Tuesday, which means that today we solve the tasks again. This time, on the topic "Free drop of bodies."

Questions with answers to free fall bodies

Question 1. How is the free fall of free fall?

Answer: You can just say that acceleration g. Directed down. In fact, if we talk more precisely, the acceleration of the free fall is directed towards the center of the Earth.

Question 2. What depends on the acceleration of free fall?

Answer: On Earth, the acceleration of free fall depends on geographic latitude, as well as from height h. Lifting the body above the surface. On other planets, this value depends on the mass M. and radius R. Heavenly body. General formula for speeding free fall:

Question 3. The body throws up vertically. How can I characterize this movement?

Answer: In this case, the body moves equally. Moreover, the time of lifting and the time of the fall of the body from the maximum height is equal.

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

Answer: It can be said that this is also a free fall. In this case, the movement should be considered relative to two axes: vertical and horizontal. Relative to the horizontal axis the body is moving evenly, but relative to the vertical - equal to the acceleration g..

Ballistics - Science, learning the features and laws of the movement of bodies, abandoned at an angle to the horizon.

Question 5. What does "free" fall mean.

Answer: In this context it is understood that the body is free from the resistance of the air.

Free Fall Tel: Definitions, Examples

Free drop is an equilibrium movement occurring under the action of gravity.

The first attempts are systematized and quantify to describe the free fall of bodies belong to the Middle Ages. True, then the misconception was widespread that the bodies of different masses fall at different speeds. In fact, there is some truth in this, because in the real world on the rate of falling strongly affects the resistance of the air.

However, if they can be neglected, the speed of falling bodies of different masses will be the same. By the way, the speed at a free fall increases in proportion to the time of the fall.

Acceleration of free falling bodies does not depend on their mass.

Examples of free fall tel:

• apple flies on Newton's head;
• parachutist jumps out of the aircraft;
• a fence falls in a hermetic tube, from which air is dumped.

With a free falling of the body, the state of weightlessness occurs. For example, in the same condition there are subjects at the space station moving in orbit around the Earth. It can be said that the station slowly, very slowly falls on the planet.

Of course, the free drop is possible not only not land, but also near any body with sufficient mass. On other comic bodies of falling will also be equivalent, but the amount of free fall will differ from the earth. By the way, before we already went out the material about gravity.

When solving problems, the acceleration G is taken to be 9.81 m / s ^ 2. In reality, its value varies from 9.832 (on the poles) to 9.78 (at the equator). This difference is due to the rotation of the earth around its axis.

Need help to solve problems in physics? Contact B.

What is a free fall? This is a drop in bodies to the ground in the absence of air resistance. In other words - drop in emptiness. Of course, the lack of air resistance is a vacuum that cannot be found on Earth under normal conditions. Therefore, we will not take the power of air resistance into account, considering it as small that it can be neglected.

Acceleration of gravity

Conducting its famous experiments on the Pisa Tower Galileo Galilei found out that all the bodies, regardless of their mass, fall on the ground equally. That is, for all bodies accelerate the free fall equally. According to the legend, the scientist then dropped the balls from the tower of different masses.

Acceleration of gravity

Acceleration of free fall - acceleration with which all bodies fall to the ground.

The acceleration of the free fall is approximately 9, 81 m C 2 and is indicated by the letter G. Sometimes, when accuracy is not fundamentally important, the acceleration of the free fall is rounded up to 10 m from 2.

Earth is not an ideal ball, and at various points of the earth's surface, depending on the coordinates and height above sea level, the value G varies. So, the greatest acceleration of the free fall - on the poles (≈ 9, 83 m C 2), and the smallest - at the equator (≈ 9, 78 m from 2).

Free drop of body

Consider a simple example of free fall. Let some body fall from the height H with zero initial speed. Suppose we raised the piano to the height H and calmly let him go.

Free drop is a straightforward movement with constant acceleration. We will send the coordinate axis from the point of the initial position of the body to the Earth. Applying kinematics formulas for straight equative movement, you can write.

h \u003d V 0 + G T 2 2.

Since the speed is equal to zero, rewrite:

From here there is an expression for the time of the body fall from the height H:

Taking into account that V \u003d G T, we will find the body speed at the time of the fall, that is, the maximum speed:

v \u003d 2 H G · G \u003d 2 H g.

Similarly, you can consider the movement of the body thrown up vertically up at a certain initial speed. For example, we throw up the ball.

Let the coordinate axis point vertically up from the body throwing point. This time the body moves equifiable, losing speed. In the highest point, the body speed is zero. Applying kinematics formulas, you can write:

Substituting V \u003d 0, we will find the lifting time for the maximum height:

The fall time coincides with the time of lifting, and the body will return to the ground through T \u003d 2 V 0 g.

The maximum lifting height abandoned vertically:

Take a look at the drawing below. It shows the charts of the velocity of bodies for three cases of movement with acceleration a \u003d g. Consider each of them, pre-clarify that in this example all numbers are rounded, and the acceleration of the free fall is taken equal to 10 m C 2.

