Problems

This section brings together the problems for the early IYPTs, as they are restored from all traced multilingual sources. Before 1994, the probelms were circulating mostly in Russian. In many cases, no “standard” English editions existed, and not all “standard” Russian editions have been yet found. When re-published or translated in the past, the problems suffered from omissions and inaccuracies, and many problems were even misattributed. Our key aim here is to provide the “critical editions” of a maximum coherence and reliability. After 1993, the problems already existed in unique, “standard” English versions, that have been continuously available up to now. They can be found in e.g. Heinz Kabelka’s collection and will be included into the Archive after verficiation against original records.


1st IYPT (1988)

Source: Problems for the 1st IYPT (Critical edition, I. M.)

The sciences nourish young people,
Give consolation to the old,
They decorate a happy life,
And they protect one in misfortune...
M. V. Lomonosov

1. Invent yourself
Suggest original projects of technical and scientific use of high-temperature superconductivity.

2. “Eternal radio”
Develop and construct a portable radio receiver that does not use power supplies. The usability parameter is x=P/Lm, where P is acoustic pressure at a distance of 1 m from the receiver, L is maximum linear dimension, and m is mass of the receiver.

3. Camera obscura
Make a group portrait of your team with a camera obscura. Validate the physical principles of achieving a good quality photograph with such a device.

4. Electric circuit
Several knots (n≤10) are interconnected with batteries of known EMF and r. Create a computer program to calculate the potential difference between the first and the second knot. Consider the time from the start of data input (tables of EMF and r values) to the moment of correct result output, as the quality criterion of the program.

5. Metrology
Determine the maximum precision of length measurement with a steel ruler.

6. Seller of vacuum
An enterprising star farer decided to supply physical laboratories worldwide with vacuum from cosmic space. What are the venture’s chances of being successful?

7. Sunset
The visible Sun disk is flattened at sunset. Measure these distortions experimentally and describe them. Calculate the theoretical ratio of horizontal and vertical dimensions of the Sun disk that is touching the horizon.

8. Color television
You have to construct a four-color television receiver. What colors would you choose as basic? Is it then necessary to modify the image capture equipment?

9. Ninth wave
   “Before me are the waves of the sea.
   There are so many. They are countless.”
   B. Pasternak
Does the “Ninth wave” phenomenon exist? Clarify this question. As a starting point, you can use the ideas from the article “Troika, semyorka, tuz...” (Znanie — sila, 1987, No. 1, pp. 97—104.)

10. Self-ignition
   “Yet also when a many-branched tree,
   Beaten by winds, writhes swaying to and fro,
   Pressing ’gainst branches of a neighbour tree,
   There by the power of mighty rub and rub
   Is fire engendered; and at times out-flares
   The scorching heat of flame, when boughs do chafe
   Against the trunks.”
   Lucretius Carus
Thus the Roman philosopher has explained the origin of forest fires. Estimate the probability of such an ignition and its role among the factors that cause fires in nature, i.e. not caused by a human activity.

11. Incandescent lamp
It is said that two 60 W light bulbs shine brighter than three 40 W bulbs. Is it true? Investigate how a small change in supplied voltage will affect light emission and a light bulb’s lifetime.

12. Spring in a city
Spring begins in a city earlier than in the countryside. Describe the main causes of this phenomenon and make numerical estimations. In particular, what would happen if one day all snow from Moscow is removed to the countryside?

13. Heat transfer
Research the heat transfer through the vertical water column in the two cases: T1<T2 and T1>T2.
                                       
“1” is water column, “2” is heat insulating tube.

14. Mesoscopics
One of the mesoscopic effects is a significant change of the resistance of a two-dimensional metal sample at low temperatures, if just a single atom within the crystal lattice is displaced. This effect can be visually illustrated if one considers the following model: small flat mirrors, with reflection coefficients equal to 1, are placed in the knots of a two-dimensional lattice n×n, n>>1. Each mirror can exist in two positions only; it can be inclined at 45° clockwise or counter-clockwise.
                                 
