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(10 points)3. Series 32. Year - P. personal power bank

Last battery percentages in your mobile phone are almost gone, your power bank is dead, or you left it at home and 230 is also not in the sight. Wouldn't it be awesome if you could have your own source of electrical energy with you all the time?

  • Suggest several different tools, which would be able to produce electrical energy just from your body resources.
  • Discuss their maximum power and efficiency. What devices could you supply with electricity using this method?
  • Discuss its effects on your health and physical condition. Which body organs would fail first?

As a possible solution, consider a system of small turbines located in your bloodstream. Support all arguments with accurate calculations.

(11 points)4. Series 30. Year - E. Mikulas's egg

Measure the surface area of a bird's (e.g. chicken's) egg.

Mikulas made pancakes.

(8 points)3. Series 30. Year - P. openhearted

Estimate the work performed by the heart pumping blood in one day. What can you compare this energy to? What percentage of the recommended daily energy intake is your estimate?

Karel's heart started pounding.

(12 points)2. Series 30. Year - E. one full fat milk, please

Milk with higher fat content should be „whiter“ – more light is scattered and less is transmitted. Conduct a measurement of the fat content of milk with the help of a color scale (contact us at fykos@fykos.czto get the pdf with the scale – you have to print it yourself). The difference in whiteness is most apparent when you add a dye to each glass of milk. You can use e.g. black ink or any other dye, but with different colors you have to create your own color scale which you have to add to your solution. Use different types of milk and mixture of milk with water. Discuss the reliability of this method of measurement.

Mára byl bledý jako stěna.

(2 points)6. Series 29. Year - 2. Optometric

Pikos' friend wears glasses. When she puts them on, her eyes seem to be smaller. Is she shortsighted or farsighted? Justify your answer.

(2 points)4. Series 29. Year - 2. Brain in a microwave

How far from a base transceiver station (BTS) do a person have to be, for the emission to be fully comparable with that of the mobile phone just next to somebody's head. Expect the BTS to broadcast uniformly into a half-space with the emission power 400 W. The emission power of a mobile phone is 1 W.

(4 points)1. Series 29. Year - 5. chernobyl

If someone would eat 5&nbspµg of the isotope of cesium ^{137}Cs, how long would it take for them to have only0,04 % of the original amount of this isotope? Assume that cesium ^{137}Cs has a half-life of 30,42 let and a biological half-life (the time it takes for half of the original amount of the material to leave the body) is approximately 5 days. Determine also, how many of the particles will have decayed in the body up till then.

Kiki was hungry after her toxikology exam.

(5 points)1. Series 29. Year - P. decompression illness

Surely you have heard before (at least in a movie) about how it is dangerous to go diving in great depths and then to immediately travel by plane. If a person were to do this he might suffer from the so called. decompression illnes. Describe as accurately as possible what physical processes the human body will undergo during this sickness(how precisely do the phyiscal laws act in this case) and say why precisely they are dangerous for a person. Is it dangerous for people to attempt the opposite sequence of events (ie. first travelling by plane then diving) Je pro lidi nebezpecná i opacná posloupnost akcí, tedy cestování letadlem a následné potápení? (when solving this you can utilise all available resources but in the end you must use your own words to describe it)

Mirek felt a sudden decrease in pressure after a successfully done exam in mathematical analysis.

(2 points)6. Series 28. Year - 1.

The Turtle A'Tuin, on the shell of which the four elephants that carry on their backs Discworld stand, isn't tiny. Let us assume that we would be bored with the sphericity of our Earth and we would want to exchange it for a circular disc with the same mass and density and with the width $h=1\;\mathrm{km}$ carried by the same turtle-elephant band. In case that the turtle would have hit with the tip of its tale into a planetoid, how long would it take for it to notice the impulse of pain, given that her tail and her brain are connected by a very long neuron? (This neuron is approximately as long as the diameter of the disc) How much earlier/later would A'tuin realise this pain (the length of the neuron is equivalent to its length 18 000 km)? For a numerical estimate assume that the speed of the spread of the signal in the large animals is the same as with normal land animals who experience a speed of $v≈120\;\mathrm{m}\cdot \mathrm{s}^{-1}$.

víte snad o lepším vymyšleném světě, než je Zeměplocha? Kiki ne!

(4 points)4. Series 28. Year - P. unnamed snack bar

Considering biochemical processes in the human body and its mechanics estimate, how much energy is used by a cyclist to rise a thousand vertical meters if the average gradient is 5 %.

Mirek and Tomas were thinking about how many hills can be climbed with a certain snack bar (not naming one due to the lack of funding).

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