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. Remains open question about what will be its speed when falling? 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 the falling object is not affected by other forces, in particular, the same air. 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 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 times 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.
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 affected by extra power resistance and its movement 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 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 free fall state in a large 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 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 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 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 overloads (1 g), so any overload greatly affects 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.
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 that 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
Conducting 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 free fall is the same. According to legend, the scientist then threw balls of different masses from the tower.
Acceleration of gravity
Acceleration of free fall - the acceleration with which all bodies fall to the Earth.
The free fall acceleration is approximately equal to 9.81 m s 2 and is denoted by the letter g. Sometimes, when accuracy is not fundamentally important, the acceleration due to gravity is rounded up to 10 m s 2 .
The earth is not a perfect sphere, and at various points earth's surface, depending on the coordinates and height above sea level, the value of g varies. So, the largest free fall acceleration is at the poles (≈ 9, 83 m s 2), and the smallest is at the equator (≈ 9, 78 m s 2) .
Free fall body
Consider a simple example of free fall. Let some body fall from a height h with zero initial velocity. Suppose we raised the piano to a height h and calmly let it go.
Free fall - rectilinear motion with constant acceleration. Let's direct the coordinate axis from the point of the initial position of the body to the Earth. Applying the formulas of kinematics for rectilinear uniformly accelerated motion, you can write.
h = v 0 + g t 2 2 .
Since the initial speed is zero, we rewrite:
From here, the expression for the time of the fall of the body from a height h is found:
Taking into account that v \u003d g t, we find the speed of the body at the time of the fall, that is, the maximum speed:
v = 2 h g · g = 2 h g .
Similarly, we can consider the motion of a body thrown vertically upwards with a certain initial velocity. For example, we throw a ball up.
Let the coordinate axis be directed vertically upwards from the point of throwing the body. This time the body moves uniformly slow, losing speed. At the highest point, the speed of the body is zero. Using kinematic formulas, we can write:
Substituting v = 0 , we find the time for the body to rise to the maximum height:
The fall time coincides with the rise time, and the body will return to Earth after t = 2 v 0 g .
Maximum height of a body thrown vertically:
Let's take a look at the figure below. It shows graphs of body velocities for three cases of motion with acceleration a = - g. Let's consider each of them, after specifying that in this example all numbers are rounded, and the acceleration of gravity is assumed to be 10 m s 2.
The first graph is the fall of a body from a certain height without initial velocity. Fall time t p = 1 s. It is easy to get from the formulas and from the graph that the height from which the body fell is equal to h = 5 m.
The second graph is the movement of a body thrown vertically upwards with an initial speed v 0 = 10 m s. Maximum lifting height h = 5 m. Rise time and fall time t p = 1 s.
The third graph is a continuation of the first. The falling body bounces off the surface and its velocity abruptly changes sign to the opposite one. The 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 about the vertical and horizontal axes.
Along the O Y axis, the body moves uniformly accelerated with acceleration g, the initial speed of this movement is v 0 y. 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 .
We present formulas for the motion of a body thrown at an angle to the horizon.
Body flight time:
t = 2 v 0 sin α g .
Body flight range:
L \u003d v 0 2 sin 2 α g.
The maximum flight range is achieved at an angle α = 45°.
L m a x = v 0 2 g .
Max lifting height:
h \u003d v 0 2 sin 2 α 2 g.
Note that in real conditions, the motion of a body thrown at an angle to the horizon can follow a trajectory that is 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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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.
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 fast, i.e. at any moment of time the bodies have the same instantaneous velocities and accelerations.
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 free fall acceleration.
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 are applicable to the free fall of bodies.
The value of the free fall speed of a body at any given time:
body movement:
In this case, instead of accelerating but, 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 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 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 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.
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 the globe: from 9.78 m/s 2 (equator value) to 9.83 m/s 2 (polar acceleration value). 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 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 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.
Video
Watch an interesting and informative video that will tell you about the speed of falling bodies.
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