Mathematical and Physical Journal
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Problem P. 4501. (January 2013)

P. 4501. A fixed U shaped small narrow tube is turned upside-down and a thread of length \ell is hanging in it as shown in the figure. Initially the length of the thread is \ell/2 in each side. This is an unstable equilibrium since friction is negligibly small.

a) If the thread begins to slide to one side what will its speed be when it is straight?

b) What will the speed of the thread be when its momentary centre of mass is just at the same level as that end of the thread which is moving up?

(4 pont)

Deadline expired on February 11, 2013.


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

Megoldásvázlat.

\(\displaystyle v_a=\sqrt{\frac{g\ell}{2}}\approx 0{,}71\sqrt{g\ell};\)

\(\displaystyle v_b=\sqrt{\left(\frac{3}{2}-\sqrt{2}\right)g\ell}\approx0{,}29\sqrt{g\ell}.\)


Statistics:

97 students sent a solution.
4 points:Antalicz Balázs, Balogh Menyhért, Barta Szilveszter Marcell, Berta Dénes, Bingler Arnold, Bugár 123 Dávid, Csáky Pál, Csathó Botond, Dávid Bence, Essig-Kacsó Attila, Fábián Kristóf, Farkas Tamás, Fehér Zsombor, Fekete Panna, Fonyó Viktória, Forrai Botond, Holczer András, Horváth János, Janzer Barnabás, Jenei Márk, Juhász Péter, Kollarics Sándor, Krokos Ádám László, Maga Balázs, Medek Ákos, Olexó Tünde, Olosz Balázs, Öreg Botond, Sal Kristóf, Sárvári Péter, Seress Dániel, Sztilkovics Milán, Tatár Dániel, Tegzes Tamás, Ürge László, Vajda Balázs, Váli Tamás, Varga Blanka, Zsiros Ádám.
3 points:16 students.
2 points:21 students.
1 point:17 students.
0 point:4 students.

Problems in Physics of KöMaL, January 2013