Assignment of Series 4 of Year 24

About the Competition Rules How to Write Solutions Results

Year 24

1 2 3 4 5 6

1 2

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

0 1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5 6

1 2 3 4 5

1 2 3 4
Brochure with solutions (cs)

1... Warm-Up

points

 

  • //Strings. //

Using dimensional analysis determine the dependance of the frequency of oscillatons of a string if you know that it depends on its length $l$, on the tension $F$ in the string and on its linear density $ρ_{l}$.

$

  • //Downward. //

You have a dumbell which consists of a short rod and two heavy discs. You wrap a string around the rod and let the dumbell fall while holding the string. What is the velocity of the dumbell? The discs have mass $M$ and radius $R$. The radius of the rod is $r$ and you can neglect its mass.

We will publish the solution to this problem soon.

2... To the Sun

points

Karel has decided to throw his notes into the Sun. Help: him calculate the necessary initial velocity of his notebook so that it reaches the Sun. You can neglect the frictional froces acting on his notebook and you can also assume that the trajectory of the Earth around the Sun is circular. You know the masses of the Earth and the Sun as well as the distance of the Earth from the Sun.

We will publish the solution to this problem soon.

3... Old clock

points

Design a shape for a sandglass so that the dependance of the height of sand on time is linear. If you do not neglect friction etc. you can gain some extra points.

We will publish the solution to this problem soon.

4... Home alone

points

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$x3x4\;\mathrm{m}$.

We will publish the solution to this problem soon.

P... Colors

points

To display a cyan blue on your monitor it has to light up both blue and red segment. If you however mix blue and red temperas you see that the resulting color is purple. Imagine that the temperas consist of small pieces and describe how does the color of a mixture of blue and red temperas depends on the size of these pieces.

We will publish the solution to this problem soon.

E... Depressed egg

points

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.

Instructions for Experimental Tasks
We will publish the solution to this problem soon.

S...

points

We will publish the solution to this problem soon.
If you are looking for the old website, you may find it at https://old.fykos.org