Series 6, Year 20

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1. three cylinder and friction


Find the condition of equilibrium (no movement) for the 3 cylinders in figure 1. The cylinders are made of material of density $ρ$, the radius of bottom cylinders is $R$, the radius of top cylinder is $r$. The coefficient of friction is same for all surfaces.

Zadal Honza Prachař, aby prověřil vaše znalosti ze statiky soustavy tuhých těles.

2. strange atmosphere

The refractive index of atmosphere of a planet of radius $R$ is can be describe by following equation: $n=n_{0}-αh$. Calculate, how high above the surface of the planet $h$ the laser beam will follow circular trajectory around the planet.

Nepoužitá úloha z archivu.

3. the square the Joker


The electric circuit in the image is made from the infinite number of wire-frame-squares. The next square is exactly sqrt(2) smaller then the previous. The resistance of used wire is $R$ per one side of the largest square. What is electrical resistance between most left and most right point?

Úlohu vymyslel Marek Pechal.

4. binary star

The magnitude of binary star is changing with 4-day period with this sequence:

side minimum: m = 3.5

maximum: m = 3.3

main minimum: m = 4.2

maximum: m = 3.3.

The larger part of binary star has higher temperature then its escort. Assuming, that the Earth is in the orbital plane of binary star, calculate magnitudes of each component and ratio of its linear dimensions. Relation between magnitude $m$ and irradiation $E$ is given by


where $E_{0}$ is some defined value.

Nepoužitá úloha z archivu.

P. how the UFO-man is looking?

In this problem question think about and animal, which communicate at radio frequency (10 Hz –100 MHz). Suggest an biological equivalent of necessary radio-electronic components.

Zadal Michael Komm doufaje, že přijdete na něco zajímavého.

E. blowing experiment

Measure what is the maximum pressure (and underpressure) which can be made by your mouth by blowing and sucking air.

O ruce vás chtěl připravit Michael Komm.

Instructions for the experimental problem

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