Mathematical and Physical Journal
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Problem P. 4573. (November 2013)

P. 4573. The coefficient of static friction between the fixed inclined plane of angle of inclination and the block of mass M, shown in the figure, is . The radii of the two alike pulleys are r and R (R>r), there is no friction at the axles, and the mass of the pulleys is negligibly small with respect to the other masses. Two pieces of rope are vertical, and one is parallel to the slope. The mass of the block at the bottom is m. At what m/M mass-ratio can the system be in equilibrium?

Data: =30o, =0,2 and .

(4 pont)

Deadline expired on December 10, 2013.

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

Megoldásvázlat. $\displaystyle 0{,}24 < \frac{m}{M} < 0{,}5$ esetén lehet egyensúlyban a rendszer.

Statistics:

 147 students sent a solution. 4 points: Antalicz Balázs, Balogh Menyhért, Béda Ármin, Berezvai Orsolya, Berta Dénes, Blum Balázs, Csáky Pál, Dányi Péter, Egyedi Balázs, Farkas Tamás, Forrai Botond, Gróf Tamás, Holczer András, Horváth János, Iván Balázs, Jeges Viktor, Juhász Péter, Kalló Kristóf, Kaposvári Péter, Kenderes Anett, Kormányos Hanna Rebeka, Kovács Péter Tamás, Mályusz Attila, Mándoki László, Marosvári Kristóf, Molnár 128 Szilárd, Nagy Kristóf 314, Németh 017 András, Németh Flóra Boróka, Olosz Balázs, Pacheco Ana Esther, Pristyák Levente, Putti Krisztián, Rózsa Tibor, Sáfrán Péter, Seress Dániel, Stein Ármin, Szántó Benedek, Szász Norbert Csaba, Szathmári Balázs, Tóth Adrián, Váli Benedek, Varju Ákos, Wiandt Péter. 3 points: 15 students. 2 points: 42 students. 1 point: 30 students. 0 point: 12 students. Unfair, not evaluated: 4 solutions.

Problems in Physics of KöMaL, November 2013