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3. Series 25. Year - 2. river ride

Lock is placed in a dam on a river in order for ships to be able to pass through. Assume the river has a flow rate of $Q=200m⁄s$ and that the lock connects places with height difference $H=4\;\mathrm{m}$ and has dimensions $s=100\;\mathrm{m}$, $d=20\;\mathrm{m}$. How many ships per day can this lock transport from the lower place to the higher place if the maximum flow rate in and out of the lock is $Q_{Z}=250m⁄s?$

Napadlo Michala při čtení tajného časopisu.

5. Series 24. Year - 1. warm up


  • blood sedimentation

Given a test tube full of human blood, how long does it take for the red cells to settle at the bottom (the so called blood sedimentation)? The usual method for such a measurement is to let the blood cells settle for an hour and than to measure the height of the cells that are already at the bottom (usually about 10 mm). We are interested in an approximate calculation. You may need to use the Stoke's relation $F=6$ π η r v$ and the value of dynamical viscosity of blood plasma $η$ = 2 Ns/m²$$.

  • different eyes

Aleš was sitting in a tram and the Sun was about 60° to the left. Because he was staring at a hot blond in front of him one of his eyes was in the shadow of his nose. When the blond noticed he was staring at her he turned his eyes to the right and he found out that he saw different color shades in each of his eyes. Describe the difference between the shades he observed with his left eye compared to his right eye. Why did this happen?

archive, Aleš

4. Series 24. Year - 3. Old clock

Design a shape for a sandglass so that the dependance of the height of sand on time is linear. If you do not neglect friction etc. you can gain some extra points.

from Nečada couple

4. Series 24. Year - 4. Home alone

Terka was playing around and spilled five liters of liquid nitrogen in her room. Couple days later she bought five liters of gasoline, brought it to her room and burned it. Could this playing around result in her being sick? To be more concrete describe the change in the temperature, pressure and oxygen concentration in her room (in both cases) if it is perfectly isolated and has dimensions 3$x3x4\;\mathrm{m}$.


3. Series 24. Year - 1. Warm-Up


  • Dr. Nec.

There are two ways to measure the amount of wood in a pile of trees. Either as the volume of pure wood in the pile or as the volume of wood together with the empty spaces in the pile. Find the conversion factor between these two units assuming the trees are cylinders of radius $r$ that are layed one on top of the others.

  • Bubbles.

A spherical cap of radius $r$ is made by blowing air into a circular surface of soap water. Estimate the velocity of air molecules hitting the surface?


3. Series 24. Year - P. Water, water and water

There are many interesting properties of water that other liquids do not possess. Some of them are listed at martin.chaplin/anmlies.html. Think of some consequences of these anomalies for the life on Earth, humans and technology.

Mára was listening to Meteor.

1. Series 24. Year - 1. floating sphere


A solid sphere of density ρ is placed between two layers of immiscible liquids (see picture). Densities of the upper and lower liquids are ρ_{1} and ρ_{2} respectively. Assume that ρ_{1} ρ < ρ_{2}. Calculate the fraction of the sphere surrounded by the upper resp. lower liquid.

Z ruských bylin vyčetl Marek

1. Series 24. Year - P. to be, or not to be

Two travelers, one fat and the other skinny, are arguing who would have better chances of surviving in extreme conditions. Tell them who will live longer in the following environments. Hot(50 °C), cold(-1 °C), after a boat accident in the Mediterranean sea, inside a hurricane, inside a heavy snow storm and in the middle of earthquake inside a city. Except of their body fat they are exactly the same. They even wear the same clothes and they do not carry anything else. Be original and remember that details matter.

Ve známém televizním pořadu viděl Honza P.

6. Series 23. Year - P. tora tora tora

In the middle of the Battle of Midway one of the Japanese pilots got thirsty. After searching the cockpit he found out that the supply management gave him only bottles with soda. What should he do in order to satisfy his thirst?

1. Series 23. Year - 4. emptying centrifuge


Lets have a tall cylindrical vessel filled with water (radius $r$, height of water $h)$ and spin it around its axis at angular speed $ω$. At the centre of bottom is a small orifice of surface area $S$, while the vessel is still rotating. How much water will escape the vessel?

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