Series 1, Year 9

Can a battleship float in a bath?

Of course, we mean the ship small or the bath large enough. In any case the volume of the water surrounding the ship is small compared to the volume of the ship (see pic. 1). Being exact, we have a ship weighting 100 tons and a bath with 1 m^{3} of water.

We have two semitransparent mirrors, either of which transmits about 1/5 of light beam and reflects the rest (this in an experimental result). When we place both mirrors perpendicularly to the direction of a parallel light beam (see pic. 2), the first idea suggests that this system transmits just 1/25 of incident light. In fact it is much more, about 1/10. Explain this „paradox“!

A capacitor formed by two parallel metal plates of area $S$ each placed in a distance $l_{1}$ one from another are charged at the voltage $U_{b}$. What work must be performed to move the plates apart to distance $l_{2}$, if we

• had disconnected,
• hadn’t disconnected

the battery..

A gas of temperature $t$ is placed in a vessel with walls the temperature of which is $t_{c}$. In what case is the gas pressure on the walls higher: when we warm the walls above or when we cool them bellow the gas temperature?

Picture 3 shows an aerial view of three steam engines with clouds of smoke (seen from above). They move steadily on three straight parallel railways. The velocity of the first engine is 50 km/h, of the third one 70 km/h; their directions are shown on the picture. At what speed does the second engine move?

When we pour powder (dry sand, flour or so) freely at one place, we get a cone with a top angle a (see pic. 4). Try to measure this angle for different materials. Can you give some explanation to your results?