The first schedule is a drop in body with some height without initial speed. Fall time T n \u003d 1 s. From the formulas and from the graph it is easy to obtain that the height with which the body fell is equal to H \u003d 5 m.

The second graph is the movement of the body, abandoned vertically upwards with the initial velocity V 0 \u003d 10 m s. Maximum lifting height H \u003d 5 m. Lifting time and time of fall T n \u003d 1 s.

The third chart is the continuation of the first. The falling body bounces off the surface and its speed changes the sign to the opposite. Further body movement can be considered on the second schedule.

The task of the body's movement abandoned at a certain angle to the horizon is closely connected with the task of free falling of the body. Thus, the movement along a parabolic trajectory can be represented as the sum of two independent movements relative to the vertical and horizontal axes.

Along the axis O y, the body moves equally to the acceleration G, the initial speed of this movement - V 0 y. Movement along the O X axis is uniform and straightforward, with an initial velocity V 0 x.

Conditions for movement along the axis about x:

x 0 \u003d 0; v 0 x \u003d v 0 cos α; a x \u003d 0.

Conditions for movement along the axis O y:

y 0 \u003d 0; v 0 y \u003d v 0 sin α; A y \u003d - g.

We give formulas for the movement of the body thrown at an angle to the horizon.

Body flight time:

t \u003d 2 V 0 sin α g.

Body flight range:

L \u003d V 0 2 SIN 2 α g.

The maximum range of flight is achieved at an angle α \u003d 45 °.

L M A x \u003d V 0 2 g.

Maximum lifting height:

h \u003d V 0 2 SIN 2 α 2 g.

It should be noted that in real conditions the movement of the body abandoned at an angle to the horizon can pass along the trajectory other than the parabolic due to the resistance of the air and the wind. The study of the movement of bodies abandoned in space is engaged in special science - Ballistics.

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The free drop of body is its equal movement, which occurs under the action of gravity. At this point, other forces that can affect the body are either absent or so small that their influence is not taken into account. For example, when the parachute is jumping from the aircraft, the first few seconds after the jump it falls in a free state. This short segment of time is characterized by a feeling of weightlessness, similar to Tedzh. We have astronauts on board the spacecraft.

History of opening phenomena

The scholars learned about the free fall of the body: Albert Saxon and Nikolai Ore was studied this phenomenon, but some of their conclusions were erroneous. For example, they argued that the speed of the incident heavy object increases directly proportional to the distance traveled. In 1545, the amendment of this mistake was made by the Spanish scientist D. Soto, who had established the fact that the speed of the incident body increases in proportion to the time that passes from the beginning of the fall of this subject.

In 1590, Italian physicist Galileo Galilee Formulated a law that establishes a clear dependence of the path incident to the incident from time to time. Also, scientists have been proven that in the absence of air resistance, all items on Earth fall with the same acceleration, although before its discovery it was assumed that heavy items fall faster.

A new value was opened - acceleration of gravitywhich consists of two components: gravitational and centrifugal accelerations. It is indicated by the acceleration of the free drop in the letter G and has a different value for different points of the globe: from 9.78 m / s 2 (indicator for the equator) to 9.83 m / s 2 (the speed of acceleration on the poles). The accuracy of indicators affect longitude, latitude, time of day and some other factors.

The standard G value is considered to be 9.80665 m / s 2. In physical calculations that do not require compliance with high accuracy, the acceleration value is taken for 9.81 m / s 2. To facilitate the calculations, it is allowed to take G equal to 10 m / s 2.

In order to demonstrate how the item falls in accordance with the opening of Galilee, scientists make such an experience: it is placed in a long glass tube. Items with different masses are placed, air from the tube. After that, the tube turns overAll items under the action of gravity are falling simultaneously to the bottom of the tube, regardless of their mass.

When the same items are placed in any Wednesday, simultaneously with the power of gravity on them there is a resistance force, therefore, objects depending on their mass, form and density will fall at different times.

Formulas for calculations

There are formulas with which you can count on various indicators associated with a free drop. They use such Legend:

1. u - the final speed with which the resulting body moves, m / s;
2. h - the height with which the body under study moves, m;
3. t - the time of moving the body under study, C;
4. g - acceleration (constant value, equal to 9.8 m / s 2).

The formula for determining the distance traveled by the incident subject with a known finite speed and time of the fall: H \u003d UT / 2.

The formula for calculating the distance traveled by the incident subject by the constant size G and the time: H \u003d GT 2/2.

The formula for determining the speed of the incident subject at the end of the fall at a well-known drop time: U \u003d GT.

The formula for calculating the velocity of the subject at the end of the fall, if the height is known, with which the studied object is dropped: U \u003d √2 GH.

If you do not delve into scientific knowledge, the household definition of free displacement implies the movement of any body in the earth's atmosphere when no foreign factors affect it, in addition to resistance to ambient air and gravity.

At various times, volunteers compete with each other, trying to establish a personal record. In 1962, the Testor-parachutist from the USSR Evgeny Andreev established a record that was listed in the Guinness Book of Records: when jumping with a parachute in a free fall, he overcame the distance of 24500 m, during the jump was not used brake parachute.

