Results after Problem 4

The list of the contest leaders after the fourth problem:

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.