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KöMaL Problems in Physics, December 2012

Please read the rules of the competition.


Show/hide problems of signs:


Problems with sign 'M'

Deadline expired on 10 January 2013.


M. 328. According to the grandmother of Judy, who always makes chocolate coconut balls for Christmas, if she forms greater balls from the mixture less coconut gratings are needed to roll in the balls. What can the truth behind her opinion be? Look for a theoretical relationship between the size of the balls and the used coconut gratings, and then check it experimentally.

(6 pont)

statistics


Problems with sign 'P'

Deadline expired on 10 January 2013.


P. 4486. Sam was courious to find the speed of the elevator in their house. For his measurement he used a bathroom scale and a stopwatch. He got into the lift at the groundfloor, stood on the the scale and recorded the readings on the scale. The reading was 50 kg when the elevator was at rest, and for 2 seconds right after the lift started to move the reading of the scale was 52 kg. What is the speed of the elevator when it moves uniformly?

(3 pont)

solution (in Hungarian), statistics


P. 4487. The e.m.f. of an older type of rechargeable battery of a mobile phone is 2.4 V, whilst its capacity to store the charges is 1100 milliampere-hour. How much energy can this battery store?

(3 pont)

solution (in Hungarian), statistics


P. 4488. The following safe distances between two cars are suggested in order to avoid rear-end collisions: for a speed of 70 km/h the safe distance is 20 m, for a speed of 100 km/h the safe distance is 30 m, for a speed of 130 km/h the safe distance is 40 m. What is your opinion about these suggestions?

(4 pont)

solution (in Hungarian), statistics


P. 4489. The same problem was P.4477 in November.

(4 pont)

solution (in Hungarian), statistics


P. 4490. A small body of mass m is placed to the top of a fixed hemisphere, and is tied by means of a rope to another body of mass M, which hangs vertically. The system is released, the small body of mass m slides along the hemisphere without friction. At which mass ratio m/M will the small body of mass m leave the surface of the hemisphere exactly at the angle of 45o? Where will the small body leave the hemisphere if M\llm, and where will it leave the surface if M\ggm?

(5 pont)

solution (in Hungarian), statistics


P. 4491. A spaceship is orbiting around the Earth. The distance between the spaceship and the surface of the Earth is the same as the radius of the Earth. Operating the rockets on the spaceship for a short time, the direction of the velocity of the spaceship is changed such that the angle between the actual radius drawn to the spaceship and the velocity is \varphi=150o. The speed and the height of the spaceship above the Earth surface is unchanged.

a) By what amount will the spaceship go further away from the surface of the Earth?

b) Without altering again the path of the spaceship, at what speed would the spaceship hit the surface of the Earth?

(Neglect the effect of air and the rotation of the Earth.)

(5 pont)

solution (in Hungarian), statistics


P. 4492. A sample of monatomic ideal gas is taken through the cyclic process shown in the figure. The temperature of the gas at state A is TA=180 K. What is the temperature of the gas at state C if the efficiency of the heat engine of this cyclic process is \eta=2/9?

(4 pont)

solution (in Hungarian), statistics


P. 4493. At least by what factor is the equivalent capacitance of three condensers of different capacitances connected in parallel greater than the equivalent capacitance of the same condensers connected in series?

(4 pont)

solution (in Hungarian), statistics


P. 4494. All the resistances of the resistors shown in the figure are R=2 M\Omega, the capacitance of the capacitor is C=1 \muF, the voltage of the battery is U=90 V. The switch K is held at its closed position in order to charge the capacitor, and then it is opened.

a) What is the reading on the ideal voltmeter before opening the switch?

b) What is the reading on the voltmeter a short time after the switch was opened?

(4 pont)

solution (in Hungarian), statistics


P. 4495. The form consisting of rings touching each other is soldered from a 1-m long metal wire of resistance 80 \Omega. (See the figure.) What is the resistance measured across the endpoints AB of the diameter of the great ring?

(4 pont)

solution (in Hungarian), statistics


P. 4496. A small object of mass m slides along a slope which is attached tangentially to a cart of mass M. In the middle of the cart a hemicylinder of radius R is attached to the cart as shown in the figure. The small object of mass m just reaches the top point A of this hemicylinder, stops there for an instant, then it falls freely and just hits the rim of the car. a) At least how long is the cart? b) What is the mass of the cart? c) From what height did the small object slide down? (m=2 kg, R=0.6 m. Friction is negligible everywhere.)A small object of mass m slides along a slope which is attached tangentially to a cart of mass M. In the middle of the cart a hemicylinder of radius R is attached to the cart as shown in the figure. The small object of mass m just reaches the top point A of this hemicylinder, stops there for an instant, then it falls freely and just hits the rim of the car.

a) At least how long is the cart?

b) What is the mass of the cart?

c) From what height did the small object slide down?

(m=2 kg, R=0.6 m. Friction is negligible everywhere.)

(6 pont)

solution (in Hungarian), statistics


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

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