Acceleration of free fall, formulas. Why do bodies in a vacuum fall the same way - training courses
Free fall is the movement of bodies only under the influence of the Earth's gravity (under the influence of gravity)
Under Earth conditions, the fall of bodies is considered conditionally free, because When a body falls in the air, there is always a force of air resistance.
An ideal free fall is possible only in a vacuum, where there is no air resistance, and regardless of mass, density and shape, all bodies fall equally quickly, i.e. at any moment in time the bodies have the same instantaneous speeds and accelerations.
You can observe the ideal free fall of bodies in a Newton tube if you pump the air out of it using a pump.
In further reasoning and when solving problems, we neglect the force of friction with 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 Earth's surface, regardless of their mass, acquire the same acceleration, called acceleration free fall.
The symbol for gravitational acceleration is g.
The acceleration of gravity on Earth is approximately equal to:
g = 9.81m/s2.
The acceleration of gravity 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 influence of a constant force. Therefore, free fall is uniformly accelerated motion.
The vector of gravity and the free fall acceleration it creates are always directed in the same way.
All formulas for uniformly accelerated motion are applicable to freely falling bodies.
The magnitude of the speed during free fall of a body at any time:
body movement:
In this case, instead of accelerating A, the acceleration of gravity is introduced into the formulas for uniformly accelerated motion g=9.8m/s2.
Under 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 falling.
In an ideal free fall, the body returns to Earth with a speed equal to the magnitude of the initial velocity.
The time the body falls is equal to the time it moves upward from the moment of the throw until it comes to a complete stop at 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 that arises in rotating systems (i.e., the influence of the Earth’s rotation around its axis is affected).
DO YOU KNOW
WHAT IS THE FALL OF BODIES IN REAL CONDITIONS?
If you shoot a gun vertically upward, then, taking into account the force of friction with the air, a bullet freely falling from any height will acquire a speed of no more than 40 m/s at the ground.
In real conditions, due to the presence of friction force against air, the mechanical energy of the body is partially converted into thermal energy. As a result, the maximum height of the body's rise turns out to be less than it could be when moving in airless space, and at any point in the trajectory during 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 movement. As the speed increases, the acceleration decreases, and 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 a disk of the same diameter from plain paper. Lift them up, holding them 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, each disk is simultaneously affected by two forces: 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 force of air resistance increases and gradually becomes equal in magnitude to the force of gravity; falling bodies begin to move evenly, but at different speeds (a heavier body has a higher speed).
Similar to the movement of a 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 disk on a heavier plastic or plywood disk, lift them to a height 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, secured 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. Below he was surrounded by enthusiastic spectators. What is the name of your umbrella? Parachute! - Lenormand answered (the literal translation of this word from French is “against the fall”).
INTERESTING
If you drill through the Earth and throw a stone there, what will happen to the stone?
The stone will fall, hitting the middle of the path maximum speed, will then 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 free fall 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 movement of objects vertically downwards or vertically upwards. This is uniformly accelerated motion, but its special type. For this motion, all formulas and laws of uniformly accelerated motion are valid.
If a body flies vertically downward, then it accelerates, in this case the velocity vector (directed vertically downward) coincides with the acceleration vector. If a body flies vertically upward, then it slows down; in this case, the velocity vector (directed upward) does not coincide with the direction of acceleration. The acceleration vector during free fall is always directed vertically downwards.
Acceleration during free fall of bodies is a constant value.
This means that no matter what body flies up or down, its speed will change the same. BUT with one caveat, if the force of air resistance can be neglected.
Acceleration due to gravity is usually denoted by a letter other than acceleration. But the acceleration due to gravity and acceleration are the same physical quantity and they have the same physical meaning. They participate equally in formulas for uniformly accelerated motion.
We write the “+” sign in 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 a vacuum, bodies of 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 bodies fall (gravity), caused by the Earth's gravitational field, is different for these bodies. For a stone it is larger (since the stone has more mass), for a feather it is smaller. But there is no dependence: the greater the force, the greater the acceleration! Let's compare, we act with the same force on a heavy cabinet and a light bedside table. Under the influence of this force, the bedside table will move faster. And in order for the closet and the bedside table to move equally, the closet must be influenced more strongly than the bedside table. The Earth does the same. It attracts heavier bodies with greater force than lighter ones. And these forces are distributed between the masses in such a way that they all fall in a vacuum at the same time, regardless of mass.
