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 different points on the 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 free fall is taken equal to 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 axis O Y the body moves uniformly accelerated with acceleration g, starting speed this movement - 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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A fall is the movement of a body in the gravitational field of the Earth. Its specificity is that it invariably takes place with continuous acceleration, which is equal to g? 9.81 m / s?. This must also be considered when the object is thrown horizontally.

You will need

• - rangefinder;
• – electronic stopwatch;
• - calculator.

Instruction

1. If the body falls freely from a certain height h, measure it with a rangefinder or any other device. Calculate speed fall body v, having found the square root of the product of the acceleration of the free fall to height and number 2, v=?(2?g?h). If, before the start of the countdown, the body had more speed v0, then add its value v=?(2?g?h)+v0 to the resulting total.

2. Example. A body freely falls from a height of 4 m at zero initial velocity. What will be his speed upon reaching the earth's surface? Calculate speed fall bodies according to the formula, considering that v0=0. Substitute v=?(2?9.81?4)?8.86 m/s.

3. measure time fall body t electronic stopwatch in seconds. Discover it speed at the end of the period of time that the movement continued by adding to the initial speed v0 the product of the time by the acceleration of the free fall v=v0+g?t.

4. Example. The stone began to fall from its original speed u 1 m/s. Discover it speed after 2 s. Substitute the values ​​of these quantities in the formula v=1+9.81?2=20.62 m/s.

5. Calculate speed fall body thrown horizontally. In this case, its movement is the result of 2 types of movement in which the body simultaneously takes part. This is uniform horizontal motion and uniformly accelerated vertical motion. As a result, the trajectory of the body has the form of a parabola. The speed of the body at any moment of time will be equal to the vector sum of the horizontal and vertical components of the speed. Since the angle between the vectors of these speeds is invariably straight, then to determine the speed fall body thrown horizontally, use the Pythagorean theorem. The speed of the body will be equal to the square root of the sum of the squares of the horizontal and vertical components in this moment time v=?(v mountains? + v vert?). Calculate the vertical component of the velocity according to the method expressed in the previous paragraphs.

6. Example. A body is thrown horizontally from a height of 6 m speed u 4 m/s. Define it speed when hitting the ground. Detect the vertical velocity component when hitting the ground. It will be the same as if the body freely fell from a given height vvert =?(2?g?h). Substitute the value in the formula and get v \u003d? (v mountains? + 2? g? h) = ? (16 + 2? 9.81? 6)? 11.56 m / s.

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 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 their 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 for Space Research (CNES, France) uses the Airbus A310 for training in weightlessness. The modification consists in the refinement of the fuel, hydraulic and some other systems in order to ensure their normal operation in conditions of short-term weightlessness, as well as the strengthening of 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 weight, that is, the force of the reaction of the support on the objects in the spacecraft, which are moving in space with the same acceleration of gravity, 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.

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 overload (1 g), so any overload greatly affects the human body. As in 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 lose consciousness at 3-5 g (depending on the direction of the overload), as 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 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.

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.

Thus, free fall is a special case of uniformly accelerated motion. 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 acceleration of free fall depends on the geographic latitude of the area, at the poles it is maximum and at the equator is minimum. In addition, the acceleration of free fall depends on the composition of the earth's crust under the place where we are. If there are deposits of heavy minerals, the value of g will be a little 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 of being on it human body. 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.

We are talking about the fact 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 acceleration of free fall 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.

The presence of minerals, deposits of 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 a mathematical pendulum, by which we measure the gravitational acceleration.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) - M.: Mnemozina, 2012.
2. Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

Homework

1. What type of motion is free fall?
2. What are the characteristics of free fall?
3. What experience shows that all bodies on Earth fall with the same acceleration?

1. Internet portal Class-fizika.narod.ru ().
2. Internet portal Nado5.ru ().
3. Internet portal Fizika.in ().

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 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 a 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 velocity 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, according to by and large, does not affect the change in speed.