Physics on balloons. Experiments with liquid nitrogen, plastic bottles and table tennis balls Laboratory tennis ball

··· VII Moscow marathon of educational subjects. Physics Day ···

G.F. TURKINA, State Educational Establishment Central Educational Institution “Teaching Technologies.
School of distance support for the education of disabled children", Moscow

Balloon physics

Physics Laboratory Instructions

Balloons are an invaluable material for observing physical phenomena and performing various physical experiments.

1. Qualitative comparison of the densities of water: hot and cold, salty and fresh - without a hydrometer.

If you are researching immiscible And not joining into a chemical reaction of liquid, then it is enough to pour small portions of them into one transparent vessel, for example, a test tube. The liquids will be distributed into layers. The density can be judged by the order of the layers: the lower the layer, the higher the density. Single-color liquids should be tinted with food coloring.

It’s another matter if liquids mix, such as hot and cold water, fresh and salt. Then we set up the “Three Little Pigs” experiment.

We place three portions of different water (hot, cold and salty cold) in three balloons, for example, red, blue and yellow. To do this, we pull, for example, a blue ball onto a water tap and fill it with cold water to the size of a slightly larger tennis ball.

Tie the ball with thread. This is the most crucial moment - there should not be even a bubble of air left inside the ball! blue “pig” - with cold water.

Pour a tablespoon of salt into the yellow ball and fill it again with cold water. Make sure there are no air bubbles in the ball. Yellow “pig” is salty.

The third, red, “pig” - with hot water. To prevent the water in it from cooling prematurely, keep it in a pan of hot water.

Pour hot water into a large container and throw the balls into it. We record how each “pig” behaves in hot water (floats on the surface, in the middle, or drowns).

Replace hot water with cold water. We describe the behavior of each ball in cold water.

Strongly salt the water in the container. We describe the behavior of balls in salt water.

WE Draw conclusions about the density of water - hot and cold, fresh and salty.

Notes

– If there is an air bubble in the balls, the result of the experiment will be false.

– You cannot keep the balls for a long time in either cold or hot water - the water in them will either cool down or heat up.

– The density of the balloon shell is slightly less than the density of water (check whether an uninflated balloon sinks or floats and draw a conclusion). This fact should be taken into account when drawing conclusions.

2. Study of the floating conditions of bodies

So, we have a ball of salt water floating in salt water. BUT, depending on the ratio of salt concentration in the ball and the pan, this “pig” can float inside the liquid, on the surface, and even sink to the bottom. Always sink: a ball with cold water in hot water, a ball with salt water in cold and hot water.

WE Draw conclusions about the dependence of the buoyant force on the ratio of the densities of the liquid and the body.

3. Study of the action of Archimedes' law in water

And these experiments are best carried out on the shore of a reservoir on a summer day in good weather or (at worst) in the bathroom. The experience is more fun in the company of friends. You will need several balls, preferably thick rubber.

Inflate the balloons to different sizes. They are light and float on the surface of the water.

Try to drown the balls. This is a fun but challenging task. You may not be strong enough to sink a large ball. When you “defeat” the Archimedes force (buoyant force), carry out the calculation and evaluate your strength: F A = gV = g· 4/3 · R 3 where F A is the Archimedes force, or buoyant force, N; – density of water (1000 kg/m3); g– free fall acceleration (9.8 m/s 2); = 3.14; R– radius of the ball, m. Estimate the radius - wrap the ball around the ball with a thread and divide the resulting length of the thread by 2 (circumference L = 2R).

4. Study of the action of Archimedes' law in the air

Montgolfier brothers in the 18th century. managed to make a large balloon, fill it with light gas (hot air) and go on an air journey. Such Balloons began to be named after the brothers-inventors hot air balloons. You will need two balloons, one of which is filled with helium.

We tie a small light toy to a helium balloon and release the balloon.

Inflate the second balloon with air and release it.

Observation. The helium balloon flies up, and the air balloon goes down.

Explanation. The density of helium is less than the density of air. The buoyant force acting on this ball is greater than the force of gravity, and it rushes upward - “floats up”. An inflated balloon is heavier than the air it displaces. He is "drowning."

5. Balloon strength test

Try to pierce the balloon with a needle so that it does not burst with noise.

Clue. This can be done in three ways: 1) on the sides, where the rubber is very stretched, glue a piece of tape and pierce the ball in this place - this is the trick clowns do in the circus; 2) where the rubber is thickest, i.e. "on top of the head"; 3) where the rubber is not tensioned - where is the thread.

Note. The hole from the needle is so small that the ball deflates unnoticeably. After successful experiments, pierce the ball through with a knitting needle or a sharp wooden stick.

6. Pressure study

We are so accustomed to the fact that an inflated balloon, hitting the point, bursts with a noise, that a balloon on nails under the weight of a load is perceived by us as a supernatural phenomenon. Nevertheless, this is a fact... You will need an applicator (Kuznetsova, Lyapko) or a board with nails evenly packed (every centimeter).

We inflate the balloon and place it on the tip of the Kuznetsov iplicator.

Carefully press down on the ball from above. We increase the pressure. Do you have the strength to press so hard that it bursts?

Observation. The most amazing thing is that the ball lying on the tips only flattens under pressure, but does not burst!

Explanation. Due to the large number of points with which the ball comes into contact, the pressure on the ball shell is insignificant, acceptable for thin rubber. A balloon on nails can withstand 60 N (6 kg load)!

7. Testing rubber for thermal strength

The sharp unpleasant smell of burnt rubber is familiar to everyone. It turns out that rubber does not always burn in a flame. You will need a ball and a candle.

Pour water into the ball and place the ball of water into the flame of the candle.

Observation. The rubber just smokes.

Explanation. The temperature of the shell, as long as there is water in it, will not rise above 100 °C, i.e. will not reach the burning temperature of rubber.

8. Study of gas laws

8.1. Boyle–Mariotte law

Gas law, independently discovered by the English scientist Boyle and the French scientist Marriott: at constant temperature and mass, the pressure of a gas is inversely proportional to its volume.

8.1.1. How do the lungs work?

The diaphragm lowers - inhale, rises - exhale. Let's make a model of the lungs and look at its work through the eyes of a physicist.

Cut off the bottom of the plastic bottle.

Place the balloon inside the bottle and pull it over the neck.

We cover the cut part of the bottle with film from another balloon (cut it with scissors) and secure it with tape.

We pull back the film and the balloon inflates; we press on the film and the balloon deflates.

Explanation. The volume of air inside the bottle is isolated. When the film is pulled back, this volume increases, the pressure decreases and becomes less than atmospheric. The ball inside the bottle is inflated with atmospheric air. When you press on the film, the volume of air in the bottle decreases, the pressure becomes greater than atmospheric pressure, and the ball deflates. Our lungs work the same way. The rubber film imitates the diaphragm, the balloon imitates the lungs. The rubber film-diaphragm lowers (retracts) - inhale, rises - exhale.

