Calculate the speed of falling body mass distance. Free fall of bodies. Acceleration of gravity

It is known that the planet Earth attracts any body to its core with the help of the so-called gravitational field. This means that the greater the distance between the body and the surface of our planet, the more it affects it, and the more pronounced

A body falling vertically downwards is still affected by the aforementioned force, due to which the body will certainly fall downwards. The question remains, what will be its speed as it falls? On the one hand, the object is influenced by air resistance, which is quite strong, on the other hand, the body is more strongly attracted to the Earth, the farther it is from it. The first one will obviously be an obstacle and reduce the speed, the second one will give acceleration and increase the speed. Thus, another question arises: is free fall possible under terrestrial conditions? Strictly speaking, bodies are possible only in a vacuum, where there are no interferences in the form of resistance to air flows. However, within the framework of modern physics, the free fall of a body is considered to be a vertical movement that does not encounter interference (air resistance can be neglected in this case).

The thing is that it is possible only artificially to create conditions where other forces, in particular, the same air, do not affect the falling object. Experimentally, it was proved that the speed of free fall of a body in a vacuum is always equal to the same number, regardless of the weight of the body. Such a movement is called uniformly accelerated. It was first described by the famous physicist and astronomer Galileo Galilei more than 4 centuries ago. The relevance of such conclusions has not lost its force to this day.

As already mentioned, the free fall of a body within the framework of everyday life is a conditional and not entirely correct name. In fact, the speed of free fall of any body is not uniform. The body moves with acceleration, due to which such a movement is described as a special case uniformly accelerated movement. In other words, every second the speed of the body will change. With this caveat in mind, we can find the free fall velocity of the body. If we do not give the object acceleration (that is, we do not throw it, but simply lower it from a height), then its initial speed will be equal to zero: Vo=0. With each second, the speed will increase in proportion to the acceleration: gt.

It is important to comment on the introduction of the variable g here. This is the free fall acceleration. Earlier, we have already noted the presence of acceleration when a body falls under normal conditions, i.e. in the presence of air and under the influence of gravity. Any body falls to the Earth with an acceleration equal to 9.8 m/s2, regardless of its mass.

Now, keeping this reservation in mind, we derive a formula that will help calculate the free fall speed of a body:

That is, to the initial speed (if we gave it to the body by throwing, pushing or other manipulations), we add the product by the number of seconds that the body took to reach the surface. If the initial speed is zero, then the formula becomes:

That is simply the product of the free fall acceleration and the time.

Similarly, knowing the speed of free fall of an object, one can derive the time of its movement or the initial speed.

The formula for calculating the speed should also be distinguished, since in this case forces will act that gradually slow down the speed of the thrown object.

In the case considered by us, only the force of gravity and the resistance of air flows act on the body, which, by and large, does not affect the change in speed.

He took two glass tubes, which were called Newton's tubes, and pumped air out of them (Fig. 1). Then he measured the fall time of a heavy ball and a light feather in these tubes. It turned out that they fall at the same time.

We see that if we remove the air resistance, then nothing will prevent either the feather or the ball from falling - they will fall freely. It is this property that formed the basis for the definition of free fall.

Free fall is the movement of a body only under the influence of gravity, in the absence of the action of other forces.

What is free fall? If you pick up any object and release it, then the speed of the object will change, which means that the movement is accelerated, even uniformly accelerated.

For the first time that the free fall of bodies is uniformly accelerated, Galileo Galilei declared and proved. He measured the acceleration with which such bodies move, it is called the acceleration of free fall, and is approximately 9.8 m / s 2.

Thus, free fall is a special case of uniformly accelerated motion. Hence, for this movement, all the equations that were obtained are valid:

for the velocity projection: V x \u003d V 0x + a x t

for the projection of movement: S x \u003d V 0x t + a x t 2 / 2

determining the position of the body at any time: x(t) = x 0 + V 0x t + a x t 2 /2

x means that we have a rectilinear movement, along the x-axis, which we traditionally chose horizontally.

If the body moves vertically, then it is customary to designate the y-axis and we will get (Fig. 2):

Rice. 2. Vertical movement of the body ()

The equations take the following absolutely identical form, where g is the free fall acceleration, h is the displacement in height. These three equations describe how to solve the main problem of mechanics for the case of free fall.

The body is thrown vertically upwards with initial velocity V 0 (Fig. 3). Find the height to which the body is thrown. We write the equation of motion of this body:

Rice. 3. Task example ()

Knowing the simplest equations allowed us to find the height to which we can throw the body.