The states of the mirrors change chaotically, so the laser beam incident on a lattice knot reflects perpendicularly from the knot in both directions with the same probability. Estimate how the output light power will change if one of the knots is replaced by an absolute light-absorbing element.

15. Copper coin
A 1-kopeck coin “fell out” of a space rocket and became an artificial planet. Estimate its lifetime as of a planet of the Solar System.

16. Trapped electrons
Several electrons (2≤n≤30) can freely move inside a circle of a radius R. What relative position of the electrons is stable?

17. Cagliostro’s resistor
Even a human being is a resistor for a school tester. Investigate the laws of parallel and series circuits with a school tester. (Traditionally, problem No. 17 has a humorous tone.)



2nd IYPT (1989)

Source: Problems for the 2nd IYPT (Critical edition, I. M.)

Squamps are hunted from the inside only.
S. Lem

1. Invent yourself
Develop and construct a device for demonstrating the wave properties of sound in air.

2. Noon
Is it possible to call “noon” the moment in the middle of the time interval between sunrise and sunset? Using a calendar, you will easily notice that throughout the year this moment “drifts” relatively to a certain moment of time. Explain the cause of this effect.

3. Tides
Estimate the heights of the tides in the Black Sea on April 1, 1989.

4. Rolling friction
Investigate how the friction force depends on speed. To be more specific, consider the rolling of a wooden puck on wood (a wooden surface of a table.)

5. Clock
You have visited a planet and you plan to return to it in ten thousand or even in a million years. What clock would you leave on this planet to measure precisely the time of your absence from the planet?

6. Rainbow
Is it possible that three or more rainbows can appear on the sky simultaneously?

7. Sparks
When knives are sharpened on a grinding wheel, sparks fly away. Most often, a single spark bursts apart in all directions at the end of its flight. Explain the phenomenon.

8. Metro
Suggest the methods and measure the speed of a metro electric train midway between two stations. The same is to be done for a bus in which you are going, if there are no reliable distance signs on the route.

9. Astronaut
What maximum travel distance may an astronaut expect

  • a. at the modern level of technical development?
  • b. in the far future, when practically all technical difficulties will be overcome?

10. Aqueous planet
What amount of water may form a planet with a constant mass

  • a. far from the Sun;
  • b. in a distance of 1 AU from the Sun?

11. Mosquito
At what maximum altitude can a mosquito fly?

12. Sand in a tube
A glass tube is installed vertically and its lower end is tightly closed with a cap. The tube is filled with some sand. During what time T will the sand flow out of the tube, when the cap is opened? Investigate the dependence of T on the following parameters: size of sand grains d, length of the tube L, diameter of the tube D, at a constant degree of packing of sand (you have to introduce and validate this parameter on your own.) We ask you not to consider high degrees of packing for comparability of the results. It is preferred that 10 cm<L<1 m.

13. Electrolytic cell
Prepare some saturated solution of table salt NaCl. Immerse two carbon electrodes (sticks from manganese-zinc battery 373 (R20)) into it so that their metal contacts are not immersed into the solution. Investigate

  • a. the current-voltage characteristic of the created electrolytic cell in the range of currents from 10 μA to 50 mA;
  • b. how does the current-voltage characteristic change as the solution is diluted?

14. Fence
A remote large object is separated from you by a picket fence. It happens that you can see the object if you do not stay near the fence, but go along the fence in a car. Explain this phenomenon. What speed is sufficient if a is width of a fence board, b width of the gaps, L is distance to the fence (L>>a, b), γ is angular size of the remote object, γ>>(a+b)/L.

15. Electron
An electron with a velocity of v=3·105 m/s flies with an impact parameter d aside a metal ball with a radius of a few centimeters. The charge of the ball changes with time under a law q(t)=q0cosωt, where q0=10-3 C, ω=108 s-1. Build a dependence plot of the deviation angle φ of the electron on the impact parameter d.

