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6. Series 27. Year - 4. insatiable spider

In a dark corner there lurks a spider that has just caught a fly and is slowly devouring it. Assume that the consumption follows such an equation:

$$\;\mathrm{A} + \mathrm B \mathop{\rightleftharpoons}_{k_{-1}}^{k_1} \mathrm{AB} \stackrel{k_2}{\longrightarrow} \mathrm C + \mathrm B\,,$$

where A is fly substrate, B are the digestive compounds (there is always enough of themu) and C is the product of digestion. AB denotes the unstable intermediate product. The reaction is of the first order, in other words the speed is directly proportional to the concentration of the said substance. Determine how long will take the spider to digest the fly and begin hunting again, if its receptors will tell it that it is hungry once the substrate reaches 10 % of the original value.

Tip Use the approximation of the stationary state of intermediate product.

Mirek reminiscing about Bestvina.

5. Series 27. Year - P. physics in flames

On what physical (or chemical) values does the temperature at which a certain material burns depend? How does it depend on them? Determine such a temperature for one such material.

Karel was musing about flames

6. Series 25. Year - E. alternative stress relief technique

Original way to get rid of an empty coke can is to pour a little bit of water into it, seal the opening and place it on a cooker. After it is hot enough throw it into a cold water and if you are lucky it will collapse so that it is ready to be recycled. Try this also without the water inside the can and explain why is the outcome different. Your goal is to crush the can into the smallest possible form. Send us a picture of your result together with the description of the conditions under which you achieved it. Warning The can will get hot, do not burn yourself!

Karel wants you to get burned.

6. Series 25. Year - P. x-ray

When you illuminate your fingers with a very intense light in order to see through them, you should notice that you can see individual vessels but the rest seems rather homogeneous. Explain why the vessels are visible but bones are not.

Michal was playing with LEDs.

5. Series 25. Year - E. sweet coffee

Together with this problem set you also received a bag with sugar or sweetener. Your task is to experimentally compare „sweetness“ of this sample with other kinds of sugar/sweeteners. You should use the attached spoon as a measure of volume. „Sweetness“ of a sample is determined from a solution of one leveled spoon of the sample in 1 dl of water. As a reference point of „sweetness“ you can use for example refined beet sugar. You should determine „sweetness“ by comparing solutions of tested samples with the reference sample. To make the measurement more valid you should ask other people to rate the samples as well. For every sample find out its composition and report your results in an appropriate way.

Hint: The regular sugar is usually refined beet sugar, but you can also get cane sugar (almost the same in composition as beet sugar), grape sugar (dextrose) and fruit sugar (fructose). Examples of sweeteners are sorbit, huxol, sucralose or aspartame. You can also use honey. We recommend to use sugars/sweeteners with similar „sweetness“. If this is the first time you participate in FYKOS just send us an email to and we will send you your sample. Warning Every substance can be dangerous in large amounts. Even distilled water is a poison. Try not to exceed recommended daily doses.

Karel has a sweet tooth.

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$x3x4\;\mathrm{m}$.


2. Series 24. Year - 2. Lennard-Jones potential

The interaction of two atoms of an inert gas can be described using the so called Lennard-Jones potenial $U(R) = 4\epsilon((\sigma/R)^12 - (\sigma/R)^6)$. Assume the motion is one-dimensional and determine the equilibrium position without using the tools of calculus. The meaning of the constants $\sigma$ and $\epsilon$ will be explained in the published solution.


3. Series 19. Year - E. vine analysis

Measure the alcohol content in cheap table vine and compare the content to the value declared on the packaging.

Našel Jarda Trnka na internetu a vzpomněl si při tom na jednoho z organizátorů.

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