8.1.2. Ball in a bottle

Place the ball inside the bottle and pull it over the neck.

Let's try to inflate the balloon.

Observation. It is impossible to inflate a balloon in a bottle!

Explanation. As the volume of the ball increases, the air, the volume of which is isolated in the bottle, is compressed, and the pressure increases. Only a person with powerful lungs (singer, swimmer) can partially cope.

Use an awl to make a hole in the bottle closer to the bottom.

We are trying to inflate the balloon again. It turns out!

When the balloon is inflated, close the hole with your finger - the balloon remains inflated!

We cut off the bottom of the plastic bottle and try to inflate the ball again.

Observation. It inflates easily if internal volume bottles communicate with the atmosphere.

8.2. Charles's Law

The gas law, discovered by the French scientist Charles, states: the higher the temperature of a gas at constant pressure and constant mass, the greater the volume it occupies.

8.2.1. Ball in a jar

We put the ball on the water tap and pour water into it so that the size of the water ball becomes slightly larger than the neck of a two- or three-liter glass jar. Tie the ball securely.

Set fire to a piece of paper and throw it into the jar.

Place the ball on the neck of the jar.

Observation. The flame in the jar goes out. The ball is pulled into the jar.

Pour hot water from the kettle into an empty jar.

Pour out the water and immediately place a ball of water on the neck of the jar.

Observation. The ball is funny being pulled into the jar.

Note. This experience proceeds more slowly than the first.

Explanation. In the first experiment, the air in the jar is heated by burning paper. When a ball is placed on the jar, it blocks the access of oxygen and combustion stops. The density of hot air is less than the density of cold air. The air in the jar quickly cools down, its density increases, its volume decreases - the ball is drawn into the jar.

In the second experiment hot water heats the jar, and the jar heats the air. The jar of air quickly cools down, and the heavy ball is sucked inside. The experiment can be carried out with an inflated balloon, but then it turns out not so bright.

8.2.2. Ball in the steam room

Inflate the balloon to medium size and tie the neck with a knot.

We measure the size of the ball with a thread and make a knot-mark (we take the thread with a reserve).

Place the ball in a bowl and pour hot water (boiling water) from the kettle over it.

We measure with a thread new size ball. Let's compare the results.

Observation. The ball increases in size before our eyes - this is confirmed by testing with a thread.

8.2.3. Ball in the cold

We inflate the balloon and securely tie the neck with a knot, but not with thread (this deflates faster).

We measure the circumference of the ball with a thread and make a knot-mark.

Place the balloon in the refrigerator for several hours (preferably in the freezer) or take it out into the cold.

After a few hours, we compare the sizes of the ball at the beginning of the experiment and at the end.

Observation. In the cold, the ball “loses a lot of weight” and “grows old” (shrinks).

8.3. Air paradox

This experience baffles many. You will need two identical balloons, a tube 10–30 cm long and 15–20 mm in diameter (the ball should fit tightly onto it).

We inflate the balloons slightly and NOT EQUALLY.

We stretch the balls onto opposite ends of the tube. To prevent the balls from deflating, we twist their necks.

We unscrew the necks - the balls communicate freely with each other through the tube.

Observation. Air flows from one ball to another. But... the small balloon inflates the big one!

Explanation. Many people believe that since there is more air mass in a larger balloon, this balloon will deflate and inflate the smaller balloon. But such reasoning is wrong. The reason for the observed phenomenon is the pressure inside the ball. The gas pressure depends on the curvature of the surface, i.e. on the radius of the sphere: the smaller the radius, the greater the pressure. (Remember the communicating vessels - water flows not from the vessel where there is less water, but from the one where the pressure is greater.) In addition, everyone knows how difficult it is to start inflating a balloon, but when the “dead” point is overcome, it then inflates easily. Consequently, the elasticity of rubber plays an important role.

Note. You can also observe the following result: the small ball “does not want” to deflate and inflate the big one. Apparently, in this case, the elasticity of rubber plays a leading role. You can make the tube yourself from thin cardboard. The main thing is that it is airtight.

9. Studying Bernoulli's law

9.1. Air kiss

One of the basic laws of hydro- and aerodynamics is Bernoulli’s law: the higher the speed of the air flow, the lower the pressure in it.

We inflate two balloons to the same size and tie a thread about a meter long to each.

We take the balls by the threads with our right and left hands so that they hang at the same level at some distance from each other.

Without touching the balls with your hands, try to connect them.

Clue. The solution is extremely simple, but not obvious: blow between the balls from above, below or from the side - it doesn’t matter.

Explanation. From Bernoulli's law it follows that the pressure in a stream of air is lower than atmospheric pressure. The force of atmospheric pressure from the sides will bring the balls together.

9.2. Ball in the stream

Inflate the balloon, turn on the hairdryer, apply a stream of air under the balloon and release the balloon.

Observation. A stream of air will lift the ball up, but it does not fly away, but hangs at a certain height.

Explanation. The ball is held steadily in the air stream, because the air pressure in the jet is below atmospheric. For any deviation of the ball to the side, atmospheric pressure returns the ball to the center of the jet, where the pressure is less.

10. Studying jet propulsion

Reactive motion is the movement of a body caused by the separation of some part of it from it at a certain speed.

10.1. Jet ball

You will need round and long balloons, tape (silk, paper or magnetic from a video cassette), and tape.

We inflate the round ball and, without tying it, release it from our hands.

We inflate the round ball again, attach a tail-stabilizer made of paper tape to it and release the ball from our hands. Comparing the flights of a ball with and without a stabilizer

Inflate a long balloon and release it.

We inflate the long balloon again, twist it slightly (as if we were squeezing out laundry) and release it from our hands. Let's compare the flights of the ball.

Inflate a round ball, press it perpendicular to the wall and release it.

We inflate the round ball again, press it sideways against the wall and release it.

Observation. If a round ball is released from your hands, it will take off and fly chaotically, throwing out a stream of air. The stabilizer tail makes the ball's flight directional.

A long ball flies in a straight path. A twisted ball rotates during flight.

A round ball, pressed perpendicularly to the wall, remains in place, does not fall and rapidly decreases in size. The ball, pressed sideways to the wall, turns perpendicular to the wall and quickly deflates.

10.2–10.4. Flight to the stars. Jet-powered toys. Water jet transport

(These experiments are spectacular, but well known, so we do not describe them.– Red.)

11. Studying electrical phenomena

Experiments on electrostatics with balloons are bright and spectacular - rubber is a good dielectric, easily electrified, and a large charge accumulates on the balloon.

11.1. Electricity from the head

Inflate the balloon and tie it.

We electrify the ball by rubbing it on our hair.

Raise the ball above your head.

Observation. Hair stretches behind the ball, which feels good.

We electrify the ball again.

Place the ball on a desk (wooden) table with the electrified side up.

Observation. The ball instantly turns over and lies on the table with its charged side. When you try to return it to its previous position, it turns over again.

