Problem P. 4340. (April 2011)
P. 4340. A small ball of mass m=0.4 kg is hanging on a thread of length =1 m, and touches another ball of mass m and of the same radius. This second ball is on a horizontal plane and is attached to one end of a horizontal spring of spring constant D=10 N/m, as shown in the figure. Initially the spring is unstretched and its other end is fixed. The simple pendulum is deflected at an angle of =20o, and it is released without any initial speed.
a) At what speed do the two balls collide? What is the percentage error that is made if the speed of the ball is calculated from the formula of the period of the pendulum.
b) How much time elapses until the pendulum gets back again to the position where its displacement is the greatest, having collided with the other ball totally elastically? (Friction is negligible.)
Deadline expired on May 10, 2011.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle a)\) 1,10 s; a hiba 1 százalék nagyságrendű.
\(\displaystyle b)\) 1,13 s.
65 students sent a solution. 5 points: Antalicz Balázs, Barta Szilveszter Marcell, Béres Bertold, Filep Gábor, Horicsányi Attila, Koncz Gabriella, Laczkó Zoltán Balázs, Maknics András, Nagy Zsolt, Pető János, Seress Dániel, Simon Sebestyén, Szabó 928 Attila, Tamási Mátyás, Tóth Balázs, Ürge László, Várnai Péter, Zsámboki Richárd. 4 points: Bingler Arnold, Bojtár Orsika, Bolgár Dániel, Csáky Pál, Cseke Zsombor, Czipó Bence, Dávid Péter, Fülep Andrea , Hoffmann Hanna, Iglói Gábor, Jéhn Zoltán, Jenei Márk, Kovács 444 Áron, Kozák Ádám András, Mázik László, Miskó Gergely, Papp Roland, Park Choong Eun, Pataki Bálint Ármin, Pázmán Koppány, Sárvári Péter, Sisák Mária Anna, Szakszon Tamás, Szélig Áron, Szemes Gábor Bence, Tuza Réka. 3 points: 7 students. 2 points: 5 students. 1 point: 6 students. 0 point: 3 students.