Problems of the International Young Physicists' Tournament

Problems 2018

Problems 2017

Problems 2016

Problems 2015

Problems 2014

Problems 2013

Problems for the 25th IYPT 2012

1. Gaussian cannon
A sequence of identical steel balls includes a strong magnet and lies in a nonmagnetic channel. Another steel ball is rolled towards them and collides with the end ball. The ball at the opposite end of the sequence is ejected at a surprisingly high velocity. Optimize the magnet's position for the greatest effect.
2. Cutting the air
When a piece of thread (e.g., nylon) is whirled around with a small mass attached to its free end, a distinct noise is emitted. Study the origin of this noise and the relevant parameters.
A long string of beads is released from a beaker by pulling a sufficiently long part of the chain over the edge of the beaker. Due to gravity the speed of the string increases. At a certain moment the string no longer touches the edge of the beaker (see picture). Investigate and explain the phenomenon.
4. Fluid bridge
If a high voltage is applied to a fluid (e.g. deionized water) in two beakers, which are in contact, a fluid bridge may be formed. Investigate the phenomenon. (High voltages must only be used under appropriate supervision - check local rules.)
5. Bright waves
Illuminate a water tank. When there are waves on the water surface, you can see bright and dark patterns on the bottom of the tank. Study the relation between the waves and the pattern.
6. Woodpecker toy
A woodpecker toy (see picture) exhibits an oscillatory motion. Investigate and explain the motion of the toy.
7. Drawing pins
A drawing pin (thumbtack) floating on the surface of water near another floating object is subject to an attractive force. Investigate and explain the phenomenon. Is it possible to achieve a repulsive force by a similar mechanism?
8. Bubbles
Is it possible to float on water when there are a large number of bubbles present? Study how the buoyancy of an object depends on the presence of bubbles.
9. Magnet and coin
Place a coin vertically on a magnet. Incline the coin relative to the magnet and then release it. The coin may fall down onto the magnet or revert to its vertical position. Study and explain the coin's motion.
10. Rocking bottle
Fill a bottle with some liquid. Lay it down on a horizontal surface and give it a push. The bottle may first move forward and then oscillate before it comes to rest. Investigate the bottle's motion.
11. Flat flow
Fill a thin gap between two large transparent horizontal parallel plates with a liquid and make a little hole in the centre of one of the plates. Investigate the flow in such a cell, if a different liquid is injected through the hole.
12. Lanterns
Paper lanterns float using a candle. Design and make a lantern powered by a single tea-light that takes the shortest time (from lighting the candle) to float up a vertical height of 2.5m. Investigate the influence of the relevant parameters. (Please take care not to create a risk of fire!)
13. Misty glass
Breathe on a cold glass surface so that water vapour condenses on it. Look at a white lamp through the misted glass and you will see coloured rings appear outside a central fuzzy white spot. Explain the phenomenon.
14. Granular splash
If a steel ball is dropped onto a bed of dry sand, a "splash" will be observed that may be followed by the ejection of a vertical column of sand. Reproduce and explain this phenomenon.
15. Frustrating golf ball
It often happens that a golf ball escapes from the hole an instant after it has been putted into it. Explain this phenomenon and investigate the conditions under which it can be observed.
16. Rising bubble
A vertical tube is filled with a viscous fluid. On the bottom of the tube, there is a large air bubble. Study the bubble rising from the bottom to the surface.
17. Ball in foam
A small, light ball is placed inside soap foam. The size of the ball should be comparable to the size of the foam bubbles. Investigate the ball's motion as a function of the relevant parameters.

Problems for the 24th IYPT 2011

Teheran, Iran

Determine the force necessary to remove a piece of adhesive tape from a horizontal surface. Investigate the influence of relevant parameters.
2. Air drying
Table utensils (dishes, cutlery, etc.), after being washed, dry differently. Investigate how the time of drying depends on relevant parameters.
3. Bouncing flame
Place a flame (e.g. from a Bunsen burner) between two charged parallel metal plates. Investigate the motion of the flame.
4. Breaking spaghetti
Find the conditions under which dry spaghetti falling on a hard floor does not break.
5. Car
Build a model car powered by an engine using an elastic air-filled toy-balloon as the energy source. Determine how the distance travelled by the car depends on relevant parameters and maximize the efficiency of the car.
6. Convection
In a container filled with a liquid, heat transport will occur when the bottom of the container is heated and the top surface is cooled. How does the phenomenon change when the container rotates about its vertical axis?
7. Cup drum
A plastic cup is held upside-down and tapped on its base. Investigate the sound produced when the open end of the cup is above, on or below a water surface.
8. Domino amplifier
A row of dominoes falling in sequence after the first is displaced is a well known phenomenon. If a row of "dominoes" gradually increases in height, investigate how the energy transfer takes place and determine any limitations to the size of the dominoes.
9. Escaping powder
When a hot wire is plunged into a beaker of water with powder (e.g. lycopodium) floating on the surface, the powder moves rapidly. Investigate the parameters that alter the speed of movement of the powder.
When a container filled with small spheres (e.g. mustard seeds) is vibrated vertically with a frequency between 1 - 10 Hz, so called Faraday heaping occurs. Explore this phenomenon.
11. Fingerprints
Fill a glass with a liquid and hold it in your hands. If you look from above at the inner walls of the glass, you will notice that the only thing visible through the walls is a very bright and clear image of patterns on your fingertips. Study and explain this phenomenon.
12. Levitating spinner
A toy consists of a magnetic spinning top and a plate containing magnets (e.g. "Levitron"). The top may levitate above the magnetic plate. Under what conditions can one observe the phenomenon?
13. Light bulb
What is the ratio between the thermal energy and light energy emitted from a small electric bulb depending on the voltage applied to a bulb?
14. Moving cylinder
Place a sheet of paper on a horizontal table and put a cylindrical object (e.g. a pencil) on the paper. Pull the paper out. Observe and investigate the motion of the cylinder until it comes to rest.
15. Slow descent
Design and make a device, using one sheet of A4 80 gram per m2 paper that will take the longest possible time to fall to the ground through a vertical distance of 2.5m. A small amount of glue may be used. Investigate the influence of the relevant parameters.
16. Smoke stream
A glass jar is covered with cellophane. A tightly folded paper tube of length 4-5 cm is inserted hermetically into the jar through the cellophane cover. The tube is oriented horizontally. If one burns the outside end of the tube the dense smoke flows into the jar. Explore this phenomenon.
17. Vikings
According to a legend, Vikings were able to navigate in an ocean even during overcast (dull) weather using tourmaline crystals. Study how it is possible to navigate using a polarizing material. What is the accuracy of the method?

