Such an experience gives grounds to consider the movement of bodies along a curved trajectory, which received speed at an angle to the horizon, as two independent movements - vertically and horizontally. Moreover, these movements proceed independently of each other and do not affect each other.
This statement, called principle of independence of movements, extends to the motion of bodies thrown at an angle to the horizon.
Since the complex curvilinear motion of a falling body can be represented as a sum of two independent simple movements vertically and horizontally, for further reasoning we will focus on analyzing the movement of the body only in the vertical direction. In this case, for simplicity, we will assume for now that the initial velocity of the body is zero.
Even the simplest observations give us grounds to be convinced that the medium in which the falling body moves has a significant influence on the nature of the motion. First of all, air acts as such a medium.
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Indeed, let us drop a steel ball and a piece of paper from the same height. A piece of paper reaches the surface of the Earth in a much longer time than a ball. It may seem that this is due to the fact that the ball is more massive than a piece of paper. However, the crumpled piece of paper reaches the Earth's surface almost simultaneously with the steel ball. Probably, the results of the experiments can be explained by the resistance that air has to the falling bodies.
A piece of paper falling from the same height and a sheet of metal equal to it in area, again, make the same movement for clearly different times. But, on the other hand, it is worth putting a paper sheet on top of a metal sheet, as it stops lagging behind the metal sheet during the fall.
After carrying out such experiments, it becomes almost obvious that the effect of air on falling bodies is significant.
It can be assumed that in airless space, different bodies, regardless of their size, shape, substance from which they are made, under the same initial conditions will fall in the same way.
This assumption can be verified by direct experiment. To do this, you can take a long, closed tube in which, for example, a feather, a piece of paper, or a pellet are placed. If you evacuate air from the tube and allow these objects to fall from the same height, you can be convinced of the validity of the assumption put forward.
A more precise experiment is also possible. For example, it is possible to directly measure the fall time from the same height of several balls that differ significantly from each other in size and mass.
Within the limits of measurement accuracy, this time turns out to be the same.
We will hardly be able to study free fall in its pure form. But if we take into account that the air has a relatively small effect on the falling small metal balls, we will take their motion in air as a free fall model.
Let us ask ourselves a question: does the body's speed remain constant when it falls or does it change?
It is plausible to assume that the speed of the falling body increases during movement.
Simple direct observation is unlikely to allow us to prove the validity of this hypothesis. However, indirect evidence suggests that this is so. Such data include, for example, the impact sound, the height of the rebound of a metal ball falling on a wooden table from different heights.
If the speed of the falling body increases with time, then the question arises: is the acceleration of the falling body constant or not?
It is possible that free fall is a kind of uniformly accelerated motion. But it is also possible that the acceleration either increases or decreases as it moves.
If the first version is taken as a working version, then the time of falling of any body from different heights should be measured and in each case the estimated acceleration should be calculated using the known formula. If the calculations carried out taking into account the measurement accuracy will give the same result, the version will find its experimental confirmation. Otherwise, you will need to check alternative versions.
A similar experiment has been carried out several times. It turned out that the acceleration of gravity in a given area of \u200b\u200bthe Earth, provided that the height above its surface (in comparison with the radius of the Earth) changes insignificantly, is a constant value. On average, the acceleration of gravity near the Earth's surface is
An analysis of a stroboscopic photograph of the movement of a body thrown at an angle to the horizon shows that the movements made by the body in the horizontal direction over equal time intervals are equal. This means that the body moves uniformly in this direction. Movements in the vertical direction, made for the same equal intervals of time, are not equal to each other.
In the ascending segment, the trajectories decrease, while in the descending segment, they increase. This is due to the accelerated nature of body movement. The symmetry of the curve indicates that the acceleration modulus remains constant throughout the entire path segment.
Since the horizontal coordinate of a body thrown at an angle to the horizon changes over time according to a linear law, and along the vertical - according to a quadratic law, the trajectory of such a movement is a parabola.
