Do you think that a feather, a plastic bottle and a coin will all fly to the ground at the same time? You can do such an experiment and make sure that the coin lands 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 is over, but some physicists did not rest on this and suggested that the force of air resistance can affect the free fall of bodies and, accordingly, such experimental results cannot be considered final.
They took a long glass tube and placed a feather, a pellet, a wooden cork and a coin in it. Then they plugged the tube, pumped air out of it, and turned it over. And then absolutely incredible things came to light.
All objects flew down the tube together and landed at the same time. For a long time they had fun like that, laughed, joked, turning the pipe 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 that one more remarkable thing is that all objects move with acceleration during free fall. Naturally, a desire arose to find out what this acceleration is equal to.
Then, using special photographs, they measured the position of a freely falling body in the absence of air resistance at different times and found that the magnitude of the acceleration of the fall was 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 gravity and a separate letter was allocated for its designation, the letter g (zh) 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.
Free fall of bodies is described by the same formulas of speed and displacement 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 initial velocity of the body is zero, only instead of the acceleration value a take the value of 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 the final speed, v_0 is the initial speed, 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 ridiculous from the point of view of everyday experience. But in fact, everything is correct and logical. Simply, a seemingly insignificant amount of air resistance for many falling bodies turns out to be quite noticeable, and therefore very much slows down their fall.
Free fall is the movement of bodies only under the influence of the Earth's gravity (under the influence of gravity)
In the conditions of the Earth, the fall of bodies is considered conditionally free, because when a body falls in an air environment, there is always an air resistance force.
An 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.
The ideal free fall of bodies can be observed in Newton's tube if air is pumped out of it with the help of a pump.
In further considerations and in solving problems, we neglect the force of friction against the air and consider the fall of bodies in 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 acceleration of free fall.
Symbol free fall acceleration - g.
The acceleration of gravity 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 value of gravity is considered constant, therefore the free fall of a body is the movement of a body under the influence of a constant force. Consequently, free fall is a uniformly accelerated motion.
The vector of the force of gravity and the acceleration of gravity created by it are always directed in the same way.
All formulas for uniformly accelerated motion are applicable for the free fall of bodies.
The magnitude of the speed during free fall of the body at any moment of time:
body movement:
In this case, instead of accelerating but, gravitational acceleration is introduced into the formulas for uniformly accelerated motion g= 9.8m / s2.
Under the conditions of an ideal fall, bodies falling from the same height reach the surface of the Earth, having the same speeds and spending the same time to fall.
In an ideal free fall, the body returns to the Earth with a velocity equal to the modulus of the initial velocity.
The time of the body falling is equal to the time of upward movement from the moment of throwing to a complete stop at the highest point of the flight.
Only at the poles of the Earth do bodies fall strictly vertically. At all other points of the planet, the trajectory of a freely falling body deviates to the east due to the Karyolis 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 IN REAL CONDITIONS?
If you shoot from the gun vertically upwards, then, taking into account the force of friction against the air, a bullet freely falling from any height will acquire a velocity of no more than 40 m / s at the ground.
In real conditions, due to the presence of a frictional force against 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 airless space, and at any point of the trajectory during descent, the speed turns out to be less than the speed during the ascent.
In the presence of friction, the falling bodies have an acceleration equal to g only at the initial moment of motion. As the speed increases, the acceleration decreases, the movement of the body tends to be uniform.
DO IT YOURSELF
How do falling bodies behave in real conditions?
Take a small disc made of plastic, thick cardboard, or plywood. Cut a disc of the same diameter out of plain paper. Raise them, holding them in different hands, to the same height and release them at the same time. A heavy disc will fall faster than a light one. Two forces act simultaneously on each disk when it falls: gravity and air resistance. At the beginning of the fall, the resultant of the 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 force of air resistance increases and gradually becomes equal in magnitude to the force of gravity, the falling bodies begin to move evenly, but at different speeds (the speed of the heavier body is higher).
Similarly to the movement of the falling disk, one can consider the movement of a parachutist falling down when 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, the air resistance acts only on the heavy lower disk, and the force of gravity imparts equal accelerations to the bodies, regardless of their masses.
ALMOST ANECDOTE
Parisian physicist Lenormand, who lived in the 18th century, took ordinary rain umbrellas, fastened 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. At the bottom, enthusiastic spectators surrounded him. What is the name of your umbrella? Parachute! - answered Lenormand (literal translation of this word from French - "against the fall").
