KöMaL Problems in Physics, February 2025

Problems with sign 'M' Deadline expired on March 17, 2025.

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M. 438. Stand up a given number of dominoes along a straight line equidistant from each other and knock the first domino. How much time will it take for the last domino to fall? How does this time depend on the distance between the dominoes?

(6 pont)

statistics

Problems with sign 'G' Deadline expired on March 17, 2025.

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G. 877. The size of a car tyre is 205/55 R16. When new, the groove depth on the tread area is 8 mm, but after a few years of use it will be halved. Will the reading on the speedometer be higher or lower due to the wear of tyres? Estimate the percentage difference.

(3 pont)

solution (in Hungarian), statistics

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G. 878. Two trolleys are standing close together on a horizontal track. One weighs 100 g, the other 150 g. The trolleys can move on the track without friction. The larger trolley is pushed by the smaller trolley such that a horizontal force of magnitude \(\displaystyle 0.5\,\mathrm{N}\) is exerted on the smaller trolley, as shown in the figure.

a) What is the common acceleration of the trolleys?

b) What is the normal force exerted between the trolleys?

c) Do the answers to the previous two questions change if the horizontal force of \(\displaystyle 0.5\,\mathrm{N}\) is exerted on the larger trolley towards the smaller trolley?

(4 pont)

solution (in Hungarian), statistics

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G. 879. The same plane cruises in clear weather at the same altitude and at the same speed. Some days it produces a very long contrail, other days a shorter one, and some days there is no contrail at all. What determines primarily whether a trail will form and how long it will be?

(3 pont)

solution (in Hungarian), statistics

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G. 880. An L-shaped luminous LED strip is mounted on the principal axis of a thin converging lens of focal length 10 cm. The longer, 4 cm long leg of the L-shape is perpendicular to the principal axis, and the shorter, 2 cm long leg is aligned with the principal axis such that its end point is \(\displaystyle 13~\mathrm{cm}\) away from the lens, as shown in the figure.

a) Construct the schematic image of the LED strip formed by the lens.

b) Calculate the length of the two parts of the image of the LED strip, the one which is parallel and the other which is perpendicular to the principal axis of the lens. What is the magnification of these parts?

(4 pont)

solution (in Hungarian), statistics

Problems with sign 'P' Deadline expired on March 17, 2025.

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P. 5625. In a riding hall, the rider goes round in a circle of 20 m radius at a constant speed of 5 m/s. The groom stands 10 m from the centre of the circle. When does the distance between the rider and the groom change at the smallest and at the fastest rate? In these two cases what are the rates at which the distance between them changes?

(5 pont)

solution (in Hungarian), statistics

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P. 5626. A motorcyclist starts from rest and travels in a circular path such that the speed of the motorcyclist increases uniformly. What is the angle turned (with respect to the initial position) until the direction of the acceleration of the motorcycle first becomes perpendicular to the direction of the initial acceleration?

(5 pont)

solution (in Hungarian), statistics

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P. 5627. A simple pendulum of length \(\displaystyle \ell\) and of mass \(\displaystyle m\) is attached to an easily rolling trolley of mass \(\displaystyle M\). The system is placed on a horizontal plane, and it is at rest initially. Then the trolley is given a slight push. After how much time will the speed of the trolley be the same again?

(5 pont)

solution (in Hungarian), statistics

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P. 5628. A pencil, which can be regarded as a uniform rod, is placed on a table top and it rests on its end with an eraser. A thread is attached to the tip of the pencil, perpendicular to the pencil, to prevent it from falling.

a) What is at least the coefficient of static friction between the eraser and the table top if the pencil does not slip when it makes an angle of \(\displaystyle 15^\circ\) with the vertical?

b) At what coefficient of friction can the pencil be ``laid down'' slowly on the table without the bottom end slipping, if the thread is perpendicular to the pencil during the whole movement?

(5 pont)

solution (in Hungarian), statistics

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P. 5629. An imaginary solar system is an almost exact replica of our solar system, except that all the linear dimensions are half the size of the real system. The density of the imaginary celestial bodies is the same as the density of the real ones. What is the orbital period of the mini-Earth in the imaginary solar system?

(4 pont)

solution (in Hungarian), statistics

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P. 5630. A gas mixture contains 7 g nitrogen and 20 g argon. What is the specific heat of the gas mixture at constant volume and constant pressure?

(4 pont)

solution (in Hungarian), statistics

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P. 5631. The electric field strength at a distance \(\displaystyle R\) from a uniformly charged, thin, very long, straight filament is well known. Compare this field strength with the electric field strength at the centre of a bent filament, having a shape of a semicircle of radius \(\displaystyle R\). The filaments have the same properties and the same linear charge density.

(5 pont)

solution (in Hungarian), statistics

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P. 5632. On one side of a large metal plate, there is a point-like ball of charge \(\displaystyle Q\) and another of charge \(\displaystyle -Q\), at a distance of \(\displaystyle d\) from each other and \(\displaystyle d/2\) from the plate. How much work is needed

a) to move the charges parallel to the plane of the plate, and separate them very far from each other,

b) to move the charges perpendicular to the plate and carry them very far away from the plate (to the same distance),

c) to move the charges very far away from the plate and from each other?

(5 pont)

solution (in Hungarian), statistics

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P. 5633. We carry out an optical experiment with a wide, parallel, homogeneous light beam. A small cube is illuminated from different directions, the surface of which

a) is sooted,

b) is silvered.

In which direction or directions will the force exerted by the light beam be the greatest?

(For the sake of simplicity, consider the sooted surface as a perfect absorber and the silvered one as perfect reflector.)

(6 pont)

solution (in Hungarian), statistics