Introductory control in physics 8kl
OPTION No. 2
Complete the sentence with one word:
1.The physical quantity that characterizes the inertia of the body is called ____________________
2. The force with which the Earth attracts bodies to itself is called
____________________
3. The force that prevents movement is called_______________________________________
4. Length measuring device ____________________
5. A wheel with a groove fixed in a cage is ___________
6. Pressure measuring device _________________
TEST
1. The smallest particles of which substances are composed are called: a) molecules, b) microparticles, c) grains.
2.Diffusion can be slowed down if: a) the bodies are cooled, b) heated, c) rearranged from one table to another.
3. What general properties are typical for solids: a) have their own shape and volume, b) easily compressible, c) practically not compressible.
4.What formula can be used to calculate the volume of the body?a) F= mg. b) p= m: v. d) V= S: te) V= abc
5. What force causes all bodies to fall to the Earth? a) friction force, b) elastic force, c) gravity, d) body weight.
6. What formula can you use to calculate the force of gravity?a) F= mgb) F= mgh. d) p= F: Se) V= S: t
7. What is the unit of measure for pressure? a) Pa b) H c) m / s d) kg
8. Which of the cosmonauts flew into space first? a) Gagarin b) Titov c) Tereshkova d) Leonov.
9. By what formula can you calculate the work?a) F= pghb) A= FSd) N= A: t
10. the body does mechanical work when a) it moves, b) a force acts on it, c) a force acts on it and it
PHYSICS TESTS 8kl.
TEST 1 Thermal motion. Temperature.
1. Diffusion occurs faster if a) the movement of molecules slows down b) the movement of molecules stops c) the speed of movement of molecules increases
2. How is warm water different from cold water?
a) the speed of movement of molecules
b) molecular structure
c) transparency
3. Which of the phenomena is thermal?
a) the rotation of the Earth around the Sun
b) rainbow
c) snow melting
4. What is the trajectory of gas molecules?
a) straight
b) curvilinear
c) along a broken line
5. In what bodies can molecules vibrate, rotate, move relative to each other?
a) in gases
b) in liquids
c) in solids
6. Body temperature is related
a) with the kinetic energy of the body
b) with the potential energy of the body
c) with average kinetic energy of molecules
TEST # 2 Internal energy
1.Kinetic energy of a body depends a) only on body mass b) only on body speed c) on mass and on body speed
2. When the body released from the hands falls a) there is a transition of potential energy into kinetic b) there is a transition of kinetic energy into potential c). Kinetic and potential energies do not change
3. The mechanical energy of a piece of plasticine that fell on the floor, a) will not change b) it will disappear without a trace c) will turn into another form of energy
4. What energy is called the internal energy of the body? a) energy of body movement b) energy of interaction of body parts c) kinetic and potential energy of body parts
5. The internal energy of a body depends a) on the speed of movement of the body b) on the temperature of the body and its state (solid, liquid, gaseous) c) on the position of the body relative to other bodies
6. Could the body be devoid of internal energy? a) can, if the body has a very low temperature b) can, if the body does not have mechanical energy c) can not under any conditions
Literature: G. V. Sypchenko
PHYSICS tests 8kl Saratov: Lyceum, 2012.-80s
Internet resource
It remains for us to consider the case when the load together with the scales makes a free fall, that is, when the scales are simply released from the hands (Fig. 129). Experience shows that during free fall, the balance arrow is set on the pool: the weight turns out to be zero. And this is understandable. After all, when the load falls under the influence of the attraction to the Earth, the spring of the balance “itself follows it” (see Fig. 129). Therefore, it does not deform. But if the spring does not deform, then no force from its side acts on the load attached to it. Therefore, the load is also not deformed and also does not act on the spring. The load became weightless.
The fact that during free fall the body weight is equal to zero follows directly from the formula
With the free fall of the body Consequently,
Under this condition, the dispute does not interact with the body.
