Mathematical and Physical Journal
for High Schools
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# KöMaL Problems in Physics, March 2013

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## Problems with sign 'M'

Deadline expired on April 10, 2013.

M. 331. Hang a tennis ball to the end of a thread and with this pendulum measure how much work is done by the air drag during one complete swing. How does this work depend on the initial displacement of the ball? Can we deduce from the measured data anything about which power of the velocity the air drag is proportional to (in case of smaller and bigger speeds)?

(6 pont)

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## Problems with sign 'P'

Deadline expired on April 10, 2013.

P. 4518. A ball of mass m bounces between two parallel walls, such that its velocity v is perpendicular to the walls.The collisions with the walls are totally elastic. What is the average force exerted by the ball on the walls, if the distance between the walls is d?

(3 pont)

solution (in Hungarian), statistics

P. 4519. Recently, one of the greatest sensation was Felix Baumgartner's stratosphere jump. The Austrian sky-diver jumped out of the capsule, lifted by a Helium balloon, at a height of 39045 metres and opened his parachute after falling for 4 minutes and 17 seconds. According to the video which can be seen on the world wide web, in the first part of his motion his speed changed as it is shown in the table below:

a) Plot the speed-time and the acceleration-time graphs of the motion in the first 64 seconds.

b) His greatest registered speed was 1300 km/h, which is 1.2 times the actual speed of sound. Estimate when would he reach this record, if only the effect of gravity is counted.

(4 pont)

solution (in Hungarian), statistics

P. 4520. The bodies arranged as shown in the figure are at rest; m1=1 kg, =30o. The rope attached to the body of mass m1 is horizontal.

a) Determine the magnitude of m2.

b) Suppose that the rope which fixes the body of mass m1 brakes. What is the acceleration of the bodies when they begin to move?

(4 pont)

solution (in Hungarian), statistics

P. 4521. A sample of air of volume V1=3 dm3 and of pressure p1=6.104 Pa is confined to a fixed vertical cylinder which is closed at its bottom by a piston of cross section A=1 dm2, which can move frictionlessly. The piston is connected to the closed end of the cylinder with a spring, designed for both compression and tension, of length L0=0.6 m and of spring constant D=1000 N/m. The system is in equilibrium in this position. The external air pressure is p0=105 Pa.

a) Find the mass of the piston.

b) The air in the piston is heated slowly. How much heat must be added to the confined air in order to reach that state when the spring does not exert any force on the piston?

(4 pont)

solution (in Hungarian), statistics

P. 4522. News: Each saved cubic metre of natural gas protects the environment from the emission of 1.7 kg of carbon-dioxide gas. 97% of the natural gas is methane.

a) What is the temperature of the methane if 1.7 kg carbon-dioxide is emitted during the burning of 1 cubic metre of methane at normal pressure?

b) How many kg Oxygen is used and how much water vapour is gained?

c) By what amount is the calorific value of 1 cubic metre of methane smaller than its heat of combustion?

(4 pont)

solution (in Hungarian), statistics

P. 4523. Five alike =0.5 metre long pendulums are made of electrically insulating threads and of small metal spheres of mass m=50 milligram. Each small sphere is given the same type of electrical charge of Q=10-7 coulomb, and the pendulums are hung at the same point. Reaching the equilibrium position, because the mutual repulsion the small spheres will be on the circumference of a horizontal circle.

a) What is the radius of this circle?

b) What would the number of revolution of the rotation of the pendulums be, if they were to rotate about a vertical axis going through the point at which they are hung, and the small spheres were to move along the circumference of the above described circle such that the spheres had no charge on them?

(5 pont)

solution (in Hungarian), statistics

P. 4524. The pointer of the linear variable resistor (rheostat), shown in the figure is initially at the middle of the rheostat. How do the readings on the meters change if the pointer is slowly moved towards the right? The resistance of the variable resistor is R and the internal resistance values of the voltmeter and the ammeter are RV and RA, respectively.

(5 pont)

solution (in Hungarian), statistics

P. 4525. The flux linkage of a circular loop of wire of radius 10 cm and of cross section 0.5 mm2, which is in uniform perpendicular magnetic field, is 6.28.10-3 Vs. What will the tension in the loop be when a current of 10 A begins to flow in it?

(5 pont)

solution (in Hungarian), statistics

P. 4526. Which planet covers greater part of the Sun during its transit: the Venus observed from the Earth, or the Earth observed from the Mars? What is the ratio of the two covered parts?

(4 pont)

solution (in Hungarian), statistics

P. 4527. By what factor the ,,efficiency'' of the Sun is greater than that of the nuclear power station at Paks? More precisely: how much more energy is liberated during the fusion of 1 kg Hydrogen into Helium, than during the fission of 1 kg Uranium?

(4 pont)

solution (in Hungarian), statistics

P. 4528. An unexpansible, flexible heavy rope is hung to two nails, held at the same height as shown in the figure. The rope is at rest in this position. The length of the rope between the nails is and the deepest point of this part of the hanging rope is at a depth of h, measured from the level of the nails. How long is the rope? (Friction is negligible.)

(6 pont)

solution (in Hungarian), statistics

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