Ultimate fall speed. Free fall of bodies. Acceleration of free fall Determine the height of the fall of the body from the final speed

The speed at which a body falls in a gas or liquid stabilizes when the body reaches a speed at which the force of gravitational attraction is balanced by the resistance force of the medium.

When larger objects move in a viscous medium, however, other effects and patterns begin to prevail. When raindrops reach a diameter of only tenths of a millimeter, so-called swirls as a result flow disruption. You may have observed them very clearly: when a car drives along a road covered with fallen leaves in the fall, dry leaves not only scatter on the sides of the car, but begin to spin in a kind of waltz. The circles they describe exactly follow the lines von Karman vortices, which received their name in honor of the Hungarian-born physicist Theodore von Kármán (1881-1963), who, having emigrated to the USA and worked at the California Institute of Technology, became one of the founders of modern applied aerodynamics. These turbulent vortices usually cause braking - they make the main contribution to the fact that a car or plane, having accelerated to a certain speed, encounters a sharply increased air resistance and is unable to accelerate further. If you have ever driven your passenger car at high speed with a heavy and fast oncoming van and the car began to “spin” from side to side, know that you have found yourself in the von Karman whirlwind and have become acquainted with it first-hand.

When large bodies free fall in the atmosphere, vortices begin almost immediately, and the maximum speed of fall is reached very quickly. For skydivers, for example, the maximum speed ranges from 190 km/h at maximum air resistance, when they fall flat with their arms outstretched, to 240 km/h when diving like a fish or a soldier.

The free fall of a body is its uniform 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, he falls free for the first few seconds after the jump. This short period of time is characterized by a feeling of weightlessness, similar to that experienced by astronauts on board a spacecraft.

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 Nicholas Ores 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, a correction to this error was made 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, Italian physicist Galileo Galilei formulated a law that establishes a clear dependence of the distance traveled by a falling object on time. Scientists have also proven 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 quantity was discovered - acceleration of gravity, which consists of two components: gravitational and centrifugal acceleration. The acceleration of gravity is denoted by the letter g and has different values for different points of 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 the indicators is affected by longitude, latitude, time of day and some other factors.

The standard value of g is considered to be 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 set up the following experiment: objects with different masses are placed in a long glass tube, and air is pumped out of the tube. After this the tube is turned over, all objects fall simultaneously to the bottom of the tube under the influence of gravity, regardless of their mass.

When the same objects are placed in any environment, simultaneously 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 associated with free fall. They use the following legend:

u is the final speed with which the body under study moves, m/s;
h is the height from which the body under study moves, m;
t is the time of movement of the body under study, 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.

Formula for calculating the distance traveled by a falling object using 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 its fall, if the height from which the object under study falls is known: u = √2 gh.

Without delving 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 other than the resistance of the surrounding air and gravity.

At various times, volunteers compete with each other, trying to set a personal best. In 1962, a test parachutist from the USSR, Evgeny Andreev, set a record that was included in the Guinness Book of Records: when jumping with a parachute in free fall, he covered a distance of 24,500 m, without using a braking parachute during the jump.

In 1960, the American D. Kittinger made a parachute jump from a height of 31 thousand m, but using a parachute-braking system.

In 2005, a record speed during free fall was recorded - 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.

Video

Watch an interesting and educational video that will tell you about the speed of falling bodies.

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, it is subject to an additional drag force and its movement depends not only on gravitational acceleration, but also on its mass, cross-section and other factors. However, a body falling in a vacuum is subject to only one force, namely gravity.

Examples of free fall are spaceships and satellites in low-Earth orbit, because the only force acting on them is gravity. The planets orbiting the Sun are also in free fall. Objects falling to the ground at low speed can also be considered freely 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 gravity on the surface of the Earth 9.8 meters per second per second (m/s²) or 32.2 feet in second per second (ft/s²). On the surface of other astronomical bodies, the acceleration of gravity will be different.

Skydivers, of course, say that before the parachute opens they are in free fall, but in reality a parachutist can never be in free fall, even if the parachute has not yet opened. Yes, a parachutist 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- fall height (m).

t- fall time (s).

