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Problems in Physics, September 2013

Please read the rules of the competition.


Problems with sign 'M'

Deadline expired on 10 October 2013.

M. 334. Place a chain made of same links to the table such that some part of the chain hangs down from the tabletop. When will the whole chain begin to slide down from the table? Using the result give an estimation to the coefficient of static friction between the table and the chain. Check your estimation with measurement as well!

(6 points)

Statistics


Problems with sign 'P'

Deadline expired on 10 October 2013.

P. 4551. There is a massless piston, which can move frictionlessly, in the middle of a 1-metre long, horizontal tube, closed at both of its ends. In the left chamber there is a sample of Oxygen gas, and in the right chamber there is Hydrogen gas at the same tempereture. The mass of the hydrogen is one-fourth of that of the Oxygen. Where is the equilibrium position of the piston?

(3 points)

Solution (in Hungarian)

P. 4552. A fisherman sitting in his boat drops his pipe into the water. The change in the level of the water is the same as if he drops his pipe into the water when he stands on the shore. What is the density of the pipe?

(4 points)

Solution (in Hungarian)

P. 4553. The operation of a hot air balloon is to be modelled by a small candle and a light plastic bag. Estimate the minimum volume of the ascending bag which is in a room of temperature 20 oC, if the average temperature of the air in the bag is 80 oC, and the total mass of the candle, the bag and the other equipments is 12 grams.

(4 points)

Solution (in Hungarian)

P. 4554. There are two tables next to each other. How much work is done on that flat parcel, which is pulled from one of the tables to the other? The coefficients of dynamic friction between the parcel and the two tabletops are different.

Data: m=18 kg; \ell=0.8 m; \mu1=0.1; \mu2=0.4. ( The weight of the parcel is distributed evenly along the surfaces of the tables that are in contact with the parcel.)

(4 points)

Solution (in Hungarian)

P. 4555. There is a 4-m long, 1.2 kg chain, wound small, at the bottom of a 2-m deep lake. At least how much work is to be performed while the chain is pulled out totally from the lake, by holding one of its end, and moving it vertically? The density of the material of the chain is 3000 kg/m3.

(4 points)

Solution (in Hungarian)

P. 4556. There is a spring of spring constant D=240 N/m between two easily rolling carts of masses m1=2 kg and m2=3 kg. The spring is kept at a compressed position by a thin thread and the compression of the spring is \Delta\ell=15 cm. The common speed of the two carts is v=2 m/s. What will their velocities be after the break of the thread?

(4 points)

Solution (in Hungarian)

P. 4557. A 0.6-kg iron cylinder is attached to the end of the spring shown in the figure, and a disc shape magnet of mass 0.2 kg sticks to the bottom of the iron cylinder. Initially the spring, the spring constant of which is 64 N/m, is unstretched, and then the system is released. During the oscillation the magnet does not fall off.

a) What is the period of the oscillation?

b) What is the greatest speed of the magnet?

c) What is the minimum force between the magnet and the iron cylinder?

(4 points)

Solution (in Hungarian)

P. 4558. There is some water and its saturated vapour above it in a container, containing a piston, at a temperature of 370 oC. The total mass of the water and its vapour is 2 kg. The initial volume of the water and its vapour together is 8 dm3.

a) What is the volume of the vapour?

b) The piston is moved into the vessel, while the temperature is kept constant, and the volume of the container is decreased to 5 dm3. What will the volume of the water vapour be in this case?

c) By how many molecules did the amount of vapour decrease?

(4 points)

Solution (in Hungarian)

P. 4559. A pen dosimeter, which contains 5 cm3 air at standard conditions, and which has a capacitance of 1 pF, is charged to 1000 V, initially. What is the absorbed doze, if after the exposure, the voltage drops to 900 V? The average ionization-energy of air is 6.88 aJ and its density is 1.3 kg/m3.

(4 points)

Solution (in Hungarian)

P. 4560. Bones of Woolly Mammuth were found in North-America. The activity C-14 originated from the youngest bones is 21% of that of in a living animal today. How many years ago did the Woolly Mammuth become extinct in North-America?

(4 points)

Solution (in Hungarian)


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    Budapest 112, Pf. 32. 1518, Hungary
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