Mathematical and Physical Journal
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Problem P. 4631. (April 2014)

P. 4631. A step ladder is placed to the smooth horizontal surface of ice. The cross section of the ladder is the same everywhere and the angle between its legs is \(\displaystyle \alpha=60^\circ\). The hinge which connects the two legs of mass 5 kg and of length of 2 m is frictionless. The thin, initially tight safety rope breaks.

\(\displaystyle a)\) What is the angle between the legs of the ladder, when the hinge does not exert any force?

\(\displaystyle b)\) What is the force exerted on the ice by the ladder at this moment?

\(\displaystyle c)\) At what speed does the hinge hit the ice?

(5 pont)

Deadline expired on May 12, 2014.

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

Megoldásvázlat. \(\displaystyle a)\) \(\displaystyle 2\,{\rm arccos}\left(\frac23 \cos\frac{\alpha}{2}\right)\approx 109{,}5^\circ\).

\(\displaystyle b)\) \(\displaystyle F= mg/2=24{,}5~\)N.

\(\displaystyle c)\) \(\displaystyle v=\sqrt{\frac{3\sqrt{3}}{2}gL}=7{,}14~\)m/s.


27 students sent a solution.
5 points:Antalicz Balázs, Asztalos Bogdán, Balogh Menyhért, Csathó Botond, Forrai Botond, Horicsányi Attila, Juhász Péter, Kovács Péter Tamás, Sal Kristóf.
4 points:Berta Dénes, Blum Balázs, Bugár 123 Dávid, Dinev Georgi, Elahe Ahmadi, Fehér Zsombor, Fekete Panna, Holczer András, Janzer Barnabás, Marosvári Kristóf, Németh Flóra Boróka, Olosz Balázs, Sárvári Péter.
3 points:1 student.
2 points:2 students.
1 point:1 student.
0 point:1 student.

Problems in Physics of KöMaL, April 2014