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

If v₀=0 and h₀=0, we have:

if the free fall time 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, 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. Typically these forces act in a direction perpendicular to the surface of contact with the support, and most often vertically upward. Weightlessness can be compared to swimming in water, but in such a way that the skin does not feel the water. Everyone knows that feeling of your own weight when you go ashore after a long swim in the sea. This is why water pools are used to simulate weightlessness when training cosmonauts and astronauts.

The gravitational field itself 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 a feeling of weightlessness arises, almost the same as in water .

Aircraft for training in zero gravity conditions 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 use in several countries. For short periods of time, lasting about 25 seconds every minute of flight, the aircraft is in a state of weightlessness, meaning there is no ground reaction for the occupants.

Various aircraft were used to simulate weightlessness: in the USSR and Russia, modified production aircraft Tu-104AK, Tu-134LK, Tu-154MLK and Il-76MDK were used for this purpose since 1961. In the United States, 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 an Airbus A310 aircraft for zero-gravity training. The modification consists of modifying 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 space flight in orbit around the Earth they talk about 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, which move through space with the same acceleration due to gravity, which is only slightly less than on Earth. For example, in the 350 km high Earth orbit in which the International Space Station (ISS) circles the Earth, the gravitational acceleration is 8.8 m/s², which is only 10% less than at the Earth's surface.

To describe the actual acceleration of an object (usually an aircraft) relative to the acceleration of gravity on the Earth's surface, a special term is usually used - overload. If you are lying, sitting, or standing on the ground, your body is subject to 1 g of force (that is, there is none). If you're on a plane taking off, you'll experience about 1.5 G's. If the same aircraft performs a coordinated tight-radius turn, passengers may experience up to 2 g's, meaning their weight has doubled.

People are accustomed to living in conditions of no overload (1 g), so any overload has a strong effect on the human body. Just as in zero-gravity laboratory aircraft, in which all fluid-handling systems must be modified to operate properly under zero-g and even negative-g conditions, humans also require assistance and similar "modification" to survive in such conditions. An untrained person can lose consciousness with an overload of 3-5 g (depending on the direction of the overload), since such an overload is sufficient to deprive the brain of oxygen, because the heart cannot supply enough blood to it. In this regard, military pilots and astronauts train in centrifuges in high overload conditions to prevent loss of consciousness during them. To prevent short-term loss of vision and consciousness, which, under working conditions, can be fatal, pilots, cosmonauts and astronauts wear altitude-compensating suits, which limit the flow of blood from the brain during overload by ensuring uniform pressure over the entire surface of the human body.

It's Tuesday, which means we're solving problems again today. This time, on the topic “free fall of bodies”.

Questions with answers about free falling bodies

Question 1. What is the direction of the gravitational acceleration vector?

Answer: we can simply say that acceleration g directed downwards. In fact, more precisely, the acceleration of gravity is directed towards the center of the Earth.

Question 2. What does the acceleration of free fall depend on?

Answer: on Earth, the acceleration due to gravity depends on latitude as well as altitude h lifting the body above the surface. On other planets this value depends on the mass M and radius R celestial body. The general formula for the acceleration of gravity is:

Question 3. The body is thrown vertically upward. How can this movement be characterized?

Answer: In this case, the body moves with uniform acceleration. Moreover, the time of rise and the time of fall of the body from the maximum height are equal.

Question 4. And if the body is thrown not upward, but horizontally or at an angle to the horizontal. What movement is this?

Answer: we can say that this is also a free fall. In this case, the movement must be considered relative to two axes: vertical and horizontal. The body moves uniformly relative to the horizontal axis, and uniformly accelerated with acceleration relative to the vertical axis g.

Ballistics is a science that studies the characteristics and laws of motion of bodies thrown at an angle to the horizon.

Question 5. What does "free" fall mean?

Answer: in this context, it is understood that when a body falls, it is free from air resistance.

Free fall of bodies: definitions, examples

Free fall is a uniformly accelerated movement occurring under the influence of gravity.

