Problèmes du FPT 2020

La liste des problèmes du tournoi international est disponible : http://2020.iptnet.info/problems/

Liste des sujets

1. Cumulative cannon

How high may a ping-pong ball jump using the setup on the video? What is the maximal fraction of the total kinetic energy that can be transferred to the ball? https://youtu.be/mPOcFSHyd9o?t=478

3. Papper tube

Roll a long paper strip into a tight tube and put it vertically on a table. Why does it often unwind in jerks? What determines the period of the jerks? https://youtu.be/G3yzSMLMRds

5. Whirlpool in a bottle

When an open bottle of water is turned upside down and slightly rotated, a whirlpool is formed. What are its characteristics? How fast can the bottle be emptied that way? What will change if the bottle is filled with sand instead? https://youtu.be/J207s0zk6Kg

6. Planetary clock

Propose the most accurate clock that measures time with a temporal resolution of a minute or less using the rotation of the Earth. The clock design should allow calibrating the clock to work even on a different  planet. With what certainty will your clock show the correct time after one year?

9. Optical compass

Bees locate themselves in space using their eyes’ sensitivity to light polarization. Design an inexpensive optical compass using polarization effects to obtain the best accuracy. How would the presence of clouds in the sky change this accuracy?

11. Flat fog

After pouring liquid nitrogen into a mug, you will notice that the mug starts to cast a mist. The mist’s border is a clearly marked thin plane at a certain height from the mug. Investigate the phenomenon.

12. Resonating glasses

When you take two glasses between your fingers, they sometimes emit a particular sound containing a frequency sweep. Investigate the phenomenon. https://youtu.be/AIZkIfoQhIU

13. Pickle night light

If you pass current from a conventional household wall socket through a pickle it will glow. Investigate this effect, including the effect of alternating current, and the use of multiple pickles in a chain. What is the mechanism (and time) for a pickle to die out?

Be very careful not to confuse the pickles with your fingers!

https://youtu.be/aab8VjzuXyM?t=39, https://youtu.be/axbAvYK9Hcw

14. Jumping bean

A simple toy called a “jumping bean” can be constructed by putting a metal ball inside of a pill capsule. Placed on an inclined surface at a certain inclination, the jumping bean will tumble down in a rather surprising way, seemingly standing up-right, flipping end to end, instead of rolling.  Investigate its motion. Find the dimensions of the fastest and slowest beans for a given inclination. https://youtu.be/Azb9bDktZVc

15. Wobbly vortex rings

It is known that a vortex cannon with a non-circular aperture may produce oscillating smoke rings. Investigate the ring shape dynamics.  https://youtu.be/N7d_RWyOv20?t=190

16. Little soldiers

Investigate and explain the phenomenon whereby metal chips, initially resting on a flat surface, suddenly arrange vertically as the support begins to vibrate intensively.