Series 2, Year 9

A ship is floating on pic. 1. Its owner had solved the problem of windless weather by attaching a powerful hair-dryer to the stern of the ship and pointng it against the sail. Consider at what conditions will the ship move forward or backward. What improvements you would suggest to make the ehgine work more efectively.

The table shows masses of several nuclei. Determine the mean distance between nucleons in the nucleus of He_{3}

<table> <tr> <th>nucleus</th> <th>neutron</th> <th>proton</th> <th>deuterium</th> <th>tritium</th> <th>helium He_{3}</th> </tr> <tr> <td>mass [10^{–27} kg]</td> <td>1,674929</td> <td>1,672623</td> <td>3,343590</td> <td>5,008271</td> <td>5,008239</td> </tr> </table>

Two cylinders of radius $R$ with parallel horizontal axis placed at distance $a$ rotate in opposite directions. A plate of mass $m$ and length $2a$ is laid on them little bit asymetrically (see pic. 2). (viz obr. 2). The coeficient of friction between the plate and the cylinders is $μ$. What will happen

• when the angular velocities of the cylinders are the same,

• when the angular velocities of the left one is two times higher than of the second one.

Imagine a cube with an electrical charge uniformly distributed with density $ρ$ in the whole volume. The intensity of electrical field in point $A$ is $\textbf{E}$. But what will be its value when we cut out a small cube of half the size of the original one (see pic. 3)?

Great Russian scientist M.V. Lomonosov in his work „On the Free Movement of Air in Mines“ discovered the causes of the permanent streams of air in mines of type shown on pic. 4. Determine their direction on condition the air temperature in the mine is constant during the year and the same in all points of the mine.

Establish the resistance of electric spiral boiler

Hint: Warm up water and measure the evolution of its temperature in time.