We electrify the ball again.

Press the ball with the electrified side to vertical wall or to the ceiling.

Observation. The ball sticks to the wall for a long time - in dry sunny weather it can hang for an hour!

Explanation. When the ball is rubbed on your head, electrons transfer from the hair to the rubber shell of the ball. The ball is charged negatively, the hair is charged positively. Oppositely charged bodies attract each other, so the hair is drawn to the ball.

A charged ball creates an electric field around itself, which affects the table, wall, ceiling - induces a charge of the opposite sign. We see electrification through influence. Oppositely charged bodies attract, which is what we observe.

Note. It is important that the hair is clean, without cosmetics (spray, gel). Electrification experiments are carried out in dry weather, because moist air is a good conductor, and charge will not accumulate on the ball.

11.2. Electricity from different sources

We inflate both balloons to the same size and tie each one with a thread 40–50 cm long.

We electrify the balls by rubbing them on hair or a piece of wool.

Observation. The balls scatter in different directions.

Place the balls on the table at a short distance from each other with the electrified side up.

Observation. The balls scatter.

Remove the charge from the balls by running your hand over them.

We electrify the balls again, but now by rubbing them against each other.

We take the balls by the threads in one hand.

Observation. The balls stick to each other.

Place the balls on the table close to each other with the electrified side up.

Observation. The balls rush towards each other.

We repeat the experiment, but charge only one ball.

Observation. The balls rush towards each other as if they were oppositely charged.

Explanation. Balls rubbed against a piece of cloth or a head are charged with a charge of the same sign, and balls rubbed against each other are charged with charges of a different sign. Likely charged bodies attract, oppositely charged bodies repel.

A charge in bodies can be induced by placing the body in an electric field (by bringing a charged ball to the body). If the body is metallic, then the phenomenon is called electrostatic induction, if a dielectric, then – dielectric polarization.

11.3. Salt columns

Pour a small pile of table salt onto a piece of cardboard.

We inflate and electrify the balloon.

We bring the electrified ball to a hill of table salt.

Observation. Small crystals of salt line up in vertical columns, stretching like “strings” towards the ball.

Explanation. Table salt is a polar dielectric. Under the influence of the electric field of the electrified ball, the positive and negative bound charges of the molecule shift in opposite directions. On the side of the charged ball in the salt crystal, a charge of opposite sign is always formed. The salt crystals are attracted to the ball, aligning themselves with one another.

Note. Granulated sugar crystals look like table salt, but the sugar molecule is non-polar, so it is less polarized. In addition, the sugar crystals are larger and heavier, which does not allow you to get good columns.

11.4. Jumpers

Sprinkle glitter confetti or finely chopped metal foil onto a sheet of cardboard.

We electrify the ball and bring it to the foil, but do not touch it.

Observation. The sparkles behave like live jumping grasshoppers. They jump up, touch the ball and immediately fly off to the side.

Explanation. Metallic sparkles are electrified in the field of the ball, but remain neutral. The sparkles are attracted to the ball, bounce, charge when touched and bounce off as similarly charged.

11.5. Snake

Place a strip of paper on the table.

We bring an electrified ball to the strip.

Observation. The strip under the ball arches and moves like a snake.

We repeat the experiment with Christmas tree rain, magnetic tape, thread.

Observation. Although the strips are made of different materials, their behavior in the electric field of the ball is the same.

11.6. Ships

We make a paper boat and put it on the water.

We electrify the ball and bring it to the boat.

Observation. The ship will follow the ball.

Lower the metal lid onto the water.

Observation. The metal lid floats towards the ball.

Place the plastic lid on the water.

We electrify the ball and bring it to the lid without touching it.

Observation. The heavy lid floats behind the ball.

Explanation. In the electric field of the ball, the paper and plastic are polarized and attracted to the ball. A charge is also induced in the metal lid. Since the friction force on the water is insignificant, the boats easily move.

11.7. Electric compass

We insert the needle into the eraser and place a paper arrow on top.

Cover the arrow with a glass jar.

We electrify the ball and bring it to the arrow.

Observation. The arrow turns behind the ball.

Explanation. The paper in the electric field of the ball is polarized. Glass does not shield the electric field.

12. Studying sound phenomena

12.1. Balloon orchestra

12.1.1. Bagpipes

You will need balloons and corrugated hoses about a meter long of different diameters (the corrugation should not be spiral). The hose can be purchased at the construction market.

We roll the corrugated hose into a ring.

We put the balloon on one end.

Inflate the balloon through the hose.

Observation. The ball is deflated, and the air, passing through the corrugated pipe, generates sound. Why not bagpipes?! Hoses of different diameters and lengths produce sounds of different pitches - the smaller the diameter of the hose, the higher the sound.

12.1.2. Drum

We inflate thick rubber balls to different sizes.

Hitting the balls with your palm is accompanied by sounds, with each ball making its own sound.

12.1.3. Squeaker

We inflate the balloon and stretch the neck with both hands - the air escaping through the narrow gap makes a sound. Once you get the hang of it, you can get sounds of different pitches.

Explanation. The escaping air causes the neck of the ball to vibrate. Vibrations create sound. The experience simulates the functioning of the vocal cords.

12.1.4. Sound Lens

Press the ball to your ear - you will hear sounds that were not heard before.

We press the ball to the radio speaker, and the ear to the ball. Even a quiet sound can be heard - the ball amplifies it. If you and a friend are separated by a balloon, and the friend whispers something, then you will hear this whisper perfectly, you just need to press the balloon to your ear.

Place the ball between the handset and your ear. We select a position so that the telephone dial tone is loudest.

Observation. If you remove the ball, the beeps become quieter.

