KöMaL Problems in Physics, March 2026
Please read the rules of the competition.
Show/hide problems of signs:
 |
Problems with sign 'M'Deadline expired on April 15, 2026. |
M. 448. Measure the maximum distance from which the text of the physics problems in a KöMaL magazine under given lighting condition is readable. The lighting of the page should be measured by the light sensor of a cell phone. How accurately can lighting be measured using this alternative method?
(6 pont)
 |
Problems with sign 'G'Deadline expired on April 15, 2026. |
G. 917. At a road cycling race, a group of breakaways is ahead of the main peloton by a time gap of \(\displaystyle T\), but for a long time, everyone has been moving at the same speed of \(\displaystyle v\). Along the route, advertising banners were placed continuously. At the sponsors' request, the television broadcast director gave the instruction that every point on the route must be shown on TV at least once. Additionally, the breakaway group and the peloton must be shown on average for the same amount of time, and alternating between the two groups should not occur more frequently than every 30 seconds. For which values of \(\displaystyle T\) and \(\displaystyle v\) can these requirements of the director be fulfilled? (The sizes of the groups are neglected.)
(4 pont)
solution (in Hungarian), statistics
G. 918. Both ends of a rope of mass 2 kg and of length 2 m are attached (close to each other) to the ceiling, and then another identical rope is thrown over the lower point of the loop. What is the tension in each rope at the seven points shown in the figure?
(4 pont)
solution (in Hungarian), statistics
G. 919. How does the boat lift at the Three Gorges Dam in China operate? How was it solved to make it work at different fore- and tailwater levels? Does the lifting force depend on the weight of the boat elevated by the lift?
https://www.erdekesvilag.hu/elkeszult-a-vilag-legnagyobb-hajoliftje-kinaban
(3 pont)
solution (in Hungarian), statistics
G. 920. An open-top, thermally insulated tank contains water at a temperature of \(\displaystyle 60~{}^\circ\mathrm{C}\). A tap above the tank is opened and water at \(\displaystyle 0~{}^\circ\mathrm{C}\) flows from it into the container at a constant rate. After 5 minutes, the temperature of the well-mixed water in the container is \(\displaystyle 40~{}^\circ\mathrm{C}\).
a) What will the temperature of the water in the tank be after another 5 minutes?
b) We let the water flow into the tank for an hour. Determine the temperature as a function of time, and plot the temperature versus time graph.
(4 pont)
 |
Problems with sign 'P'Deadline expired on April 15, 2026. |
P. 5715. At rest, the string of a simple pendulum is vertical, and its bob almost reaches the ground. The length of the string is \(\displaystyle \ell\). The pendulum is displaced horizontally and released. When the angle between the string of the pendulum and the vertical is \(\displaystyle \alpha\), the string is suddenly burned. At what angle \(\displaystyle \alpha\) does the bob fly farthest from its equilibrium position, and what is this distance? (The air drag can be neglected.)
(5 pont)
solution (in Hungarian), statistics
P. 5716. A disc of mass \(\displaystyle m\) can move on a horizontal frictionless surface of a table. The disc is connected to a body of mass \(\displaystyle M\) by an inextensible rope that passes through a hole in the table (the friction between the rope and the tabletop is also negligible). The disc initially moves on a circular path of radius \(\displaystyle R\) when it is slightly pushed radially. What is the period of the oscillation of the body of mass \(\displaystyle M\)?
(5 pont)
solution (in Hungarian), statistics
P. 5717. According to another version of the legend of Dido, the princess landed her ship on an almost straight coastline in North Africa. She asked the local king for as much land as she could enclose with a 4 km fence. Designing the wall, she also considered that land located within 1 km of the coast is worth twice as much per unit area as land farther inland. What is the size and the shape of the area Dido set aside for herself if her goal was to obtain the most valuable possible territory? (See exercise P. 5700. in the January 2026 issue of our magazine.)