Let us separately consider the issue of emerging air resistance. Let's take two identical sheets of paper. We will crumple one of them and at the same time let go of them. A crumpled leaf will fall to the ground sooner. Here different time falling is not related to body weight and gravity, but is caused by air resistance.
Consider a body falling from a certain height h without initial speed. If the coordinate axis of the OU is directed upward, aligning the origin of coordinates with the surface of the Earth, we obtain the main characteristics of this movement.
A body thrown vertically upward moves uniformly with the acceleration of gravity. In this case, the velocity and acceleration vectors are directed in opposite directions, and the velocity module decreases over time.
IMPORTANT! Since the rise of a body to its maximum height and the subsequent fall to ground level are absolutely symmetrical movements (with the same acceleration, just one slower and the other accelerated), then the speed with which the body lands will be equal to the speed with which it tossed up. In this case, the time the body rises to the maximum height will be equal to the time the body falls from this height to ground level. Thus, the entire flight time will be double the time of rise or fall. The speed of a body at the same level when rising and falling will also be the same.
Do you think that a feather dropped from a roof will reach the ground at the same time? plastic bottle and a coin? You can do this experiment and make sure that the coin lands first, the bottle second, and the feather will dangle in the air for a long time and may not even reach the ground if it is picked up and carried away by a sudden breeze.
Is free-falling bodies really that 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 ends, but some physicists did not rest on this and suggested that the free fall of bodies can be influenced by the force of air resistance and, accordingly, such experimental results cannot be considered final.
They took a long glass tube and placed a feather, a pellet, a wooden stopper and a coin in it. Then they plugged the tube, pumped the air out of it and turned it upside down. And then absolutely incredible things were discovered.
All the objects flew down the tube together and landed at the same time. For a long time they had fun like this, laughing, joking, turning the tube over and being surprised, until they suddenly realized that in the absence of air resistance forces, all objects fall to the ground equally.
Moreover, another remarkable thing turned out to be that all objects move with acceleration during free fall. Naturally, there was a desire to find out what this acceleration was 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 established that the magnitude of the acceleration of the fall was the same in all cases. It is approximately 9.8 m/s^2.
Acceleration of free fall: essence and formulas
This value is the same for bodies of absolutely any mass, shape and size. This quantity was called the acceleration of gravity and a separate letter was allocated to denote it, the letter g (zhe) of the Latin alphabet.
g is always equal to 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 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 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 velocity, v_0 is the initial velocity, s is the displacement, t is the time, g is the free fall 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. It’s just that the seemingly insignificant amount of air resistance for many falling bodies turns out to be quite noticeable, and therefore very much slows down their fall.
Instructions
Convert the height from which the body falls into SI units - meters. The free fall acceleration is given in the reference book already converted into 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 problems, other planets are indicated, for example, the Moon (1.62 m/s2), Mars (3.86 m/s2). When both initial quantities are given 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 unnecessary here; it can be cited in order to check how well you know.
To 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 the speed of the body was 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 find out the speed of the body falling, m. It is clear that when h = y (that is, at the initial moment of fall) the speed is zero, and when 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 back and jumps again).
To reduce the impact force after free fall ends, parachutes are used. Initially, the fall is free and occurs in accordance with the above equations. Then the parachute opens and a smooth deceleration occurs due to air resistance, which cannot now be neglected. The patterns described by the above equations no longer apply, and further decrease in height occurs slowly.
Mars ranks fourth in distance from 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 hue of the surface is given by iron oxide contained in the soil.
