Free fall is the movement of bodies only under the influence of the Earth's attraction (under the influence of gravity)
Under the conditions of the Earth, the fall of bodies is considered conditionally free, because When a body falls in air, there is always an air resistance force.
An ideal free fall is possible only in a vacuum, where there is no air resistance force, and regardless of mass, density and shape, all bodies fall equally quickly, i.e. at any time the bodies have the same instantaneous speeds and acceleration.
It is possible to observe the ideal free fall of bodies in a Newton's tube if air is pumped out of it with a pump.
In further reasoning and in solving problems, we neglect the force of friction against air and consider the fall of bodies under terrestrial conditions to be ideally free.
ACCELERATION OF GRAVITY
In free fall, all bodies near the surface of the Earth, regardless of their mass, acquire the same acceleration, called the acceleration of free fall.
The symbol for free fall acceleration is g.
The free fall acceleration on Earth is approximately equal to:
g = 9.81m/s2.
Free fall acceleration 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 action of a constant force. Therefore, free fall is uniformly accelerated motion.
The vector of gravity and the acceleration of free fall created by it are always directed in the same way.
All formulas for uniformly accelerated motion applicable to free falling bodies.
The value of the free fall speed of a body at any given time:
body movement:
In this case, instead of accelerating a, the free fall acceleration is introduced into the formulas for uniformly accelerated motion g=9.8m/s2.
Under conditions of ideal fall, bodies falling from the same height reach the Earth's surface, having the same speeds and spending the same time on falling.
In ideal free fall, the body returns to Earth with a speed equal to the initial velocity modulus.
The time of the fall of the body is equal to the time of upward movement from the moment of the throw to a complete stop in highest point 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 arising in rotating systems (i.e., the influence of the Earth's rotation around its axis affects).
DO YOU KNOW
WHAT IS THE FALL OF BODIES UNDER REAL CONDITIONS?
If a gun is fired vertically upwards, then, taking into account the force of friction against the air, a bullet freely falling from any height will acquire a speed of no more than 40 m / s near the ground.
In real conditions, due to the presence of a friction force on the air, the mechanical energy of the body is partially converted into thermal energy. As a result, the maximum lifting height of the body turns out to be less than it could be when moving in an airless space, and at any point of the trajectory during the 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 motion. As the speed increases, the acceleration decreases, 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 out a disk of the same diameter from plain paper. Raise them, holding in different hands, to the same height and release at the same time. A heavy disk will fall faster than a light one. When falling, two forces act simultaneously on each disk: 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 air resistance force increases and gradually compares in magnitude with the force of gravity, the falling bodies begin to move evenly, but at different speeds (a heavier body has a higher speed).
Similarly to the motion of a falling disk, one can consider the motion of a parachutist falling down while jumping from an airplane from a great height.
Place a light paper disc on top of a heavier plastic or plywood disc, lift them up 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, fixed 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. Downstairs he was surrounded by enthusiastic spectators. What is the name of your umbrella? Parachute! - answered Lenormand (the literal translation of this word from French is "against the fall").
INTERESTING
If the Earth is drilled through and a stone is thrown into it, what will happen to the stone?
The stone will fall, gaining maximum speed in the middle of the path, then it will fly by inertia and reach the opposite side of the Earth, and its final speed will be equal to the initial one. The free fall acceleration 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 a starting speed stone is equal to zero, then the period of oscillation of the stone in the mine is equal to the period of revolution of the satellite near the surface of the Earth, regardless of how the straight mine is dug: through the center of the Earth or along any chord.
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.
So free fall is special case uniformly accelerated movement. 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 free fall acceleration depends on geographical latitude terrain, at the poles it is maximum and at the equator is minimum. In addition, the gravitational acceleration depends on which composition earth's crust under 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 Oh? 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.
It's about 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? Earth 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.
Presence of minerals, deposits 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 mathematical pendulum, by which we measure the acceleration of free fall.
Bibliography
- Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) - 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?
- Internet portal Class-fizika.narod.ru ().
- Internet portal Nado5.ru ().
- Internet portal Fizika.in ().
Free fall is the motion of a body under the influence of gravity alone.
A body falling in the air, in addition to the force of gravity, is affected by the force of air resistance, therefore, such a movement is not a free fall. Free fall is the fall of bodies in a vacuum.
The acceleration imparted to the body by gravity is called free fall acceleration. It shows how much the speed of a freely falling body changes per unit time.
Free fall acceleration is directed vertically downwards.
Galileo Galilei installed ( Galileo's law): all bodies fall to the surface of the Earth under the influence of gravity in the absence of resistance forces with the same acceleration, i.e. free fall acceleration does not depend on the mass of the body.
You can verify this using a Newton tube or a stroboscopic method.
Newton's tube is a glass tube about 1 m long, one end of which is sealed and the other is equipped with a tap (Fig. 25).
