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, the 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 gravity.

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

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

v₀ - initial speed (m/s).

v- final vertical speed (m/s).

h₀ - initial height (m).

h- drop height (m).

t- fall time (s).

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

If a v₀=0 and h₀=0, we have:

if the time of free fall is known:

if the free fall distance is known:

if the final speed of free fall is known:

These formulas are used in this free fall calculator.

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

By itself, the gravitational field cannot create pressure on your body. Therefore, if you are in a 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 speak 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 Earth orbit at a height of 350 km, in which the International Space Station (ISS) flies around the Earth, gravitational acceleration is 8.8 m/s², which is only 10% less than on the Earth's surface.

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 at 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.

Tuesday, which means that today we are solving problems again. This time, on the topic free fall tel."

Questions with answers to the free fall of bodies

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

Answer: one can simply say that the acceleration g directed down. In fact, to be more precise, the acceleration of free fall is directed towards the center of the Earth.

Question 2. What does free fall acceleration depend on?

Answer: On Earth, the free fall acceleration depends on geographical latitude, as well as on the height h lifting the body above the surface. On other planets, this value depends on the mass M and radius R celestial body. General formula to accelerate free fall:

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

Answer: In this case, the body moves uniformly accelerated. Moreover, the time of rise and the time of falling of the body from the maximum height are equal.

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

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 relative to the vertical axis with acceleration g.

Ballistics is a science that studies the features 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 the body, when falling, is free from air resistance.

Free fall of bodies: definitions, examples

Free fall is a uniformly accelerated motion 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, the speed of falling is greatly affected by air resistance.

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.

Examples of free falling bodies:

• an apple flies on Newton's head;
• parachutist jumps out of the plane;
• the feather falls in a sealed tube from which the air is pumped out.

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

Of course, free fall is possible not only not on the 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 free fall acceleration will differ from the earth's. By the way, earlier we already published a material about gravity.

When solving problems, the acceleration g is considered to be 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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13 free-falling body in airless space is subjected to the acceleration of free fall g =\u003d 9.81 m / s 2, there is no resistance force Q. Therefore, the speed of falling bodies in airless space over time will constantly increase under the influence of the acceleration of free fall V=gt.

When falling in the air on a body, in addition to the acceleration of free fall, the air resistance force Q will act in the opposite direction :

When the body's gravity G=mg will be balanced by the resistance force Q, there will be no further increase in the free fall velocity of the body, that is, equilibrium is reached:

This means that the body has reached the critical equilibrium velocity of fall:

It can be seen from the formula that the critical speed of falling bodies in the air depends on the weight of the body, the coefficient of resistance of the body C x the area of ​​​​the resistance of the body. The drag coefficient C x of a person can vary over a wide range. Its average value C x = = 0.195; the maximum value is about 150%, and the minimum is 50% of the average.

Usually instead of midsection (S) Conventionally, the square of the height of the body is taken -. Everyone knows their own growth. Taking the amount of growth squared is enough for the calculation, that is:

The maximum value of the drag coefficient is obtained when the body is positioned flat face down, the minimum value is obtained when the position is close to a vertical fall upside down.

On fig. 54 shows the change in the drag coefficient of the paratrooper's body depending on his position. 0° corresponds to falling of the body flat face down, 90° corresponds to falling head first, 180° corresponds to falling flat on the back.

Such a range of change in the drag coefficient gives the following possible values ​​of the equilibrium parachute fall velocity in air of normal density (that is, at our operating altitudes). When falling head down - 58-60 m / s; when falling flat - 41-43 m / s. For example, with the weight of a parachutist

90 kg, height 1.7 m, density 0.125, average

drag coefficient C x = 0.195, the rate of fall will be equal to:

If, under these conditions, the fall is continued upside down, then the equilibrium speed of fall will be approximately 59 m/s.

When performing a complex of figures in free fall, the drag coefficient fluctuates around its average value. When the weight of a parachutist changes by 10 kg, the speed of his fall changes by approximately 1 m / s, that is, by 2%.

From all of the above, it becomes clear why paratroopers try to achieve maximum fall speed before performing figures. It should be noted that when the body falls in any position, the equilibrium speed is reached at 11-12 seconds. Therefore, it makes no sense for a skydiver to do acceleration longer than 12-16 s. At the same time, a great effect is not achieved, however, the height is lost, the supply of which is never superfluous.

For clarity, we can give an example: the maximum fall speed when jumping from a height of 1000 m is reached at the 12th second of the fall. When jumping from a height of 2000 m - at 12.5 seconds, and when jumping from a height of 4000 m - at 14 seconds.

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

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

The thing is that it is possible only artificially to create conditions where other forces, in particular, the same air, do not affect the falling object. Experimentally, it was proved that the speed of free fall of a body in a vacuum is always equal to the same number, regardless of the weight of the body. Such a movement is called uniformly accelerated. It was first described famous physicist and astronomer Galileo Galilei over 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 and the time.

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

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

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

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 in different time: first a pellet, then a cork, and finally a 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