Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# KöMaL Problems in Physics, March 2018

Show/hide problems of signs:

## Problems with sign 'M'

Deadline expired on April 10, 2018.

M. 376. A half-litre bottle is filled with water and is made swing about a horizontal axis, which is perpendicular to the bottle's symmetry axis, and goes through the cap of the bottle. Measure the period of the pendulum for different initial angular displacements. Will the result change if the water is frozen in the bottle?

(6 pont)

statistics

## Problems with sign 'G'

Deadline expired on April 10, 2018.

G. 629. Once, when Nasreddin Hodja shouldered his heavy pack and got on his donkey with the pack, he was asked why he did not put his pack to the donkey. He answered: ,,Because that would be cruelty to animals, I am heavy enough for this poor little thing''.

$\displaystyle a)$ Why is this answer wrong?

$\displaystyle b)$ Draw the forces acted upon the objects mentioned in the story.

(3 pont)

solution (in Hungarian), statistics

G. 630. Why does the surface of the water in a rotating container have concave shape?

(3 pont)

solution (in Hungarian), statistics

G. 631. A current of 2 A is flowing through a 30 g copper wire across which there is a voltage of 1.2 V. What should the voltage across that copper wire be which is also 30 g, but twice as long as the other one and the same 2 A current flows through it?

(3 pont)

solution (in Hungarian), statistics

G. 632. A plane, which is flying at a speed of 900 km/h, uses 4 litres of fuel (kerosene) in each second. What distance is covered in each minute by that car which has a fuel consumption of 6.4 litres of petrol per 100 km and which needs the same amount of petrol in 5 hours as the amount of kerosene consumed by the plane while it covers a distance of one kilometre?

(4 pont)

solution (in Hungarian), statistics

## Problems with sign 'P'

Deadline expired on April 10, 2018.

P. 5012. Team Hungary won men's 5000 m short track speed skating relay gold at PyeongChang Winter Olympic Games and claimed champion in a time of 6:31.971 and set a new Olympic record. The short track of total length 111.12 m consists of two straight and two semi-circular segments with radius 8.5 m. Estimate the skaters' angle of lean in the turns of the track.

(4 pont)

solution (in Hungarian), statistics

P. 5013. The total mass of the trolley, which has small light wheels, and the ring of radius $\displaystyle R=1$ m on the trolley is $\displaystyle m$ (see the figure). A small point-like object of mass $\displaystyle m$ is placed to the bottom of the ring. The small object is given an initial speed of $\displaystyle v_0$. What is the value of $\displaystyle v_0$ if the trolley just rises from the ground when the object reaches the topmost point of the ring? Friction is negligible everywhere.

(5 pont)

solution (in Hungarian), statistics

P. 5014. At what speed should a projectile be projected on the Moon, in order that the height to which it rises is $\displaystyle p$ percent of the radius of the Moon? Let the values of $\displaystyle p$ be the following: $\displaystyle p=1$, $\displaystyle 10$ and $\displaystyle 100$. (Give your answers to 2 significant figures.)

(4 pont)

solution (in Hungarian), statistics

P. 5015. The star called 55 Cancri has the same diameter and mass as the Sun has. Its innermost planet Janssen has an orbital period of 17.76 hours. Determine the average distance between the star and the planet in astronomical units, which is the average distance between the Sun and the Earth.

(4 pont)

solution (in Hungarian), statistics

P. 5016. There is a uniform-density rod on the horizontal tabletop. We would like to bring the rod slowly to a vertical position with a force which is exerted at one end of the rod and which is perpendicular to the rod during the whole process. What is the least value of the coefficient of static friction, if the rod does not slip?

(5 pont)

solution (in Hungarian), statistics

P. 5017. A heating element is built into a boiler of 10 liters. The element has such a small power that it is unable to heat the water to its boiling point. After heating the water totally, during the first minute after ceasing the heating the temperature of the water decreases by $\displaystyle 1~{}^\circ$C. What is the power rating of the heating element if the water equivalent of the calorimeter is 3 kg?

(4 pont)

solution (in Hungarian), statistics

P. 5018. If fuel is burnt in a heat engine and a heat pump is operated with the heat engine then more heat can be transferred into the flat than in the case when the fuel is burnt in a stove. Let the flat be the low temperature heat reservoir of the heat engine and the high temperature heat reservoir of the heat pump. The cold temperature heat reservoir of the heat pump can be the air of the street. Suppose that the efficiency of the heat engine is $\displaystyle \eta_1$, and that the efficiency of the heat pump if it was operated as a heat engine would be $\displaystyle \eta_2$. Calculate the factor by which the heat transferred to the flat by means of the heat engine and the pump is greater than the heat transferred to the flat by burning the fuel in the stove.

(5 pont)

solution (in Hungarian), statistics

P. 5019. An electron of energy 1.5 eV is moving in a uniform vertical magnetic field of induction $\displaystyle 2\cdot10^{-3}$ T, such that the angle between its velocity vector and the horizontal is $\displaystyle 30^\circ$. How many times does it cross the same induction line while it descends 20 cm?

(4 pont)

solution (in Hungarian), statistics

P. 5020. A circular hole on a screen is illuminated by a coherent laser beam perpendicular to the screen. Behind the screen and perpendicular to the optical axis a CCD-detector sheet was placed. By what percent does the illumination of the pixel on the optical axis (the intensity of the incident light beam) decrease if one-sixth of the hole is covered by an opaque sheet having a circular sector shape?

(5 pont)

solution (in Hungarian), statistics

P. 5021. At most how much energy can be gained by an – initially stationary – electron if it collides with another particle of energy 1 MeV, if the particle is a

$\displaystyle a)$ proton;

$\displaystyle b)$ electron;

$\displaystyle c)$ positron?

(4 pont)

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P. 5022. The lengths of two threads are $\displaystyle L$ and $\displaystyle 2L$. At the ends of the threads there are point-like objects of mass $\displaystyle m$. The objects have the same $\displaystyle Q$ charge. What is the angle between the two threads which are fixed at the same point in equilibrium?

Data: $\displaystyle L=20$ cm, $\displaystyle m=1$ g, $\displaystyle Q=2.8\cdot10^{-7}$ C.

(6 pont)

solution (in Hungarian), statistics