Mathematical and Physical Journal
for High Schools
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# Problem P. 4036. (January 2008)

P. 4036. A small body of negligible size slides with a speed of v onto a long cart, which can move easily. The mass of the small body and the cart are the same. In the middle of the cart there is a slope which has a shape of a circular arc of central angle of 45o and of radius R. The small body slides along the slope and then it falls exactly to the end of the cart. What is the length of the cart? (Friction is negligible.)

Data: v=5 m/s, R=0.4 m.

(5 pont)

Deadline expired on February 11, 2008.

### Statistics:

 83 students sent a solution. 5 points: Almási 270 Gábor András, Béres Bertold, Deli Gábor, Filep Tibor, Hartstein Máté, Kovács 235 Gábor, Lovas Lia Izabella, Maknics András, Matolcsi Csaba, Nagy 648 Donát, Pásztor Ádám Viktor, Rárósi Dávid. 4 points: Balassa Péter, Blázsik Zoltán, Deák Zsolt, Demeter Dániel, Fonyó Dávid, Gaál Alexisz Tamás, Gulyás Máté, Harsányi Szabolcs, Iván Dávid, Kovács 888 Gábor, Kovács Attila, Krämer Zsolt, Kupcsik Réka, Marák Károly, Nagy Loránd, Najbauer Eszter Éva, Ölvedi Tibor, Pálovics Péter, Papp Ádám, Somogyi József, Szolnoki Lénárd, Tamási Mátyás, Tolnai Gábor, Tolner Ferenc, Tószegi Károly, Török 125 Csaba, Túri Attila, Varga 777 Ádám. 3 points: 26 students. 2 points: 5 students. 1 point: 1 student. 0 point: 9 students. Unfair, not evaluated: 2 solutionss.

Problems in Physics of KöMaL, January 2008