Mathematical and Physical Journal
for High Schools
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Problem P. 4601. (January 2014)

P. 4601. An easily moveable, thermally insulated piston of negligible mass confines a sample of air of volume V0=8 litre, at a temperature of T0=300 K, into a thermally insulated cylinder of cross section A=1dm2. The cylinder is fixed to a horizontal table. The pressure of the confined air is the same as the atmospheric pressure p0=105 Pa. A piece of thread is attached to the centre of the piston, it lies in the line of the axis of the cylinder and leads through a pulley. A weight of mass m=25 kg is attached to the other end of the thread as shown in the figure. Holding the weight, any part of the thread is straight, but loose.

The weight is released without any push. To an accuracy of 1% determine the

a) temperature of the air in the cylinder, when the weight is at its lowermost position;

b) the acceleration of the piston at the lowermost position of the weight;

c) the greatest speed of the piston during the process. (The mass of the thread and the pulley and friction are negligible.)

(5 pont)

Deadline expired on February 10, 2014.

Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. \(\displaystyle a)\) 256 K=\(\displaystyle -17~^\circ\)C.

\(\displaystyle b)\) \(\displaystyle 7,1~{\rm m/s}^{2}\).

\(\displaystyle c)\) 1,3 m/s.


38 students sent a solution.
5 points:Antalicz Balázs, Asztalos Bogdán, Balogh Menyhért, Berta Dénes, Csathó Botond, Fehér Zsombor, Fekete Panna, Forrai Botond, Holczer András, Horicsányi Attila, Janzer Barnabás, Juhász Péter, Kaposvári Péter, Marosvári Kristóf, Németh Flóra Boróka, Olosz Balázs, Öreg Botond, Sal Kristóf, Sárvári Péter, Szathmári Balázs, Virágh Anna.
4 points:Berczi Benjámin, Blum Balázs, Büki Máté, Krokos Ádám László, Rózsa Tibor.
3 points:1 student.
2 points:3 students.
1 point:5 students.
0 point:1 student.
Unfair, not evaluated:2 solutions.

Problems in Physics of KöMaL, January 2014