Free Fall: Discovery Story and Historical Significance. Law of falling bodies Falling speed does not depend on weight

In Ancient Greece, mechanical movements were classified into natural and forced. The fall of a body to the Earth was considered a natural movement, some inherent desire of the body “to its place”,
According to the idea of ​​the greatest ancient Greek philosopher Aristotle (384-322 BC), a body falls to the Earth faster, the greater its mass. This idea was the result of primitive life experience: observations showed, for example, that apples and apple tree leaves fall at different speeds. The concept of acceleration was absent in ancient Greek physics.
For the first time, the great Italian scientist Galileo Galilei (1564 - 1642) spoke out against the authority of Aristotle, approved by the church.

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, my father was rescued. Galileo from the walls of the monastery and give him a good education at home, introduce him to the society of musicians, writers, artists.
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. Influenced by the works of Archimedes, Galileo became interested in geometry and mechanics and left 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. During the Padua period of Galileo's life (1592 - 1610), the scientist's activities reached their peak. At this time, the laws of free fall of bodies and 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 topography of the Moon, the satellites of Jupiter, the structure of the Milky Way, the 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 of 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 in the list of prohibited books).
Galileo had to disguise his ideas. In 1632, he published a remarkable book, “Dialogue Concerning Two World Systems,” in which he develops 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 summarized his many years of fruitful activity.”
In 1637 he became blind, but continued his 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 movements. He first introduced the concepts of uniform and accelerated motion and began the study of mechanical motion by measuring distances and times of motion. Galileo's experiments with uniformly accelerated motion of a body on an inclined plane are still repeated in all schools of the world.
Galileo paid special attention to the experimental study of the free fall of 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 from the tower at the same time. Contrary to Aristotle's opinion, they reached the surface of the Earth almost simultaneously: the bomb was only a few inches ahead of the ball. Galileo explained this difference by the presence of air resistance. This explanation was then fundamentally new. The fact is that since the times of Ancient Greece, the following Idea about the mechanism of movement of bodies has been established: when moving, the body leaves behind a void; nature is afraid of emptiness (there was a false principle of fear of emptiness). The 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 some 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 in motion. In the case of free fall, the force of attraction is constantly acting on the body, and the results of this action are continuously summed up, because according to the law of inertia, the action once caused is conserved. This idea is the basis of his logical construction, which led to the laws of free fall.
Galileo determined the acceleration of gravity with a large error. In the Dialogue he states that the ball fell from a height of 60 m in 5 seconds. This corresponds to the value g, almost two times less than the true one.
Galileo, naturally, could not accurately determine g, because I didn't have a stopwatch. The hourglass, water clock, or pendulum clock he invented did not contribute to accurate timekeeping. The acceleration of gravity was determined quite accurately only by Huygens in 1660.
To achieve greater measurement accuracy, Galileo looked for ways to reduce the speed of fall. This led him to experiments with an inclined plane.

Methodological note. When talking about Galileo's work, it is important to explain to students the essence of the method he used to establish 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 need to be verified by experience. Only the coincidence of theory with experience leads to conviction of the justice of the law. To do this you need to measure. Galileo harmoniously combined the power of 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 measuring small periods of time.
Galileo reduces the speed 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 along 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. It was sent into a small vessel, which was pre-weighed. The period of time was measured by the increment in the weight of the vessel! By launching a ball from half, a quarter, etc., the length of an inclined plane, Galileo established that the distances traveled were related to the squares of the time of movement.
Repetition of these experiments of Galileo can serve as the subject of useful work in a school physics circle.

Free fall is one of the most interesting physical phenomena, which has attracted the attention of scientists and philosophers since ancient times. In addition, it is one of those processes that any schoolchild can experiment with.

Aristotle's "philosophical error"

The first to undertake the scientific substantiation of the phenomenon that is now known as free fall were ancient philosophers. They, naturally, did not carry out any experiments and experiments, but tried to characterize it from the point of view of their own philosophical system. In particular, Aristotle argued that heavier bodies fall to the ground at greater speed, explaining this not by physical laws, but only by the desire of all objects in the Universe for order and organization. It is interesting that no experimental evidence was produced, and this statement was perceived as an axiom.

Galileo's contribution to the study and theoretical justification of free fall

Medieval philosophers questioned Aristotle's theoretical position. Not being able to prove this in practice, they were nevertheless confident that the speed with which bodies move towards the ground, without taking into account external influences, remains the same. It was from these positions that the great Italian scientist G. Galileo considered free fall. After conducting numerous experiments, he came to the conclusion that the speed of movement of, for example, copper and gold balls towards the ground is the same. The only thing that prevents this from being installed visually is the presence of air resistance. But even in this case, if you take bodies with a sufficiently large mass, they will land on the surface of our planet at approximately the same time.