Size: px

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Transcript

1 Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 1 1. With uniformly accelerated motion, a material point with a mass m = 100 g passes in the first two equal successive time intervals, τ = 4 s each, a path S 1 = 24 m and S 2 =64 m. Determine the initial speed, acceleration of the moving point and its kinetic energy after time T = 5 s after the start of movement. 2. A block of mass m = 2.5 kg is held on an inclined plane, forming an angle α = 30° with the horizon in the first experiment, and an angle β = 60° with the horizon in the second. The sliding friction coefficient between the block and the plane is µ = 0.77. The block is released. By what percentage is the friction force greater in the first case than in the second? 3. A material point with mass m = 1 kg is thrown at an angle α = 45 o to the horizon with a speed v o = 40 m/s. What is the ratio of its kinetic energy after one and two seconds of flight? 4. Two skaters with masses m 1 = 60 kg and m 2 = 30 kg, standing on ice, push off from each other and slide in opposite directions. The distance between them after stopping is L = 100 m. Determine the displacement of each of the skaters from the starting position if the coefficients of friction of their skates on the ice are the same. 5. A weight suspended on a light inextensible thread of length l = 30 cm rotates freely in a vertical plane. At the top point of the trajectory, the speed of the weight is v = 2 m/s. Determine how many times greater is the tension force of the thread at the bottom point of the trajectory than at the top? Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 2 1. The first car of the train passed by the observer standing on the platform in t 1 = 1 s, and the second car in t 2 = 1.5 s. The length of the car is L = 24 m. Find the acceleration of the train and its speed at the beginning of the observation. Assume that the motion of the train is uniformly variable, and the spatial gap between the cars is negligible. 2. A block of mass m = 2 kg located on a horizontal surface acquires an acceleration of a = 7 m/s 2 under the influence of a force F = 20 N acting on it parallel to this surface. What will be the acceleration of this block if the same force is directed from the surface, making an angle α = 30° with it? 3. A material point with mass m = 1 kg is thrown at an angle α = 45 o to the horizon with a speed v o = 40 m/s. How different is its potential energy after one and two seconds of flight? 4. Skaters, whose masses m 1 = 60 kg and m 2 = 70 kg, sharply push off from each other and slide in opposite directions. How many times do the coefficients of sliding friction of their skates on ice differ if the movements of the skaters before they stop are the same? 5. A load of mass m, suspended on a light inextensible thread, rotates in a circle in horizontal plane around a vertical axis (conical pendulum). The length of the thread is known and equal to L. The elastic force arising in the thread during the rotation of the ball is constant and equal to T. Find the kinetic energy of the ball K.

2 Entrance exam in physics at the Scientific and Research Center of Moscow State University (10th grade 2016) Option 3 1. Two identical buses left city A for city B according to a schedule with an interval of τ = 12 minutes. They took turns, with an interval of T = 14 minutes, overtaking the same cyclist traveling to city B. How many times is the speed of the buses greater than the speed of the cyclist? 2. A straight, light and inextensible thread lies on a smooth horizontal table. One of the ends of the thread is fixed, and on the other there is a small washer with a mass m = 100 g. The washer is given a speed v = 10 m/s in a direction perpendicular to the thread. In this case, an elastic force F = 3.14 N appears in the thread. Find the modulus of change in the momentum vector of the washer and its kinetic energy after a time τ = 1 s after the onset of the force. 3. The projectile at the highest point of the trajectory at a height of H = 125 m exploded into two fragments with masses m 1 = 1 kg and m 2 = 1.5 kg. The speed of the projectile before the explosion at this point is v 0 = 100 m/s. The speed of the larger fragment turned out to be horizontal (coinciding in direction with v 0) and equal to 250 m/s. Determine the distance between the points of impact of both fragments. Air resistance can be neglected. 4. A body of mass m = 2 kg thrown vertically upward fell back after a time T = 10 s. Determine its kinetic energy at the moment of the throw and the potential energy measured from the place of the throw, after a time τ = 4 s after the throw. Ignore air resistance. 5. The plane makes a “dead loop” in the vertical plane at a constant speed v = 360 km/h. Find the weight of a pilot with mass M = 70 kg at the lower and upper points of the loop, if at the middle point of the loop he presses on the seat of the chair with F = 1.4 kn. What is the difference between the potential energies of the pilot at the top and bottom points of the “dead loop”? Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 4 1. Two electric trains departed from Tambov to Michurinsk with an interval of τ = 10 minutes at speeds of v = 30 km/h each. At what speed did the freight train move along the same railway line in the direction of Tambov, if the electric trains passed by it with an interval of T = 4 minutes? 2. A straight, light and inextensible thread lies on a smooth horizontal table. One of the ends of the thread is fixed, and on the other there is a small washer with mass m = 10 g. The washer is given a speed v = 20 m/s in the direction perpendicular to the thread. In this case, an elastic force F = 6.28 N appears in the thread. Find the magnitude of the displacement vector of this washer during the time τ = 0.10 s after the onset of the force. 3. A projectile fired from a gun at a certain angle to the horizontal breaks into two equal parts at the top point of the trajectory at a height of H = 125 m. One of the fragments returns to the gun along the same trajectory. Determine at what distance from the gun the second fragment will fall if at the moment of explosion the projectile had a speed of V = 250 m/s? Ignore air resistance. 4. A body is thrown vertically upward from the Earth’s surface with an initial speed v o = 30 m/s. At what height will the kinetic energy of the body be twice as great as its potential energy (potential energy is measured from the point of the throw)? Air resistance is not taken into account. 5. A mathematical pendulum oscillates in a vertical plane, deviating from the vertical axis at an angle α = 45 o. How many times is the acceleration of the pendulum at the bottom point of the trajectory greater than its acceleration at the extreme position? Air resistance can be neglected.

3 Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 5 1. A ball thrown vertically downward with a speed v 0 = 10 m/s falls from a height h = 75 m. Divide this height into three parts, to pass each of which the same time is required. Neglect air resistance to motion. 2. A light, inextensible thread is thrown across a light, stationary block, from which three identical weights are suspended: two on one side of the block, and a third on the other. The weights were released and they began to move. How many times do the gravitational force of one of the weights and the elastic force of the thread between the first and second weights (located on one side of the block) differ from each other? Ignore friction. 3. A man with mass M = 60 kg moves from the bow to the stern of the boat. How far will a boat of length L = 3 m move if its mass m = 120 kg? What will be the speed of the boat relative to the water when the man reaches the stern and stops? Neglect water resistance. 4. The initial speed of a bullet with mass m = 10 g (when leaving the gun) is V = 600 m/s. At what angle to the horizon did it fly out of the gun barrel if its kinetic energy at the highest point of the trajectory is W = 450 J? 5. A mathematical pendulum of mass m was deflected by an angle α from the vertical and released. Determine the elastic force of the thread when the pendulum passes the equilibrium position. Friction can be neglected. Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 6 1. During the last second of free fall, the body traveled a distance of h = 45 m. How long and from what height did the body fall if it was thrown vertically down with a speed v 0 = 20 m /With? Air resistance can be neglected. 2. A weightless, inextensible thread is thrown through a light stationary block, suspended from the ceiling using a dynamometer, to the ends of which weights of mass m 1 = 2 kg and m 2 = 3 kg are attached. Determine the dynamometer readings and the speed module of the loads after a time τ = 3 s after the start of their movement. 3. A person with a mass M = 80 kg moves from the stern to the bow of a boat, the length of which is L = 5 m. What is the mass of the boat if during this transition it moved in still water in the opposite direction by L = 2 m? What will be the speed of the boat when a person moves to its bow and stops? Neglect water resistance. 4. Determine the kinetic energy of a body of mass m = 1 kg thrown horizontally with a speed v = 20 m/s at the end of the fourth second of its movement. Air resistance can be neglected. 5. A heavy ball of mass m is suspended on a light and inextensible thread that can support the weight P. At what smallest angle from the vertical should the thread be deflected so that the ball, passing the equilibrium position, breaks it? Friction can be neglected.