The reason for weightlessness lies in the fact that the force of universal gravity imparts the same acceleration to the body and its support. Therefore, any body that moves only under the influence of the forces of universal gravity is in a state of weightlessness.
It is in such conditions that a freely falling body is found.
This amazing fact is illustrated by the following interesting experiment (Fig, 130). There is a block on the tripod, through which the thread is thrown. At the end of this thread is suspended a cup with two weights of a sufficiently large mass. The top weight fits snugly against the bottom. The other end of the string is attached to a tripod. A strip of tissue paper is placed between the weights. Its free end is held motionless in the hand. If the load is lowered slowly, then the paper, stretching, breaks, because the resting friction force acts on the clamped end of the strip. Now we replace the strip of paper with a new one and repeat the experiment so that the weight falls freely. If the load falls, the strip of paper remains unbreakable in your hands. This means that during the fall, the weights did not press on each other and the static friction force was zero. This proves that weights in free fall are in a state of weightlessness.
Exercise # 31
1. Is a body thrown vertically upward in a state of weightlessness? Disregard air friction.
2. To the frame, which can slide along two guide rods (Fig. 131), various weights are suspended on two identical springs. If you burn the thread with which the frame is fixed, the frame will fall freely (friction is small and can be neglected) and the deformation of the springs will disappear. Explain why the deformations of the springs disappear when the frame falls freely.
Tasks in mechanics (dynamics), on the topic
Vertical movement due to gravity
From the manual: GDZ to the Rymkevich problem book for grades 10-11 in physics, 10th edition, 2006
Find the free fall acceleration of the ball from Figure 31, taken from a stroboscopic photograph. The interval between shots is 0.1 s, and the side of each grid square in a life-size photo is 5 cm
DECISION
During free fall, the first body was in flight 2 times longer than the second. Compare the final velocities of bodies and their displacements
DECISION
G. Galileo, studying the laws of free fall (1589), threw various objects without initial speed from an inclined tower in the city of Pisa, the height of which was 57.5 m. How long did objects fall from this tower and what is their speed when hitting the ground
DECISION
A swimmer, jumping from a five-meter platform, plunged into the water to a depth of 2 m.How long and with what acceleration did he move in the water
DECISION
The body freely falls from a height of 80 m.What is its movement in the last second of the fall
DECISION
How long did the body fall if in the last 2 s it passed 60 m?
DECISION
What is the displacement of a freely falling body in the nth second after the start of the fall
DECISION
What initial velocity must be imparted to the stone when it is thrown vertically down from a 20 m high bridge so that it reaches the water surface in 1 s? How long would the fall of a stone from the same height take if there was no initial velocity
DECISION
One body falls freely from the height h1; simultaneously with it, another body begins to move from a greater height h2. What should be the initial velocity u0 of the second body for both bodies to fall simultaneously
DECISION
An arrow fired vertically upward from the bow fell to the ground after 6 seconds. What is the initial speed of the boom and the maximum lifting height
DECISION
How many times is the height of rise of a body thrown vertically upwards on the Moon than on Earth, at the same initial velocity?
DECISION
How many times should the initial speed of a body thrown vertically upward be increased in order for the lifting height to increase by 4 times
DECISION
From a point located at a sufficiently high altitude, two bodies are simultaneously thrown with the same velocity v0 \u003d 2 m / s: one vertically upward and the other vertically downward. What will be the distance between the bodies in 1 s; 5 s; after a period of time equal to
DECISION
When throwing the ball vertically upwards, the boy gives him a speed that is 1.5 times greater than the girl. How many times higher will a ball thrown by a boy go
DECISION
An anti-aircraft gun projectile, fired vertically upward at a speed of 800 m / s, reached the target after 6 s. At what altitude was the enemy plane and what was the speed of the projectile upon reaching the target? How do the real values \u200b\u200bof the required quantities differ from the calculated ones?