Basic principles of free fall

From his experiments, Galileo made two important conclusions. Firstly, the speed of fall of absolutely any body, regardless of its mass and the material from which it is made, is the same. Secondly, the acceleration with which a given object moves remains constant, that is, the speed increases by the same amount over equal periods of time. Subsequently, this phenomenon was called free fall.

Modern calculations

However, even Galileo himself understood the relative limitations of his experiments. After all, no matter what bodies he took, he was unable to ensure that they hit the earth’s surface at the same time: it was impossible to fight air resistance in those days. Only with the advent of special equipment, with the help of which the air was completely pumped out of the tubes, was it possible to experimentally prove that free fall actually takes place. In quantitative terms, it turned out to be approximately 9.8 m/s^2, but subsequently scientists came to the conclusion that this value varies, albeit extremely slightly, depending on the height of the object above the ground, as well as on geographical conditions.

The concept and meaning of free fall in modern science

Currently, all scientists are of the opinion that free fall is a physical phenomenon consisting in the uniformly accelerated movement of a body placed in airless space towards the surface of the earth. In this case, it does not matter at all whether any external acceleration was given to this body or not.

Universalism and constancy are the most important characteristics of this physical phenomenon

The universality of this phenomenon lies in the fact that the speed of free fall of a person or a bird's feather in a vacuum is absolutely the same, that is, if they start at the same time, they will also reach the surface of the earth at the same time.

Free fall is the movement of bodies only under the influence of the Earth’s gravity (under the influence of gravity)

Under Earth conditions, the fall of bodies is considered conditionally free, because When a body falls in the air, there is always a force of air resistance.

An ideal free fall is possible only in a vacuum, where there is no air resistance, and regardless of mass, density and shape, all bodies fall equally quickly, i.e. at any moment in time the bodies have the same instantaneous speeds and accelerations.

You can observe the ideal free fall of bodies in a Newton tube if you pump the air out of it using a pump.

In further reasoning and when solving problems, we neglect the force of friction with the air and consider the fall of bodies in terrestrial conditions to be ideally free.

ACCELERATION OF GRAVITY

During free fall, all bodies near the surface of the Earth, regardless of their mass, acquire the same acceleration, called the acceleration of gravity.
The symbol for gravitational acceleration is g.

The acceleration of gravity on Earth is approximately equal to:
g = 9.81m/s2.

The acceleration of gravity is always directed towards the center of the Earth.

Near the surface of the Earth, the magnitude of the force of gravity is considered constant, therefore the free fall of a body is the movement of a body under the influence of a constant force. Therefore, free fall is uniformly accelerated motion.

The vector of gravity and the free fall acceleration it creates are always directed in the same way.

All formulas for uniformly accelerated motion are applicable to freely falling bodies.

The magnitude of the speed during free fall of a body at any time:

body movement:

In this case, instead of accelerating A, the acceleration of gravity is introduced into the formulas for uniformly accelerated motion g=9.8m/s2.

Under conditions of an ideal fall, bodies falling from the same height reach the surface of the Earth, having the same speeds and spending the same time falling.

In an ideal free fall, the body returns to Earth with a speed equal to the magnitude of the initial velocity.

The time the body falls is equal to the time it moves upward from the moment of the throw to a complete stop at the highest point of the flight.

Only at the Earth's poles do bodies fall strictly vertically. In all other points of the planet, the trajectory of a freely falling body deviates to the east due to the Cariolis force that arises in rotating systems (i.e., the influence of the Earth’s rotation around its axis is affected).

DID YOU KNOW

WHAT IS THE FALL OF BODIES IN REAL CONDITIONS?

If you shoot a gun vertically upward, then, taking into account the force of friction with the air, a bullet freely falling from any height will acquire a speed of no more than 40 m/s at the ground.

In real conditions, due to the presence of friction force against air, the mechanical energy of the body is partially converted into thermal energy. As a result, the maximum height of the body's rise turns out to be less than it could be when moving in airless space, and at any point in the trajectory during descent, the speed turns out to be less than the speed on the ascent.

In the presence of friction, falling bodies have an acceleration equal to g only at the initial moment of movement. As the speed increases, the acceleration decreases, and the motion of the body tends to be uniform.

DO IT YOURSELF

How do falling bodies behave in real conditions?

Take a small disk made of plastic, thick cardboard or plywood. Cut a disk of the same diameter from plain paper. Raise them, holding them in different hands, to the same height and release them at the same time. A heavy disk will fall faster than a light one. When falling, each disk is simultaneously affected by two forces: the force of gravity and the force of air resistance. At the beginning of the fall, the resultant force of gravity and the force of air resistance will be greater for a body with a larger mass and the acceleration of a heavier body will be greater. As the speed of the body increases, the force of air resistance increases and gradually becomes equal in magnitude to the force of gravity; falling bodies begin to move evenly, but at different speeds (a heavier body has a higher speed).
Similar to the movement of a falling disk, one can consider the movement of a parachutist falling down when jumping from an airplane from a great height.