4 Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 7 1. An arrow with a mass m = 100 g is released from a tower with a height of H = 45 m in the horizontal direction with a speed v 0 = 40 m/s. What will be the modulus of its momentum at the moment of its fall? Air resistance can be ignored. 2. After what time after the launch, the speed of the block, which was given a speed v 0 up the inclined plane, will again become equal to v 0. The coefficient of friction between the block and the plane is equal to µ, and the angle formed by it with respect to the horizon line is equal to β (tg β > µ). 3. The boat is standing motionless in the lake. Fishermen sit at the stern and bow of the boat at a distance L = 5 m from each other. The masses of the fishermen are m 1 = 50 kg and m 2 = 70 kg, and the mass of the boat is M = 250 kg. Please determine how many meters the boat will move after the fishermen change places? Neglect water resistance. The movement of fishermen relative to the boat can be considered uniform. 4. A body is thrown from a tower with a height of H = 45 m in a horizontal direction at a speed of V = 15 m/s. After how many seconds will the kinetic energy of the body double? Air resistance can be neglected. 5. A small ball of mass m = 2 kg, suspended on an inextensible and weightless thread of length L = 1 m, oscillates in the vertical plane. The elastic force in the thread at the moment when it forms an angle α = 60° with the vertical is equal to T = 12 N. What will be the elastic force in the thread when the ball passes the equilibrium position? Friction forces can be neglected. Entrance exam in physics at the Scientific Research Center of Moscow State University (10th grade 2016) Option 8 1. A projectile with a mass m = 17 kg flies out of a gun barrel at an angle α = 30 o to the horizon with a speed v 0 = 640 m/s. How long after the shot will the projectile be at an altitude of H = 1200 m for the first time? Air resistance can be neglected. 2. The block was pushed up an inclined plane forming an angle β = 30° with the horizontal. After a time τ = 2 s after starting, it stopped, and after a time T = 4 s after stopping, it returned to the starting point. What is the coefficient of sliding friction? 3. A cart with a mass M = 120 kg moves straight along horizontal rails without friction at a speed v = 6 m/s. A person with a mass m = 70 kg jumps off it in the horizontal direction at an angle α = 30 0 to the direction of movement of the cart. In this case, the speed of the cart decreased by v = 1 m/s. What was the speed of the person u during the jump relative to the ground? 4. A pebble with mass m = 0.3 kg is thrown from a tower in a horizontal direction with some speed. After time τ = 1 s, the velocity vector made an angle α = 30 o with the horizon. Please find the kinetic energy of the pebble at this moment. 5. A ball of mass m is suspended on a light inextensible thread. The thread was placed horizontally and the ball was released. Find the dependence of the elastic force of the thread on the angle α formed by it with the vertical? Friction forces can be neglected.

5 Physics 2016 for those entering grade 11 Option 1 1. A body with mass m = 5 kg begins to move without an initial speed under the influence of a variable force, the dependence of which on time is presented on the graph. Find the body's speed v at the end of the fifth second. 2. The spring was compressed by x 1 = 2 cm, doing work A 1 = 0.12 J. What work A 2 must be done to compress it another x 2 = 1 cm? F, H 3. An air bubble rises from the bottom of a reservoir of depth H. Neglecting water vapor pressure and surface tension forces, find the dependence of the volume V of the bubble on the depth h of its immersion if its volume at the bottom is V 0. The process of the bubble’s ascent is considered isothermal. 4. In a certain process, the work done on the gas is A" = 100 J, its internal energy increased by U = 80 J, and the temperature increased by T = 10 K. Find the heat capacity of the gas C in this process. 5. At what speed v reach the anode electron tube electrons emitted by the cathode, if the voltage between the anode and cathode U = φa φк = 200V? Neglect the initial velocities of the electrons (as well as the gravitational field) t, s Physics 2016 for those entering grade 11 Option 2 1. Two parallel slats move in opposite directions sides with velocities v 1 = 6 m s and v 2 = 4 m s. A ball of radius r = 10 cm is clamped between the slats, rolling along them without slipping. Find the speed v of its center and the angular speed ω of its rotation. 2. A small body of mass m , sliding with speed v on a horizontal surface, enters a moving slide of the same mass (at rest on the same surface), rises to a height H, less than the height of the slide, and slides back off it.Find the final speed u acquired by the slide. Ignore friction. 3. An ideal gas is contained in a vertical cylinder, closed at the top by a easily movable piston of mass m and area S. The volume of gas is equal to V 0. What will be the volume of gas V if the cylinder is moved vertically upward with acceleration a? Atmospheric pressure is equal to p 0, the gas temperature is constant. 4. An ideal monatomic gas, expanding isobarically, receives a portion of heat Q = 10 J. Find the work A performed by it if the initial and final volumes of the gas are equal, respectively, V1 = 1 l and V2 = 2 l. 5. Positive point charges q1 = 2 10 C and q2 = 5 10 C, located in a vacuum, act on each other with a force F = 0.25N. Determine the field strength E at a point located in the middle between the charges. 6 t v 6 N m u=?

6 Physics 2016 for those entering grade 11 Option 3 1. Find the acceleration a of a body of mass m 2, in the system shown in the figure, if the other end of the thread is not attached to a load of mass m 1 > m 2, but is wound on a weightless reel of radius r, located inside it and rotating with angular velocity ω = const. The system is perfect. 2. A small ball is on a smooth horizontal table and rotates uniformly in a circle of radius l. The ball is connected to the fixed center of this circle by a weightless elastic band, the elongation of which obeys Hooke's law. Find the length l 0 of an unstretched elastic band if the ratio of the potential (elastic) energy of the system to its kinetic energy is n = 0.2. 3. When an ideal gas in a closed vessel was heated to T = 30º K, its pressure p increased by 10%. What is the initial temperature T of the gas? 4. An aluminum blank with a mass M = 0.5 kg lying on an anvil is struck by a hammer with a mass m = 4 kg. During an impact lasting time τ = 0.1 s, an average force F cp = 2 kN acts on the blank. How many degrees will the blank heat up if the specific heat capacity of aluminum is c = 0.9 J/g deg? 5. An uncharged capacitor with a capacity of 2C is connected to a capacitor with capacity C, charged to voltage U. Find the amount of heat Q released in the connecting wires if C = 30 μF and U = 100V. t 2 r t 1 ω Physics 2016 for those entering grade 11 Option 4 1. A point makes a linear motion along the x axis. The dependence of the projection of its velocity on this axis on time is shown in the figure. Graphically depict the x(t) dependence. At the initial moment, the point was at the origin of coordinates. 2. A body is launched upward along an inclined plane forming an angle α = 45 with the horizon, giving it a certain initial speed. How much heat Q will be released in the system if it is known that after the body reaches the top point, its potential energy has increased by U = 5 J, and the coefficient of friction between the body and the plane is µ = 1? 3. The cubic crystal lattice of iron contains one iron atom per elementary cube, which can be repeated to obtain the entire crystal lattice. Determine 3 the distance r 0 between the nearest iron atoms if its density is ρ = 78, gcm/, and its molar mass is µ = 56 gmol/. 4. Two ideal monatomic gases of equal concentrations are in identical vessels at the same temperatures. The mass of a molecule of the first gas is t, and the second is 2t. Which gas exerts greater pressure on the walls of the vessel and by how much? Compare also the average kinetic energies per molecule in each gas. 5. On the same horizontal line at a distance r from each other there are point charges q and 2q. Point M is located strictly above the charge q at the same distance r from it. Find the angle α that the equipotential surface passing through this point forms with the horizontal at point M. v x 2τ 4τ 5τ t

