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11th_IPhO_1979

11th_IPhO_1979 - Problems of the XI International Olympiad...

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Problems of the XI International Olympiad, Moscow, 1979 The publication has been prepared by Prof. S. Kozel and Prof. V.Orlov (Moscow Institute of Physics and Technology) The XI International Olympiad in Physics for students took place in Moscow, USSR, in July 1979 on the basis of Moscow Institute of Physics and Technology (MIPT). Teams from 11 countries participated in the competition, namely Bulgaria, Finland, Germany, Hungary, Poland, Romania, Sweden, Czechoslovakia, the DDR, the SFR Yugoslavia, the USSR. The problems for the theoretical competition have been prepared by professors of MIPT (V.Belonuchkin, I.Slobodetsky, S.Kozel). The problem for the experimental competition has been worked out by O.Kabardin from the Academy of Pedagogical Sciences. It is pity that marking schemes were not preserved. Theoretical Problems Problem 1. A space rocket with mass M =12t is moving around the Moon along the circular orbit at the height of h =100 km. The engine is activated for a short time to pass at the lunar landing orbit. The velocity of the ejected gases u = 10 4 m/s. The Moon radius R M = 1,7·10 3 km, the acceleration of gravity near the Moon surface g M = 1.7 m/s 2 Fig.1 Fig.2 1). What amount of fuel should be spent so that when activating the braking engine at point A of the trajectory, the rocket would land on the Moon at point B (Fig.1)? 2). In the second scenario of landing, at point A the rocket is given an impulse directed towards the center of the Moon, to put the rocket to the orbit meeting the Moon surface at point C (Fig.2). What amount of fuel is needed in this case? 1

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Problem 2. Brass weights are used to weigh an aluminum-made sample on an analytical balance. The weighing is ones in dry air and another time in humid air with the water vapor pressure P h =2·10 3 Pa. The total atmospheric pressure ( P = 10 5 Pa) and the temperature ( t =20° C) are the same in both cases. What should the mass of the sample be to be able to tell the difference in the balance readings provided their sensitivity is m 0 = 0.1 mg ? Aluminum density ρ 1 = 2700 kg/m 3 , brass density ρ 2 =.8500 kg/m 3 . Problem 3 .During the Soviet-French experiment on the optical location of the Moon the light pulse of a ruby laser (λ= 0,69 μm) was directed to the Moon’s surface by the telescope with a diameter of the mirror D = 2,6 m. The reflector on the Moon’s surface reflected the light backward as an ideal mirror with the diameter d = 20 cm. The reflected light was then collected by the same telescope and focused at the photodetector. 1) What must the accuracy to direct the telescope optical axis be in this experiment? 2) What part of emitted laser energy can be detected after reflection on the Moon, if we neglect the light loses in the Earth’s atmosphere? 3) Can we see a reflected light pulse with naked eye if the energy of single laser pulse E = 1 J and the threshold sensitivity of eye is equal n =100 light quantum?
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11th_IPhO_1979 - Problems of the XI International Olympiad...

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