The magnitude of the acceleration of free fall depends on the geographic latitude of the area, at the poles it is maximum and at the equator is minimum. In addition, the acceleration of free fall depends on the composition of the earth's crust under the place where we are. If there are deposits of heavy minerals, the value of g will be a little more, if there are voids, then it will be a little less. This method is used by geologists to determine deposits of heavy ores or gases, oil, it is called gravimetry.

If we want to accurately describe the motion of a body falling on the surface of the Earth, then we must remember that air resistance is still present.

The Parisian physicist Lenormand in the 18th century, having fixed the ends of the spokes on an ordinary umbrella, jumped from the roof of the house. Encouraged by his success, he made a special umbrella with a seat and jumped from a tower in the city of Montellier. He called his invention a parachute, which in French means "against falling."

Galileo Galilei was the first to show that the time of a body falling to the Earth does not depend on its mass, but is determined by the characteristics of the Earth itself. As an example, he cited an argument about the fall of a body with a certain mass over a period of time. When this body is divided into two identical halves, they begin to fall, but if the speed of the fall of the body and the time of fall depend on the mass, then they should fall more slowly, but how? After all, their total mass has not changed. Why? Maybe one half prevents the other half from falling? We arrive at a contradiction, which means that the assumption that the rate of fall depends on the mass of the body is unfair.

Therefore, we come to the correct definition of free fall.

Free fall is the movement of a body only under the influence of gravity. No other forces act on the body.

We are accustomed to using the gravitational acceleration value of 9.8 m/s 2 , this is the most convenient value for our physiology. We know that gravitational acceleration will vary by geographic location, but these changes are negligible. What are the values of the free fall acceleration on other celestial bodies? How to predict whether a comfortable existence of a person is possible there? Recall the free fall formula (Fig. 4):

Rice. 4. Table of acceleration of free fall on the planets ()

The more massive the celestial body, the greater the acceleration of free fall on it, the more impossible the fact that a human body is on it. Knowing the acceleration of free fall on various celestial bodies, we can determine the average density of these celestial bodies, and knowing the average density, we can predict what these bodies consist of, that is, determine their structure.

We are talking about the fact that measurements of the acceleration of free fall at various points on the Earth are the most powerful method of geological exploration. In this way, without digging holes, not storming wells, mines, it is possible to determine the presence of minerals in the thickness of the earth's crust. The first way is to measure the gravitational acceleration with the help of geological spring balances, they have a phenomenal sensitivity, up to millionths of a gram (Fig. 5).

The second way is with the help of a very precise mathematical pendulum, because, knowing the period of oscillation of the pendulum, you can calculate the acceleration of free fall: the smaller the period, the greater the acceleration of free fall. This means that by measuring the acceleration of free fall at different points on the Earth with a very accurate pendulum, you can see whether it has become larger or smaller.

What is the norm for the magnitude of the acceleration of free fall? The globe is not a perfect sphere, but a geoid, that is, it is slightly flattened at the poles. This means that at the poles the value of the acceleration of free fall will be greater than at the equator, at the equator it is minimal, but at the same geographical latitude it should be the same. This means that by measuring the acceleration of free fall at different points within the same latitude, we can judge by its change the presence of certain fossils. This method is called gravimetric exploration, thanks to which oil deposits were discovered in Kazakhstan and Western Siberia.

The presence of minerals, deposits of heavy substances or voids can affect not only the magnitude of the acceleration of free fall, but also its direction. If we measure the gravitational acceleration near a large mountain, then this massive body will affect the direction of the gravitational acceleration, because it will also attract a mathematical pendulum, by which we measure the gravitational acceleration.

Bibliography

Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemozina, 2012.
Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

Homework

What type of motion is free fall?
What are the characteristics of free fall?
What experience shows that all bodies on Earth fall with the same acceleration?

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In classical mechanics, the state of an object that moves freely in a gravitational field is called free fall. If an object falls in the atmosphere, an additional drag force acts on it and its motion depends not only on gravitational acceleration, but also on its mass, cross section and other factors. However, only one force acts on a body falling in a vacuum, namely gravity.

