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Results after Problem 4

The list of the contest leaders after the fourth problem:

Points   Name Country School Physics teacher
10,157   SZABÓ Attila Hungary Leőwey Klára High School, Pécs Simon Péter, Dr Kotek László
7,6476   Nikita Sopenko Russia Lyceum No.14, Tambov Valeriy Vladimirovich Biryukov
6,8666   Lars Dehlwes Germany Ohm-Gymnasium Erlangen Martin Perleth
6,7301   Jakub Šafin Slovak Pavol Horov Secondary, Michalovce Jozef Smrek
6,0833   Ivan Tadeu Ferreira Antunes Filho Brazil Colégio Objetivo, Lins, São Paulo  
6,0244   Ilie Popanu Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
5,6695   Brahim Saadi Algeria Preparatory School for Science & Technology of Annaba Derradji Nasreddine
5,1968   Jakub Supeł  Poland 14th School of Stanisław Staszic, Warsaw Włodzimierz Zielicz
5,0589   Ion Toloaca Moldova liceul "Mircea Eliade" Igor Iurevici Nemtov; Andrei Simboteanu
4,919   Alexandra Vasileva Russia Lyceum "Second School", Moscow A.R. Zilberman, G.F. Lvovskaya, G.Z. Arabuly 
4,1057   Dinis Cheian Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
3,9424   Papimeri Dumitru Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
3,8105   Kohei Kawabata Japan Nada High School  
3,7997   Nadezhda Vartanian Russia Smolensk Pedagogical Lyceum Mishchenko Andrei Anatolievich
3,7517   Luís Gustavo Lapinha Dalla Stella Brazil Colégio Integrado Objetivo, Barueri, Brazil Ronaldo Fogo
3,4738   Cristian Zanoci Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
3,4205   Bharadwaj Rallabandi India Narayana Jr. College, Basheer Bagh, India Vyom Sekhar Singh
2,5937   Mikhail Shirkin Russia Gymnasium of  Ramenskoye  Petrova Elena Georgyevna
2,1   Krzysztof Markiewicz Poland XIV Highschool in Warsaw Robert Stasiak
2   Jaan Toots Estonia Tallinn Secondary Science School Toomas Reimann
1,4641   Hideki Yukawa Japan Nada high school  
1,3896   Petar Tadic Montenegro Gimnazija ,,Stojan Cerovic" Niksic Ana Vujacic
1,21   Midhul Varma India Vidyadham Junior, Hyderabad  Manikanta Kumar
1   Task Ohmori Japan Nada High School T.Hamaguchi
1   Sharad Mirani  India Prakash Higher Secondary School Ruchi Sadana, Sunil Sharma
1   Lev Ginzburg Russia Advanced Educational Scientific Center, MSU, Moscow I.V. Lukjanov, S.N. Oks
0,9801   Mekan Toyjanow Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
0,81   Meylis Malikov Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
0,81   Liara Guinsberg Brazil Colégio Integrado Objetivo, São Paulo, Brazil Ronaldo Fogo
0,792   Ulysse Lojkine  France Lycée Henri IV, Paris M. Lacas
0,72   Rajat Sharma India Pragati Vidya Peeth,Gwalior Mr. Rakesh Ranjan
0,5648   Ng Fei Chong Malaysia SMJK Chung Ling, Penang  
0,5648   Lorenzo Comoglio  Italy Liceo Scientifico del Cossatese e Valle Strona Chiara Bandini

Points for Problem No 4:

2,7183   Ilie Popanu
2,5937   SZABÓ Attila
2,1436   Nikita Sopenko
2,1436   Nadezhda Vartanian
2,1222   Jakub Supeł 
1,6105   Bharadwaj Rallabandi
1,5944   Lars Dehlwes
1,4641   Hideki Yukawa
1,2755   Jakub Šafin
1,21   Midhul Varma
1,1   Papimeri Dumitru
1,1   Kohei Kawabata
1   Alexandra Vasileva
1   Cristian Zanoci
1   Krzysztof Markiewicz
0,891   Ion Toloaca
0,792   Dinis Cheian
0,792   Ulysse Lojkine 
0,648   Ivan Tadeu Ferreira Antunes Filho
0,5648   Ng Fei Chong
0,5184   Petar Tadic

Correct solutions (ordered according to the arrival time; best solutions in bold):

1. Szabó Attila (Hungary)

2. Jakub Supeł (Poland)

3. Nadezhda Vartanian (Russia)

4. Nikita Sopenko (Russia)

5. Lars Dehlwes (Germany)

6. Ilie Popanu (Moldova)

7. Jakub Šafin (Slovak)

8. Bharadwaj Rallabandi (India)

9. Hideki Yukawa (Japan)

10. Midhul Varma (India)

11. Dinis Cheian (Moldova)

12. Ion Toloaca (Moldova)

13. Kohei Kawabata (Japan)

14. Cristian Zanoci (Moldova)

15. Ng Fei Chong (Malaysia)

16. Alexandra Vasileva (Russia)

17. Papimeri Dumitru (Moldova)

18. Krzysztof Markiewicz (Poland)

19. Ivan Tadeu Ferreira Antunes Filho (Brazil)

20. Petar Tadic (Montenegro)

21. Ulysse Lojkine (France)

The number of incorrect solutions: 13

The overall number of registered participants: 238 from 41 countries

 

For the last two weeks, a small hint was given: it is helpful to consider the motion of the balls in the connector frame of reference. For the last three days, relatively detailed hints were given: (1) Note that in the lab system of reference, there is only one force applied to each of the balls: the rod tension. Due to the Newton II law, once you know the tensions, you can obtain immediately the accelerations. (2) Force balance for the connector allows you to find, how the tensions in different rods are related to each other, ie. to express T2 and T3 in terms of T1. (3) In order to advance further with the solution, it is helpful to consider the motion of the balls in the connector frame of reference, where they perform circular motions: the radial (centripetal) acceleration is caused by the the tension in rod, together with the force of inertia; the tangential acceleration is caused only by the force of inertia (because there is no bending stress in the rods). So, you have three equations (the force balance for each of the balls, projected onto the direction of the respective rod), and three unknowns (two components of the connector acceleration, and the tension  T1. This system can be solved geometrically, arithmetically using trigonometric functions, or performing symbolic vectorial calculations; the length of the solution depends on the route you choose.



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