Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Exercises and problems in Physics
September 2004

Please read The Rules of the Problem Solving Competition.

Experimental problem

M. 253. Measure what minimum torque is needed to break a wooden skewer. Carry out as many measurements as you can.

(6 points)

Theoretical problems

It is allowed to send solutions for any number of problems, but final scores of students of grades 9-12 are computed from the 5 best score in each month. Final scores of students of grades 1-8 are computed from the 3 best scores in each month.

P. 3722. The mass center of the homogeneous plate shown in the figure is in point A. What is the ratio b/a?

(3 points)

P. 3723. Why does ice build up on the inner wall of the deep-freezer section of a refrigerator? Can it be prevented?

(3 points)

P. 3724. We want to flip over one of its edges a cube of edges l and mass m with a homogeneous mass distribution. We lift the cube with vertical force acting in the mid point of one edge. a) Calculate and plot the necessary force F as a function of height h. b) How much work is done while flipping the cube slowly over?

(4 points)

P. 3725. While heating up from 20 oC to 80 oC a 120 liter electric boiler filled entirely with water, water is dripping through the safety valve. Can a half-liter vessel contain the water dripping out?

(4 points)

P. 3726. Two men are trying to start a broken-down car by pushing it. The mass of the car is 1750 kg and the mass of the driver is 80 kg. To ignite the engine the car must roll at a speed of 8 km/h. When can the driver release the clutch if one man pushes the car with a force of 335 N and the other one with 405 N? The gripping force between the tyres and the road is 500 N. P. 3727. A certain amount of air heated at constant pressure absorbs 2.1 kJ of heat. a) To what extent does the internal energy of the gas change? b) How much work is done by the gas?

(3 points)

P. 3728. On the sunny side of the Venus the air pressure is 9 .106 Pa and the temperature is 740 K. On the surface of the Earth the pressure is 105 Pa and the temperature of the sunny side can reach 320 K. All these suggest that the atmosphere of planet Venus is denser than Earth's atmosphere. Is this supposition true?

(4 points)

P. 3729. How much can the temperature of the water in a 50 mx25 mx2 m size pool be raised with the energy released by a single gram of 235 Uranium isotope in a nuclear power plant?

(4 points)

P. 3730. In position A of the switch the capacitor of 684 nF is connected to a 40 V battery. We move the switch from position A to B. The inductivity of the coil is 30 mH and its ohmic resistance is negligible. How much is voltage DB 0.3 ms after moving the switch?

(4 points)

P. 3731. The resistance of a piece of thin wire of length L is R. A square with a side length L is prepared of that thin wire and the middle points of the sides are connected with the same kind of wire. This process can be continued resulting in smaller and smaller squares, theoretically an infinite number of them. a) How long wire is needed to do this? b) How much is the resultant resistance between points A and B?

(5 points)

Send your solutions to the following address:

    KöMaL Szerkesztőség (KöMaL feladatok),
    Budapest 112, Pf. 32. 1518, Hungary
or by e-mail to:

Deadline: 11 October 2004