Problems for the 23rd IYPT 2010

Vienna, Austria

1. Electromagnetic cannon
A solenoid can be used to fire a small ball. A capacitor is used to energize the solenoid coil. Build a device with a capacitor charged to a maximum 50V. Investigate the relevant parameters and maximize the speed of the ball.
2. Brilliant pattern
Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the pattern created on a screen. Study and explain the structure of the pattern.
3. Steel balls
Colliding two large steel balls with a thin sheet of material (e.g. paper) in between may "burn" a hole in the sheet. Investigate this effect for various materials.
4. Soap film
Create a soap film in a circular wire loop. The soap film deforms when a charged body is placed next to it. Investigate how the shape of the soap film depends on the position and nature of the charge. Investigate and explain the phenomenon.
5. Grid
A plastic grid covers the open end of a cylindrical vessel containing water. The grid is covered and the vessel is turned upside down. What is the maximal size of holes in the grid so that water does not flow out when the cover is removed?
6. Ice
A wire with weights attached to each end is placed across a block of ice. The wire may pass through the ice without cutting it. Investigate the phenomenon.
Two similar flasks (one is empty, one contains water) are each connected by flexible pipes to a lower water reservoir. The flasks are heated to 100°C and this temperature is held for some time. Heating is stopped and as the flasks cool down, water is drawn up the tubes. Investigate and describe in which tube the water goes up faster and in which the final height is greater. How does this effect depend on the time of heating?
8. Liquid light guide
A transparent vessel is filled with a liquid (e.g. water). A jet flows out of the vessel. A light source is placed so that a horizontal beam enters the liquid jet (see picture). Under what conditions does the jet operate like a light guide?
9. Sticky water
When a horizontal cylinder is placed in a vertical stream of water, the stream can follow the cylinder's circumference along the bottom and continue up the other side before it detaches. Explain this phenomenon and investigate the relevant parameters.
10. Calm surface
When wind blows across a water surface, waves can be observed. If the water is covered by an oil layer, the waves on the water surface will diminish. Investigate the phenomenon.
11. Sand
Dry sand is rather 'soft' to walk on when compared to damp sand. However sand containing a significant amount of water becomes soft again. Investigate the parameters that affect the softness of sand.
12. Wet towels
When a wet towel is flicked, it may create a cracking sound like a whip. Investigate the effect. Why does a wet towel crack louder than a dry one?
13. Shrieking rod
A metal rod is held between two fingers and hit. Investigate how the sound produced depends on the position of holding and hitting the rod?
14. Magnetic spring
Two magnets are arranged on top of each other such that one of them is fixed and the other one can move vertically. Investigate oscillations of the magnet.
15. Paper anemometer
When thin strips of paper are placed in an air flow, a noise may be heard. Investigate how the velocity of the air flow can be deduced from this noise?
16. Rotating spring
A helical spring is rotated about one of its ends around a vertical axis. Investigate the expansion of the spring with and without an additional mass attached to its free end.
17. Kelvin's dropper
Construct Kelvin's dropper. Measure the highest voltage it can produce. Investigate its dependence on relevant parameters.

Problems for the 22nd IYPT 2009

Tianjin, China

1. Stearin engine
A candle is balanced on a horizontal needle placed through it near its centre of mass. When the candle is lit at both ends, it may start to oscillate. Investigate the phenomenon. Maximize the output mechanical power of the system.
2. Coupled compasses
Place a compass on a table. Place a similar compass next to the first one and shake it gently to make the needle start oscillating. The original compass' needle will start oscillating. Observe and explain the behaviour of these coupled oscillators.
3. Resonating modes
Place a mobile phone inside a metallic container with a hole in it. Investigate under what conditions the mobile phone starts to ring after calling it.
4. Ghostly images
When a photo is taken with a flash, bright "disks" may appear as shown in the picture. Investigate and explain the phenomenon.
5. Stop a drip
To prevent dripping from a bottle after pouring, it can be turned slightly. Investigate the motion of the bottle for no drop to fall.
Put a plastic cup on a thin layer of liquid on a flat solid surface. Make the cup rotate. On what parameters does the rotational deceleration of the cup depend?
7. Skateboarder
A skateboarder on a horizontal surface can accelerate from rest just by moving the body, without touching external support. Investigate the parameters that affect the motion of a skateboard propelled by this method.
8. Air pocket
A vertical air jet from a straw produces a cavity on a water surface. What parameters determine the volume and depth of the cavity?
9. Drying
Investigate the drying process of a vertical wet paper sheet. How does the boundary of drying move?
10. Optical tube
Look down a cylindrical metal tube which is shiny on the inside. You will notice dark and light bands. Investigate the phenomenon.
11. Transformers
The "simple transformer law" relates output voltage to input voltage and turns ratio. Investigate the importance of frequency and other parameters in determining the non-ideal behaviour of transformers.
12. Hot ball
Put a hot metal ball on parallel horizontal rails. The ball starts to move. Investigate the phenomenon.
13. Sand ripples
Investigate how the formation of sand ripples under shallow water depends on various parameters.
14. Bouncing drop
Investigate the motion of water droplets falling on a hydrophobic surface (e.g. coated with soot or teflon).
15. Electro-oscillator
A mass is hung from the middle of a horizontal wire. When a current is passed through the wire, the mass may start to oscillate. Describe and explain this phenomenon.
16. Electromagnetic motor
Attach a strong light magnet to the head of a steel screw. The screw can now hang from the terminal of a battery. Completing the circuit by a sliding contact on the magnet causes the screw to rotate. Investigate the parameters that determine the angular velocity of the screw.
17. Corrugation
After traffic has used an unpaved road for some time the surface of the road gets a "wave" structure with a well defined wavelength. Investigate and explain this phenomenon.

Problems for the 21st IYPT 2008

Trogir, Croatia

1. Tipcat
Place a small wooden stick over the edge of a desk. Hit the end of the stick overhanging the table so that it flies away. How is the flight distance related to the relevant parameters? What is the condition for a maximum horizontal distance?
2. Winged seed
Investigate the motion of falling winged seeds such as those of the maple tree.
3. Pin-hole Camera
Study the characteristics of a pin-hole camera and find the conditions for the camera to achieve optimum image quality.
4. Cymbal
Discharging an electronic flash unit near a cymbal will produce a sound from the cymbal. Explain the phenomenon and investigate the relevant parameters.
5. Voltaic cell
Make a voltaic cell using paper tissues as a salt bridge. Study and explain how the electromotive force of this battery depends on time.
6. Liquid stain
When a drop of liquid such as coffee dries on a smooth surface, the stain usually remains at the edge of the drop. Investigate why the stain forms at the edge and what parameters affect the characteristics of the stain.
7. Making a Splash
A solid object is dropped into water from a height of 50 cm. Investigate the factors that would minimize the splash.
8. Astroblaster
When a large ball is dropped, with a smaller one stacked on top of it, onto a hard surface, the smaller ball will often rise much higher than it would if dropped onto the same surface by itself while the larger ball hardly bounces at all. Investigate this phenomenon and design a multiple-ball system, using up to 4 balls, that will reach the greatest elevation of the top ball.
9. Flute
Drill a hole into the side of a tube that is open at one end and produce a sound by blowing the open end. Investigate the pitch and timbre of the sound of your flute and how they depend on the position and the diameter of the hole.
10. Kaye Effect
When a thin stream of shampoo is poured onto a surface, a small stream of liquid occasionally leaps out. This effect lasts less than a second but occurs repeatedly. Investigate this phenomenon and give an explanation.
11. Gutter
When a thin layer of water flows along an inclined gutter different wave patterns are sometimes observed. Study this phenomenon.
12. Geyser
Support a long, vertical tube containing water. Heat the tube directly from the bottom and you will observe that the water erupts. Arrange for the water to drain back into the tube to allow repeated eruptions. Investigate the parameters that affect the time dependence of the process.
13. Spinning ice
Pour very hot water into a cup and stir it so the water rotates slowly. Place a small ice cube at the centre of the rotating water. The ice cube will spin faster than the water around it. Investigate the parameters that influence the ice rotation.
Construct a homopolar electric generator. Investigate the electrical properties of the device and find its efficiency.
15. Gelation
Hot gelatine solution becomes a gel upon cooling. Investigate the electric conductivity as a function of temperature as it gels. Explain the results obtained.
16. Black spoon
Blacken a spoon using a candle flame. If you immerse the spoon in water it appears glossy. Investigate the phenomenon and determine the optical properties of such a "mirror".
17. Heat engine
Build a heat engine powered only by the difference between the day and night air temperatures without using direct sunlight. Determine its efficiency.