INTERESTING
If the earth is drilled through and a stone is thrown there, 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 acceleration of gravity 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 velocity 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 direct shaft is dug: through the center of the Earth or along any chord.
Instructions
Convert the height from which the body falls into SI units - meters. Acceleration of free fall is given in the reference book already translated into units of this system - meters divided by seconds. For the Earth in the middle lane, it is 9.81 m / s 2. In the conditions of some problems, other planets are indicated, for example, the Moon (1.62 m / s 2), Mars (3.86 m / s 2). When both initial values are specified in SI units, the result will be in units of the same system - seconds. And if the condition indicates body weight, ignore it. This information is superfluous here, it can be cited in order to check how well you know.
To fall, multiply the height by two, divide by the acceleration of gravity, and then extract the square root from the result:
t = √ (2h / g), where t is time, s; h - height, m; g - acceleration of gravity, m / s 2.
The task may require finding additional data, for example, about what was the speed of the body at the moment of touching the ground or at a certain height from it. In general, calculate the speed as follows:
New variables have been introduced here: v is the speed, m / s and y is the height where you want to know the speed of the body falling, m. It is clear that at h = y (that is, at the initial moment of falling) the speed is zero, and at y = 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 and bounces again).
To reduce the force of impact after the end of free fall, parachutes are used. Initially, the fall is free and follows the above equations. Then the parachute opens, and there is a smooth deceleration due to air resistance, which can no longer be neglected. The regularities described by the above equations no longer apply, and further decrease in height is slow.
Mars ranks fourth in terms of remoteness of the Sun and seventh in size of 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 is given by the iron oxide contained in the soil.
You will need
- An amateur telescope or powerful binoculars
Instructions
The opposition of the Earth and Mars but
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 opposite direction to the Sun. Such oppositions are repeated every 26 months in different parts of the Earth and Mars but. These are the most favorable times for observing red with amateur telescopes. Once every 15-17 years, great confrontations occur: at the same time, the distance to Mars but is minimal, and itself reaches its maximum 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 oppositions. Surface details are available for observation only during these periods when the angular diameter of the planet reaches maximum value... A large amateur telescope has access to many interesting details on the planet's surface, the seasonal evolution of the polar caps Mars a and signs of Martian dust storms. In a small telescope you can see “ dark spots"On the surface of the planet. You can also see the polar caps, but only during great confrontations. Much depends on the experience of observations and on atmospheric conditions. So, the more the observing experience, the smaller the telescope can be for "capturing" Mars and details of its surface. Lack of experience is not always compensated by expensive and powerful telescope.
Where to looking for
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, the planet is in the constellation Gemini, in the northern sky. FROM Mars visible in the constellation Cancer. It is located between the constellations Leo and Gemini.
note
If the experience of observation is small, you should wait for a period of confrontation.
Sources:
- Mars in 2019
- mars telescope in 2019
To find acceleration free fall, drop a sufficiently heavy body, preferably metal, from a certain height and time fall, then use the formula to calculate acceleration free fall... Or measure the force of gravity that acts on a body of known mass and divide the value of the force by that mass. Can be used mathematical pendulum.
You will need
- electronic and ordinary stopwatch, metal body, scales, dynamometer and mathematical pendulum.
Instructions
Finding acceleration free fall Free falling body Take a metal body, and attach it to a bracket on some, which immediately measure in meters. At the bottom, stop a special platform. Attach the bracket and platform to the electronic stopwatch. The height should be chosen so that the resistance can be. It is recommended to choose heights from 2 to 4 m. After that, detach the body from the bracket, as a result, it will begin to fall freely. After about the platform, the stopwatch will record the time fall in . After that, divide the altitude 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 your body weight in kilograms on a scale with high precision. Then, take a dynamometer and hang this body on it. But it will show the value of gravity in newtons. Then divide the gravity value by the body weight. As a result, you will get acceleration free fall.
Finding acceleration free fall using a math Take a math pendulum (a body suspended by a sufficiently long string) and make it oscillate by first measuring the strings in meters. Turn on the stopwatch and count a number of oscillations and note the time in seconds for which they were produced. 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 evenly 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 air, gaining speed, the force of its resistance is found using Newton's laws, and the force of air resistance can also be found from the law of conservation of mechanical energy and special aerodynamic formulas.
Free fall- this is the movement of the body under the influence of only gravity.
A body falling in the air, in addition to 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 that imparts gravity to the body is called acceleration of gravity... It shows how much the speed of a freely falling body changes per unit of time.
Free fall acceleration is directed vertically downward.