7 Physics 2016 for those entering grade 11 Option 5 1. A small body is thrown vertically upward from the roof of a skyscraper. At the moment when it reaches the maximum height h above the throwing point, another small body is thrown from this point (throwing) with a speed v directed horizontally from the skyscraper. How does the distance s between the bodies change (while they are both in the air) depending on the flight time t of the second body? Neglect air resistance. 2. A stationary ball of mass m = 10 g, hanging on a light inextensible thread of length l = 45 cm, is hit by a bullet of the same mass flying horizontally at a certain speed v and gets stuck in it. What should this speed be for the thread to break if 2 its strength limit T max = 3mg? In calculations, take g = 10 ms /. 3. In a vertical cylinder under the piston, the lower plane of which S makes an angle α = 30º with the horizon, there is air. Piston mass m = 6 kg, α cylinder cross-sectional area S = 20 cm 2 5, atmospheric pressure p0 = 10 Pa. What mass m 1 must be placed on the piston so that the volume of air under it in the cylinder is halved? Neglect friction and consider the process isothermal. 4. One mole of an ideal monatomic gas is transferred from state 1 with parameters p1, V1, T 1 to state 2 with parameters p2, V2, T 2 by performing work A on it. Find the change U in its internal energy. 5. To what maximum potential φ can a solitary conducting ball of radius r = 3 cm in air be charged if the electric field strength at which breakdown occurs in air is E = V/m? Physics 2016 for those entering grade 11 Option 6 1. In which direction and with what magnitude of acceleration should the middle block be moved so that a load of mass m remains at rest? The system is perfect. N α 2. A ball slides from a high stand onto a stationary cart with sand and gets stuck in it. How will the initial a= change? m is the speed of the cart after the ball falls, if the height H of the stand is doubled? 2m There is no friction between the cart and the floor, the angle α remains unchanged. 3. Two ideal gases at the same temperatures and pressures have densities equal to, respectively, ρ 1 = 0.4 kg/m 3 and ρ 2 = 0.6 kg/m 3. What density ρ will a mixture of these gases have under the same conditions, if the masses of the mixed gases are the same? 4. A children's balloon filled with helium has a volume V = 3 liters and is under normal conditions (i.e., at atmospheric pressure and temperature t 0 = 0 C). The ball is lowered to a depth of h = 1 m into a bath of hot water at a temperature of t = 90 C. Find the work A done by helium when heated at a given depth. Neglect the pressure caused by the shell of the ball. 5. Two identical flat capacitors are connected in parallel and charged to a voltage U 0 = 150 V. Find the voltage U on the capacitors if, after disconnecting them from the source, one of the capacitors has reduced the distance between the plates by n = 2 times.

8 Physics 2016 for those entering grade 11 Option 7 1. Two small bodies are thrown simultaneously from one point in space at a certain height with equal velocities v = 10 ms /, but in different directions: one horizontally, the other at an angle α = 60 k horizon. Find the distance s between the bodies (while they are in flight) after time t = 25, s, if the velocity vectors lie in the same vertical plane. Neglect air resistance. 2. A body moving rectilinearly is subject to a constant force directed along the velocity for some time. Find the average speed v cf of the body during the action of the force, if during this time the magnitude of the body’s momentum has increased by p = 3 kg m/s, and its kinetic energy has increased by w = 12 J. 3. A piece of cork floats first in water, and then In oil. In what case is the Archimedes force F greater and by how many times? Density ratio of oil and water = 0.9. ρм ρв 4. A “laboratory” tennis ball filled with helium falls without initial speed from a height h = 6 m onto a solid surface and is elastically reflected from it. Find the maximum increase T in the temperature of the gas inside the ball during the impact if the initial temperature of helium is T = 300 K, the mass of the ball is m = 150 g, its volume is V = 0.3 l, and the pressure inside it is p = 3 atm. Neglect air resistance as the ball falls. The shell of the ball is considered inextensible. 5. The plates of a flat capacitor, carrying opposite charges of equal magnitude, are moved apart, doubling the distance between them. How will the electric field strength E and the potential difference U between them change? Neglect edge effects. Physics 2016 for those entering grade 11 Option 8 1. A small ball of mass m, suspended on a soft weightless tensile thread (elastic band), rotates uniformly in a horizontal plane in a circle (conical pendulum). To what angular velocity ω must this pendulum be spun so that the length of the thread increases by δ = 1 (compared to the length in the unstretched state)? Assume 3 that the elongation of the elastic band x obeys Hooke’s law F = kx, where the coefficient k is known. 2. What distance S will the lower prism travel when the upper one touches the plane? The dimensions and masses of the bodies are shown in the figure. At the initial moment the system was at rest. There is no friction. 3. What is the gas pressure p in an electric light bulb, the volume of which is V = 1 liter, if when the tip of the light bulb is broken off under the surface of water at a depth of h = 1 m, m = 998.7 g of water enters the light bulb? Atmospheric pressure is normal. The process is considered isothermal. 4. An ideal monatomic gas, expanding isobarically, receives a portion of heat Q = 10 J. Find the increase U of its internal energy if its initial and final temperatures, respectively, are T1 = 300 K and T2 = 400 K. b m М v α v d ω t

9 5. A solitary conducting ball of radius R = 10 cm, carrying a charge q = 10-8 C, is surrounded by an uncharged concentric conducting spherical shell of radius 2R. Find the potential difference U = φ1 φ2 between the ball and the shell.

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MINISTRY OF EDUCATION AND SCIENCE OF THE RF Tomsk State University of Control Systems and Radioelectronics (TUSUR) Department of Physics MINISTRY OF EDUCATION AND SCIENCE OF THE RF Tomsk State University

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I. V. Yakovlev Materials on physics MathUs.ru Inclined plane Problem 1. A block of mass was placed on a smooth inclined plane with an angle of inclination and released. Find the acceleration of the block and the pressure force of the block

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Postponed tasks (88) A ball thrown vertically upward with speed υ fell to the surface of the Earth after some time. Which graph corresponds to the dependence of the velocity projection on the OX axis on the time of movement?

