5th Round of 24th year

Select year

Series

1. ... warm up( points)

* 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?

2. ... sailing on the moon( points)

Sometimes the Moon can look like a little ship. What are the conditions (time and place) for this to happen? If you get stuck with this problem you can consult a software like Celestia.

3. ... heavy chain( points)

A chain of mass $m$ and length $l$ is hanging right above a scale. Initially it is at rest but then it starts falling. How does the scale's reading depend on the length $x$ of the chain that is already laying on the scale? Assume that the size of single chain cells is negligible.

4. ... green revolution( points)

In 2000 a new nuclear waste repository was built. The first waste arrived and the government decided that every year the amount of newly delivered waste must be reduced by five percent. Assume for simplicity that the half-life of nuclear waste is 100 years (in reality it is much longer). Find out what year are the people in nearby villages going to receive the highest amount of radiation.

P. ... chordates( points)

As you know the amount of positive charges in the Universe is the same as the amount of negative charges. An argument for this statement is that if it were not so the repulsive electric force would be greater than the attractive gravitational force and objects would not hold together. However is this equilibrium perfect? What if there are more positive charges than negative ones and the electric force just reduces the gravitational attraction? Describe an experiment that would enable us to find out any discrepancy from this equilibrium. What is the minimum discrepancy we would be able to measure with such an experiment? As a measure of this discrepancy you can take the ratio of total charge/(positive charge-negative charge) in some large volume.

E. ... chordates( points)

Create an apparatus that will enable you to fix a string of variable length in such a way that the tension in the string is the same for all lengths. Find the relationship between the main frequency of the string and its length. To process the sound you may use some software like Audacity.

S. ... aviation( points)

* How would you draw (using only drawing-compass and a ruler) the Zhukovsky profil?

  • Draw the streamlines around the Zhukovsky profile. Choose the parameters $d/l$ and $m/l$ so that they have real world justification.
  • What is the lifting force acting on a square board? On a semicircular board?
  • Draw the profile of a wing that corresponds to the Kármán–Trefftz transform.
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