DECISION
The body is thrown vertically upward at a speed of 30 m / s. At what height and after what time the body speed (modulo) will be 3 times less than at the beginning of the ascent
DECISION
The BALL has been thrown vertically upward twice. The second time he was told a speed 3 times faster than the first time. How many times higher does the ball rise on the second throw?
DECISION
The body is thrown vertically upward at a speed of 20 m / s. Write the equation of motion y \u003d y (t). Find after what time interval the body will be at a height: a) 15 m; b) 20 m; c) 25 m. Indication. Direct the Y-axis vertically upward; assume that at t \u003d 0 y \u003d 0
DECISION
A ball was thrown vertically upward at a speed of 20 m / s from a balcony 25 m above the ground. Write the formula for the dependence of the coordinate on time y (t), choosing as the origin: a) the throwing point; b) the surface of the earth. Find how long it takes for the ball to fall to the ground.
1. You are well aware that bodies fall to the ground if they are not supported by a support, suspension thread, hand, etc. When a body falls, its speed increases, that is, the falling of the bodies is an accelerated motion.
If we simultaneously release the metal and paper mugs from a certain height of the same size and observe their movement, we will notice that the metal circle will fall to the ground before the paper one. It can be assumed that the falling time of bodies depends on their mass. To make sure of this, take two identical sheets of paper, crumple one of them and simultaneously release them from our hands. The crumpled piece of paper will fall to the ground earlier. Consequently, different times of fall are not related to the mass of the bodies.
It is obvious that a crumpled sheet of paper and a smooth one experience different air resistance when dropped. This assumption can be confirmed experimentally.
Take a thick-walled tube, one end of which is sealed, and the other is equipped with a tap. A pellet, a piece of cork and a bird's feather are embedded in the tube (Fig. 33). If you quickly turn the tube over, these bodies will fall to its bottom. You can see that the pellet will fall before everyone else, and the feather - later than all the bodies. If you now pump out air from the tube and turn it over again by closing the tap, then all three bodies will reach the bottom of the tube at the same time, despite the fact that they have different shapes and weights. Consequently, all bodies in an airless space (in a vacuum) fall with the same acceleration, which is called free fall acceleration.
The fall of bodies in airless space is called free fall.
2. The free fall of bodies is a uniformly accelerated motion.
The free fall acceleration is always directed to the center of the Earth and has the same value for all bodies at the same initial position relative to the Earth's surface.
Indeed, as you already know, the modulus of movement of a body during uniformly accelerated motion without an initial velocity is calculated by the formula: s \u003d. From the experience described above, it follows that a pellet, a piece of cork and a bird's feather make the same movements at the same time intervals, so they all move with the same acceleration.
A body thrown vertically upward also moves uniformly with the acceleration of gravity. In this case, the velocity and acceleration vectors of the body are directed in opposite directions, and the velocity modulus decreases with time.
3. Free fall acceleration is denoted by the letter g... As you know from the 7th grade physics course, the acceleration of free fall depends on the geographical latitude of the area. At the latitude of Moscow near the surface of the Earth, it is equal to 9.81 m / s 2. When solving problems, if high accuracy of the result is not required, take g \u003d 10 m / s 2.
Free fall acceleration depends on the height of the body above the Earth's surface. The higher the body is lifted, the weaker it is attracted to the Earth and the less the acceleration of gravity. For example, for passenger aircraft, the maximum lift of which is about 10 km above sea level, the acceleration due to gravity at this height is 9.78 m / s 2. The heights at which modern fighters fly are characterized by a more significant decrease in the acceleration of gravity. So, at an altitude of 18 km, it is equal to 9.72 m / s 2.
The acceleration of gravity is even less important at altitudes where the orbits of artificial earth satellites and space stations are located. Thus, the maximum height of the first artificial Earth satellite relative to sea level was 947 km. The acceleration due to gravity at this height is 7.41 m / s 2.