Examples of free fall are spaceships and satellites in Earth orbit, because they are affected by the only force - gravity. The planets orbiting the Sun are also in free fall. Objects falling to the ground at a low speed can also be considered free-falling, since in this case the air resistance is negligible and can be neglected. If the only force acting on objects is gravity, and there is no air resistance, the acceleration is the same for all objects and is equal to the acceleration of free fall on the Earth's surface of 9.8 meters per second per second second (m/s²) or 32.2 feet per second per second (ft/s²). On the surface of other astronomical bodies, the free fall acceleration will be different.

Skydivers, of course, say that before opening the parachute they are in free fall, but in fact, a skydiver can never be in free fall, even if the parachute has not yet been opened. Yes, a skydiver in "free fall" is affected by the force of gravity, but he is also affected by the opposite force - air resistance, and the force of air resistance is only slightly less than the force of gravity.

If there were no air resistance, the speed of a body in free fall would increase by 9.8 m/s every second.

The speed and distance of a freely falling body is calculated as follows:

v₀ - initial speed (m/s).

v- final vertical speed (m/s).

h₀ - initial height (m).

h- drop height (m).

t- fall time (s).

g- free fall acceleration (9.81 m/s2 at the Earth's surface).

If a v₀=0 and h₀=0, we have:

if the time of free fall is known:

if the free fall distance is known:

if the final speed of free fall is known:

These formulas are used in this free fall calculator.

In free fall, when there is no force to support the body, there is weightlessness. Weightlessness is the absence of external forces acting on the body from the floor, chair, table and other surrounding objects. In other words, support reaction forces. Usually these forces act in a direction perpendicular to the surface of contact with the support, and most often vertically upwards. Weightlessness can be compared to swimming in water, but in such a way that the skin does not feel the water. Everyone knows this feeling of your own weight when you go ashore after a long swim in the sea. That is why pools of water are used to simulate weightlessness during training of cosmonauts and astronauts.

By itself, the gravitational field cannot create pressure on your body. Therefore, if you are in a state of free fall in a large object (for example, in an airplane), which is also in this state, no external forces of interaction between the body and the support act on your body and there is a feeling of weightlessness, almost the same as in water .

Weightless training aircraft designed to create short-term weightlessness for the purpose of training cosmonauts and astronauts, as well as for performing various experiments. Such aircraft have been and are currently in operation in several countries. For short periods of time, which last about 25 seconds during each minute of flight, the aircraft is in a state of weightlessness, that is, there is no support reaction for the people in it.

Various aircraft were used to simulate weightlessness: in the USSR and in Russia, since 1961, modified production aircraft Tu-104AK, Tu-134LK, Tu-154MLK and Il-76MDK have been used for this. In the US, astronauts have trained since 1959 on modified AJ-2s, C-131s, KC-135s, and Boeing 727-200s. In Europe, the National Center for Space Research (CNES, France) uses the Airbus A310 for training in weightlessness. The modification consists in finalizing the fuel, hydraulic and some other systems in order to ensure their normal operation in conditions of short-term weightlessness, as well as strengthening the wings so that the aircraft can withstand increased accelerations (up to 2G).

Despite the fact that sometimes when describing the conditions of free fall during a space flight in orbit around the Earth, one speaks of the absence of gravity, of course gravity is present in any spacecraft. What is missing is weight, that is, the force of the support reaction on objects in the spacecraft that are moving through space with the same gravitational acceleration, which is only slightly less than on Earth. For example, in a 350 km low Earth orbit, in which the International Space Station (ISS) flies around the Earth, the gravitational acceleration is 8.8 m/s², which is only 10% less than on the Earth's surface.

To describe the real acceleration of an object (usually an aircraft) relative to the acceleration of free fall on the surface of the Earth, a special term is usually used - overload. If you are lying, sitting or standing on the ground, your body is affected by an overload of 1 g (that is, there is none). On the other hand, if you are in an airplane taking off, you experience about 1.5 g. If the same aircraft makes a coordinated tight turn, the passengers may experience up to 2 g, meaning their weight has doubled.

People are accustomed to living in the absence of overload (1 g), so any overload greatly affects the human body. As with zero gravity laboratory aircraft, in which all fluid handling systems must be modified in order to function correctly in zero (weightlessness) and even negative G conditions, people also need help and a similar "modification" to survive in such conditions. An untrained person can pass out with 3-5 g (depending on the direction of the overload), as this is enough to deprive the brain of oxygen, because the heart cannot pump enough blood into it. In this regard, military pilots and astronauts train on centrifuges in high overload conditions to prevent loss of consciousness during them. To prevent short-term loss of vision and consciousness, which, under the conditions of work, can be fatal, pilots, cosmonauts and astronauts put on altitude-compensating suits that limit the outflow of blood from the brain during overloads by providing uniform pressure on the entire surface of the human body.

