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KöMaL Füzetek 1: Tálalási javaslatok matematika felvételire

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Exercises and problems in Physics
September 1999

Please read The Conditions of the Problem Solving Competition.

New experimental problem:

M. 208. Measure the density of the material of a table-tennis ball as accurately as you can. Give an error estimation. (6 points)

New problems:

P. 3264. The value at "cement 600" shows that the cross-sectional area of 1 cm2 of a concrete plate is capable to hold the weight of 600 kg. Using ten times higher safety standard how high concrete tower can be made of this kind of cement? The density of concrete is 2500 kg/m3. (3 points)

P. 3265. The water runs into an insulated vessel from two taps. The first tap gives 7 litres water per minute with temperature 12 oC, while the other gives 4 litres per minute with 60 oC. The cold water tap has been open for 8 minutes. How long should the hot water tap be open to get finally 36 oC water in the vessel? (3 points)

P. 3266. In hail a piece of ice hits onto the roof of a car with a speed of 6 m/s. How high does it bounce back at most if 60%of its kinetic energy is lost in the collision? (3 points)

P. 3267. There are two identical open test-tube in a garden. One of them is in shadow, the other is placed on a very sunny place. There is no wind at all. In which test-tube is bigger the energy of air

    a) if the thermal expansion of glass is negligible;

    b) if the thermal expansion of glass is not negligible?

(4 points)

P. 3268. A glass of carbonated water is on the table. Approximately how many CO2 molecules are in a bubble of diameter 1 mm? (4 points)

P. 3269. A simple pendulum is hung on a frictionless chart of mass M. The mass of the bob is m, the length of the string is l. Fixing the chart the pendulum is displaced a little bit and released. After measuring the period the experiment is repeated not fixing the chart. How does the period of the pendulum change? (4 points)

P. 3270. A satellite has a circular orbit of radius r=2R around the Earth of radius R=6370 km. In an instant it gets an extra velocity directed to the centre of the Earth. The change of magnitude of its linear momentum is equal the magnitude of momentum of the satellite before.

    a) Find the velocity of the satellite just after the change of its momentum.

    b) Find the minimum distance of the satellite from the centre of the Earth after changing its momentum.

    c) What is its velocity at the closest point?

(5 points)

P. 3271. The diameter of the objective lens of a Kepler telescope (of magnification 5) is 84 mm, its focal length is 1 m, the diameter of its ocular (eyepiece) lens is 12 mm. Find the maximum visual angle of this telescope to observe stars at the same time. (5 points)

P. 3272. Suppose the rest heat of nuclear power station in Paks of power 1800 MW and efficiency 30 % is using for melting the ice cover of the frozen lake Balaton of thickness 10 cm. For how long would this quantity of ice melt? What surface should be covered with solar cells constructing a solar power station having a peak power identical with the permanent electric power of Paks? (The intensity of the solar radiation on the surface of the Earth is approximately 1 kW/m2.) (4 points)

P. 3273. There is a very small hole on a heatable furnace. In the vicinity of the furnace the temperature of air is 0 oC, while the temperature inside is 57 oC. In sufficient time the pressure in the furnace becomes steady. Estimate this steady pressure. (6 points)

Send your solutions to the following address:

KöMaL Szerkesztőség (KöMaL feladatok), Budapest Pf. 47. 1255, Hungary

or by e-mail to: megoldas@komal.elte.hu.

Deadline: 15 October 1999

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