In 1960, the American D. Kittinger made a parachute jump from a height of 31 thousand m, but using a parachute brake unit.

In 2005, a record speed was recorded with a free drop - 553 km / h, and after seven years a new record was installed - this speed was increased to 1342 km / h. This record belongs to the Austrian parachutist Felix Baumgarter, which is known worldwide with its dangerous tricks.

Video

Look at an interesting and informative video that will tell you about the speed of falling tel.

Free drop is the movement of telly only under the action of attraction of the Earth (under the action of gravity)

In the conditions of land, the fall of the bodies is considered conditionally free, because When the body is falling in the air, the air resistance force always occurs.

The perfect free drop is possible only in vacuo, where there is no strength of the resistance of the air, and independently of the mass, density and forms, all the bodies fall equally quickly, that is, at any time of the body have the same instantaneous speeds and acceleration.

You can observe the perfect free drop in the phone in Newton's tube, if you pull out air from it.

In further reasoning, and when solving the tasksprovement, the force of friction about the air and consider the fall of bodies on earthly conditions perfectly free.

ACCELERATION OF GRAVITY

With a free drop, all the bodies near the surface of the Earth, regardless of their mass, acquire the same acceleration, called the acceleration of the free fall.
Conditional designation of acceleration of free fall - g.

Acceleration of free fall on Earth is approximately possible:
G \u003d 9.81m / C2.

Acceleration of free fall is always directed towards the center of the Earth.

Near the surface of the Earth, the amount of gravity is considered constant, so the free fall of the body is the movement of the body under the action of constant strength. Consequently, the free fall is an equilibrium movement.

The gravity vector and the free fall created by it is always the same.

All formulas for an equilibrium movement are applicable to free falling tel.

Speed \u200b\u200bvalue with free body fall at any time:

body Moving:

In this case, instead of acceleration but, In the formula for an equilibrium movement, an acceleration of free fall is introduced g. \u003d 9.8 m / c2.

In the conditions of the ideal drop falling from the same height of the body reach the surface of the earth, possessing the same speeds and spending the same time to fall.

Under the perfect free fall, the body returns to the ground at a speed, the value of which is equal to the module of the initial speed.

The time of the body fall is equal to the time of movement up from the moment of the throw until a complete stop in the highest point of the flight.

Only on the poles of the body of the body are falling strictly vertically. In all other points of the planet, the trajectory of a free falling body deviates to the east due to the power of the cariolis arising in rotating systems (that is, the influence of the rotation of the Earth around its axis affects).

DO YOU KNOW

And what is the drop in bodies in real conditions?

If you shoot from a gun vertically up, then, given the force of friction about the air, freely falling from any height of the bullet will acquire a speed of no more than 40 m / s.

In real conditions, due to the presence of friction force on air, the mechanical energy of the body partially goes into thermal. As a result, the maximum height of the lifting of the body turns out to be less than it could be when driving in an airless space, and at any point of the trajectory, during the descent, the speed is less than the speed on the rise.

In the presence of friction, falling bodies have an acceleration equal to G, only in the initial moment of movement. As the speed increases, the acceleration decreases, the movement of the body tends to uniform.

DO IT YOURSELF

How do falling bodies behave in real conditions?

Take a small disk from plastics, thick cardboard or plywood. Cut the disc from the usual paper of the same diameter. Raise them, keeping in different hands, to the same height and simultaneously release. Heavy disk will fall faster than light. On each disk acts when there are two strength at the same time: the strength of gravity and the power of air resistance. At the beginning of the fall, the complex strength of gravity and the strength of the resistance of the air will be more at the body with a greater mass and acceleration of a heavier body will be greater. As the body rate increases, the air resistance force increases and gradually compared in magnitude with the force of gravity, the falling bodies begin to move evenly, but at different speeds (in a heavier body speed above).
Similar to the movement of the incident disc, you can consider the movement of a falling parshetist when jumping from an airplane from a high height.

Put a lightweight paper disk on a heavier plastic or plywood, lift them to height and simultaneously release. In this case, they will fall at the same time. Here, the resistance of the air acts only on a heavy bottom disk, and the strength of gravity informs the bodies equal acceleration in independence on their masses.

Almost joke

Parisian physicist Lenorman, who lived in the 18th century, took ordinary rain umbrellas, fastened the ends of the arms and jumped off the roof of the house. Then he was encouraged by a special umbrella with a wicker seat and rushed down the tower in Montpellier. At the bottom of him surrounded by enthusiastic spectators. What is your umbrella called? Parachute! - answered Lenorman (literal translation of this word from French - "against fall").

INTERESTING

If the land is drilled through and throw a stone there, what will happen to a stone?
The stone will fall, typing the maximum speed in the middle of the way, then flies on the inertia and will reach the opposite side of the Earth, and its final speed will be equal to the initial one. Acceleration of the free fall within the earth is proportional to the distance to the center of the Earth. The stone will move as a load on the spring, according to the law of the throat. If the initial speed of the stone is zero, then the period of hesitation of the stone in the mine is equal to the period of the satellite's appeal near the earth's surface, regardless of how the triggers direct mine: through the center of the Earth or for any chord.