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 acceleration free fall.
Symbol free fall acceleration - 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 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 modulus initial speed.
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. Pick them up by 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 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).
Under terrestrial conditions, g depends on geographical latitude terrain.
It has the greatest value at the pole g=9.81 m/s 2 , the smallest - at the equator g=9.75 m/s 2 . Reasons for this:
1) diurnal rotation 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 maximum height, and then moves downward with uniform acceleration. 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
What do you think, will the feathers dropped from the roof reach the ground at the same time, plastic bottle and coin? One can make such an experiment and make sure that the coin will land first, the bottle second, and the feather will hang in the air for a long time and may not reach the ground at all if it is picked up and carried away by a sudden breeze.
Is the free fall of bodies so free?
Accordingly, we conclude that the free fall of bodies does not obey any one rule, and all objects fall to the ground in their own way. Here, as they say, the fairy tale would end, but some physicists did not calm down on this and suggested that the free fall of bodies could be influenced by the force of air resistance and, accordingly, such experimental results cannot be considered final.
They took a long glass tube and put a feather, a shotgun, a wooden cork and a coin into it. Then they plugged the tube, bled the air out of it, and turned it upside down. And then some incredible things happened.
All objects flew down the tube together and landed at the same time. For a long time they had fun like that, laughing, joking, turning the tube over and wondering, until they suddenly realized that in the absence of air resistance forces, all objects fall to the ground in the same way.
Moreover, it turned out one more wonderful thing, that all objects during free fall move with acceleration. Naturally, there was a desire to find out what this acceleration is equal to.
Then, with special photographs, they measured the position of a freely falling body in the absence of air resistance at different points in time and found that the magnitude of the fall acceleration is the same in all cases. It is equal to approximately 9.8 m / s ^ 2.
Free fall acceleration: essence and formulas
This value is the same for bodies of absolutely any mass, shape and size. This value was called the acceleration of free fall and a separate letter was allocated for its designation, the letter g (zhe) of the Latin alphabet.
g is always 9.8 m/s^2. Strictly speaking, there are more decimal places, but for most calculations this approximation is sufficient. A more accurate value is taken into account if necessary for more accurate calculations.
The free fall of bodies is described by the same velocity and displacement formulas as any other uniformly accelerated motion:
v=a*t ,and s=((v^2) - (v_0^2)) / 2*a or s= a*(t^2) / 2 if the body's initial velocity is zero, but instead of the acceleration value a take the value g. And then the formulas take the form:
v = g*t , s =((v^2)-(v_0^2))/2*g or s = g*(t^2)/2 (if v_0 = 0), respectively,
where v is final velocity, v_0 is initial velocity, s is displacement, t is time, g is gravitational acceleration.
The conclusion that the free fall of any body occurs in the same way, at first glance, seems absurd from the point of view of everyday experience. But in fact, everything is correct and logical. Simply, the seemingly insignificant amount of air resistance for many falling bodies turns out to be quite noticeable, and therefore greatly slows down their fall.
Instruction
Convert the height from which the body falls to SI units - meters. Free fall acceleration is given in the handbook already converted to units of this system - meters divided by seconds. For the earth on middle lane it is 9.81 m/s 2 . In the conditions of some tasks, other planets are indicated, for example, the Moon (1.62 m/s 2), Mars (3.86 m/s 2). When both initial values are given in SI units, the result will be in units of the same system - seconds. And if the condition specifies body weight, ignore it. This information is superfluous here, it can be brought in order to check how well you know.
To make a body fall, multiply the height by two, divide by the acceleration due to gravity, and then take the square root of the result:
t=√(2h/g), where t is time, s; h - height, m; g - free fall acceleration, m/s 2 .
The task may require finding additional data, for example, about what was the speed of the body at the moment it touched the ground or at a certain height from it. In general, calculate the speed like this:
New variables are introduced here: v - speed, m/s and y - height, where you want to know the speed of the fall of the body, m. 0 (at the moment of touching the ground, just before the body stops), the formula can be simplified:
After touching the ground has already occurred, and the body has stopped, the speed of its fall is again equal to zero (unless, of course, it springs back and bounces again).
To reduce the force of impact after the end of free fall, parachutes are used. Initially, the fall is free and occurs according to the above equations. Then the parachute opens, and there is a smooth deceleration due to air resistance, which now cannot be neglected. The patterns described by the above equations no longer apply, and further decrease in height is slow.
Mars ranks fourth in distance to the Sun and seventh in size to the planets solar system. It got its name in honor of the ancient Roman god of war. Sometimes Mars called the red planet: the reddish tint of the surface gives the iron oxide contained in the soil.
You will need
- Amateur telescope or powerful binoculars
Instruction
The opposition of the Earth and Mars a
When the Earth is exactly between the Sun and Mars ohm, i.e. at a minimum distance of 55.75 million km, this ratio is called opposition. At the same time, he Mars is in the direction opposite to the sun. Such confrontations are repeated every 26 months in different parts of the Earth and Mars a. These are the most favorable moments for observations of red in amateur telescopes. Once every 15-17 years, great confrontations take place: at the same time, the distance to Mars but minimally, but itself reaches its greatest angular size and brightness. The last great confrontation was on January 29, 2010. The next one will be July 27, 2018.
