ipho96theory - PART 4 Theoretical Competition Exam...

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97 PART 4 Theoretical Competition Exam commission page 98 Problems in English 99 Solutions in English page 106 Problems in three other languages and back-translations of these page 117 Examples of student papers page 130 Photos from the grading process page 140 Example of «Old Masters´» original theoretical work. (From: The collected papers of Albert Einstein, Vol. 4, 1995)
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98 Per Chr. Hemmer Chief examiner Commission for the Theoretical Competiton: Per Chr. Hemmer Alex Hansen Eivind Hiis Hauge Kjell Mork Kåre Olaussen Norwegian University of Science and Technology, Trondheim & Torgeir Engeland Yuri Galperin Anne Holt Asbjørn Kildal Leif Veseth University of Oslo
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99 27 th INTERNATIONAL PHYSICS OLYMPIAD OSLO, NORWAY THEORETICAL COMPETITION JULY 2 1996 Time available: 5 hours READ THIS FIRST : 1. Use only the pen provided 2. Use only the marked side of the paper 3. Each problem should be answered on separate sheets 4. In your answers please use primarily equations and numbers, and as little text as possible 5. Write at the top of every sheet in your report: Your candidate number (IPhO identification number) The problem number and section identification, e.g. 2/a Number each sheet consecutively 6. Write on the front page the total number of sheets in your report This set of problems consists of 7 pages.
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100 PROBLEM 1 (The five parts of this problem are unrelated) a) Five 1 resistances are connected as shown in the figure. The resistance in the conducting wires (fully drawn lines) is negligible. Determine the resulting resistance R between A and B. (1 point) ___________________________________________________________________________ b) A skier starts from rest at point A and slides down the hill, without turning or braking. The friction coefficient is µ . When he stops at point B, his horizontal displacement is s . What is the height difference h between points A and B? (The velocity of the skier is small so that the additional pressure on the snow due to the curvature can be neglected. Neglect also the friction of air and the dependence of µ on the velocity of the skier.) (1.5 points) c) A thermally insulated piece of metal is heated under atmospheric pressure by an electric current so that it receives electric energy at a constant power P . This leads to an increase of the absolute temperature T of the metal with time t as follows: [] Tt T at t () ( ) . =+ 00 14 1 Here a, t 0 and T 0 are constants. Determine the heat capacity CT p () of the metal (temperature dependent in the temperature range of the experiment). (2 points)
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101 d) A black plane surface at a constant high temperature T h is parallel to an- other black plane surface at a constant lower temperature T l . Between the plates is vacuum. In order to reduce the heat flow due to radiation, a heat shield consisting of two thin black plates, thermally isolated from each other, is placed between the warm and the cold surfaces and parallel to these. After some time stationary conditions are obtained.
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ipho96theory - PART 4 Theoretical Competition Exam...

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