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Problems for the calculation task (EnMI) in mechanics 2013/14 1. Kinematics 1. A stone is thrown vertically upward from a height of 10 m with an initial speed of 8 m/s. Create an equation of motion in three versions by placing

I. V. Yakovlev Materials on physics MathUs.ru Open Olympiad Phystech-lyceum 2015 Physics, grade 11 1. On a thin transparent horizontal table lies a thin converging lens with a focal length F = 70

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4. Falling ball. A basketball thrown into a hoop begins to fall vertically from the basket without any initial speed. At the same moment, from a point located at a distance I from the ring, a tennis ball is thrown into the falling ball (Fig. 4.1). With what initial speed was the tennis ball thrown if the balls collided at a distance h from the ring?

L The question posed implies that you need to find the vector of the initial speed of the tennis ball, i.e. its direction (angle a) and module (y0). If we solve the problem in the original (laboratory) frame of reference, then the line of reasoning may be as follows. We write down expressions for the movements of both balls during the time t from the beginning of the movement until they meet, then we project them onto the vertical and horizontal directions (Fig. 4.2). In re-
|0 I. KINEMATICS

As a result, we arrive at the system of equations

A = 4-, I -A = y„sina-<--С-,

* (!) V1r-Raa = y0 cos a-t.

Here R is the height of the ring above the point of throwing the tennis ball, and K/2-R2 is the horizontal distance to the ring (Fig. 4.2).

In the system of three equations (1) there are four unknown quantities: d0, oc, t and R. Therefore, it may seem that the problem does not have a single solution. However, it is not. Indeed, substituting A from the first equation into the second, we get

H-v0sina-t. (2)

Dividing this equation term by term by the third equation of system (1), we find the expression for tan a:

Tga = tf/J/>-Н\ (3)

Now using fig. 4.2, you can see that the angle a at which the initial speed of the tennis ball should be directed actually corresponds to the direction from the point of throwing onto the ring. The true direction of the initial velocity va is shown in Fig. 4.3. So, you need to throw the tennis ball exactly in the direction of the ring. The magnitude of its initial velocity can be found by substituting t = V2h/g from the first equation of system (1) into equation (2).
5. AT THE TARGET WITH THE LOWEST INITIAL SPEED 17

Considering that I/sin a-1, we get

v0 - l/t - I ]/~ g/2h.

But all these transformations can be avoided if, from the very beginning, we go to the reference system associated with the basketball, i.e., freely falling with acceleration sr - in this reference system there is a basketball,

naturally, is motionless, and the tennis player moves uniformly and rectilinearly with a speed v0 - Obviously, this speed<ой должна быть направлена на баскетбольный мяч. Через время t=l!v0 мячи столкнутся. В лабораторной системе отсчета за это время баскетбольный мяч опустится на расстояние

whence for v0 we obtain the previous expression (4). Using this problem as an example, we see that in some cases it is convenient to transition to an accelerated moving frame of reference. ^

5. At the target with the lowest initial speed. It is necessary to hit a target with a stone from the surface of the earth, which is located at a height h and at a horizontal distance s. At what minimum initial speed of the stone is this possible? Neglect air resistance.

A At first glance, it seems that the initial speed of the stone will be the smallest if the top point of its trajectory coincides with the target (Fig. 5.1a).

Maybe you thought so too? This illusion is so strong that a similar solution to a similar problem

Rice. 4.2. Projections of ball movements

Rice. 4.3. The true direction of the vector r>0 of the initial speed

I. KINEMATICS

can be found in some reputable textbooks on solving physical problems. However, even without solving the problem, it is easy to see that this is not the case. Indeed, we will mentally reduce the height at which the target is located. In this case, the point where the stone hits continues, according to the assumption, to remain the top point of the trajectory (Fig. 5.16), including in the limiting case A = 0. But it is quite obvious that in order to hit a target on the ground, it is enough to simply throw a stone to the target (Fig. 5.16). So, the assumption that the target coincides with the highest point of the stone's flight path is incorrect.

The fallacy of this assumption becomes even more obvious if we notice that the required initial speed must increase as h -> 0.

The above analysis is an example of checking the solution of a problem by passing to the limit to the answer is either obvious or

From the above qualitative analysis we can conclude that the target should always be on the descending branch of the trajectory (Fig. 5.1b). Let us remind you once again that we are looking for a trajectory with a minimum initial speed.

Let's start solving the problem.

Let a stone be thrown at an angle a to the horizontal and hit the target. Its horizontal movements s and vertical h can be recorded in the following way:

S=v0 cos a-t, h=vo sin a-t-gt2/2.

Since we are not interested in the stone's flight time t, we exclude it from these equations. Expressing t from the first equation

First stage: preparing the solution. Typically, a tennis ball is made from natural rubber. Raw rubber arrives at the plant in 70- to 250-pound bales. To make it softer, it must be thoroughly ground. And in order to obtain the various required properties of the future ball (strength, color, hardness), various powders are added to the rubber. The rubber compound is then placed in a tank of solvent and after a few hours a sticky dough is obtained. To obtain the mass of the required consistency, it is necessary to mix the dough with a large amount of solvent.

Second stage: composition. In general, pressure balls are usually made from natural rubber containing a high load of fine filler for low gas permeability. The composition (by weight) is as follows: natural rubber - 100 black - reinforcing filler - 30 clay - 32 zinc oxide - 9 sulfur - 3.5 diphenylguanidine (DPG) - 2 cyclohexylbenthiazylsulfenamide (HBS) - 1

Third stage: extrusion. At this stage, long strips are cut from the rubber mass, from which small granules are squeezed out using an extruder (forming device) (this is similar to squeezing toothpaste from a tube). The granules are then cooled.

Fourth stage: form. The pellets are loaded into a hydraulic press which converts them into hemispheres (ball halves), usually within 2 and a half minutes at 150º. Next, the hemispheres are removed from the forming sheets using figured knives.

Fifth stage: polishing. The edges of the hemisphere are rough, so to ensure their smooth gluing, it is necessary to sand them using a grinding wheel. After grinding, a vulcanizing rubber solution is applied to the edges of the polished hemisphere.

Stage six: hardening and inflation. There are two methods of inflating or increasing the pressure in a tennis ball. The first method is the use of chemicals. Chemicals for inflation are usually sodium nitrite and ammonium chloride, which produce nitrogen during the molding process. The compressed air method is much more complicated. The two halves of the sphere are brought together and air enters. The closing of the hemispheres occurs in stages as follows: a) The press is closed until the edges of the hemispheres touch each other; b) In this position, the internal area of ​​the cell with hemispheres is isolated from the atmosphere by rubber o-ring; c) Compressed air is introduced at the required pressure into the area of ​​the cell with hemispheres; d) Pressure cells with hemispheres are brought together, thus trapping compressed air between the hemispheres; e) The balls are then heated until the rubber solution vulcanizes and cooled. The balls are typically pressurized to about 12 psi. inch. Due to the fact that rubber compounds are easily permeable to gas, the pressure in them is gradually lost, and after a few months the balls will not be suitable for play. Therefore, they are sold in special jars that maintain the pressure of the balls.

Seventh stage: coating with solution. To smooth out the rough surface of the ball, it is polished and coated with a special rubber solution.

