Mathematical and Physical Journal
for High Schools
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Problem P. 4443. (April 2012)

P. 4443. A soap film of surface tension \sigma is created in the frame, shown in the figure. The diameter of the frame is \ell. A piece of unstretched hair of length \ell, and of young modulus E joins the points P and Q. By what amount will the hair be elongated if the film in the right hand side is pricked by a hot pin. (The two endpoints of the hair are fixed and its weight is negligible. For small angles use the approximation: sin \alpha\approx\alpha-\alpha3/6.)

(6 pont)

Deadline expired on May 10, 2012.

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

Megoldásvázlat. A megnyúlás

\Delta \ell=\frac{\ell}{6}\left(\frac{6\ell\sigma}{EA} \right)^{\frac{2}{3}}.


13 students sent a solution.
6 points:Szabó 928 Attila.
5 points:Barta Szilveszter Marcell, Czipó Bence, Juhász Péter, Koncz Gabriella, Papp Roland, Sárvári Péter, Szélig Áron, Trócsányi Péter, Vajda Balázs.
4 points:3 students.

Problems in Physics of KöMaL, April 2012