Galileo Galilei established ( 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. the acceleration of gravity does not depend on body weight.
You can verify this using the Newton tube or the 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
Place three different objects in the tube, such as a pellet, a cork, and a 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 geographic latitude terrain.
Highest value it has at the pole g = 9.81 m / s 2, the smallest - at the equator g = 9.75 m / s 2. The reasons for this:
1) 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.
Free fall acceleration depends on the body's height h above the planet's surface. If we neglect the rotation of the planet, it can be calculated by the formula:
Where G- gravitational constant, M- 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 gravity decreases. If we neglect the rotation of the planet, then on the surface of the planet with radius R
To describe it, you can use the formulas for uniformly accelerated motion:
speed equation:
kinematic equation describing the free fall of bodies: 
,
or in projection on the axis 
.
The movement of a body thrown vertically
A free falling body can move in a straight line or along curvilinear trajectory... It depends on the initial conditions. Let's take a closer look at this.
Free fall without initial velocity ( = 0) (fig. 26).
With the selected coordinate system, the motion of the body is described by the equations: 
.
From the last formula, you can find the time of the body falling from a height h:
Substituting the found time into the formula for the velocity, we obtain the module of the body's velocity at the moment of falling:.
The movement of a body thrown vertically upward with an initial velocity (fig. 27)
Fig. 26 Fig. 27
The movement of the body is described by the equations:
It can be seen from the equation of speed that the body moves equally slowly upward, reaches maximum height, and then moves downward with uniform acceleration. Taking into account that at y = hmax the speed and at the moment the body reaches its initial position y = 0, we can find:
The time of lifting the body to the maximum height;
Maximum body lifting height;
Body flight time;
The projection of the speed at the moment the body reaches its original position.
The movement of a body thrown horizontally
If the speed is not directed vertically, then the movement of the body will be curvilinear.
Consider the motion of a body thrown horizontally from a height h with a speed (Fig. 28). We will neglect the air resistance. To describe the movement, it is necessary to select two coordinate axes - Ox and Oy. The origin of coordinates is compatible with the initial position of the body. Figure 28 shows that,,,.
Fig. 28
Then the motion of the body will be described by the equations:
Analysis of these formulas shows that in the horizontal direction the speed of the body remains unchanged, i.e. the body moves evenly. In the vertical direction, the body moves uniformly with acceleration g, i.e. just like a body falling freely without initial velocity. Let's find the equation of the trajectory. For this, from equation (3) we find the time
Free fall is the movement of objects vertically downward or vertically upward. This is a uniformly accelerated movement, but its special kind. For this motion, all formulas and laws of uniformly accelerated motion are valid.
If the body flies vertically downward, then it is accelerated, in this case the velocity vector (directed vertically downward) 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 free fall acceleration vector is always directed vertically downward.
The free fall acceleration of bodies is constant.
This means that whatever body is flying up or down, its speed will change in 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 other than acceleration. But free fall acceleration and acceleration are one and the same physical quantity and they have the same physical meaning... Participate in the same way in 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 masses land at the same time. Whatever one may say, whether they are in a vacuum or in air, their mass is different. The answer is simple. The force that makes the bodies fall (gravity) caused by the gravitational field of the Earth is different for these bodies. For a stone, it is larger (since a stone has more mass), for a feather it is less. But there is no dependence here: the greater the force, the greater the acceleration! Let's compare, we act with equal force on a heavy wardrobe and a light bedside table. Under the influence of this force, the bedside table will move faster. And in order for the cabinet and the bedside table to move in the same way, the cabinet must be influenced more strongly than the bedside table. The Earth is doing the same. It attracts heavier bodies with greater 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.
Let us consider separately the question of the arising air resistance. Take two identical sheets of paper. We crumple one of them and simultaneously 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 due to air resistance.
Consider the fall of a body from a certain height h without initial speed. If the coordinate axis OU is directed upwards, aligning the origin of coordinates with the Earth's surface, we will receive the main characteristics of this movement.
A body thrown vertically upward moves uniformly with the acceleration of gravity. In this case, the vectors of velocity and acceleration are directed in opposite directions, and the modulus of velocity decreases with time.
IMPORTANT! Since the rise of the body to the 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 will land will be equal to the speed with which it thrown up. In this case, the time for the body to rise to the maximum height will be equal to the time of the body falling from this height to the ground level. Thus, the entire flight time will be twice the rise or fall time. The speed of the body at the same level when lifting and falling will also be the same.