The first attempts to systematically and quantitatively describe the free fall of bodies date back to the Middle Ages. True, at that time there was a widespread misconception that bodies of different masses fall at different speeds. In fact, there is some truth in this, because in the real world, air resistance greatly affects the speed of falling.

However, if it can be neglected, then the speed of falling bodies of different masses will be the same. By the way, the speed during free fall increases in proportion to the time of fall.

The acceleration of freely falling bodies does not depend on their mass.

The free fall record for a person currently belongs to the Austrian skydiver Felix Baumgartner, who in 2012 jumped from a height of 39 kilometers and was in free fall for 36,402.6 meters.

Examples of free falling bodies:

an apple flies onto Newton's head;
a parachutist jumps out of a plane;
the feather falls in a sealed tube from which the air has been evacuated.

When a body falls in free fall, a state of weightlessness occurs. For example, objects in a space station moving in orbit around the Earth are in the same state. We can say that the station is slowly, very slowly falling onto the planet.

Of course, free fall is possible not only on Earth, but also near any body with sufficient mass. On other comic bodies, the fall will also be uniformly accelerated, but the magnitude of the acceleration of free fall will differ from that on Earth. By the way, we have already published material about gravity before.

When solving problems, the acceleration g is usually considered equal to 9.81 m/s^2. In reality, its value varies from 9.832 (at the poles) to 9.78 (at the equator). This difference is due to the rotation of the Earth around its axis.

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He took two glass tubes, which were called Newton's tubes, and pumped the air out of them (Fig. 1). Then he measured the time of fall 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 air resistance, then nothing will stop 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 other forces.

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

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

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

for velocity projection: V x = V 0x + a x t

for displacement projection: S x = V 0x t + a x t 2 /2

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

x means that our movement is rectilinear, along the x axis, which we traditionally chose horizontally.

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

Rice. 2. Vertical body movement ()

The equations take on the following absolutely identical form, where g is the acceleration of free fall, 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 upward with an initial speed V 0 (Fig. 3). Let us find the height to which the body is thrown. Let us write down the equation of motion of this body:

Rice. 3. Example task ()

Knowledge of the simplest equations allowed us to find the height to which we can throw a body.

The magnitude of the acceleration due to gravity depends on the geographic latitude of the area; it is maximum at the poles and minimum at the equator. 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 larger, if there are voids there, 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 movement 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 secured the ends of the knitting needles to 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 Montelier. He called his invention a parachute, which translated from French means “anti-fall.”

Galileo Galilei was the first to show that the time a body falls to Earth does not depend on its mass, but is determined by the characteristics of the Earth itself. As an example, he cited a discussion 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 body’s fall 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 is preventing the other half from falling? We arrive at a contradiction, which means that the assumption that the speed of falling depends on the mass of the body is unfair.

Therefore, we arrive at 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 the acceleration due to gravity will vary depending on geographic location, but these changes are insignificant. What values does the acceleration of gravity take on other celestial bodies? How to predict whether a person can live comfortably there? Let us recall the formula for free fall (Fig. 4):

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

The more massive the celestial body, the greater the acceleration of free fall on it, the more impossible it is for a human body to be on it. Knowing the acceleration of gravity 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 are made of, that is, determine their structure.

The point is that measuring the acceleration of gravity at various points on the Earth is a powerful method of geological exploration. In this way, without digging holes, without drilling wells or mines, you can determine the presence of minerals in the thickness of the earth's crust. The first method is to measure the acceleration of gravity using geological spring balances; they have phenomenal sensitivity, up to millionths of a gram (Fig. 5).

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

What is the norm for the magnitude of the acceleration of gravity? The globe is not a perfect sphere, but a geoid, that is, slightly flattened at the poles. This means that at the poles the value of the acceleration due to gravity 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 gravity 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 it 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 gravity, but also its direction. If we measure the acceleration of gravity near a large mountain, then this massive body will influence the direction of the acceleration of gravity, because it will also attract the mathematical pendulum, the method by which we measure the acceleration of gravity.

Bibliography

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

Homework

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

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