Problems for the 20th IYPT 2007

Seoul, Korea

1. Filament
There is a significant current surge when a filament lamp is first switched on. Propose a theoretical model and investigate it experimentally.
Suspend a Slinky vertically and let it fall freely. Investigate the characteristics of the Slinky's free-fall motion.
3. Water jets
What can be observed when two water jets collide at different angles?
Pull a thread through the button holes as shown in the picture. The button can be put into rotating motion by pulling the thread. One can feel some elasticity of the thread. Explain the elastic properties of such a system.
A razor blade is placed gently on a water surface. A charged body brought near the razor makes it move away. Describe the motion of the razor if an external electric field is applied.
6. Rheology
It has been said that if you are sinking in soft mud, you should not move vigourously to try to get out. Make a model of the phenomenon and study its properties.
7. Crickets
Some insects, such as crickets, produce a rather impressive sound by rubbing together two parts of their body. Investigate this phenomenon. Build a device producing a sound in a similar way.
8. Condensation
Water droplets form on a glass filled with cold water. Explain the phenomenon and investigate the parameters that determine the size and number of droplets on the glass.
9. Ink Droplet
Place a droplet of ball pen ink on a water surface. The droplet begins to move. Explain the phenomenon.
10. Steam Boat
A boat can be propelled by means of a candle and metal tubing with two open ends (an example is shown in the picture). Explain how such a boat is propelled and optimize your design for maximum velocity.
11. Water Ski
What is the minimum speed needed to pull an object attached to a rope over a water surface so that is does not sink. Investigate the relevant parameters experimentally and theoretically.
12. Fluid lens
Develop a fluid lens system with adjustable focus. Investigate the quality and possible applications of your system.
13. Balloon
Measure the change of the optical properties of the skin of a balloon during its inflation.
14. Earthquake
Suggest a mechanism that makes buildings resistant to earthquakes. Perform experiments and explain the results.
15. Blowpipe
Investigate the motion of a projectile inside a blowpipe. Determine the conditions for maximum exit velocity when blown by mouth.
Arrange a corrugated drainage pipe, or similar, on an incline. Allow water to flow through the pipe and then carefully stop the flow. Investigate the behaviour of the system when water is dropped into the pipe.
17. Ice Bulge
Fill a plastic tray with water. When frozen, under certain conditions, a bulge can appear on the surface. Investigate this phenomenon.

Problems for the 19th IYPT 2006

Bratislava, Slovakia

1. Froth
Investigate the nature of the decay in height of the "froth" or "foam" on a liquid. Under what conditions does the froth remain for the longest time?
If small non-transparent objects are illuminated with light, patterns in the shadows are observed. What information can be obtained about these objects using these patterns?
3. Duck's cone
If one looks at the wave pattern produced by a duck paddling across a pond, this reminds one of Mach's cone. On what parameters does the pattern depend?
4. Whispering Gallery
The Whispering Gallery at St Paul's Cathedral in London, for example, is famous for the fact that the construction of the circular gallery makes a whisper against its walls on one side of the gallery audible on the opposite side of the gallery. Investigate this phenomenon.
5. Probability
A coin is held above a horizontal surface. What initial conditions will ensure equal probability of heads and tails when the coin is dropped and has come to rest?
6. Wet cleaning
A wet rag is hard to drag when it is spread out and pulled across the floor. What does the resistive force depend on?
7. Airglider
A paper sheet is on a table. If one blows along the table the sheet begins to glide over it. Determine the flight characteristics of the paper.
8. Electrostatics
Propose and make a device for measuring the charge density on a plastic ruler after it has been rubbed with a cloth.
9. Sound and foam
Investigate the propagation of sound in foam.
10. Inverted pendulum
It is possible to stabilise an inverted pendulum. It is even possible to stabilise an inverted multiple pendulum (one pendulum on top of the other). Demonstrate the stabilisation and determine on which parameters this depends.
11. Singing tube
A tube open at both ends is mounted vertically. Use a flame to generate sound from the tube. Investigate the phenomenon.
12. Rolling magnets
Investigate the motion of a magnet as it rolls down an inclined plane.
13. Sound
Measure the speed of sound in liquids using light.
14. Cellular materials
Investigate the behaviour of a stream of fluid when it strikes the surface of a sponge-like material.
15. Heat and temperature
A tube passes steam from a container of boiling water into a saturated aqueous salt solution. Can it be heated by the steam to a temperature greater than 100°C? Investigate the phenomenon.
16. Hardness
A steel ball falls onto a horizontal surface. If one places a sheet of paper onto the surface with a sheet of carbon paper on top of it, a round trace will be produced after the impact. Propose a hardness scale based on this method.
17. Magnetohydrodynamics
A shallow vessel contains a liquld. When an electric and magnetic field are applied, the liquid can start moving. Investigate this phenomenon and suggest a practical application.

Problems for the 18th IYPT 2005

Winterthur, Switzerland

1. Dragonfly
Propose a model of how a dragonfly flies. Investigate the major parameters and validate your model.
2. The two ball problem
Two balls placed in contact on a tilted groove sometimes do not roll down. Explain the phenomenon and find the conditions, under which it occurs.
3. Avalanche
Under what conditions may an avalanche occur? Investigate the phenomenon experimentally.
4. Hydraulic jump
When a smooth column of water hits a horizontal plane, it flows out radially. At some radius, its height suddenly rises. Investigate the nature of the phenomenon. What happens if a liquid more viscous than water is used?
5. Mirage
Create a mirage like a road or desert mirage in a laboratory and study its parameters.
6. Noise
When a droplet of water or other liquid falls on a hot surface, it produces a sound. On what parameters does the sound depend?
7. The bouncing plug
A bathtub or sink is filled with water. Remove the plug and place a plastic ball over the plughole. As the water drains the ball starts to oscillate. Investigate the phenomenon.
8. Windcar
Construct a car which is propelled solely by wind energy. The car should be able to drive straight into the wind. Determine the efficiency of your car.
9. Sound in the glass
Fill a glass with water. Put a tea-spoon of salt into the water and stir it. Explain the change of the sound produced by the clicking of the glass with the tea-spoon during the dissolving process.
10. Flow rate
Combine powdered iron (iron filings) with a vegetable oil. Connect two containers with plastic tubing and allow the mixture to drain through the tube. Develop an external mechanism to control the flow rate of the mixture.
11. Water droplets
If a stream of water droplets is directed at a small angle to the surface of water in a container, droplets may bounce off the surface and roll across it before merging with the body of water. In some cases the droplets rest on the surface for a significant length of time. They can even sink before merging. Investigate these phenomena.
12. Ball spin
Spin can be used to alter the flight path of balls in sport. Investigate the motion of a spinning ball, for example a table-tennis or tennis ball, in order to determine the effect of the relevant parameters.
13. Hard starch
A mixture of starch (e.g. cornflour or cornstarch) and a little water has some interesting properties. Investigate how its "viscosity" changes when stirred and account for this effect. Do any other common substances demonstrate this effect?
14. Einstein - de Haas Experiment
When you apply a vertical magnetic field to a metallic cylinder suspended by a string it begins to rotate. Study this phenomenon.
15. Optical tunnelling
Take two glass prisms separated by a small gap. Investigate under what conditions light incident at angles greater than the critical angle is not totally internally reflected.
16. Obstacle in a funnel
Granular material is flowing out of a vessel through a funnel. Investigate if it is possible to increase the outflow by putting an "obstacle" above the outlet pipe?
17. Ocean "Solaris"
A transparent vessel is half-filled with saturated salt water solution and then fresh water is added with caution. A distinct boundary between these liquids is formed. Investigate its behaviour if the lower liquid is heated.

