Mathematical and Physical Journal
for High Schools
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Problem P. 4538. (April 2013)

P. 4538. A frictionless slope, having a cross section of a quadrant of radius R=20 cm, is attached to a moveable cart as shown in the figure. The horizontal surface of the cart is rough, the coefficient of friction is =0.8. A point-like object falls freely from a height, measured from the plateau of the cart, of h=2R onto the top of the slope, and arrives tangentially. It slides along the path and just stops at the end of the cart. How long is the cart?

(5 pont)

Deadline expired on May 10, 2013.

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

Megoldásvázlat. A kocsi hossza $\displaystyle \left(\frac{2}{\mu}+1\right)R=70~$cm. (A $\displaystyle m$ és $\displaystyle M$ adatokra nincs szükségünk.)

Statistics:

 79 students sent a solution. 5 points: Asztalos Bogdán, Bingler Arnold, Blum Balázs, Czipó Bence, Dinev Georgi, Forrai Botond, Janzer Barnabás, Kovács-Deák Máté, Reitz Angéla, Szabó 928 Attila, Virágh Anna, Zsiros Ádám. 4 points: Antalicz Balázs, Béda Ármin, Büki Máté, Csáky Pál, Csathó Botond, Emri Tamás, Farkas Tamás, Fehér Zsombor, Fekete Panna, Garai Zoltán, Holczer András, Jenei Márk, Juhász Péter, Kacz Dániel, Kollarics Sándor, Krokos Ádám László, Mezősi Máté, Nagy Zsolt, Olosz Balázs, Pristyák Levente, Sal Kristóf, Sárvári Péter, Seress Dániel, Sisák Mária Anna, Szathmári Balázs, Székely Bálint, Sztilkovics Milán, Tanner Martin, Tuhári Richárd, Váli Tamás, Vasvári Ádám Viktor. 3 points: 11 students. 2 points: 1 student. 1 point: 1 student. 0 point: 19 students. Unfair, not evaluated: 4 solutionss.

Problems in Physics of KöMaL, April 2013