V International Physics Olympiad for Schoolchildren

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V INTERNATIONAL PHYSICS
SCHOOL OLYMPICS

From July 2 to July 11, 1971, the V International Physics Olympiad for schoolchildren of socialist countries was held in Bulgaria. 5 participants were invited from each country. Two schoolchildren (one from Poland and one from Czechoslovakia) were unable to come due to illness. In total, 33 schoolchildren from 7 countries took part in the Olympiad: Bulgaria, Hungary, East Germany, Poland, Romania, USSR and Czechoslovakia.

The entire program of the Olympiad was prepared by the Organizing Committee of Bulgaria. The program included solving 4 theoretical problems (5 hours were allotted for their solution) and performing 1 experimental problem (5 hours were allotted for it).

Achievements were assessed by the total number of points scored by participants, awarded by the International Jury, established from the leaders of each team from the 7 countries participating in the Olympiad. The highest number of points for each theoretical task is 10, for an experimental task - 20 (10 for completing its theoretical part and 10 for the experiment and its design). Thus, the maximum number of points was 60.

None of the participants scored 60 points. The highest number - 48 - had two schoolchildren: Adam Tichy from Hungary and Karl Shafernik from Czechoslovakia. Both of them received first prizes.

A total of 5 first prizes were awarded.

From the Soviet Union, 5 tenth graders participated in the Olympiad: Alexey Abrikosov (Moscow), Sergey Budnik (Dnepropetrovsk), Andrey Varlamov (Kyiv), Vitas Saldzhukas (Vilnius), Alexander Sitszerev (Osinovka village, Mogilev region). All of them are winners of the 1971 All-Union Physics Olympiad.

All our schoolchildren successfully performed at the V International Physics Olympiad and received corresponding certificates and prizes. The first prize went to Andrey Varlamov (45 points), the second prize went to Alexey Abrikosov (44 points). A. Abrikosov was also awarded a special attribute for the largest number of flawlessly completed tasks (4 out of 6 tasks were awarded the highest points and praise). This year, as at previous Olympiads, in accordance with the established system, only individual championships were considered and there were no team competitions.

Below are the tasks of the V International Physics Olympiad 1971.

1. A smooth wedge with mass M has a triangular cross-section with base angles θ₁ and θ₂. On the wedge there are two smooth masses m₁ and m₂, connected to each other by an inextensible thread thrown over a small block attached to the top of the wedge. Neglect the masses of the thread and the block in comparison with the masses of the weights and the wedge. The whole system started from scratch. With what acceleration a₀ will the wedge slide if it is on a perfectly smooth horizontal plane and if the system is left to its own devices? Express the acceleration of the weights relative to the wedge a’ through the acceleration of the wedge. At what ratio of masses m₁ and m₂ will the wedge be motionless, and the loads will slide along the wedge?

2. A glass tube with a cross section of S = 1 cm² is sealed at one end, filled with hydrogen and positioned vertically so that the upper end is sealed and the lower end is lower.