Problems for the 17th IYPT 2004

Brisbane, Australia

1. Misty
Invent and construct a device that would allow the size of a droplet of a mist to be determined using a sound generator.
2. Stubborn Ice
Put a piece of ice (e.g. an ice cube) into a container filled with vegetable oil. Observe its motion and make a quantitative description of its dynamics.
3. Electric Pendulum
Use a thread to suspend a suitable ball between the plates of a capacitor. When the plates are charged the ball will start to oscillate. What does the period of the oscillations depend on?
4. Dusty Blot
Describe and explain the dynamics of the patterns you observe when some dry dust (e.g. coffee powder or flour) is poured onto a water surface. Study the dependence of the observed phenomena on the relevant parameters.
5. Sea-shell
When you put a sea-shell to your ear you can hear 'the sea'. Study the nature and the characteristics of the sound.
6. Seebeck Effect
Two long metal strips are bent into the form of an arc and are joined at both ends. One end is then heated. What are the conditions under which a magnetic needle placed between the strips shows maximum deviation?
7. Coin
Stand a coin on its edge upon a horizontal surface. Gently spin the coin and investigate the resulting motion as it settles.
8. Pebble Skipping
It is possible to throw a flat pebble in such a way that it can bounce across a water surface. What conditions must be satisfied for this phenomenon to occur?
9. Flow
Using a dc source, investigate how the resistance between two metallic wires dipped into flowing water (or water solution) depends upon the speed and direction of the flow.
10. Two Chimneys
Two chimneys stand on a box with one transparent side. Under each chimney there is a candle. A short period after the candles are lit one flame becomes unstable. Examine the case and present your own theory of what is happening.
11. String Telephone
How do the intensity of sound transmitted along a string telephone, and the quality of communication between the transmitter and receiver, depend upon the distance, tension in the line and other parameters? Design an optimal system.
12. Kundt's Tube
In a 'Kundt's Tube' type of experiment the standing waves produced can be made visible using a fine powder. A closer look at the experiment reveals that the regions of powder have a sub-structure. Investigate its nature.
13. Egg White
White light appears red when it is transmitted through a slice of boiled egg white. Investigate and explain this phenomenon. Find other similar examples.
14. Fountain
Construct a fountain with a 1m 'head of water'. Optimise the other parameters of the fountain to gain the maximum jet height by varying the parameters of the tube and by using different water solutions.
15. Brazil Nut Effect
When a granular mixture is shaken the larger particles may end up above the smaller ones. Investigate and explain this phenomenon. Under what conditions can the opposite distribution be obtained?
16. Small Fields
Construct a device based upon a compass needle and use your device to measure the Earth's magnetic field.
17. Didgeridoo
The 'didgeridoo' is a simple wind instrument traditionally made by the Australian Aborigines from a hollowed-out log. It is, however, a remarkable instrument because of the wide variety of timbres that it produces. Investigate the nature of the sounds that can be produced and how they are formed.

Problems for the 16th IYPT 2003

Uppsala, Sweden

1. Motion of a kite
On windy days one can see kites flying in the wind. Often, one-string kites move an a stable track, which looks like a number 8. Why does a kite move in such a way? Are there other stable tracks?
2. Water drops
Investigate and explain the movement of raindrops on a window pane.
3. Transparent film
If you cover printed text with a piece of transparent polyethylene film you can still easily read it. As you gradually lift up the film, the text becomes increasingly blurred and may even disappear. Study the properties of the film. On what parameters of the film is the phenomenon based?
4. Bright spots
Blow a soap bubble and allow it to rest an a liquid surface or a glass plate. When illuminated by sunlight, bright spots can be observed on the bubble. Investigate and explain the phenomenon.
5. Bubbles at an Interface
Certain liquids can be layered one above the other with a sharp interface between them. If the surface tensions of the liquids are different, then an interesting phenomenon can be observed. Blow bubbles of different sizes into the lower liquid and observe their behaviour near the interface. Investigate and explain the phenomenon.
6. Freezing soft drinks
On opening a container of cold soft (carbonated) drink the liquid inside sometimes freezes. Study the relevant parameters and explain the phenomenon.
7. Oscillating box
Take a box and divide it into a number of small cells with low walls. Distribute some small steel balls between the cells. When the box is made to oscillate vertically, the balls occasionally jump from one cell to another. Depending on the frequency and the amplitude of the oscillation, the distribution of the balls can become stable or unstable. Study this effect and use a model to explain it.
8. Heat engine
Construct a heat engine from a U-tube partially filled with water (or another liquid), where one arm of the tube is connected to a heated gas reservoir by a length of tubing, and the other arm is left open. Subsequently bringing the liquid out of equilibrium may cause it to oscillate. On what does the frequency of the oscillation depend? Determine the pV diagram of the working gas.
9. Falling chimney
When a tall chimney falls it sometimes breaks into two parts before it hits the ground. Investigate and explain this.
10. Tungsten lamp
The resistance of the tungsten filament in a light bulb shows a strong temperature dependence. Build and demonstrate a device based on this characteristic.
11. Light scattering
Construct an optical device for measuring the concentration of non-soluble material in aqueous colloid systems. Use your device to measure the fat content of milk.
12. Boiled egg
Construct a torsion viscometer. Use it to investigate and explain the differences in the 'viscous' properties of hens' eggs that have been boiled to different extents.
13. Electro-osmosis
Develop a device that will drain wet sand, with the aid of an electrical voltage but without significant heating.
14. Rotating disk
Find the optimum way of throwing a 'frisbee' as far as possible. Explain your findings.
15. Vortices
Make a box that has a hole in its front wall and a membrane as its back wall. Hitting the membrane creates a vortex that propagates out from the hole. Investigate the phenomenon and explain what happens when two vortices interact.
16. Pot and ice
It is sometimes argued that to cool a pot effectively one should put ice above it. Estimate to what extent this is more effective than if the ice is put under the pot.
17. Prometheus Problem
Describe and demonstrate the physical mechanism, based on friction, which allowed our ancestors to make fire. Estimate the time needed to make fire in this way.

