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P. 4591. There are 4 positively charged small balls of mass m at the vertices of a regular tetrahedron of edges L. The balls are connected with insulating threads of negligible mass. Three balls have a charge of Q, and the fourth is charged to 2Q.

a) At the same instant the three threads which connect the charge of 2Q with the others are cut. Determine the initial acceleration of the balls at the instant when the threads are cut.

b) To what speed will the balls accelerate?

(5 points)

Deadline expired on 10 January 2014.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldásvázlat. $\displaystyle a)$ $\displaystyle a_{2Q}=3 \cdot a_{Q}=\sqrt{24}\,\frac{kQ^2}{mL^2}.$

$\displaystyle b)$ $\displaystyle v_{Q}=\frac13v_{2Q}=\sqrt{\frac{kQ^2}{mL}}.$

Statistics on problem P. 4591.
 44 students sent a solution. 5 points: Antalicz Balázs, Balogh Menyhért, Bartók Imre, Csathó Botond, Di Giovanni Márk, Fehér Zsombor, Fekete Panna, Forrai Botond, Holczer András, Horicsányi Attila, Janzer Barnabás, Juhász Péter, Kaposvári Péter, Kovács Péter Tamás, Nagy Zsolt, Olosz Balázs, Sal Kristóf, Seress Dániel, Subicz Mátyás, Tanner Martin. 4 points: Beregi Ábel, Berta Dénes, Géczi Péter Attila, Hu Jia Lin, Marosvári Kristóf, Öreg Botond, Pázmán Zalán, Sárvári Péter, Trócsányi Péter. 3 points: 12 students. 2 points: 3 students.

• Problems in Physics of KöMaL, December 2013

•  Támogatóink: Morgan Stanley