Earth with its free fall acceleration g. According to Newton's law of universal gravitation, two bodies attract each other in proportion to their masses and inversely as the square of the distance between the bodies.
On the other hand, the weight of a body mass m equals P = mg. In the absence of other forces, the weight of a body on Earth will be equal to the force of mutual attraction between the Earth and the body itself, i.e. F=P. We reduce by m and we get the formula shown in the topmost picture:
The sign of approximate equality, apparently, is caused by taking into account the uneven distribution of density in the body of the Earth.
Now suppose that at a distance of, say, one kilometer from our Earth, there is another planet that has exactly the same characteristics. Such a peculiar twin - Earth 2 .
What forces are acting on it? Only one: the force of gravity from the Earth. Under the influence of this force, the Earth 2 rush towards the earth at a speed v=gt.
But the gravitational force from the Earth also acts on the Earth 2 ! Those. our planet will also "fall" to the Earth at an ever-increasing speed 2 . It is clear that at any moment of time both these speeds are identical in absolute value and always directed oppositely - both Earths are equal in their physical characteristics.
Approach speed v1 will be equal to v 1 = gt - (-gt) = 2gt.
Now we will place instead of the Earth2, say, the Moon. The moon has free fall acceleration g Moon about 6 times smaller than the earth. So, under the action of the same law of universal gravitation, the Moon will fall to the Earth with acceleration g, and the Earth to the Moon with acceleration g Moon. Then the speed of approach v2 will be different than in the first case, namely:
v 2 = gt + g of the Moon *
t = (g + g of the Moon) * t.
Value g + g Moons about 1.7 times less than the value 2g.
What happens? The distance between the bodies (falling height) is the same, but the falling speeds are different. But we are assured that the time of fall is the same for bodies of any mass! Then we get a contradiction: the height of the fall is the same, the time is the same, but the speeds are different. This is not how physics should be. Unless, of course, an error has crept into my reasoning.
Another thing is that for practical calculations, the accuracy is quite enough, if we do not take into account the acceleration of free fall of the body that falls to the Earth: it is too small compared to the value g due to the incomparability of the masses of the Earth and the falling body. The mass of our planet is about 6 × 10 24 kg, which is really incomparable with any body falling to the Earth.
However, the statement in textbooks that in the absence of air resistance all bodies fall to the Earth with the same speed should be recognized as incorrect. The statement that they fall with the same acceleration is also false. With practically the same - yes, with mathematically and physically exactly the same - no.
Such textbook statements distort the correct perception of the real picture of the world.
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 alone the study of the laws of free fall of 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 (Fig. 1.80).
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 free fall of heavy balls of the same diameter, studied the laws of motion of bodies along an inclined plane and the motion of bodies thrown at an angle to the horizon.
The results of these observations allowed Galileo to discover one of the most important laws 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 various points 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 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 of universal gravitation (gravity), which was created by A. Einstein at the beginning of our century. Einstein called this theory general theory 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 are those of 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, verified the validity of Galileo's law with an accuracy of up to the twelfth decimal place when determining the numerical value
From everyday life, we know that the earth's gravity causes bodies, freed 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, i.e., 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 earth's crust more and the free fall acceleration 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.
|
h, km |
g, m/s 2 |
h, km |
g, m/s 2 |
Table 2. Acceleration of free fall for some cities.
|
Geographical coordinates (GMT) |
Height above sea level, m |
Free fall acceleration, m/s 2 |
||
|
Longitude |
Latitude |
|||
|
Washington | ||||
|
Stockholm | ||||
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 up, the velocity vector of the body and the acceleration vector of free fall are directed in opposite sides, so 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.