16. Information
How many bits of information did you receive after having read the problems of a YPT? How many bits of information would you receive when looking at a geographic map with the size of a paper sheet?

17. Karlsson
With what rate should Karlsson eat jam not to get thinner during the flight?



3rd IYPT (1990)

Source: Problems for the 3rd IYPT (Critical edition, I. M.)

Victories do not attract him.
For him growth means: profound defeat
at the hands of ever greater adversaries.
R. M. Rilke

1. Invent yourself — a physical photo contest
Submit to a contest the photographs of a rapidly occurring physical phenomenon. Explain in your commentaries the physical value of these photographs.

2—4. Ball and piston
A horizontal piston oscillates up and down. The coordinate of the piston’s surface is defined with an expression x=x0cosωt. At an arbitrary moment, a small ball is dropped without initial speed onto the piston from a height H.
                                 

2. Up to what altitude will the ball bounce after the first collision with the piston? For this case, consider the collision as absolutely elastic, and H>x0.

3. The system “forgets” the initial conditions after a big number of collisions. Estimate up to what maximum altitude a ball may bounce after many collisions. What is the average bounce altitude? Consider that the surfaces of the ball and of the piston are not damaged at collisions.

4. Let a ceiling be at a height H above the piston. In this case, stationary solutions are possible. Find some of them and research their stability. Consider H=1 m, H>>x0, g=10 m/s2 for numerical estimations. Consider the restoration coefficient of ball collisions with the piston and with the ceiling, as k=0.8.

5. Planet
What is the maximum possible size of a cube-shaped planet?

6. Evaporation-condensation
A Ï-shaped soldered glass tube contains some water.
                                     
If there is an initial difference of water levels H, then the water levels will become equal after some time. Estimate the rate of this equalization for a given H and T=const,

  • a. if there is no air in the tube
  • b. if there is some air in the tube, at normal atmospheric pressure.

7. Cylinder in a tube
A cylinder is moving towards the closed end in a long tube filled with water.
                             
The inner diameter of the tube is D, diameter of the cylinder is d, the cylinder length is L, D-d=h, L>D, h<<D. How does the resistance force depend on the speed of cylinder? Compare the theoretical estimations with the experimental results.

8. Segner’s wheel
A Segner’s wheel rotates due to the reactive force of streams flowing out of the nozzles, when the wheel is placed into the water. Will it rotate backwards in a reverse regime, if the water is sucked into the nozzles, not flowing out of them? It is recommended to look through the book Surely You’re Joking, Mr. Feynman! (a partial Russian translation can be found in the “Nauka i zhizn” magazine, 1986, No. 12.)

9. Franklin’s wheel
Rotation of a little metal bar with pointed spearheads in a well-known “Franklin’s wheel experiment” is explained by the existence of “electric wind”. Explain why the wheel rotates if one places it between the plates of a parallel-plate capacitor and charges the capacitor with an electrostatic generator. If the Franklin’s wheel is replaced with a dielectric disk, will such a disk rotate between the plates of a parallel-plate capacitor charged with an electrostatic generator?

10. Electret
150 years ago, M. Faraday predicted electrets as electrostatic analogues to permanent magnets. Manufacture an electret and research its properties.

11. Color of a cloud
   “Clouds in the skies above, heavenly wanderers,
   Long strings of snowy pearls stretched over azure plains!
   Exiles like I, you rush farther and farther on...”
   M. Yu. Lermontov
Explain the observed colors of white clouds and rain bearing clouds.

12. Border of a cloud
An observed border of a cloud is often sharp. It is especially evident from onboard an airplane. Evaluate the “diffuseness” of the cloud’s border.

13. Cosmonauts cloud (a fantasy with physical sense)
A large number of cosmonauts form a “cosmonauts cloud” in the outer space. Initially each of them has a football with him. Starting from a certain moment, cosmonauts begin throwing these balls one to another (without losing them). Describe the evolution of the “cosmonauts cloud”. In order not to limit your imagination, we offer you to choose on your own the initial conditions, the rules of throwing the balls, and other parameters of the “cloud”. The only important aspects are that the choice of model should be logically validated; the conclusions should be supported with quantitative estimations; the number of described evolutions should not exceed two.

