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(2 points)1. Series 26. Year - 1. paper

Try to find out dimensions, mass and density of a regular A4 paper (one that you would use in a printer). Given these values estimate its average thickness.

Karel was eating a piece of paper.

(5 points)1. Series 26. Year - P. airship

What is the minimal wind speed necessary to blow away a paper lying on a flat table?

Karel does not like wind.

(4 points)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 points)5. Series 25. Year - P. lightsaber

Design a lightsaber that looks and works in a similar way as the ones from Star Wars movies but using only knowledge and technology available to us.

Remembering old FYKOS camps.

(8 points)1. Series 25. Year - E. suffering of gummy bears

Find out experimentally at least three different physical properties of gummy bears candy. You should explore even how do these properties depend on the candy's color. Some possible properties you can measure are melting temperature, Young's modulus, maximal tension, absorbency (change in volume or mass after being in water for certain amount of time), density, conductivity, index of refraction, solubility, dependence of any of the preceding properties on temperature or anything else you can think of.

Karel

6. Series 24. Year - 3. airplane

How long does it take before the Sun rises and sets as seen from an air-plane that flies in the ecliptic plane? In the same situation how long is a day? What about night? Necessary information like typical height at which air-planes fly can be surely found on the Internet. Answer these questions for an air-plane flying both east and west.

6. Series 24. Year - E. the discworld

Think of as many ways to verify that the Earth is spherical as you can. If you do verify this statement find a way to measure the radius of the Earth.

6. Series 24. Year - P. the water porter

How much water can be taken out of a swimming pool (in one trial) using only your hair (assume you have a lot of them)?

4. Series 24. Year - E. Depressed egg

Determine the maximum height a typical egg can fall from without breaking itself. How does the result change if you wrap the egg in some protective material which is not thicker than 5$\;\mathrm{mm}?$ Try couple of different materials.

Karel

3. Series 24. Year - 1. Warm-Up

 

  • Dr. Nec.

There are two ways to measure the amount of wood in a pile of trees. Either as the volume of pure wood in the pile or as the volume of wood together with the empty spaces in the pile. Find the conversion factor between these two units assuming the trees are cylinders of radius $r$ that are layed one on top of the others.

  • Bubbles.

A spherical cap of radius $r$ is made by blowing air into a circular surface of soap water. Estimate the velocity of air molecules hitting the surface?

Jakub

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