Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# KöMaL Problems in Physics, December 2007

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## Problems with sign 'M'

Deadline expired on January 11, 2008.

M. 283. Fill a carton of juice with some water and tilt it such that its shortest edge is at rest on the table and if it is left it turns back to its original equilibrium position. Measure the maximum angle of tilting as a function of the mass of the water poured to the carton.

(6 pont)

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## Problems with sign 'P'

Deadline expired on January 11, 2008.

P. 4023. Would the longest night of the year last longer or shorter in Hungary if the Earth had no atmosphere?

(3 pont)

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P. 4024. The power rating of resistor R3 shown in the figure is 15 W. The reading on the ammeter is 500 mA and the reading on the voltmeter is 10 V. Find the resistances of R1 and R3. What is the electromotive force of the supply?

(3 pont)

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P. 4025. A handhold mirror contains a plane mirror on one of its side and a concave mirror of radius of curvature of 30 cm on its other side. You hold the plane mirror 15 cm from your face and notice a spot. By what factor will the image of the spot be enlarged if you turn the mirror, but still keep it at a distance of 15 cm from your face?

(4 pont)

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P. 4026. In 1993 in the Spanish city Salamanca Javier Sotomayor won the high jump with a height of 245 cm, which was a new world record. Estimate the initial speed of the jump.

(4 pont)

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P. 4027. The volume of a balloon, filled loosely with Helium, increases if it is taken to a warm room from a cold street. Somebody stated that if we measure the increase of the upthrust exerted on the balloon, we can estimate the heat absorbed by the balloon. Is he right?

(4 pont)

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P. 4028. The bore diameter (inner diameter of the cylinder) of an older-type four-cylinder, four-stroke automobil engine is 92 mm. The piston stroke length is also 92 mm. The average gauge pressure in the cylinder during power stroke is 5.6.105 Pa. The number of revolution of the main axle is 4500 rev/min. Calculate the theoretical'' power of the engine.

(5 pont)

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P. 4029. A 2 kg body, moving on a frictionless horizontal track, reaches another object of 3 kg made of the same material, moving in front of the 2-kg object, and collides with it totally inelastically. Their common speed after the collision is 4 m/s. Due to the collision the temperature of the two objects, which was initially the same, is increased, though only by 0.006 oC. The specific heat capacities of the two objects are the same: .

a) What were the initial speeds of the colliding objects before the collision?

b) What percent of the initial kinetic energy is transferred to increase of the internal energy of the two objects?

(4 pont)

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P. 4030. A house, situated 100 m to the South of a straight road running East--West, contains a television set which is receiving signals from a distant transmitter, also situated South of the road, operating at a frequency of 60 MHz. A bus, travelling along the road in a westerly direction, causes the received signal to fluctuate in intensity, the rate of fluctuation is 2 Hz when the bus is opposite the house and (temporarily) reduces to zero when it is 200 m further along the road. Find the speed of the bus and the direction of the transmitter.

(5 pont)

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P. 4031. A positron of speed , collides with an electron which was initially at rest, and they annihilate. One of the created photon travels perpendicularly to the original direction of the velocity of the positron.

a) In what direction is the other photon emitted?

b) What is the ratio of the energies of the two photons?

(5 pont)

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P. 4032. A uniform metal disc is rotated about an axle, which goes through its centre and which is perpendicular to it. The disc is in uniform magnetic field, the magnetic induction is parallel to the axis of rotation. Usually electromotive force is induced between the rim of the disc and its axle. Though if we are clever we can rotate the disc in such way that no e.m.f. induced between the rim and the axle. How should we rotate the disc if the magnetic induction at the disc is 10-8 T.

(5 pont)

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