Mathematical and Physical Journal
for High Schools
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Problem P. 4485. (November 2012)

P. 4485. Two alike balls are suspended next to each other and can swing in the plane of the figure on threads of length \ell. One ball is displaced by a distance of d and then released (d\ll\ell). The balls collide inelastically, their velocities decrease by a factor of k at each collision, with respect to the system of their centre of mass (0<k<1 is the collision number).

How will the balls move? What will the amplitude of the swings be after many collisions?

(6 pont)

Deadline expired on December 10, 2012.


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

Megoldásvázlat. \(\displaystyle d/2\). (A golyók összimpulzusa minden ütközés után ugyanakkora lesz, a relatív sebességük pedig fokozatosan nullára csökken.)


Statistics:

36 students sent a solution.
6 points:Barta Szilveszter Marcell, Buttinger Milán, Czipó Bence, Dinev Georgi, Essig-Kacsó Attila, Fehér Zsombor, Filep Gábor, Garami Anna, Holczer András, Horváth András Levente, Janzer Barnabás, Jenei Márk, Juhász Péter, Kollarics Sándor, Kovács 444 Áron, Papp Roland, Reitz Angéla, Sal Kristóf, Sárvári Péter, Szabó 928 Attila, Trócsányi Péter, Ürge László, Vajda Balázs.
4 points:3 students.
3 points:1 student.
1 point:2 students.
0 point:7 students.

Problems in Physics of KöMaL, November 2012