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Problems in Physics, November 2006

Please read the rules of the competition.


Problems with sign 'M'

Deadline expired on 11 December 2006.

M. 273. The display of a solar cell powered calculator turns off if some part of the solar cell is covered. (Use a calculator which does not have a back-up battery.) Find the limit case, and examine the relationship between the area of the uncovered surface and the intensity of light. Shading the uncovered part of the solar cell with semi-permeable foils investigate how the absorption of light depends on the number of layers.

(6 points)

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Problems with sign 'P'

Deadline expired on 11 December 2006.

P. 3923. In a thermally insulated container there was some water at a temperature of 30\,{}^\circ\rm
C, then 1 kg ice at temperature -30\,{}^\circ\rm C was added. How much water was initially in the container if

a) there was no phase change;

b) the total amount of ice melted;

c) the total amount of water froze?

(4 points)

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P. 3924. If a bulb, rated at 15 W and 230 V, and another bulb rated at 100 W and 230 V are connected in series and a voltage supply of 230 V is applied the 15 W bulb operates as if it was connected to the 230 V voltage supply, but the 100 W bulb does not operate at all. Explain the phenomenon.

(4 points)

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P. 3925. What is the colour of the sky above our head in the day-time observed

a) from the ground;

b) from a sail-plane;

c) from a jet fighter;

d) from a space station revolving around the Earth;

e) from the Moon?

(4 points)

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P. 3926. The two ends of a rubber string of negligible mass are fixed at the same height, such that the string is un-stretched. A small object is attached to the string in its midpoint, thus the angle of depression of the string is \alpha=30o. Then the small object is charged and vertical electric field is applied. Initially the depression angle of the string increases to \alpha1=45o, then the electric field is changed and the depression angle increases to \alpha2=60o. By what factor is the electric field in the second case more than that of in the first case?

(4 points)

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P. 3927. Two small moons revolve around a planet. The period of one of them is 24 hours and the period of the other is 81 hours. The second moon is 2.5 times further from the surface of the planet than the first one. Find the average density of the planet. (The moons revolve along circular paths.)

(4 points)

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P. 3928. Sid has a very good sense of music. One day when he walked home he was surprised to experience that the change in the pitch of the sound of the horn of a passing car changed exactly by one major second (a whole tone). When he got home he could calculate the speed of the car. Did the driver keep the speed limit in towns?

(4 points)

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P. 3929. A disc of mass m=12 kg and of radius R=0.1 m slides down without rolling along smooth, frictionless inclined plane, which ends in a horizontal plane without break. The disc starts at a height of h=1.25 m (it has no initial speed and it does not rotate), and lands on the top of a cart of mass M=6 kg, which can move easily. The coefficient of kinetic friction between the cart and the disc is \mu=0.4. The disc begins to roll without sliding when it is in the middle of the cart.

a) How long is the cart?

b) What is the greatest speed of the cart?

c) How long does it take for the disc to go through the cart?

(5 points)

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P. 3930. The circuit of a carbon arc lamp is shown in the figure (to ignite the lamp the carbon electrodes are touched together, then they are slowly drawn apart.) The voltage across the gap between the carbon rods as a function of the current can be given by the following formula: U=A+\frac{B}{I}, where A and B are constants.

a) If the voltage of the battery U0. can be considered constant what is the resistance of the multiplier Rmax , that should be connected in series to ignite the lamp.

b) Find the stable current if the resistance of the multiplier is R<Rmax .

Data: A=30 V, B=20 W, U0=100 V, R=50 \Omega.

(5 points)

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P. 3931. What is the greatest and the smallest speed with which a comet revolving around the Sun could strike the Earth if there was no air around the Earth?

(5 points)

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P. 3932. Why can those radioactive isotopes (natural) exist in the Earth which have much shorter half-life than the age of the Earth?

(4 points)

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    KöMaL Szerkesztőség (KöMaL feladatok),
    Budapest 112, Pf. 32. 1518, Hungary
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