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Massless rod of length $L$ is attached to an arch of top angle 2φ and radius $R$. A mass $m$ is glued to the rod's end (see picture). Assume that the body's motion is two-dimensional.

• Find the condition necessary for the system to be stable.
• What is the period of oscillations of the body about its equilibrium point?

Two travelers, one fat and the other skinny, are arguing who would have better chances of surviving in extreme conditions. Tell them who will live longer in the following environments. Hot(50 °C), cold(-1 °C), after a boat accident in the Mediterranean sea, inside a hurricane, inside a heavy snow storm and in the middle of earthquake inside a city. Except of their body fat they are exactly the same. They even wear the same clothes and they do not carry anything else. Be original and remember that details matter.

Returning home from an observatory, watching the sunrise, Janap discovered an easy way to calculate the temperature of the Sun. We do give away that the Earth is an absolute black body with a temperature of 0° C.

Construct a thermometer using the materials available at home. Base the calibration of the degree scale on well-known temperatures. Do not forget to attach a photograph of the end result of your efforts.

The movement of point mass is restricted on straight line by 2 end points. At the beginning the point mass $m$ is moving at speed $v$. The end point starts to move away at speed $v_{1}<<v$. How will the energy of point mass change?

We are going to the north pole. Having snowmobile helping to bring them north, we need into the cooler some antifreeze. What is the ideal concentration of alcohol in water, more precisely what is dependence of melting point on alcohol concentration? If you have good freezer, then measure, what concentration will freeze at some specific temperature.

Do not forgot, that this task is experimental.

The capillary of medical thermometer is at its bottom thinner, to stop mercury to return back to the reservoir at the base, which allows us to read the maximum reached temperature. From June 2009 it is forbidden to sell such thermometers. At this historical occasion, take the opportunity and explain us, why the capillary narrowing works only in one direction – only when heating. Because while cooling down the mercury cannot go through the narrow point back.

Marek has a piston of area $S$ filled with ideal gas in equilibrium ($p$, $V$ a $T)$. On this piston a stone falls down from the height $h$. Mass of stone is $m(see$ picture). Piston is pushed down and then comes up again and remains in a new position. How depends this new position on the mass of stone and the falling height? Is it possible for piston to become in equilibrium higher then the original position? How will change the temperature of gas?

How will the temperature increase, if there are two person under duvet instead of one.

Assume a pressure cooker, which is filled with half of water and remaining half is filled with air. Then it is closed that no water vapor or air can escape. The cooker with water is slowly heated. At what temperature will water start to boil? What phases are present inside the pressure cooker during increasing temperature?