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).

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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.

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 fact 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 without 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.

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:

1. u is the final speed with which the body under study moves, m/s;
2. h is the height from which the body under study moves, m;
3. t is the time of movement of the body under study, s;
4. 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, test parachutist from the USSR Evgeniy 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.

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, to be more precise, 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 free fall is:

Question 3. The body is thrown vertically upward. How can you characterize this movement?

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 kind of 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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What is free fall? This is the fall of bodies to the Earth in the absence of air resistance. In other words, falling into the void. Of course, the absence of air resistance is a vacuum, which cannot be found on Earth under normal conditions. Therefore, we will not take the force of air resistance into account, considering it so small that it can be neglected.

Acceleration of gravity

Carrying out his famous experiments on the Leaning Tower of Pisa, Galileo Galilei found out that all bodies, regardless of their mass, fall to the Earth in the same way. That is, for all bodies the acceleration of gravity is the same. According to legend, the scientist then dropped balls of different masses from the tower.

Acceleration of gravity

Gravity acceleration is the acceleration with which all bodies fall to the Earth.

The acceleration of gravity is approximately 9.81 m s 2 and is denoted by the letter g. Sometimes, when accuracy is not fundamentally important, the acceleration of gravity is rounded to 10 m s 2.

The Earth is not a perfect sphere, and at different points on the earth's surface, depending on the coordinates and altitude above sea level, the value of g varies. Thus, the greatest acceleration of gravity is at the poles (≈ 9.83 m s 2), and the smallest is at the equator (≈ 9.78 m s 2).

Free fall body

Let's look at a simple example of free fall. Let some body fall from a height h with zero initial speed. Let's say we raised the piano to a height h and calmly released it.

Free fall is a rectilinear movement with constant acceleration. Let's direct the coordinate axis from the point of initial position of the body to the Earth. Using kinematics formulas for rectilinear uniformly accelerated motion, we can write:

h = v 0 + g t 2 2 .

Since the initial speed is zero, we rewrite:

From here we find the expression for the time of falling of a body from a height h:

Taking into account that v = g t, we find the speed of the body at the moment of falling, that is, the maximum speed:

v = 2 h g · g = 2 h g .

Similarly, we can consider the motion of a body thrown vertically upward with a certain initial speed. For example, we throw a ball up.

Let the coordinate axis be directed vertically upward from the point of throwing the body. This time the body moves equally slow, losing speed. At the highest point the speed of the body is zero. Using kinematics formulas, we can write:

Substituting v = 0, we find the time for the body to rise to its maximum height:

The time of fall coincides with the time of rise, and the body will return to Earth after t = 2 v 0 g.

Maximum lifting height of a body thrown vertically:

Let's take a look at the picture below. It shows graphs of body velocities for three cases of motion with acceleration a = - g. Let's consider each of them, having previously specified that in this example all numbers are rounded, and the acceleration of free fall is assumed to be 10 m s 2.

The first graph is a body falling from a certain height without an initial speed. Fall time tp = 1 s. From the formulas and from the graph it is easy to see that the height from which the body fell is h = 5 m.

The second graph is the movement of a body thrown vertically upward with an initial speed v 0 = 10 m s. Maximum lifting height h = 5 m. Rising time and falling time t p = 1 s.

The third graph is a continuation of the first. The falling body bounces off the surface and its speed sharply changes sign to the opposite. Further movement of the body can be considered according to the second graph.

The problem of the free fall of a body is closely related to the problem of the motion of a body thrown at a certain angle to the horizon. Thus, movement along a parabolic trajectory can be represented as the sum of two independent movements relative to the vertical and horizontal axes.

Along the O Y axis the body moves uniformly with acceleration g, the initial speed of this movement is v 0 y. The movement along the O X axis is uniform and rectilinear, with an initial speed v 0 x.

Conditions for movement along the O X axis:

x 0 = 0 ; v 0 x = v 0 cos α ; a x = 0 .

Conditions for movement along the O Y axis:

y 0 = 0 ; v 0 y = v 0 sin α ; a y = - g .

Let us give formulas for the motion of a body thrown at an angle to the horizontal.

Body flight time:

t = 2 v 0 sin α g .

Body flight range:

L = v 0 2 sin 2 α g .

Maximum flight range is achieved at angle α = 45°.

L m a x = v 0 2 g .

Maximum lifting height:

h = v 0 2 sin 2 α 2 g .

Note that in real conditions, the movement of a body thrown at an angle to the horizon can take place along a trajectory different from parabolic due to air and wind resistance. The study of the movement of bodies thrown in space is a special science - ballistics.

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