Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem P. 4426. (March 2012)

P. 4426. On a smooth horizontal tabletop there is a spring, one of its end is braced, and at the other end there is a ball of mass M=1.15 kg at rest. Another ball of mass m=1.00 kg hangs on a vertical thread of length =0.30 m and touches the previoussly mentioned one. The ball on the thread is displaced to the horizontal and released without any initial speed. The velocity of the ball at which it reaches the horizontal is parallel to the symmetry axis of the spring. The collision of the two balls is totally elastic. a) What should the spring constant of the spring be, in order that the second collision of the balls occurs at the same position as the first one did? b) How much time elapses between the two collisions? c) After the first collision what is the maximum distance between the two balls? (Friction and the mass of the spring are negligible.)

(5 pont)

Deadline expired on April 10, 2012.

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

Megoldás. $\displaystyle a)$ 37,6 N/m.

$\displaystyle b)$ 0,55 s.

$\displaystyle c)$ kb. 43 cm.

### Statistics:

 88 students sent a solution. 5 points: Agócs Fruzsina, Barta Szilveszter Marcell, Bogye Balázs, Bojtár Orsika, Bolgár Dániel, Csáky Pál, Csathó Botond, Csóka József, Czigány Máté Gábor, Demeter Dániel, Fekete Panna, Filep Gábor, Forman 123 Ferenc, Fülep Andrea , Garai Zoltán, Holczer András, Horicsányi Attila, Janzer Barnabás, Janzer Olivér, Jenei Márk, Kollarics Sándor, Koncz Gabriella, Kovács 444 Áron, Laczkó Zoltán Balázs, Medek Ákos, Nagy Lajos, Nagy Zsolt, Öreg Botond, Öreg Zsombor, Papp Roland, Pázmán Zalán, Pölöskei Péter Zsolt, Sárvári Péter, Seres Imre, Seress Dániel, Sisák Mária Anna, Szabó 928 Attila, Szigeti Bertalan György, Szilágyi 585 Dezső, Tilk Bence, Tóth Balázs, Ürge László. 4 points: 18 students. 3 points: 16 students. 2 points: 9 students. 1 point: 2 students. Unfair, not evaluated: 1 solution.

Problems in Physics of KöMaL, March 2012