You will need
- Amateur telescope or powerful binoculars
Instructions
Confrontation between 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 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 observing red in amateur telescopes. Once every 15-17 years, great confrontations occur: the distance to Mars a minimally, and 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 confrontations. Surface details are available for observation only during these periods, when the angular diameter of the planet reaches maximum value. A large amateur telescope reveals many interesting details on the surface of the planet, the seasonal evolution of the polar caps Mars and also signs of Martian dust storms. Through 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 observation experience and atmospheric conditions. So, the greater the observational experience, the smaller the telescope can be for “catching” Mars and details of its surface. Lack of experience is not always compensated by 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, the planet is in the constellation Gemini, which is in the northern sky. WITH Mars visible in the constellation Cancer. It is located between the constellations Leo and Gemini.
note
If the observation experience 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 falls, drop a fairly heavy body, preferably metal, from a certain height and note the time falls, then use the formula to calculate acceleration free falls. Or measure the force of gravity that acts on a body of known mass and divide the force value by this mass. You can use a mathematical pendulum.
You will need
- electronic and regular stopwatch, metal body, scales, dynamometer and mathematical pendulum.
Instructions
Finding acceleration free falls freely falling body Take a metal body and attach it to a bracket on some, which you immediately measure in meters. Stop the special platform below. Attach the bracket and platform to the electronic stopwatch. The height must be selected in such a way that resistance can be achieved. It is recommended to choose heights from 2 to 4 m. After this, disconnect the body from the bracket, as a result it will begin to fall freely. After reaching the platform, the stopwatch will record the time falls V . After this, divide the height value by the time value taken in , and multiply the result by 2. Get the acceleration value free falls in m/s2.
Finding acceleration free falls through force Measure body weight in kilograms on a scale 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 gravity value by your body weight. As a result you will get acceleration free falls.
Finding acceleration free falls using a mathematical one 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 certain number of vibrations and note the time in seconds during which they were produced. After this, 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 falls.
For determining strength resistance air create conditions under which the body begins to move uniformly and linearly 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- This is the movement of a body under the influence of gravity only.
In addition to the force of gravity, a body falling in the air is affected by the force of air resistance, therefore, such a movement is not free fall. Free fall is the fall of bodies in a vacuum.
The acceleration imparted to a body by gravity is called acceleration of free fall. It shows how much the speed of a freely falling body changes per unit time.
The 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 the mass of the body.
You can verify this using a Newton tube or the stroboscopic method.
A Newton tube is a glass tube about 1 m long, one end of which is sealed and the other is equipped with a stopcock (Fig. 25).
Fig.25
Let's place three different objects in 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 at different times: first the pellet, then the cork, and finally the feather. But this is how bodies fall when there is air in the tube (Fig. 25, a). As soon as we pump out the air 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 the geographic latitude of the area.
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) daily rotation of the Earth around its axis;
2) deviation of the Earth’s shape from spherical;
3) heterogeneous distribution of the density of earth rocks.
The acceleration of free fall depends on the height h of the body above the surface of the planet. If we neglect the rotation of the planet, it can be calculated using the formula:
Where G- gravitational constant, M- mass of the planet, R- radius of the planet.
As follows from the last formula, with increasing height of the body 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 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 onto the axis 
.
Movement of a body thrown vertically
A freely falling body can move rectilinearly or along a curved path. It depends on the initial conditions. Let's look at this in more detail.
Free fall without initial speed ( =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 a body falls from a height h:
Substituting the found time into the formula for speed, we obtain the modulus of the body's speed at the moment of fall: .
Movement of a body thrown vertically upward with initial speed (Fig. 27)
Fig.26 Fig.27
The movement of the body is described by the equations:
From the velocity equation it can be seen that the body moves uniformly slow upward, reaches its maximum height, and then moves uniformly accelerated downward. Considering that at y=hmax the speed and at the moment the body reaches the initial position y=0, we can find:
Time to raise the body to maximum height;
Maximum height lifting the body;
Body flight time;
Projection of velocity at the moment the body reaches its initial position.
Movement of a body thrown horizontally
If the speed is not directed vertically, then the movement of the body will be curvilinear.
Let us consider the movement of a body thrown horizontally from a height h with speed (Fig. 28). We will neglect air resistance. To describe the movement, it is necessary to select two coordinate axes - Ox and Oy. The origin of the coordinates is compatible with the initial position of the body. From Fig. 28 it is clear 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 uniformly. In the vertical direction, the body moves uniformly with acceleration g, i.e. just like a body freely falling without initial speed. Let's find the equation trajectories. To do this, from equation (3) we find the time