6th_IPhO_1972 - Problems of the 6th International Physics...

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Problems of the 6 th International Physics Olympiad (Bucharest, 1972) Romulus Pop Civil Engineering University, Physics Department 1 Bucharest, Romania The sixth IPhO was held in Bucharest and the participants were: Bulgaria, Czechoslovakia, Cuba, France, German Democratic Republic, Hungary, Poland, Romania, and Soviet Union. It was an important event because it was the first time when a non-European country and a western country participated (Cuba), and Sweden sent one observer. The International Board selected four theoretical problems and an experimental problem. Each theoretical problem was scored from 0 to 10 and the maximum score for the experimental problem was 20. The highest score corresponding to actual marking system was 47,5 points. Each team consisted in six students. Four students obtained the first prize, seven students obtained the second prize, ten students obtained the third prize, thirteen students had got honorable mentions, and two special prizes were awarded too. The article contains the competition problems given at the 6 th International Physics Olympiad (Bucharest, 1972) and their solutions. The problems were translated from the book published in Romania concerning the first nine International Physics Olympiads 2 , because I couldn’t find the original English version. Theoretical problems Problem 1 (Mechanics) Three cylinders with the same mass, the same length and the same external radius are initially resting on an inclined plane. The coefficient of sliding friction on the inclined plane, μ, is known and has the same value for all the cylinders. The first cylinder is empty (tube) , the second is homogeneous filled, and the third has a cavity exactly like the first, but closed with two negligible mass lids and filled with a liquid with the same density like the cylinder’s walls. The friction between the liquid and the cylinder wall is considered negligible. The density of the material of the first cylinder is n times greater than that of the second or of the third cylinder. Determine: a) The linear acceleration of the cylinders in the non-sliding case. Compare all the accelerations. b) Condition for angle α of the inclined plane so that no cylinders is sliding. c) The reciprocal ratios of the angular accelerations in the case of roll over with sliding of all the three cylinders. Make a comparison between these accelerations. d) The interaction force between the liquid and the walls of the cylinder in the case of sliding of this cylinder, knowing that the liquid mass is m l . Solution Problem 1 1 E-mail: p[email protected] 2 Marius Gall and Anatolie Hristev, Probleme date la Olimpiadele de Fizica, Editura Didactica si Pedagogica – Bucuresti, 1978 1
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The inertia moments of the three cylinders are: ( 29 , 2 1 4 4 1 1 h r R I - = π ρ 2 4 2 2 2 1 2 1 mR h R I = = π ρ , ( 29 , 2 1 3 4 4 2 h r R I - = π ρ (1) Because the three cylinders have the same mass : ( 29 h R h r R m 2 2 2 2 1 π ρ π ρ = - = (2) it results: 2 1 2 1 2 2 2 , 1 1 1 ρ ρ ρ ρ = - = - = n n R R r (3)
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