备考全国高中物理竞赛11thipho1979电子教案.docx

1、备考全国高中物理竞赛11thipho1979电子教案备考2014年全国高中物理竞赛-11th_IPhO_1979Problems 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

2、, 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 theoretica

3、l 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 ProblemsProblem 1. A

4、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 = 104 m/s. The Moon radius RM = 1,7103 km, the acceleration of gravity near the

5、 Moon surface gM = 1.7 m/s2 Fig.1 Fig.21). 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 towar

6、ds 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?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

7、 with the water vapor pressure Ph =2103 Pa. The total atmospheric pressure (P = 105 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 m0 = 0.1 mg ?Aluminum density

8、 1= 2700 kg/m3, brass density 2=.8500 kg/m3.Problem 3.During the Soviet-French experiment on the optical location of the Moon the light pulse of a ruby laser (= 0,69 m) was directed to the Moons surface by the telescope with a diameter of the mirror D = 2,6 m. The reflector on the Moons surface refl

9、ected 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 det

10、ected after reflection on the Moon, if we neglect the light loses in the Earths 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?4) Suppose the Moons surface reflects = 10% o

11、f the incident light in the spatial angle 2 steradian, estimate the advantage of a using reflector.The distance from the Earth to the Moon is L = 380000 km. The diameter of pupil of the eye is dp = 5mm. Plank constant is h = 6.610-34 Js.Experimental Problem Define the electrical circuit scheme in a

12、“black box” and determine the parameters of its elements. List of instruments: A DC source with tension 4.5 V, an AC source with 50 Hz frequency and output voltage up to 30 V, two multimeters for measuring AC/DC current and voltage, variable resistor, connection wires.Solution of Problems of the XI

13、International Olympiad, Moscow, 1979Solution of Theoretical ProblemsProblem 1. 1) During the rocket moving along the circular orbit its centripetal acceleration is created by moon gravity force:,where R = RM + h is the primary orbit radius, v0 -the rocket velocity on the circular orbit:Since it yiel

14、ds (1)The rocket velocity will remain perpendicular to the radius-vector OA after the braking engine sends tangential momentum to the rocket (Fig.1). The rocket should then move along the elliptical trajectory with the focus in the Moons center. Denoting the rocket velocity at points A and B as vA a

15、nd vB we can write the equations for energy and momentum conservation as follows: (2)MvAR = MvBRM (3)Solving equations (2) and (3) jointly we findTaking (1) into account, we get .Thus the rocket velocity change v at point A must be Since the engine switches on for a short time the momentum conservat

16、ion low in the system “rocket-fuel” can be written in the form(M m1)v = m1uwhere m1 is the burnt fuel mass.This yieldsAllow for v u we find 2) In the second case the vector is directed perpendicular to the vector thus givingBased on the energy conservation law in this case the equation can be written as (4)and from the mome