Observation conditions
If you have an amateur telescope, you should look for Mars in the sky in opposition. Surface details are available for observation only during these periods, when the angular diameter of the planet reaches its maximum value. large amateur telescope many interesting details on the surface of the planet are available, the seasonal evolution of the polar caps Mars and signs of Martian dust storms. In a small telescope one can see dark spots on the surface of the planet. You can also see the polar caps, but only during the great confrontations. Much depends on the experience of observations, and on atmospheric conditions. So, the more observational experience, the smaller the telescope can be for "catching" Mars and the details of its surface. Lack of experience is not always compensated by an expensive and powerful telescope.
Where to look
in the evening and Mars visible in red-orange light, and in the middle of the night in yellow. In 2011 Mars can be observed in the sky until the end of November. Until August, a planet in the constellation of Gemini, which is in the northern sky. With Mars seen in the constellation Cancer. It lies between the constellations Leo and Gemini.
note
If the experience of observations is small, you should wait for the opposition period.
Sources:
- Mars in 2019
- mars through a telescope in 2019
In order to find acceleration free fall, drop a fairly heavy body, preferably a metal one, from a certain height and note the time fall, then use the formula to calculate acceleration free fall. Or measure the force of gravity acting on a body of known mass and divide the value of the force by that mass. You can use a mathematical pendulum.
You will need
- electronic and conventional stopwatch, metal body, scales, dynamometer and mathematical pendulum.
Instruction
Finding acceleration free fall freely falling body Take a metal body and attach it to the bracket on some , which you immediately measure in meters. At the bottom, stop the special platform. Attach the bracket and platform to the electronic stopwatch. The height must be chosen in such a way that the resistance can be. It is recommended to choose heights from 2 to 4 m. After that, disconnect the body from the bracket, as a result, it will begin to fall freely. After about the platform, the stopwatch will fix the time fall in . Then divide the height value by the time value taken in and multiply the result by 2. Get the acceleration value free fall in m/s2.
Finding acceleration free fall through force Measure body weight in kilograms on the scales with high accuracy. Then, take a dynamometer and hang this body on it. But it will show the value of gravity in newtons. Then divide the value of gravity by the mass of the body. As a result you will get acceleration free fall.
Finding acceleration free fall using mathematical Take a mathematical pendulum (a body suspended on a sufficiently long thread) and make it oscillate, having previously measured the threads in meters. Turn on the stopwatch and count a number of oscillations and note the time in seconds for which they were made. After that, divide the number of oscillations by the time in seconds, and raise the resulting number to the second. Then multiply it by the length of the pendulum and the number 39.48. As a result, we get acceleration free fall.
For determining strength resistance air create conditions under which the body will begin to move uniformly and rectilinearly under the influence of gravity. Calculate the value of gravity, it will be equal to the force of air resistance. If a body moves in the air, picking up speed, its resistance force is found using Newton's laws, and the air resistance force can also be found from the law of conservation of mechanical energy and special aerodynamic formulas.
Free fall is the movement of objects vertically downwards or vertically upwards. This is a uniformly accelerated movement, but a special kind of it. All formulas and laws of uniformly accelerated motion are valid for this motion.
If the body flies vertically downwards, then it accelerates, in this case the velocity vector (directed vertically downwards) coincides with the acceleration vector. If the body flies vertically upwards, then it slows down, in this case the velocity vector (directed upwards) does not coincide with the direction of acceleration. The acceleration vector in free fall is always directed vertically downwards.
Acceleration in the free fall of bodies is a constant value.
This means that no matter what body is flying up or down, its speed will change the same way. BUT with one caveat, if the force of air resistance can be neglected.
Free fall acceleration is usually denoted by a letter different from acceleration. But gravitational acceleration and acceleration are the same physical quantity and they have the same physical meaning. They participate equally in the formulas for uniformly accelerated motion.
We write the "+" sign in the formulas when the body flies down (accelerates), the "-" sign - when the body flies up (slows down)
Everyone knows from school physics textbooks that in a vacuum a pebble and a feather fly the same way. But few people understand why in the vacuum of the body different weight land at the same time. Like it or not, whether they are in a vacuum or in air, their mass is different. The answer is simple. The force that causes bodies to fall (gravity) caused by the Earth's gravitational field is different for these bodies. It is larger for a stone (since the stone has more mass), for a feather it is smaller. But there is no dependence here: the greater the force, the greater the acceleration! Compare, act with the same force on heavy cabinet and a light nightstand. Under the influence of this force, the nightstand will move faster. And in order for the cabinet and bedside table to move in the same way, it is necessary to act on the cabinet more strongly than on the bedside table. The Earth does the same. It attracts heavier bodies with more force than light ones. And these forces are so distributed among the masses that as a result they all fall in a vacuum at the same time, regardless of the mass.
Separately, consider the issue of emerging air resistance. Take two identical sheets of paper. We crumple one of them and at the same time release it from our hands. The crumpled leaf will fall to the ground earlier. Here, the different fall times are not related to body mass and gravity, but are due to air resistance.
Consider a body falling from a certain height h no initial speed. If the OS coordinate axis is directed upwards, aligning the origin of coordinates with the Earth's surface, we obtain the main characteristics of this movement.
A body thrown vertically upwards moves uniformly with the acceleration of free fall. In this case, the velocity and acceleration vectors are directed in opposite directions, and the velocity modulus decreases with time.
IMPORTANT! Since the rise of the body to its maximum height and the subsequent fall to the ground level are absolutely symmetrical movements (with the same acceleration, just one slowed down and the other accelerated), the speed with which the body lands will be equal to the speed with which it tossed up. In this case, the time for the body to rise to the maximum height will be equal to the time for the body to fall from this height to the ground level. Thus, the entire flight time will be double the time of ascent or fall. The speed of the body at the same level during the ascent and during the fall will also be the same.