Place a light paper disk on a heavier plastic or plywood disk, lift them to a height and release them at the same time. In this case they will fall at the same time. Here, air resistance acts only on the heavy lower disk, and gravity imparts equal accelerations to the bodies, regardless of their masses.

ALMOST A JOKE

The Parisian physicist Lenormand, who lived in the 18th century, took ordinary rain umbrellas, secured the ends of the spokes and jumped from the roof of the house. Then, encouraged by his success, he made a special umbrella with a wicker seat and rushed down from the tower in Montpellier. Below he was surrounded by enthusiastic spectators. What is the name of your umbrella? Parachute! - Lenormand answered (the literal translation of this word from French is “against the fall”).

INTERESTING

If you drill through the Earth and throw a stone there, what will happen to the stone?
The stone will fall, picking up maximum speed in the middle of the path, then fly further by inertia and reach the opposite side of the Earth, and its final speed will be equal to the initial one. The acceleration of free fall inside the Earth is proportional to the distance to the center of the Earth. The stone will move like a weight on a spring, according to Hooke's law. If the initial speed of the stone is zero, then the period of oscillation of the stone in the shaft is equal to the period of revolution of the satellite near the surface of the Earth, regardless of how the straight shaft is dug: through the center of the Earth or along any chord.

From everyday life we ​​know that gravity causes bodies freed from bonds to fall to the surface of the Earth. For example, a load suspended on a thread hangs motionless, but as soon as the thread is cut, it begins to fall vertically down, gradually increasing its speed. A ball thrown vertically upward, 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 downward also gradually increases its speed under the influence of gravity. The body can also be thrown at an angle to the horizontal or horizontally...

Usually bodies fall in the air, so in addition to the gravity of the Earth, they are also affected by air resistance. And it can be significant. Let's take, for example, two identical sheets of paper and, having crumpled one of them, we drop both sheets at the same time from the same height. Although gravity is the same for both leaves, we will see that the crumpled leaf reaches the ground faster. This happens because the air resistance for it is less than for an uncrumpled piece of paper. 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 falling bodies occur in airless space.

To make sure that in the absence of air both light and heavy bodies fall equally, you can use a Newton 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. The tube contains three bodies: a pellet, a piece of foam sponge and a light feather. If the tube is quickly turned over, the pellet will fall the fastest, then the sponge, and the feather will reach the bottom of the tube last. This is how bodies fall when there is air in the tube. Now let’s pump the air out of the tube and, closing the tap after pumping, turn the tube over again, we will see that all the bodies fall at 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 every body near the Earth’s surface 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 acceleration of free fall and is designated by the letter . It is directed vertically down towards the center of the Earth. The value of the gravitational acceleration near the Earth's surface can be calculated using the formula
(the formula is obtained from the law of universal gravitation), g=9.81 m/s 2.

The acceleration of free fall, like the force of gravity, depends on the height above the Earth's surface (
), on the shape of the Earth (the Earth is flattened at the poles, so the polar radius is less than the equatorial radius, and the acceleration of gravity at the pole is greater than at the equator: g n =9.832 m/s 2 , g uh =9.780 m/s 2 ) and from deposits of dense earth rocks. In places of deposits, for example, iron ore, the density of the earth's crust is greater and the acceleration of gravity is also greater. And where there are oil deposits, g less. Geologists use this when searching for minerals.

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

Table 2. Free fall acceleration for some cities.

Since the acceleration of free fall near the surface of the Earth is the same, the free fall of bodies is uniformly accelerated motion. This means that it can be described by the following expressions:
And
. 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 downward, the velocity vector of the body and the acceleration vector of free fall 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 divided into two: uniformly accelerated vertically and uniformly horizontally. Then to describe the motion of the body, you need to add two more equations: 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 any other planet or its satellite, one can determine the approximate value of the acceleration of gravity 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.

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

This is a universal 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 bodies fall differently under normal conditions. A heavy ball falls quickly, a light sheet of paper falls slowly and along a complex trajectory (Fig. 1.80).

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

Experiments suggest that these differences are due to the action of air on moving bodies. This air resistance is also used practically, for example when jumping with a parachute. The fall of a parachutist before and after the parachute opens 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, 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 to this idea. In 1583, in Pisa, he made the first observations of the peculiarities of the free fall of heavy balls of the same diameter, studied the laws of the motion of bodies on 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 of modern mechanics, which is called Galileo’s law: all bodies under the influence of gravity fall to the Earth with the same acceleration.

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

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

At different points on the globe, the numerical value of the acceleration of gravity is not the same. It varies approximately from at the pole to at the equator. Conventionally, the value is taken as the “normal” value of the acceleration of gravity. We will use this value when solving practical problems. For rough calculations, sometimes we will take the 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 and allows us to understand and explain many features of the structure of our Universe.

Galileo's law, called the principle of equivalence, became 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 the general theory of relativity.

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