Problem P. 4545. (May 2013)
P. 4545. Two cylinder shaped vessels of cross section A are fixed vertically to a trolley, which was initially at rest. The two vessels are connected with a thin horizontal tube which is equipped with a tap. The distance between the axes of the vessels is L. The vessel in the left hand side is filled with some liquid of density ; and at this time the total mass of the system at rest is m.
After opening the tap what is the speed of the cart at the moment when the speed of the water levels in the vessels is v? (Rolling friction, friction in the bearings and air-drag are negligible.)
Deadline expired on June 10, 2013.
Sorry, the solution is available only in Hungarian. Google translation
Megoldásvázlat. \(\displaystyle vAL\varrho/m.\)
47 students sent a solution. 5 points: Antalicz Balázs, Asztalos Bogdán, Balogh Menyhért, Berta Dénes, Bingler Arnold, Blum Balázs, Buttinger Milán, Büki Máté, Csáky Pál, Csathó Botond, Dinev Georgi, Emri Tamás, Fehér Zsombor, Fekete Panna, Filep Gábor, Forrai Botond, Holczer András, Janzer Barnabás, Jenei Márk, Juhász Péter, Kacz Dániel, Kasza Bence, Kovács 444 Áron, Kovács-Deák Máté, Kozár Eszter, Mihály 930 Ákos, Nagy Zsolt, Olosz Balázs, Öreg Botond, Papp Roland, Sal Kristóf, Sárvári Péter, Seress Dániel, Sisák Mária Anna, Szabó 928 Attila, Sztilkovics Milán, Tanner Martin, Tegzes Tamás, Trócsányi Péter, Váli Tamás, Varju Ákos, Wiandt Péter. 4 points: Demeter Dániel, Pázmán Zalán. 3 points: 1 student. 2 points: 1 student. 1 point: 1 student.