Cím:	The Problems of the 1996 Eötvös Contest
Füzet:	1997/április, 257. oldal	PDF  |  MathML
Témakör(ök):	Eötvös Loránd (korábban Károly Irén)

A szöveg csak Firefox böngészőben jelenik meg helyesen. Használja a fenti PDF file-ra mutató link-et a letöltésre.   1. A treetrunk lies horizontally on the ground. Its diameter is 20 cm. What is the minimal velocity with which a grasshopper should spring away from the ground in order to leap over the treetrunk? (Air resistance should be neglected!)   2. A closed, cylindrical vessel of height 3 dm contains air at temperature 300 K and pressure ${10}^5$ Pa. By cooling, and heating from outside, respectively, we lower the temperature of the base to 270 K and raise the temperature of the top to 300 K and then we keep them at these temperatures. (The thermal conductivity of the sidewall of the vessel is zero.) a) Does the pressure of the gas change in comparison to the original state? b) Estimate the shift of the center of mass of the enclosed gas!   3. A plastic ball of diameter 1 cm is hanging from an insulating thread. The ball carries an electric charge of ${10}^{-8}$ C, distributed uniformly on its surface. We bring the ball above a broad, big vessel with salty water in it such that the lowest part of the ball be at a height of 1 cm above water level. The surface of the water beneath the ball will rise a little. How big is that rise? (The role of the surface tension can be neglected, the density of the salty water may be taken $1000\text{kg/<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math>}$.)