Problems for the 15th IYPT 2002

Odessa, Ukraina

1. Heat engine
A tall glass cylinder is half-filled with hot water and topped up with cold water. A small ampule, containing a few drops of ether or alcohol (and closed off by a rubber pipette cap), is then put in. Describe the phenomena occurring in the system. How does the motion of the ampule change with time?
2. Spider's web
A spider's thread looks like a string of pearls. What is the reason for this? Make experiments to investigate the relevant parameters.
3. Flying colours
Why do flags flutter in the wind? Investigate experimentally the airflow pattern around a flag. Describe this behaviour.
4. Hazy
The colour of a distant forest appears not green, but hazy blue. What is the minimum distance at which this phenomenon is observed? How do weather conditions affect this? Is it possible that a forest can appear grey?
5. Pond-skater
It is known that unwettable small bodies can float on water due to the surface tension force. Construct a floating raft based on this principle and calculate its static and dynamic parameters.
6. Stop and start
Sometimes a flow of traffic can experience sudden stops and starts for no apparent reason. Build a physical model to explain why this occurs.
7. Ohm's Law for a liquid
It is often said that electric current "flows". Is this the only analogy between electric current and the flow of a liquid? Investigate theoretically and experimentally other analogies between these two things.
8. Charged sand
Fine, well-dried quartz sand is poured out of a short thin tube into a conical metallic vessel connected to an electrometer. Investigate the behaviour of the sand stream as the vessel fills up. What changes if the stream is lit by a UV-lamp?
9. Chromatography
Put a drop of coloured liquid on a piece of absorbant paper. Describe quantitatively the observed phenomena.
10. Sound cart
Construct and demonstrate a device that can be propelled solely by sound. Investigate its properties.
11. Equilibrium
Fill a glass with water up to the point where a convex meniscus is formed. Place a table tennis ball on the surface of the water. Investigate and explain the stability of its equilibrium. Repeat your experiment with other liquids?
12. Electroconductivity
How can you measure the electroconductivity of salt solutions without using direct contact electrodes? Analyse the problem and demonstrate your device.
13. Spinning ball
A steel ball of diameter 2-3 cm is put on a horizontal plate. Invent and construct a device, which allows you to spin the ball at high angular velocity around a vertical axis. The device should have no mechanical contact with the ball.
14. Torn sail
Determine the dependence of the efficiency of a sail on its degree of perforation. What would be the effect of using a fishing net as a sail?
15. Pulsating air bubble
Trap an air bubble of radius 1-2 cm under an inverted watch glass beneath a water surface. Introduce alcohol into the bubble through a thin tube, controlling and adjusting the rate of flow until the bubble pulsates rhythmically. Study the phenomenon and explain your observations.
16. Elastic pendulum
Study and describe the behaviour of a pendulum where the bob is connected to a spring or an elastic cord rather than to a stiff rod.
17. Bottle battle
Take two opened glass bottles of cola and knock one against the other. After a short while, the cola spurts out of one of the bottles. Investigate and explain the phenomenon.

Problems for the 14th IYPT 2001

Espoo, Finland

1. Electrostatic motor
Is it possible to create a motor which works by means of an electrostatic field? If yes, suggest how it may be constructed and estimate its parameters.
2. Singing saw
Some people can play music on a handsaw. How do they get different pitches? Give a quantitative description of the phenomenon.
3. Tuning dropper
Make the music resonator shown in the picture. Investigate the conditions that affect the pitch. Can you observe amplification of external sounds? If yes, how can you explain this?
4. Dancing sand clock
Investigate the trickling of sand when a sand clock (egg-timer) is placed on a vibrating base.
5. Rubber heat machine
Investigate the conversion of energy in the process of deformation of rubber. Construct a heat machine, which uses rubber as the working element and demonstrate how it works.
6. Fractal diffraction
Produce, demonstrate and analyse diffraction pictures of fractal structures of different orders.
7. Cracks
When drying a starch solution, you will see cracks forming. Investigate and explain this phenomenon.
8. Speedometer
Two electrodes of different metal are immersed in an electrolyte solution. Investigate the dependence of the measured potential difference on the relative motion of electrodes and their shapes.
9. Pouring out
Investigate how to empty a bottle filled with a liquid as fast as possible, without external technical devices.
10. Water stream pump
Construct and demonstrate a water stream vacuum pump. What is your record value for the minimum pressure?
11. Rolling balls
Place two equal balls in a horizontal, V-shaped channel, with the walls at 90 degrees to each other, and let the balls roll towards each other. Investigate and explain the motion of the balls after the collision. Make experiments with several different kinds of ball pairs and explain the results.
12. Reaction
Make an aqueous solution of gelatine (10g gelatine in 90ml of water), heat it to 80 degrees C in a water bath and mix it with a solution of potassium iodide. Pour the solution in a test tube and cool it. Pour a solution of copper sulphate on the surface of the gel. Find a physical explanation to the observed phenomena.
13. Membrane electrolyser
In an electrolyser, containing a membrane which completely divides the space between two inert electrodes, the pH-value of the diluted salt solution will change substantially after electrolysis. Investigate how this difference depends on the pore size of the membrane.
One end of a thread is immersed in a vessel filled with water. The other end hangs down outside without contact with the outer wall of the vessel. Under certain conditions, one can observe drops on that end of the thread. What are those conditions? Determine how the time of appearance of the first drop depends on relevant parameters.
15. Bubbles in magnetic field
Observe the influence of an alternating magnetic field (50 or 60 Hz) on the kinetics of gas bubbles in a vessel filled with water. The bubbles can be generated by blowing air into the water.
Investigate and explain the light produced, when adhesive tape is ripped from a smooth surface.
17. Seiches
Seiching is a phenomenon shown by long and narrow deep lakes. Due to changes in atmospheric pressure, the water of the lake can start moving in such a way that its level at both ends of the lake makes periodic motions, which are identical, but out of phase. Make a model that predicts the period of seiching (depending on appropriate parameters) and test its validity.