If there were no air resistance, the speed of a body in free fall would increase by 9.8 m/s every second.

The speed and distance of a freely falling body is calculated as follows:

v₀ - initial speed (m/s).

v- final vertical speed (m/s).

h₀ - initial height (m).

h- drop height (m).

t- fall time (s).

g- free fall acceleration (9.81 m/s2 at the Earth's surface).

If a v₀=0 and h₀=0, we have:

if the time of free fall is known:

if the free fall distance is known:

if the final speed of free fall is known:

These formulas are used in this free fall calculator.

Free fall of a body is its uniformly variable motion, which occurs under the influence of gravity. At this moment, other forces that can act on the body are either absent or so small that their influence is not taken into account. For example, when a skydiver jumps from an airplane, the first few seconds after the jump, he falls in a free state. This short period of time is characterized by a feeling of weightlessness, similar to that experienced by astronauts on board a spacecraft.

The history of the discovery of the phenomenon

Scientists learned about the free fall of a body back in the Middle Ages: Albert of Saxony and Nikolai Orem studied this phenomenon, but some of their conclusions were erroneous. For example, they argued that the speed of a falling heavy object increases in direct proportion to the distance traveled. In 1545, this error was corrected by the Spanish scientist D. Soto, who established the fact that the speed of a falling body increases in proportion to the time that passes from the beginning of the fall of this object.

In 1590, the Italian physicist Galileo Galilei formulated a law that establishes a clear dependence of the path traveled by a falling object on time. The scientists also proved that in the absence of air resistance, all objects on Earth fall with the same acceleration, although before its discovery it was generally accepted that heavy objects fall faster.

A new value was discovered - acceleration of gravity, which consists of two components: gravitational and centrifugal accelerations. The free fall acceleration is denoted by the letter g and has a different value for different points on the globe: from 9.78 m / s 2 (indicator for the equator) to 9.83 m / s 2 (acceleration value at the poles). The accuracy of indicators is affected by longitude, latitude, time of day and some other factors.

The standard value of g is considered to be equal to 9.80665 m/s 2 . In physical calculations that do not require high accuracy, the acceleration value is taken as 9.81 m / s 2. To facilitate calculations, it is allowed to take the value of g equal to 10 m / s 2.

In order to demonstrate how an object falls in accordance with Galileo's discovery, scientists arrange such an experiment: objects with different masses are placed in a long glass tube, air is pumped out of the tube. After that, the tube is turned over, all objects under the action of gravity fall simultaneously to the bottom of the tube, regardless of their mass.

When these same objects are placed in any medium, along with the force of gravity, a resistance force acts on them, so objects, depending on their mass, shape and density, will fall at different times.

Formulas for calculations

There are formulas that can be used to calculate various indicators related to free fall. They use such conventions:

u is the final speed with which the investigated body moves, m/s;
h is the height from which the investigated body moves, m;
t - time of movement of the investigated body, s;
g - acceleration (constant value equal to 9.8 m / s 2).

The formula for determining the distance traveled by a falling object at a known final speed and time of fall: h = ut /2.

The formula for calculating the distance traveled by a falling object from a constant value g and time: h = gt 2 /2.

The formula for determining the speed of a falling object at the end of the fall with a known fall time: u = gt.

The formula for calculating the speed of an object at the end of the fall, if the height from which the object under study falls is known: u = √2 gh.

If you do not delve into scientific knowledge, the everyday definition of free movement implies the movement of a body in the earth's atmosphere, when it is not affected by any extraneous factors, except for the resistance of the surrounding air and gravity.

At various times, volunteers compete with each other, trying to set a personal record. In 1962, a test skydiver from the USSR, Evgeny Andreev, set a record, which was entered in the Guinness Book of Records: while skydiving in free fall, he overcame a distance of 24,500 m, during the jump, a braking parachute was not used.

In 1960, the American D. Kittinger made a parachute jump from a height of 31 thousand meters, but using a parachute-brake installation.

In 2005, a record speed was recorded in free fall - 553 km / h, and seven years later a new record was set - this speed was increased to 1342 km / h. This record belongs to the Austrian skydiver Felix Baumgartner, who is known throughout the world for his dangerous stunts.