(5 pont)
solution (in Hungarian), statistics
P. 5718. Before inflation, Thomas and Blaise measured the mass of a rubber balloon to be \(\displaystyle 1.5~\mathrm{g}\). After they blew up and tied the spherical balloon, which had a volume of \(\displaystyle 8.0~\mathrm{dm}^3\), the blown balloon was put on the scale again; this time the measured mass was \(\displaystyle 2.0~\mathrm{g}\). Finally, they connected the inflated balloon to one arm of a thin U-shaped glass tube that was partially filled with water. The other arm of the tube remained open to the atmosphere. After releasing the tie of balloon, they observed that a height difference of 50 cm developed between the water levels in the two arms of the tube.
a) How many \(\displaystyle \mathrm{cmH}_2\mathrm{O}\) (centimetre of water) is the total pressure of the air closed into the inflated balloon?
b) According to Blaise, the mass of the air blown into the balloon is the difference between the values obtained during weighing, i.e., \(\displaystyle 0.5~\mathrm{g}\). Thomas, on the other hand, claims that when inflated, the balloon contains much more air, almost 10 g. Which boy is right? How many grams of air was blown into the balloon? At the place of the measurements, the air pressure is \(\displaystyle 10^5~\mathrm{Pa}\), the temperature is \(\displaystyle 27~{}^\circ\mathrm{C}\). The molar mass of air is \(\displaystyle 29~\mathrm{g}/\mathrm{mol}\), and the density of water is \(\displaystyle 1~\mathrm{g}/\mathrm{cm}^3\).
(4 pont)
solution (in Hungarian), statistics
P. 5719. The radius of the circumcircle of a regular \(\displaystyle n\)-gon is \(\displaystyle R\). Charges of \(\displaystyle q\), \(\displaystyle 2q\), \(\displaystyle 3q\), \(\displaystyle \ldots\), \(\displaystyle nq\) are placed at the vertices of the polygon. Determine the electric field at the centre of the polygon.
(5 pont)
solution (in Hungarian), statistics
P. 5720. The figure shows a circuit which consists of a resistor of resistance \(\displaystyle R=100~\Omega\), a coil of inductance \(\displaystyle L=1~\mathrm{H}\), and four identical capacitors of capacitance \(\displaystyle C=20~\mu\mathrm{F}\). An AC generator with frequency of \(\displaystyle f=50~\mathrm{Hz}\) and r.m.s. (root-mean-square) voltage of \(\displaystyle U_{\mathrm{eff}}=220~\mathrm{V}\) is connected to points \(\displaystyle A\) and \(\displaystyle B\).
a) What is the active power of the circuit?
b) How should the capacitance value \(\displaystyle C\) be modified to get zero reactive power?
(5 pont)
solution (in Hungarian), statistics
P. 5721. A ray of light enters the plane surface of a glass block with a refractive index of \(\displaystyle 1.5\) from air.
a) What is the angle of incidence if the angle between the incident and refracted rays is \(\displaystyle 30^\circ\)?
b) What can be the maximum angle between the incident and refracted rays?
(4 pont)
solution (in Hungarian), statistics
P. 5722. Estimate the order of the momentum uncertainty of an electron confined in a space of the order of an atomic nucleus. To what velocity does this correspond according to the laws of classical (non-relativistic) physics?
(4 pont)
solution (in Hungarian), statistics
P. 5723. The figure shows a two-legged ladder-like structure. The thin, uniform density rods placed in a vertical plane are joined with a light frictionless hinge. The length of the rods is \(\displaystyle \ell\), they each has mass of \(\displaystyle m\), and on their lower ends there are light castors that ensure that the rods can move frictionlessly apart on the horizontal surface. Initially, the angle of the two rods is \(\displaystyle 2\alpha\). From this position, the rods start to move without any push. While sliding apart, the rods remain in the initial vertical plane.
a) At what speed does the hinge \(\displaystyle C\) strike the horizontal plane?
b) What is the acceleration of the points \(\displaystyle A\), \(\displaystyle B\) and \(\displaystyle C\) right after the starting moment?
c)
(6 pont)
Upload your solutions above.