Problems for the 13th IYPT 2000

Budapest, Hungary

1. Invent for yourself
Suggest a contact-free method for the measurement of the surface tension coefficient of water. Make an estimate of the accuracy of the method.
2. Tuning fork
A tuning fork with resonant frequency of about 100 Hz is struck and held horizontally, so that its prongs oscillate up and down. A drop of water is placed on the surface of the upper prong. During the oscillation of the tuning fork standing waves appear on the surface of the drop and change with time. Explain the observed phenomena.
3. Plasma
Investigate the electrical conductivity of the flame of a candle. Examine the influence of relevant parameters, in particular, the shape and polarity of the electrodes. The experiments should be carried out with a voltage not exceeding 150V.
4. Splash of water
Measure the height reached by splashes of water when a spherical body is dropped into water. Find a relationship between the height of the splashes, the height from which the body is dropped, and other relevant parameters.
5. Sparkling water
Bubbles in a glass of sparkling water adhere to the walls of the glass at different heights. Find a relationship between the average size of the bubbles and their height on the side of the glass.
6. Transmission of signals
Using a bulb, construct the optimum transmitter of signals without any modulation of the light beam between transmitter and receiver. Investigate the parameters of your device. The quality of the device is defined by the product of the information rate (bits/sec) and the distance between transmitter and receiver.
7. Merry-go-round
A small, light, ball is kept at the bottom of a glass filled with an aqueous solution and then set free. Select the properties of the solution, so that a moving up time of several seconds is achieved. How will this time change if you put your glass on the surface of a rotating disk?
8. Freezing drop
Drops of melted lead or tin fall from some height into a deep vessel filled with water. Describe and explain the shape of the frozen drops as a function of height of fall.
Use efficient methods to collect as much radioactive material as you can in a room. Measure the half-life of the material you have collected.
10. Liquid fingers
When a layer of hot salt solution lies above a layer of cold water, the interface between the two layers becomes unstable and a structure resembling fingers develops in the fluid. Investigate and explain this phenomenon.
11. Throwing stone
A student wants to throw a stone so that it reaches the greatest distance possible. Find the optimum mass of the stone that should be used.
12. Tearing paper
Tear a sheet of paper and investigate the path along which the paper tears.
13. Rolling can
A can partially filled with water rolls down an inclined plane. Investigate its motion.
14. Illumination
Two bulbs, 100 and 40 watts, respectively, illuminate a table tennis ball placed between them. Find the position of the ball, when both sides of the ball appear to be equally lit. Explain the result.
15. Cooling water
Two identical open glasses, filled with hot and warm water, respectively, begin to cool under normal room conditions. Is it possible that the glass filled with hot water will ever reach a lower temperature than the glass filled with warm water? Make an experiment to investigate this and explain the result.
16. Coloured sand
Allow a mixture of differently coloured, granular materials to trickle into a transparent, narrow container. The materials build up in distinct bands. Investigate and explain this phenomenon.
17. A strange sound
Pour hot water into a cup containing some cappuccino or chocolate powder. Stir slightly. If you then knock the bottom of the cup with a teaspoon you will hear a sound of low pitch. Study how the pitch changes when you continue knocking. Explain the phenomenon.

Problems for the 12th IYPT 1999

Vienna, Austria

1. Rotation
A long rod, partially and vertically immersed in a liquid, rotates about its axis. For some liquids this causes an upward motion of the liquid on the rod and for others, a downward motion. Explain this phenomenon and determine the essential parameters on which it depends.
2. Ionic Motor
An electrolyte (an aqueous solution of CuSO4, NaCl, ...) in a shallow tray is made to rotate in the field of a permanent magnet (a small "pill" placed under the tray). An electric field is applied from a 1.5 V battery in such a way that one electrode is in the form of a conducting ring immersed in the electrolyte - the other is a tip of a wire placed vertically in the centre of the ring. Study the phenomenon and find possible relationships between the variables.
3. Magic Motor
Construct a DC motor without a commutator, using a battery, a permanent magnet and a coil. Explain how it functions.
 Sketch of experimental setup Photography of setup
4. Soap Film
Explain the appearance and development of colours in a soap film, arranged in different geometrical ways.
5. Dropped Paper
If a rectangular piece of paper is dropped from a height of a couple of meters, it will rotate around its long axis whilst sliding down at a certain angle. What parameters does the angle depend on?
6. Singing Glass
When rubbing the rim of a glass containing a liquid a note can be heard. The same happens if the glass is immersed in a liquid. How does the pitch of the note vary depending on different parameters?
7. Heated Needle
A needle is hanging on a thin wire. When approached by a magnet, the needle will be attracted. When heated, the needle will return to its original position. After a while the needle is attracted again. Investigate this phenomenon, describe the characteristics and determine the relevant parameters.
8. Energy Converter
A body of mass 1 kg falls from a height of 1 m. Convert as much as possible of the released potential energy into electrical energy and use that to charge a capacitor of 100 µF.
9. Air Dryer
During a time span of 4 minutes collect as much water as possible from the air in the room. The mass of the equipment must not exceed 1 kg. Its initial temperature should be equal to ambient (room) temperature. The water should be collected in a glass test tube, provided by the jury.
10. Charged Balloon
An air-filled balloon rubbed with wool or dry paper may stick to the ceiling and stay there. Investigate this phenomenon and measure the charge distribution on the surface of the balloon.
11. Billiard
Before a pool-billiard game starts, 15 balls form an equilateral triangle on the table. Under what conditions will the impact of the white ball (16th ball) produce the largest disorder of the balls?
12. Flour Craters
If you drop a small object in flour, the impact will produce a surface structure which looks like a moon crater. What information about the object can be deduced from the crater?
13. Gas Flow
Measure the speed distribution of the gas flow in and around the flame of a candle. What conclusions can be drawn from the measurements?
14. Wheat Waves
The wind blowing through a wheat field creates waves. Describe the mechanism of the wave formation and discuss the parameters which determine the wavelength.
15. Bright Spots
Bright spots can be seen on dew drops if you look at them from different angles. Discuss this phenomenon in terms of the number of spots, their location and angle of observation.
16. Liquid Diode
Make an electrochemical diode and investigate its properties, in particular the frequency dependence.
17. Sound from Water
When you heat water in a kettle you hear a sound from the kettle before the water starts to boil. Investigate and explain this phenomenon.

Problems for the 11th IYPT 1998

Donaueschingen, Germany

1. Invent yourself
Construct an aeroplane from a sheet of paper (A4, 80 g/m^2). Make it fly as far and/or as long as possible. Explain why it was impossible to reach a greater distance or a longer time.
2. Popping body
A body is submerged in water. After release it will pop out of the water. How does the height of the pop above the water surface depend on the initial conditions (depth and other parameters)?
3. Spinning disc
Investigate and explain the phenomenon of spinning annular disc as they progress down a straight, cylindrical rod. If the rod is moved upwards at a defined velocity, the disc spins at constant height. Investigate the mechanism.
4. Water streams
A can with three holes in the side-wall at the same height slightly above the bottom is filled with water. The water will escape in three separate streams. By gently touching the streams with a finger they may unite. Investigate the conditions for this to happen.
5. Water jet
If a vertical water jet falls down onto a horizontal plate, standing waves will develop on the surface of the jet. Investigate the dependence of this phenomenon on different parameters.
6. Mount Everest
Can you see Mount Everest from Darjeeling?
7. Air bubble
An air bubble rises in a water-filled, vertical tube with inner diameter 3 to 5 mm. How does the velocity of the rising bubble depend on its shape and size?
8. Trick
It is known that a glass filled with water and covered with a sheet of paper may be turned upside down without any loss of water. Find the minimum amount of water to perform the trick successfully.
9. Woven textiles
Look at a point-like light source through different woven textiles. Describe what you see. What is the explanation of the phenomenon?
10. Repeated freezing
While a vessel filled with an aqueous solution of a volatile fluid, e.g., ammonia, ethanol or acetone, is being cooled, repeated freezing and melting may be observed near the surface. Describe and explain the phenomenon.
11. Current system
In a Petri dish (shallow bowl), small metal balls, e.g., 2 mm in diameter, are immersed in a layer of castor oil. The inner rim of the dish contains an earthed metal ring. Above the centre of the dish there is a metal needle which does not touch the oil surface. Investigate what happens when the voltage between needle and earth is about 20 kV.
Warning: The high voltage should be obtained by means of a safe generator, e.g., an electrostatic generator!
12. Powder conductivity
Measure and explain the conductivity of a mixture of metallic and dielectric powders with various proportions of the two components.
13. Rope
How is it possible that a very long and strong rope can be produced from short fibers? Prepare a rope from fibers and investigate its tensile strength.
14. Water rise
Immerse the end of a textile strip in water. How fast does the water rise in the strip and what height does it reach? In which way do these results depend on the properties of the textile?
15. Luminescent sugar
Investigate and explain the light produced when sugar crystals are pulverized. Are there other substances with the same property?
16. Strange motion
Make a mixture of ammonium nitrate and water, proportion 5 to 1. When the mixture is heated to about 100 deg C it melts. When it cools, it crystallizes and you may observe a strange motion below the surface. Investigate and explain the phenomenon.
Safety rules: Do not heat the ammonium nitrate without water, preferably use a water bath! Use protection glasses during the experiment!
17. Icicles
Investigate and explain the formation of icicles.