4 * . Free fall was studied by an Italian scientist, one of the founders of classical mechanics, Galileo Galilei (1564-1642) at the end of the XVI century. He dropped from the Leaning Tower of Pisa a ball weighing about 200 g and a body weighing 40 kg, having a cigar-like shape. Contrary to popular belief at the time, bodies reached the Earth's surface almost simultaneously. The ball was only a few centimeters behind. Galileo did not have accurate instruments for measuring time, he used an hourglass, so the value of the acceleration due to gravity was measured by him with a large error. In particular, in his work "Dialogue on the two most important systems of the world - Ptolemaic and Copernican" Galileo argued that bodies fell from a height of 60 m for 5 s and, based on these data, obtained the value of the acceleration of gravity almost 2 times less than that obtained in present time.
To improve the accuracy of the experiment on the study of uniformly accelerated motion and free fall, in particular, Galileo investigated the sliding of balls from an inclined plane. He experimentally established the proportionality of the path traversed by the ball to the square of time and the law of the ratio of the paths traversed by it in successive equal intervals of time.
5. An example of solving the problem
Two bodies simultaneously begin to move: one vertically upward at a speed of 20 m / s, the other vertically downward from a height of 60 m without an initial speed. Determine the time and coordinate of the meeting point for tel.
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Given: |
Decision |
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v 01 \u003d 20 m / s v 02 = 0 h \u003d 60 m g \u003d 10 m / s 2 |
Let us connect the frame of reference to the Earth. As the origin of coordinates, we take the point from which the first body was thrown from the surface of the Earth, the axis OY direct it upwards, we will take the moment of throwing the bodies as the starting point of time (Fig. 34). |
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t? y? |
We write the equation of motion in projections onto the axis OY:
y = y 0 + v 0y t + .
For the first body, this equation is:
y 1 = y 01 + v 01y t + .
Considering that y 01 = 0; v 01y = v 01 ; g y = –g, we get
y 1 = v 01 t – .
The equation of motion for the second body:
y 2 = y 02 + v 02y t + .
Insofar as y 02 = h; v 02y = 0; g y = –gthen
y 2 = h – .
At the moment the bodies meet, their coordinates will be the same: y 1 = y 2 = y... Then v 01 t –= h – ; v 01 t = h.
Hence the meeting time for bodies t = ;
t \u003d\u003d 3 sec.
We find the coordinate of the meeting place of the bodies from the equation of motion of the first body.
y \u003d 20 m / s 3 s - \u003d 15 m.
Answer: t \u003d 3 s; y \u003d 15 m.
Self-test questions
1. What movement is called free fall?
2. What kind of mechanical movement is free fall?
3. How to experimentally prove that the acceleration of gravity is the same for all bodies at a given point in space?
4. What determines the acceleration of gravity?
Assignment 8
1. The ball falls to the ground from a height of 20 m with an initial velocity of zero. How long will it take to reach the Earth's surface? What speed will the ball acquire when it hits the Earth's surface? At what height relative to the Earth will the ball be located 1 second after the start of the fall? What speed will it have at this moment in time? Neglect air resistance.
2. Based on the data of task 1, plot the dependences of the speed projection on the axis Y and the ball speed modulus versus time, if the axis Y directed: a) vertically down; b) vertically up.
3. At what height relative to the Earth's surface will two balls meet if one is thrown vertically upward at a speed of 10 m / s, and the other falls from a height of 10 m without an initial speed? The balls start moving at the same time. What speed relative to the Earth will the balls have at this height? Neglect air resistance. Plot the graphs of the dependence of the coordinates of each ball on time and determine the time and coordinate of the meeting place * according to the schedule.
4 * . Calculate the acceleration due to gravity using the data obtained by Galileo.
5. Plot the graphs of the dependence of the projection of the velocity of bodies on time according to the data of the problem considered in § 8 *. Using this data, plot the dependence of the coordinates of each body on time and graphically determine the time and coordinate of the meeting place of the bodies.