14. Fractal?
A grandmother is winding woolen thread into a spherical thread ball. How does the mass of the ball depend on its diameter?

15. Light in a tube
Look through a glass tube at a light (tube diameter is ca. 5 mm, length is ca. 25 cm.) Explain the origin of the observed circles.

16. Interference
Take two photo plates (9×12 cm), well-washed from emulsion. If they are tightly pressed (lapped) one to another, the interference bands can be observed in the reflected light. If the plates are laid on the table and the upper one is pressed in the middle part with a finger, the interference pattern looks like concentric circles. When the finger is removed, the circles “run away” from the centre. Carry out such an experiment and explain the observed phenomena. Evaluate theoretically how fast do the circles “run away” as the loading is removed.

17. Scientific Organization of Labor — SOL
You have to hammer 1989 similar nails (l=50 mm, d=2.5 mm) into a wooden bar. What hammer would you choose to perform this job quicker and better? (More specifically: what are the mass of the hammer and the length of its handle?)

  • a. for a pine bar
  • b. for an oak bar.



4th IYPT (1991)

Source: Problems for the 4th IYPT (Critical edition, I. M.)

Is this black currant?
No, it is red currant.
But why is it white?
Because it is still green.

1. Invent yourself
Propose a cycle of demonstrations and experiments that can help to explain and visually demonstrate the physical nature of sound waves and the properties of sound.

2. Fortune teller
When molten paraffin is made to drip from a candle into a saucer with water, different solidified shapes are obtained, like a “lens”, a “boat”, an “inkblot”. Study the shape of the solidified droplets in dependence of altitude of their fall.

3. Geyser
A strong ceramic resistor in the shape of a hollow cylinder is placed into water so that the axis of the cylinder is vertical, and the top plane is slightly below the water level. If electric current is passed through the resistor, the resistor, just like a geyser, periodically ejects portions of hot water upwards. Calculate and study experimentally the dependence of the eruption periods of the “geyser” on the power consumed by the resistor from the power supply unit.

4. Self excitation
A strong hum sometimes happens on the concerts of newbie rock bands, when the microphone appears close to the speaker that reproduces the signals amplified from this very microphone. How do the frequency and the amplitude of the produced sound oscillations depend on the distance between the microphone and the speaker, and on their mutual orientation?

5. Cosmic monument
A particular supercivilization is eager to create a cosmic monument, an isolated planetary system of three planets, of which one should move along a trajectory close to an equilateral triangle. What mutual ratios of masses and of velocities for planets would you recommend? Develop also a project for a nearly square-shaped orbit.

6. Radiometer
Construct a device that measures the level of radiation. Use it to locate the major sources of radiation in everyday life.

7. Runner
Estimate the maximum speed that a person can run with. Compare it with the experimental values. In your opinion, what will be the world record in 100 m sprint in the year 2000?

8. Photograph of a television screen
The motion of a camera’s shutter and its speed may be studied through taking photographs of a television image. With this technique, measure the exposure time of your camera and the speed of the shutter.

9. Passive motor
An apple dropped from a balcony of a multi-storey building will calmly descend into the hands of your friend, if you attach to the apple a propeller cut out of dense paper. Explain the principle of work for such a parachute and study the dependence of the drag force on the descent rate and on the sizes of the propeller’s blades.

10. Blowgun
A small knitting needle, with two rounded pieces of polyurethane foam strung onto it, is shot out of a blowgun. Find the optimal blowpipe size to shoot such a projectile. What maximum projectile speed did you succeed to achieve?

11. Gold cube
A cubic planet of pure gold evolves around the Sun and keeps one of its facets turned towards it. Estimate the difference of temperatures of the planet facets.

12. Little boat
A light little boat floats on the surface of a liquid electrolyte. When electric current is passed through the electrolyte, the boat starts moving. Estimate the speed of the boat.