Problems for the 10th IYPT 1997

Cheb, Czech Rebublic

1. Invent yourself
Construct and demonstrate a device which moves in a definite direction under chaotic influence.
2. Coin
From what height must a coin with heads up be dropped, so that the probability of landing with heads or tails up is equal?
3. Paper
How does the tensile strength of paper depend on its humidity?
4. Electron Beam
An electron beam is cast upon a planparallell plate of known homogenous material. Some of the electrons get through it, some do not. Try to simulate processes taking place, e.g. using Monte Carlo method and compare your results with the ones described in literature.
5. Blue Blood
Human blood is known to be red, but the veins seem to be blue. Explain this phenomenon and illustrate it by a model.
6. Magic Tube
A compressor blows air into Ranque-Hilsch T-shaped tube at a pressure of 0,5 Mpa or higher so that the air begins to circulate. In such a case hot air is coming out from one end of the tube and cold air from the opposite one. Find out which end of the tube is the "hot" one and explain the difference of the temperatures obtained. Investigate the parameters this difference depends on.
7. Water Jet
A water jet streaming vertically downwards from a tube is divided into drops at some distance from the tube. Choose the conditions under which the length of the unseparated jet is largest. What maximum length did you obtain?
8. Floatation
A piece of chocolate, which is dropped into a glass of soda water, periodically sinks and goes back to the surface. Investigate the dependence of the period of these oscillations on various parameters.
A water jet falling onto a horizontal plane spreads out radially. At some distance from the center the thickness of the layer increases dramatically. Explain the phenomenon.
10. Cooling the Earth
How would the temperature of the Earth change with time, if the Sun suddenly stopped radiating?
11. Candle Generator
Construct a device for charging an electric capacitor (1000 nF / 100 V) using the energy of a candle burning for a period of one minute.
12. Static Friction
A force of motion friction is known to be independent on the rubbing surface area of a body. How does the static friction depend on the rubbing surface area?
13. Tea Cup
If one fills a cup with hot tea (60 °C - 80 °C), a thin layer of steam emerges above the surface. One can see that some parts of the steam layer disappear suddenly and reappear after a few seconds. Investigate and explain this phenomenon.
14. Rain
On a long-time exposure photograph of night rain taken in the light of a projector, the tracks of drops appear interrupted. Explain this phenomenon.
15. Cell and Accumulator
How does the voltage-current characteristics of a cell and of an accumulator change during discharging?
16. Roget's Spiral
The Roget's Spiral is a device where a source of current is connected to a vertically suspended spring, the lower end of which dipped into mercury. Mercury is a highly dangerous chemical substance and thus the experiments with it are not permitted. Substitute the mercury with a less dangerous substance and investigate the functioning of this device.
17. Leap
To make a leap it is necessary to squat. How does the height of a leap depend on the depth of the squat?

Problems for the 9th IYPT 1996

Kutaissi, Georgia

1. Invent yourself.
Invent and solve yourself a problem concerning the ozone holes.
2. Paper clot.
Crumple arbitrarily a sheet of paper A4 in your hand. This clot can be approximated by a sphere. Making many of this clots and measuring their average diameters a histogram of distribution of diameters can be plotted. Try to explain the result obtained. Make more comprehensive investigation of the dependence of the average diameter of a clot on the parameters which you consider important.
3. Cycle racing
According to the forecast of specialists two very strong and "absolutely identical" sportsmen had to show equal time in a highway race for 100 km. But, alas, one sportsman lagged behind. Later it was found out that some malefactor adjusted a nut of mass 5 g to the rim of the rear wheel of his bicycle. For what time is the victim?
4. Self formation of a pile.
A horizontal rigid plate vibrates vertically at a frequency of the order of 100 Hz. A cone-shaped pile of fine dispersed powder (e.g. lycopod or talc) which is heaped up on the plate remains stable at small amplitudes of the vibration. If the amplitude is increased the cone decays. Further increase of the amplitude yields a distribution confined by a sharp border and at still higher amplitudes a pile appears again. Investigate and explain this phenomenon.
5. Auto oscillations.
Produce and investigate auto oscillating system containing thermistor as a single non-linear element.
6. Water generator.
If some volume of water is frozen from one side, a potential difference appears across the ice-water frontier. Measure this potential difference and explain the phenomenon.
7. Sun.
In the centre of the Sun suddenly an extra quantity of energy is produced which is equal to the energy emitted by the Sun per year. How will the parameters of the Sun observed on the Earth change during one year?
8. Surface Information.
Develop a method for transferring information by the waves on the surface of water. Investigate the angular characteristics of the emitter and the receiver ( the antennas ) which you constructed.
9. Floor-polisher.
A device stands on two identical disks lying flat on a horizontal surface. The disks can rotate in opposite directions at a given velocity. Investigate how the value of a force providing a uniform motion this device along a horizontal plane depends on the velocity of this motion and the velocity of rotation of these disks.
10. Soap bubbles.
Dip the ring of a children's toy for blowing out soap bubbles into a soap solution and blow on the film formed in the ring. At what velocity of the air flux blown into the ring will the bubbles form? How must the velocity of the air flux be adjusted to produce the bubble of maximum size?
11. Candle
Some candles twinkle before dying out. Investigate and explain this phenomenon.
12. Motor car.
A car driven at constant power moves onto a wet section of a straight road. How will its speed change when the thickness of the water layer increases slightly and linearly with the distance?
13. Grey light.
Construct a source of light which would seem to be grey.
14. Coherer.
It is known that a glass tube with two electrodes and metallic filings between them (coherer) has different resistance in d.c. and a.c. circuits. Investigate the frequency dependence of the coherer's resistance.
15. Salt water oscillator.
A cup with a small hole in its bottom containing salt water is partially immersed in a big vessel with fresh water and fixed. Explain the mechanism of the observed periodical process and investigate the dependence of its period on different parameters. To visualize the process, the water in the cup should be coloured.
16. Hail
Explain the mechanism of hail formation and propose your own method to prevent the hailing.
17. Gloves
Some people refuse to wear gloves in winter because they suppose to feel colder than without gloves. Others prefer to wear mittens instead. What is your opinion?

