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Imagine hitting one end of an iron rod and observing the resulting sound waves. Describe (using drawings) the time dependence of the wavefronts in the plane of the rod. We are especially interested in what the wavefronts would look like at two particular moments. The first one is the time when the sound wave reaches the other end of the rod, and the second one is the moment the wave reaches the original end of the rod after reflecting at the other end. Do not forget to describe how did you construct your drawings. You can assume that there are only longitudinal oscillations of the rod, and that its diameter is negligable compared to its length. The ratio of the speed of sound in the rod and in the air is $β=v_{rod}⁄v_{air}≈10$.

Imagine a bent tube of length $l$ that is full of water and whose lower end is submerged in a container (see \ref {S6U3_trubice}). We rotate the tube once per time $T$. Calculate the pressure that causes the water to flow out of the container. You can neglect viscosity and the pressure due to the column of water in the vertical part of the tube.

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!

What is the mass percentage of Earth's atmosphere that escapes to the outer space each year? Assume the atmosphere reaches 10 km above the ground, the pressure is everywhere the same (equal to the pressure at sea level) and it consists of ideal gas at tepmperature 300K whose molecular speeds obey the Maxwell-Boltzmann distribution. Also assume that the gravitational field is homogeneous.

• How would you draw (using only drawing-compass and a ruler) the Zhukovsky profil?
• Draw the streamlines around the Zhukovsky profile. Choose the parameters $d/l$ and $m/l$ so that they have real world justification.
• What is the lifting force acting on a square board? On a semicircular board?
• Draw the profile of a wing that corresponds to the Kármán–Trefftz transform.

Consider the double doors of a building, between which is in the middle even in closed position small gap, where air can flow. Each wing has a spring that returns it to the starting (closed) position. Wing is displaced and then released. What will happen be the other wing?

If you are not quite sure, try it first (e.g. Ke Karlovu 5, Faculty of Science, Prague, …).

Titan (satellite of Saturn) is very cold (surface temperature is 94 K) with nitrogen atmosphere, with icy surface and hydrocarbon lakes on the surface. Radium of Titan is 5150 km, mass is 1 ⁄ 45 mass of the Earth, thickness if its atmosphere is 200 km and pressure on the surface is 1,5 bar.

Based on previous facts calculate acceleration due to gravity on the surface and estimate density of atmosphere. Comparing with parameters of birds at earth conditions decide, if feathered person could fly on Titan.

Get a inflatable ball, blow it up, make a knot on the orifice and measure how its volume is changing in time. Try to find out, how many percent of the surface is taken by pores, through which the air is escaping.

In this set of questions we will visit the world of science fiction. Space is filled with many space ships – one of them is Rama (A. C. Clarke: Rendezvous with Rama, Rama II, The Garden of Rama, Rama Revealed). Rama is large intergalactic ship constructed by extra-terrestrial civilisation and came to Solar system. Lets discuss some challenges, which are facing us.

Rama has a shape of cylinder of length 54 km and internal diameter 16 km. It is filled inside by air. Rama has its own gravity, which comes from rotating around its axis once per every four minutes. On inside surface the pressure of air is 1 bar.

The entrance to Rama is an orifice in the centre of one of its basis. Before removing the space suit, lets think, if on axis is breathable air, what is its density comparing to density on cylinder surface. Assume the temperature is the same everywhere.

Finally you got onto the surface of Rama. Suddenly it started to shake and you think the rotation speed has changed. How you can measure the rotation speed? Can you find more than one experiment?