4th_IPhO_1970

# 4th_IPhO_1970 - Problems of the IV International Olympiad Moscow 1970 The publication is prepared by Prof S Kozel Prof V.Orlov(Moscow Institute of

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Problems of the IV International Olympiad, Moscow, 1970 The publication is prepared by Prof. S. Kozel & Prof. V.Orlov (Moscow Institute of Physics and Technology) The IV International Olympiad in Physics for schoolchildren took place in Moscow (USSR) in July 1970 on the basis of Moscow State University. Teams from 8 countries participated in the competition, namely Bulgaria, Hungary, Poland, Romania, Czechoslovakia, the DDR, the SFR Yugoslavia, the USSR. The problems for the theoretical competition have been prepared by the group from Moscow University stuff headed by professor V.Zubov. The problem for the experimental competition has been worked out by B. Zvorikin from the Academy of Pedagogical Sciences. It is pity that marking schemes were not preserved. Theoretical Problems Problem 1. A long bar with the mass M = 1 kg is placed on a smooth horizontal surface of a table where it can move frictionless. A carriage equipped with a motor can slide along the upper horizontal panel of the bar, the mass of the carriage is m = 0.1 kg. The friction coefficient of the carriage is μ = 0.02. The motor is winding a thread around a shaft at a constant speed v 0 = 0.1 m/s. The other end of the thread is tied up to a rather distant stationary support in one case (Fig.1, a), whereas in the other case it is attached to a picket at the edge of the bar (Fig.1, b). While holding the bar fixed one allows the carriage to start moving at the velocity V 0 then the bar is let loose. Fig. 1 Fig. 2 By the moment the bar is released the front edge of the carriage is at the distance l = 0.5 m from the front edge of the bar. For both cases find the laws of movement of both the bar and the carriage and the time during which the carriage will reach the front edge of the bar. 1

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Problem 2. A unit cell of a crystal of natrium chloride (common salt- NaCl) is a cube with the edge length a = 5.6 ּ 10 -10 m (Fig.2). The black circles in the figure stand for the position of natrium atoms whereas the white ones are chlorine atoms. The entire crystal of common salt turns out to be a repetition of such unit cells. The relative atomic mass of natrium is 23 and that of chlorine is 35,5. The density of the common salt ρ = 2.22 ּ 10 3 kg/m 3 . Find the mass of a hydrogen atom. Problem 3. Inside a thin-walled metal sphere with radius R= 20 cm there is a metal ball with the radius r = 10 cm which has a common centre with the sphere. The ball is connected with a very long wire to the Earth via an opening in the sphere (Fig. 3). A charge Q = 10 -8 C is placed onto the outside sphere. Calculate the potential of this sphere, electrical capacity of the obtained system of conducting bodies and draw out an equivalent electric scheme. Fig. 3
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## This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.

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4th_IPhO_1970 - Problems of the IV International Olympiad Moscow 1970 The publication is prepared by Prof S Kozel Prof V.Orlov(Moscow Institute of

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