
Problems with sign 'P'
Deadline expired on 12 November 2012. 
P. 4465. Why can your breath be seen in cold weather?
(3 pont)
solution (in Hungarian), statistics
P. 4466. The trolley pole of electric train engines  big current flows through them  often sparks. The same current flows through the wheels into the rails as well. Why doesn't the wheels spark?
(3 pont)
solution (in Hungarian), statistics
P. 4467. A police car parking on the hard shoulder of a highway, is passed by a car at a speed of 108 km/h. (This is the greatest speed at which this car can travel.) After a short time it turns out in the police car that the passing car is a stolen one. The police car starts to chase the car ten seconds after the stolen car passed it. The maximum speed of the fourwheel drived police car is 162 km/h. The coefficient of static friction between the road and the wheels is 0.4. In order not to reach the traffic in the city it would be good to catch the escaping car in a distance of 1.5 km. Is it possible?
(4 pont)
solution (in Hungarian), statistics
P. 4468. A circular piece of radius r is cut out of a disc of radius R as shown in the figure. At what ratio of r/R will the centre of mass of the remaining piece be closer to the centre of the disc than R/100?
(4 pont)
solution (in Hungarian), statistics
P. 4469. Two balls of masses m_{1} and m_{2} are hanged at the same point, with threads of equal lengths, and displaced towards the left and the right with the same angle measured from the vertical. They are both released at the same moment, and collide totally inelastically. The positions of the balls are described by their height above the horizontal plane which is through the lowest point of their paths. (Air resistance is negligible.) Give the ratio of the greatest height reached by the balls after the collision to the initial height.
(4 pont)
solution (in Hungarian), statistics
P. 4470. The containers of A and B are connected by a short and thin tube. The volume of container A is three times as much as that of container B. Initially in both containers there is air at a temperature of 20 ^{o}C and at a pressure of 10^{5} Pa. Then container A is heated to a temperature of 100 ^{o}C, and is kept at this temperature while the temperature of B is still 20 ^{o}C. By what percent does the mass of the gas in each container change, and what will the pressure be in them?
(4 pont)
solution (in Hungarian), statistics
P. 4471. Two batteries of voltage 3 V is connected in parallel. Their internal resistances are 3 , and 2 . Then an external resistor of resistance 10 is connected to the batteries. What will the terminal voltage and the current through the batteries be?
(4 pont)
solution (in Hungarian), statistics
P. 4472. There are two coils wined around the same closed iron core. Their inductances on this iron core are measured to be 4 henry, and 9 henry. Then the two coils are connected in series. What will the equivalent inductance be?
(5 pont)
solution (in Hungarian), statistics
P. 4473. 0.06 mass percent of the human body is potassium, and 0.012% of this is the potassium isotope of atomic mass number 40. This isotope is radioactive, it decays, and its half life is 1.3 miliard years. How many decays occur in each second in the body of a 60kg man due to the potassium in the human body?
(4 pont)
solution (in Hungarian), statistics
P. 4474. Estimate the size of that Aluminium ball which can stay at rest in the Solar system. Where can it stay at rest? (Neglect the effect of planets and moons and the particle currents in the Solar system.) The solar luminosity is 3.8^{.}10^{26} W, its mass is 1.989^{.}10^{30} kg, and the density of Aluminium is 2700 kg/m^{3}.
(5 pont)
solution (in Hungarian), statistics