Mathematical and Physical Journal
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# KöMaL Problems in Physics, October 2007

Please read the rules of the competition.

Show/hide problems of signs:

## Problems with sign 'M'

Deadline expired on November 12, 2007.

M. 281. According to a housewife if water at a temperature of 100 oC, is poured from the kettle to the cup from a height of 15-20 cm, than the water in the cup will be colder than if the water is poured at the height of the rim of the cup.

Check with measurement whether she is right or wrong.

(6 pont)

statistics

## Problems with sign 'P'

Deadline expired on November 12, 2007.

P. 4003. On a running training the runners run at a speed of v=5 m/s along a straight path, forming an L=35 m long column. Their coach runs towards them at a speed of u=2 m/s. The first runner turns back and runs in the same direction as the coach, still at a speed of v, when he meets the coach, and so do all the runners when they meet their coach.

a) How much time elapses between the turn of the first and the last runner?

b) How long is the column when they all run in the same direction as the coach?

(4 pont)

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P. 4004. The kinetic energy of a cart of mass 4 kg, moving on a straight horizontal track is 50 J. It collides with another cart of mass 6 kg, which was at rest, and they are coupled.

By what amount does the kinetic energy of the system of the two carts decreased?

(3 pont)

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P. 4005. The walls of a room, which has a shape of a cuboid, are plane mirrors. The distance between the walls are a and b. A horizontal beam of light is generated at one of the walls, the angle between the light beam and this wall is alpha.

How much time elapses until the light reaches the same wall?

(3 pont)

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P. 4006. The two ends of a uniform thin rod of length 2l and of mass m can move without friction along a circular path of radius R. The rod is released from the vertical position.

Find the force exerted by the ends of the rod on the path when the rod passes the horizontal position.

(5 pont)

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P. 4007. In a sample of Helium gas an atom of speed 800 m/s reaches another atom of speed 600 m/s, which moves in the same direction, and they collide elastically. What can be the angle between the velocity vectors after collision?

(5 pont)

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P. 4008. On the dashboard of modern cars the warning sign shows that the roads are icy even when the thermometer measuring the outside temperature shows 3 oC. Explain how can the surface of the road cool down below 0 oC, even under these circumstances.

(4 pont)

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P. 4009. The voltage of the rechargeable battery of a car is 12 V. In order to generate sparks in the spark plug a voltage of 5 kV is needed. How is it possible to produce 5000 V from 12 V direct voltage?

(4 pont)

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P. 4010. Two capacitors of capacitances C1 and C2 are given charges of Q1 and Q2, respectively and connected in series such that the the positively charged plate of one of them is connected to the negatively charged plate of the other. What is the voltage between the plates of the two condensers which are not connected, and what are the voltages between the plates of each condenser?

(4 pont)

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P. 4011. Below the fixed end of the insulating horizontal thread, at a distance equal to the length of the thread there is a fixed charge, which has the same charge as the charge of the small body of mass m at the end of the thread as shown in the figure. The body is released and when it is at the lowest position the angle between the thread and the horizontal is 30o.

a) Find the mass of the moving body.

b) Find the tension at the lowest position.

c) By what factor is the acceleration of the body at the lowest position is greater than the initial acceleration?

(5 pont)

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P. 4012. A plane mirror is placed 25 cm away from a concave spherical mirror perpendicularly to the principal axis of the concave mirror. Where should we place a candle if the images of the flames formed by the two mirrors are at the same distances from the object? The radius of then concave mirror is 40 cm.

(4 pont)

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