13. Wooden cube
A cube is cut out of a single piece of wood. The edge of the cube is much smaller than the diameter of the tree trunk from which it was cut out. Propose a method to determine the direction of wood fibers in the cube (the positive orientation of fibers is from the roots to the top of the tree.)

14. Moon
Determine experimentally the ratio of brightnesses (illuminances) of sunlit and dark sides of the Moon at different lunar phases. Compare them with the theoretical estimations.

15. Glider
Construct a glider that is driven by a piece of soap. Your glider must win in two competitions: in racing against time for a distance of 50 cm and in floating for a longest range in a given direction (separate gliders may be constructed for each competition.) The linear dimensions of the glider may not exceed 6.28 cm. In the second competition, the glider may not carry more than 0.5 g of soap.

16. Sunset
The Sun becomes red at sunset. What are the colors of the Moon, of Venus and of a bright star when they are they are low on the horizon?

17. Epigraph
In our opinion, the epigraph to the Tournament problems may serve as a basis for serious researches as well as for excellent jokes. We expect both of these from you.



5th IYPT (1992)

Source: Problems for the 5th IYPT (Critical edition, I. M.)

1. Invent it yourself
“Magnetic suspension” may be used in high speed trains of the future. Design and make an experimental model of such a suspension.

2. Unicycle
Circus actors often perform riding tricks on unicycles. There may be a range of wheel sizes. What is the largest possible diameter of the wheel?

3. The dam
There is a saying in Russian, “money goes like water through sand.” However, sand dams hold water. What should be the thickness of the dam in order to retain water whose level behind the dam is 10 m?

4. Swing
A special swing (trapeze) is used to train air and space pilots. This device is able to make a loop around the horizontal axis. What minimum time is necessary to build up the motion of the swing from the rest at the equilibrium position, to an amplitude of 180°?

5. High jumper
There is a saying in Russian, “one cannot jump over his own head.” But many high jumpers do this easily. Estimate the maximum height a man will be able to get over in high jumps and in pole vaulting, in the year 2000?

6. Matches
What is the minimum necessary mass of “sulfur” in the head of a match to make it blaze up?

7. Steel rod
A steel rod 8 mm in diameter is bent at an angle of 90°. What is the position and value of the maximum local temperature rise?

8. Boiling
A tall cylindrical vessel is partly filled with water and is put with its open end into a wide-mouthed vessel which is also filled with water. If we get the water to the boiling point and then cool it down, the level of the water in the cylinder will change. Study experimentally the correlation between the height of the water column in the cylinder and the temperature, under repeated heating and cooling. Explain the phenomena observed.

9. Fountain
There is a fountain called Samson in Peterhof. Water spurts out of it to a height of more than 20 meters. Suggest how to construct a fountain YPTon which could provide the maximum height of the spurt at a given power of the pump. What is the height if the power of the pump is 1 kW?

10. Fuse
A thin brass wire can be used as a fuse. Find the correlation between the critical current and the wire diameter.

11. Hopfield model
Develop the algorithms for storing images in computer memory and for distinguishing them.

12. Butterflies
Butterflies find each other by smell. Estimate the “transmitter” strength and the “receiver” sensitivity of butterflies.

13. Topsy-turvy world
Some medical publications state that 0—2 months old babies see the objects around them up side down. Give your arguments “for or against.”

14. Laser
A laser beam is directed perpendicularly to the wall of a transparent glass tank filled with water. If the beam passes through the tank above or below the level of the water in the tank, we can observe a spot on the screen behind the tank. If the beam passes along the level of the water we observe a vertical line. Explain the origin of the line and calculate its parameters.

15. Incandescent lamp
Estimate the amplitude of temperature variations of the spiral filament of a light bulb powered by alternating current.

16. The depth of field
Find experimentally the dependence of the depth of field of a camera on the aperture diameter of the objective. Give the theoretical explanation of the dependence obtained.

