# Series 4, Year 20

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### 1. shopping for mineral water

You may remember buying plastic bottle of your favourite drink in supermarket. The bottle placed on the belt starts spinning trying to stay on the spot. Why this happen?

Analyse following situation: the bottle in rest is placed on the belt perpendicularly to the direction of belt movement.

Suddenly the belt starts moving at constant speed $v=10\;\mathrm{cm}/s$. What will be the speed of the bottle. First analyse following idealisations: (1) approximate bottle by a solid cylinder, (2) the bottle is full of liquid water which does not like to be turned. For simplicity assume negligible viscosity, then include viscosity to your calculations.

Úlohu vymyslel Jano Lalinský na nákupu v TESCU.

### 2. plum wine in china

In our popular Chinese restaurant in Prague they give to each guest with the receipt small glass of plum wine. The wine is served in small ceramic bowl with double bottom (figure 1). The top bottom is glass and you can see picture of sitting girl (figure 2). When the glass is emptied the girl disappears (figure 3). Explain what happens. The empty bowl is in figure 4.

Vymyslel Honza po několikáté návštěvě zmíněné restaurace.

### 3. finishing of Temelin (nuclear power station)

Estimate thickness of water needed to shield radiation from nuclear reactor of power 980 MW in proposed new block of nuclear power station Temelin. The total energy released by fission from Uranium is split following: 82% goes to kinetic energy of fragments, 6% goes to neutrinos, 6% goes to neutrons and remaining 6% goes to energy of gamma photons.

**Hint:** Probability of particle passing through a material into the depth $d$ is probably equal to e^{$-σnd}$, where $n=N/V$ is density of molecules of material (in our case number of water molecules in 1 m3 ) and $σ$ is effective cross section for absorption of particle on molecule of water. Unit of cross section is surface, therefore m^{2} but often is used unit barn = 100 fm2) and depends on energy of particles. The values of cross section can be found on Internets or in tables.

Úloha řešil Karel Tůma na zkoušce z jaderné fyziky.

### 4. Koch's snow flake

Calculate the moment of inertia of Koch's flake made from homogeneous sheet with respect to the axis going through the center of flake perpendicular to the paper. Assume the mass of flake to be $m$ and radius $a$.

**Hint:** Koch's flake is a shape created by iterative process of connecting equilateral triangles each three times smaller than previous to the previous object (see picture). The diameter of Koch's flake is distance of vertices on the opposite sides.

Problém si s chutí vyřešil Marek Pechal.

### P. greasy paper

When the drop of oil falls onto a sheet paper it makes it transparent. Explain what happens. Find in your life another examples of the same effect, but in different situation.

Na problém narazil Peter Zalom při čtení o sněhových vločkách, když mu kapka oleje dopadla na papír.

### E. friction

Measure dependence of sliding friction between two materials (pick your own) as it depends on the surface of friction force and mass of the body. Do not forgot to describe exact experimental configuration.

Úloha napadla Honzu Prachaře při čtení Feynmanoých přednášek z fyziky.