Fig.25
Let's put three different objects into the tube, for example, a pellet, a cork, and a bird's feather. Then quickly turn the tube over. All three bodies will fall to the bottom of the tube, but at different times: first the pellet, then the cork, and finally the feather. But this is how bodies fall when there is air in the tube (Fig. 25, a). One has only to pump out the air with a pump and turn the tube over again, we will see that all three bodies will fall simultaneously (Fig. 25, b).
In terrestrial conditions, g depends on the geographic latitude of the area.
Highest value it has at the pole g=9.81 m/s 2 , the smallest - at the equator g=9.75 m/s 2 . Reasons for this:
1) the daily rotation of the Earth around its axis;
2) deviation of the shape of the Earth from spherical;
3) non-uniform distribution of the density of terrestrial rocks.
The free fall acceleration depends on the height h of the body above the surface of the planet. It, if we neglect the rotation of the planet, can be calculated by the formula:
where G is the gravitational constant, M is the mass of the planet, R is the radius of the planet.
As follows from the last formula, with an increase in the height of the body's rise above the surface of the planet, the acceleration of free fall decreases. If we neglect the rotation of the planet, then on the surface of the planet with a radius R
To describe it, you can use the formulas of uniformly accelerated motion:
speed equation:
kinematic equation describing the free fall of bodies: 
,
or in the projection on the axis 
.
Movement of a body thrown vertically
A freely falling body can move in a straight line or along a curved path. It depends on the initial conditions. Let's consider this in more detail.
Free fall without initial velocity ( =0) (Fig. 26).
With the chosen coordinate system, the movement of the body is described by the equations: 
.
From the last formula, you can find the time the body falls from a height h:
Substituting the found time into the formula for velocity, we obtain the modulus of the body's velocity at the moment of fall: .
The motion of a body thrown vertically upwards with initial velocity (Fig. 27)
Fig.26 Fig.27
The motion of the body is described by the equations:
From the velocity equation, it can be seen that the body moves uniformly slow up, reaches its maximum height, and then moves uniformly accelerated down. Considering that at y=hmax the speed and at the moment when the body reaches the initial position y=0, we can find:
The time of lifting the body to the maximum height;
Maximum lifting height of the body;
Time of flight of the body;
The projection of the speed at the moment the body reaches its initial position.
Movement of a body thrown horizontally
If the velocity is not directed vertically, then the motion of the body will be curvilinear.
Consider the motion of a body thrown horizontally from a height h with a speed (Fig. 28). Air resistance will be neglected. To describe the movement, it is necessary to choose two coordinate axes - Ox and Oy. The origin of coordinates is compatible with the initial position of the body. It can be seen from Fig. 28 that , , , .
Fig.28
Then the motion of the body will be described by the equations:
The analysis of these formulas shows that in the horizontal direction the speed of the body remains unchanged, i.e. the body moves uniformly. In the vertical direction, the body moves uniformly with acceleration g, i.e. just like a free-falling body with no initial velocity. Let's find the trajectory equation. To do this, from equation (3) we find the time
The speed of a body falling in a gas or liquid stabilizes when the body reaches a speed at which the gravitational attraction force is balanced by the resistance force of the medium.
When larger objects move in a viscous medium, however, other effects and regularities begin to dominate. 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 autumn, dry leaves do not just scatter on the sides of the car, but begin to spin in a kind of waltz. The circles they describe exactly follow the lines Vortex von Karman, which received their name in honor of the Hungarian-born engineer-physicist Theodore von Karman (Theodore von Kármán, 1881-1963), who, having emigrated to the United States and worked in California Institute of Technology, became one of the founders of modern applied aerodynamics. These turbulent eddies usually cause braking - they make the main contribution to the fact that a car or aircraft, having accelerated to a certain speed, encounters a sharply increased air resistance and is unable to accelerate further. If you have ever driven around at high speed in your passenger car with a heavy and fast oncoming van and the car began to “drive” from side to side, you should know that you fell into the von Karman whirlwind and got to know him firsthand.
In the free fall of large bodies in the atmosphere, turbulences begin almost immediately, and the limiting speed of fall is reached very quickly. For parachutists, for example, the speed limit ranges from 190 km/h at maximum air resistance, when they fall flat with their arms outstretched, to 240 km/h when diving as a "fish" or "soldier".
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. So if you are in free fall big object(for example, in an airplane) that is also in this state, your body is not affected by any external forces interaction of the body with the support 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 space research(CNES, France) use an 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 the weight, that is, the reaction force of the support on the objects that are in spaceship, which are moving in space with the same free fall acceleration, which is only slightly less than on Earth. For example, in low-Earth orbit at a height of 350 km, 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.
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To describe the actual acceleration of an object (usually aircraft) regarding 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.