Problems for the 8th IYPT 1995

Spala, Poland

1. Think up a problem yourself (paradox)
2. Boiling water
Some people say it is important to put a lid on the pot when you want to boil water for tea to save energy and time. Investigate this phenornenon and determine the energy and time saving.
3. Drop
A drop of salted water drying on a smooth surface creates a system of rings. Investigate and explain this phenomenon.
4. Gravitational spacecraft
A spacecraft (having a shape of a dumb-bell of variable length) can shift from the Earth orbit (300 km above the Earth surface) to the Moon orbit without the use of jets. Calculate the time taken by such a manoeuver.
5. Sound
Transfer the electric energy stored in a capacitor of 0.1 mF charged to the voltage of 30 V into the energy of the sound, with the highest efficiency possible. No external energy sources are allowed. Determine the fraction of energy converted into sound in the discharge.
6. Curtain
A light curtain (light scatters on dust particles) is used in some theatres. Suggest the design of a light curtain, which allows its effective action with the minimum power supplied for one meter of stage width?
7. Three discs
Investigate collisions of three homogeneous, rigid discs which can move in a plane. At first two discs are at rest. The third disc:
a) collides at exactly the same time with two other discs,
b) collides at first with one of the discs.
8. Carpet
When a carpet is rolled into a cylinder it sometimes unrolls by itself or with the help of a gentle push. Determine the factors on which the speed of the rolling carpet depends.
9. Ice cream
Obtain super-cooled water in an experimental setup. By how many degrees below 0°C did you manage to super-cool it? What can be the record in this experiment? Determine the freezing point of water.
10. Cathode -ray tube
While a well-known physicist A. First watched a football match by TV, another well-known physicist B. Second made a hole of diameter 0.001 mm in the cathode-ray tube. Did A. First manage to see the football match up to the end?
11. Moon light
It is possible to set paper on fire using a lens and solar radiation. Could it be possible using lunar instead of solar light? If yes - invent an optimal optical system for such a purpose. If not - what should the Moon be like, for being this possible?
12. Tinder box
When someone strikes two pieces of flint rock, sparks are created. Investigate and explain this phenomenon.
13. Air lens
Lenses are usually made of solids and sometimes made of liquids. Construct an optical lens made of air in such a way that light can travel through the lens without crossing any material but air. Determine on which factors the focal length of an air lens depends.
14. Frozen lake
The water surface of a lake is in winter exposed to cold air at a fixed temperature below zero. There is no wind. Determine the thickness of the ice layer, as a function of time.
15. Bottle
A plastic bottle of a capacity between 1 and 2 litres completely filled with water is "accidentally" dropped on the floor from the height H = 1 m. What maximum height can the spray reach and why? Determine the minimal height from which the bottle should be dropped to burst?
16. Oscillation of plates
Water has been poured on a horizontal glass plate and a second glass plate placed on it. If the lower plate is oscillating in a horizontal plane, at certain amplitudes and frequencies, the upper plate begins to oscillate in vertical direction. Investigate and describe this phenomenon. Is there any difference when you use another liquid?
17. Epic Hero
An epic Russian hero Ilya Muromets had once thrown his mace weighing forty poods (1 pood = 16 kg) and in forty days this mace fell at the same place. Estimate the parameters of the throw of the hero.

Problems for the 7th IYPT 1994

Netherlands

Think up a problem yourself
(problems 1, 2, 3) Invent yourself and solve a problem on the given theme
1. Optics
Think up and solve a problem connected with employing a thin lens of a large focal length.
2. Compass
"In sledge trips we use liquid compasses, the most exact of the small ones. But you understand of course that due to proximity to the magnetic pole the arrow usually points downwards. To make it horizontal, its opposite end is balanced with a weight". (From the letter of Cherry-Garrad, member of the last expedition of R. Scott.) Use the context of this quotation to formulate a problem.
3. Magnetization
A cylindrical permanent magnet falling inside a copper tube is found to move at an almost constant velocity, the slower the thicker and the walls of the tube. Use this fact to formulate a problem (See also 14).
Gravitation machine
(problems 4, 5, 6). A horizontal plate (a vibrator) oscillates harmonically up and down. A steel ball put an the surface of the plate starts jumping higher or lower. For the experimental device one may successfully use a ferrite core in a coil connected to an alternating current generator (a sound generator). The butt-end of the ferrite core will play the part of the vibrating horizontal plane. Steel balls of diameter 1 or 2 mm are suitable for the experiment. The glass tube approximately 1m long can also be very helpful.
1. Upper boundary
Measure experimentally the maximum height to which the ball rises to and explain the result.
2. Distribution function
Determine experimentally what part of a sufficiently large time interval the ball is in the range of heights H, H+ dH and explain the result.
3. Acceleration
The mechanical energy of the ball changes after every impact. The mean mechanical energy (averaged over all successive impacts) increases at the beginning of the process and then tends to a constant value. Try to obtain experimentally the time dependence of the mean mechanical energy of the ball.
4. Aspen leaf
Even in windless weather aspen leaves tremble slightly. Why does an aspen leaf tremble?
5. Superball
A highly elastic ball (a superball) falls on a horizontal surface from a small height (4cm or less) and recoils several times. What is the number of impacts of the superball against a table?
6. Meteorite
A meteorite of mass 1000 tons flies directly to the sun. Can modern instruments register the fact of its fall on the Sun?
7. Water dome
A vertical water jet falls on the butt-end of a cylindrical bar and creates a bell-like water dome. Explain this phenomenon and evaluate the parameters of the dome.
8. Siphon
A rubber tube is used as a siphon to flow water from one vessel into another. The vessels are separated by a high partition and the levels of water in them are different. If one withdraws the tube from one vessel, lets the pole of air enter it and then puts the tube into the water again, the action of the siphon may be resumed or not. Investigate this phenomenon.
9. Boiling
Put a metallic ball heated to the temperature 150°C - 200°C into hot water at the temperature close to 100°C and observe the process of intensive evaporation of the water. Explain the observed phenomenon.
10. Spirits
A closed vessel (a bottle) contains spirits - pure or substantially diluted by water. Suggest a method of estimation of the concentration of spirits without opening the vessel.
11. Magnetic friction
To investigate the phenomenon described in the problem 3 we suggest to create the device containing the following elements:
1. a copper plate (or a set of plates) 0.3 to 15 mm thick. The length and the width of the plate may be chosen according to one's convenience, but they should be large enough to avoid the effect of the boundaries;
2. a cylindrical electromagnet with a flat butt-end;
3. a device providing free motion of the flat butt-end of the electric magnet over the horizontal surface of the copper plate. It is very important that the gap between the magnet and the plate is small as possible and constant everywhere;
4. the push providing the uniform motion of the magnet at a given velocity over the plate surface.
Introduce the following notation: T - the push (and the force of magnetic friction), v - the velocity of the magnet, h - the thickness of the plate. Investigate and determine experimentally the dependence of T on h at v = constant for several values of v.
12. Transmission of energy
Transmit without wires to a distance of 3 meters the largest possible part of the energy stored in a capacitor having capacity of C = l0µF charged to voltage U = 100V. Measure this energy. Your device should not contain energy sources. Naturally the capacitor itself must not be transported.
13. The Moon and the Sun
"If you are asked what is more important, The Sun or the Moon, you should answer the Moon. For the Sun shines in daytime when there is enough light without it", says a joke. When is it possible to see the Sun and the Moon at the same time? Calculate the schedule of the events for the European countries during 1994.
14. Straw
The Russian proverb says "Had I known the place where I fell, I would have laid some straw there". How much straw should be laid to guarantee a safe fall?