Eighth stage: covering with tennis cloth. For the manufacture of tennis balls two types of cloth are used. These are "Melton Cloth", a cloth that has a high wool content, and "Needle Cloth", a more synthetic cloth. The cloth comes in 100-meter rolls. On one side it is covered with a vulcanizing solution. A special machine is used to cut blanks into shapes resembling dumbbells in cross-section. Using an automated wrapping machine, a rubber ball, initially treated with glue, is wrapped with two felt pieces, which are tightly fixed to its surface. Next, the balls are once again subjected to the vulcanization process.

Ninth stage: molding. The ball is placed in a molding press and heated, the rubber core of the ball and the ends of the cloth harden, and a smooth seam is formed. The molded ball is cooled and removed from the press. This molding leaves the fabric very smooth and compressed, with a crease where the mold closed.

Tenth stage: steaming. At this stage, the tennis balls are immersed in an atmosphere filled with vapor, the cloth swells, becomes more raised and soft, after this operation the fold across the ball disappears.

Eleventh stage: finishing. At this stage, the balls are checked and evaluated according to international standards of tennis organizations (ITF, USTA), and the brand name is also applied. They are packaged in sealed jars that maintain pressure during storage. The balls are now ready to go.

Dear friends and partners! We only sell balls approved by the International Tennis Association (ITF).

Tennis balls

An average tennis ball weighs about 57 grams and has a diameter of about 6.36 centimeters. A quality tennis ball should be elastic, bouncy and durable. But still, the durability of the ball depends not only on the quality, but also on the surface of the court on which it will be played.

Initially tennis balls were made of leather, later in the mid-19th century they began to be made of rubber. The color of the balls also changed; until 1970 there were only white balls. Later, yellow balls gradually began to appear at tournaments; they are more visible to both spectators and the athletes themselves.

Modern tennis balls They are produced mainly in bright yellow color and have fluorescent coatings. But, nevertheless, the rules do not prohibit playing with white balls, which existed before the 70s of the last century.
Leading companies engaged in the manufacture of tennis equipment use wool from Australian or New Zealand sheep for cloth. Such sheep are grazed in special meadows where certain herbs grow. There is a special schedule for cutting them. The friction between the ball's pile and the court surface at the moment of rebound affects its speed and height.
According to the density of the pile, tennis balls are divided into 2 groups: standard and elite balls
The "standard" group includes tennis balls with loose pile, they have normal wear resistance.. “Extra” has thicker pile, and often they have reinforced rubber - such a ball is designed for long-term use.
These are Slazenger Extra Life, Dunlop Fort Elite, Babolat RG FO, Wilson Australian Open and other balls.

There are also balls that have a waterproof fleecy surface (Hydroguard). According to manufacturers, such balls are for tennis 70% more water resistant than conventionally coated balls. An example of such balls is Slazenger Championship Hydroguard, Slazenger
Wimbledon

Balls used on slow clay courts are slightly larger in size than balls used on fast courts and have a higher rebound speed.
The most popular brands of clay balls are Babolat Roland Garros, Dunlop Fort Clay Court, Wilson Tour Red Clay, Tretorn Serie +

For fast surfaces, balls with normal or slightly slower rebound are used, with good cloth resistance to abrasion on hard surfaces. These balls are: Wilson US Open, Head ATP Tour,
Babolat RG AC, Slazenger Wimbledon, Slazenger Championship, Dunlop Fort AC, Tretorn Tournament.

Everyone knows that tennis balls They quickly lose pressure after opening the can. And in 1 hour of play, internal pressure decreases by 2-5%, and therefore both rebound and speed decrease. After 3-5 hours it becomes impossible to play normally with this tennis ball. Therefore, if you can afford it, then preferably every new workout play with a new tennis ball.

Tennis balls Also used in tennis guns, such balls can withstand the strong pressure of the gun shafts on the tennis ball. Tretorn Micro X balls are most often used in tennis guns; inside the ball, instead of air, there is a special foam composition.

Tennis balls can be stored in plastic jars for up to 2 years, and in metal jars for up to 4 years. But you should take into account that the production date is not indicated on the cans, so if you are offered a product with a low cost, then there is a possibility that it is a stale product.
Therefore, it is better to purchase balls from reputable online stores with a large turnover of tennis balls,
for example, in the online store "Raketlon".
The jars can hold 3 or 4 balls. Once the packaging is opened, the balls should be stored at a temperature of 5-15°C. Cans of tennis balls are packaged in cardboard boxes that hold 18 or 24 cans. Training balls can also be packaged in plastic buckets, most often containing 72 balls.
How to choose and purchase correctly tennis ball for quality training?

Tennis balls , in which there is no excess pressure (Pressureless), are mainly manufactured by Tretorn (Sweden). Their main advantage is durability, without the need for storage in special packaging.
For beginner tennis players, it is best to play with a tennis ball with a normal or slightly slow bounce. As a rule, these are tournament balls for fast surfaces.
Balls that spend a long time in the basket also slow down.
For children 4-5 years old who are taking their first steps in tennis, special tennis balls , they are larger in size and made of elastic foam rubber .

For teaching children older ones make lightweight balls (easy play program), which have less internal pressure. According to this training program, and it is approved in all countries,
kids are playing lightweight tennis balls on a reduced court, up to approximately 10 years.
Tennis balls for this program come in 3 types.
Red (red-yellow color) tennis balls (Red) - oversized balls with 75% loss of rebound, for ages 4-6 years
Orange tennis balls (orange-yellow) - balls with 50% loss, age 6-8 years
Green tennis balls (charcoal yellow) - balls with 25% loss, age 7-10 years
From experience it follows that it is impossible to give any specific recommendation in choosing a ball based on the brand and manufacturer. Because all well-known companies produce balls of both high and medium quality, as well as budget balls of a lower training level.
Raketlon employees are always ready to listen to you carefully and give qualified advice
by choosing a tennis ball for your game, your surface.
Buy tennis balls Through the Raketlon online store you can:

Arkhangelsk, Murmansk, Smolensk, Bryansk, Kursk, Belgorod, Voronezh, Lipetsk, Tula, Volgograd, Rostov-on-Don, Krasnodar, Saratov, Penza, Samara, Ufa, Kazan, Izhevsk, Yoshkar-Ola, Orenburg, Perm, Kirov, Ekaterinburg, Chelyabinsk, Nizhny Novgorod, Kurgan, Tyumen, Syktyvkar, Tyumen, Khanty-Mansiysk, Salekhard, Yaroslavl, Ivanovo, Ryazan, Tver, Kaluga, Tomsk, Novosibirsk, Barnaul, Kemerovo, Novokuznetsk, Krasnoyarsk, Irkutsk, Chita, Yakutsk, Magadan, Blagoveshchensk, Khabarovsk, Vladivostok , Yuzhno-Sakhalinsk, Okha, Komsomolsk-on-Amur, Nakhodka, as well as in the Republic of Belarus (Minsk) and Kazakhstan (Almaty).