17. Rain bubbles
Some people suppose that if there are bubbles on the surfaces of water pools during the rain, the rain will be long, but others think they are a sign of the close end of the rain. Who is right?



6th IYPT (1993)

Source: Problems for the 6th IYPT (Critical edition, I. M.)

1. Think up a problem yourself
Invent a problem in which an object is moving in some way and then changes its state of motion abruptly as a result of some influence. In this process interesting phenomena may arise which you must explain by, for example, making experiments and performing the necessary calculations.

2—5. Gravitation
Imagine that the gravitational constant G decreases slowly from April 1, 1993 until May 1, 1994 by 10% and keeps this value afterwards. How would this process in the given time interval and up to the date of the VI International YPT opening affect the universe as a whole and, in particular,

2. the Sun;

3. the Earth;

4. aviation and astronautics;

5. things important for you personally.

6. Gagarin’s record
In April 1961 Yury Gagarin set a world record for the fastest round-the-world orbit space flight. Suggest the cheapest way of beating this record. Note that not every record may be officially recognized.

7. Pressure and temperature
Explain why the pressure inside a house and outdoors are practically the same or become equal briefly, while the temperature may be substantially different. What is the characteristic equalizing time for pressures and temperature in- and outdoors? What is the answer to this question in the case of spacecraft?

8. Dominoes
Dominoes are placed vertically at a small distance from each other in a long row on a table surface. Make the first domino fall and the “wave of the falls” will proceed along the row. Calculate and measure experimentally the maximum speed of this wave.

9—10. Gun
The picture shows an electromagnetic gun circuit. It can launch metal rings.
                  
(S, C, K) is a power supply consisting of
   S, a source of constant voltage in the range 10—300 V,
   C, a capacitor with C=1000 μF,
   K, a switch;
L is an induction coil;
F is a ferromagnetic core;
R is a metal ring projectile with mass from 1 to 100 g.
Cn is a converter (some device that converts the energy passing from the capacitor to inductance L in a way you need.) This element does not contain energy sources. It may be completely absent from your gun.
You are to construct, make and demonstrate the electromagnetic gun. It is worth mentioning that the demonstration of your gun will take place with the power supply (elements S, C and K) presented by the Organizing Committee of the YPT. Develop two variants of the gun:

9. A long-range gun is to be constructed to shoot a ring to a maximum altitude. The control parameter is the quantity H=kh/U2, where k=10000 V2, h is the height of the projectile, U is the voltage to which the capacitor is charged.

10. A gun-lift is to be constructed to achieve the maximum work of lifting a weight (ring). The control parameter is W=mgh, where m is the mass of the ring, g=10 m/s2.

11. Recharge
You are given a capacitor C=1000 μF charged to 10 V and an uncharged capacitor Cx=1 μF. Using a self-constructed device containing no energy sources charge the capacitor Cx to the maximum possible voltage.

12. Transmission of energy
You are given a capacitor C=1000 μF charged to 300 V. Transmit without wires to a distance of 5 meters the largest possible proportion of the energy stored in the capacitor and measure it. Your device should be without energy sources.

13. Microwave oven
Why it is not recommended to cook eggs with unbroken shells in a microwave oven?

14. Boiling
A metal ball at room temperature is plunged into a thermos filled with liquid nitrogen. Describe the observed process of intense vaporization of nitrogen and find the time dependence of vaporization intensity q(t) [gs-1]. We ask you to use balls from 2 to 4 cm in diameter.

15. Fence
A picture of a moving bicycle wheel is strongly distorted by being observed through a fence. How much is the wheel distorted and why?

16. Grand Unification
According to modern views Grand Unification is possible at energy of about 1024 eV. Estimate the parameters of an accelerator capable of producing particles of such energy.

17. Karate
Karate is power, speed, force and beauty! Develop objective quantitative criteria making it possible to confer a “black belt” to a karate fighter. Maybe, you’ll become the inventor of a BB (black belt) device badly needed by referees or you’ll create a KM (karate meter) complex which is even more necessary for karate fighters for improving their skill.