KöMaL Problems in Physics, October 2025
Please read the rules of the competition.
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Problems with sign 'M'The deadline is: November 17, 2025 24:00 (UTC+01:00). |
M. 443. Using the light sensor of a mobile phone, show that light intensity is inversely proportional to the square of the distance from a point source of light. How should we choose the experimental conditions in order to prove this relationship as accurately as possible?
(6 pont)
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Problems with sign 'G'The deadline is: November 17, 2025 24:00 (UTC+01:00). |
G. 897. One end of a thread is fixed and a heavy body is attached to the other end. The thread will break if the mass of the body is greater than \(\displaystyle M\). Now the thread is laid on a horizontal table, a body of mass \(\displaystyle m\) is attached to one end, and the other end is pulled in the direction opposite to the body, with an acceleration of \(\displaystyle a\). The coefficient of friction between the body and the table is \(\displaystyle \mu\). What is the maximum magnitude of the acceleration if the thread does not break?
(3 pont)
This problem is for grades 1–10 students only.
G. 898. A car of weight \(\displaystyle 16\,000~\mathrm{N}\) is standing on a horizontal surface. All four wheels of the car push the ground with the same force. A bicycle carrier is then attached to the hitch of the car, to which three bicycles are attached symmetrically, as shown in the picture (i.e. the load is applied to the centre of the bicycle carrier).
By how much does the force exerted by the wheels of the car on the ground change?
The three bicycles and the bicycle carrier together weigh \(\displaystyle 800~\mathrm{N}\), the line of action is at a distance of \(\displaystyle 30~\mathrm{cm}\) from the ball of the hitch. The distance between the front and rear axles of the car is \(\displaystyle 2.8~\mathrm{m}\), the ball of the hitch is \(\displaystyle 1~\mathrm{m}\) horizontally from the rear axle.
(3 pont)
This problem is for grades 1–10 students only.
G. 899. What is at least the average current drawn by an electric car while it accelerates to \(\displaystyle 100~\mathrm{km}/\mathrm{h}\) in \(\displaystyle 2.7~\mathrm{s}\)? The car has a nominal voltage of \(\displaystyle 800~\mathrm{V}\) and a mass of \(\displaystyle 2500~\mathrm{kg}\).
(3 pont)
This problem is for grades 1–10 students only.
G. 900. Is it possible to choose the resistances of the resistors (other than zero) such that the effective resistance in figures a) and b) are equal?
(4 pont)
This problem is for grades 1–10 students only.
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Problems with sign 'P'The deadline is: November 17, 2025 24:00 (UTC+01:00). |
P. 5670. Two motorcyclists are riding on two roads, which cross each other perpendicularly. The speed of one is \(\displaystyle v_1\), the speed of the other is \(\displaystyle v_2\), and their minimum distance from each other is \(\displaystyle d_0\). What is their distance from the crossroad at this moment? For simplicity, consider both vehicles point-like.
(5 pont)
P. 5671. There are three small holes in a plate, fixed in a horizontal plane 3, 4, and 5 units apart. One end of each of three flexible thin threads are tied together, the other ends are threaded through the holes and 2, 3, and 4 units of mass are hung over the hanging ends (see the figure). Friction between the threads and the table is negligible.
Construct the position of the knot at equilibrium.
(5 pont)
P. 5672. Standing on the Equator, a satellite passes just above our heads, orbiting at a distance of \(\displaystyle 400~\mathrm{km}\) from the surface of the Earth. At most for how long can we see the satellite?
(4 pont)
P. 5673. A piston with a mass of \(\displaystyle 0.5~\mathrm{kg}\) divides the air in a fixed horizontal cylindrical tank into two parts. The walls of the tank and the piston have good thermal insulation, and the piston can move frictionlessly (see the figure). Initially, the piston is fixed in such a position that the volume of air in the left part is \(\displaystyle 3~\mathrm{dm}^3\) and the pressure is \(\displaystyle 100~\mathrm{kPa}\), while in the other part the volume is \(\displaystyle 2~\mathrm{dm}^3\) and the pressure is \(\displaystyle 200~\mathrm{kPa}\). At this state the temperature of the air in both parts is \(\displaystyle 300~\mathrm{K}\).
The piston is released from its clamping.
a) After releasing the piston from the clamping, what is the maximum speed to which the piston accelerates?
b) What will be the maximum temperature of the air column on the left?
(5 pont)
P. 5674. A heat engine operates between a body of heat capacity \(\displaystyle C\), which was initially at a temperature of \(\displaystyle T\), and a large heat reservoir of constant temperature \(\displaystyle T_0\).
Consider the two cases \(\displaystyle T=T_0 +\Delta T\) and \(\displaystyle T=T_0 -\Delta T\). In which case can we gain more work?
(5 pont)
P. 5675. There are point-like charges of \(\displaystyle 400~\mathrm{nC}\) at the vertices of an equilateral triangle of side \(\displaystyle 30~\mathrm{cm}\). The adjacent charges are connected by insulating threads.
a) What is the tension in the threads?
b) What is the tension in the threads, when a \(\displaystyle 200~\mathrm{nC}\) point-charge is placed at the centroid of the triangle?
(4 pont)
P. 5676. In the circuit shown in the figure, the electromotive force of the voltage supply is \(\displaystyle 20~\mathrm{V}\), the resistances of the resistors are \(\displaystyle R_1=50~\Omega\) and \(\displaystyle R_2=150~\Omega\), and the capacitor has a capacity of \(\displaystyle 20~\mu\mathrm{F}\). Initially, switch K is closed.
a) What is the charge on the capacitor when the switch is closed?
b) Until the steady state is reached after the switch is opened, how much does the energy of the capacitor change and how much heat is dissipated in resistor \(\displaystyle R_1\)? The internal resistance of the voltage supply is negligible.
(5 pont)
P. 5677. To the terminals of a battery of \(\displaystyle 1.5~\mathrm{V}\), a resistor of \(\displaystyle 1~\mathrm{k}\Omega\) is connected with two copper wires of length \(\displaystyle 20~\mathrm{cm}\), and of radius \(\displaystyle 1~\mathrm{mm}\). The copper has one conduction electron per atom.
a) Calculate the drift speed of the conduction electrons in the wire.
b) How long would it take for an electron to travel at this speed from the battery to the resistor?
(5 pont)
P. 5678. One end of a spring with a spring constant \(\displaystyle D\) is attached to the ceiling of a lift, and the other end is attached to a body with mass of \(\displaystyle m\). Initially, the body is at rest. Suddenly the lift starts to move upwards with a constant acceleration of \(\displaystyle a\), and after a time \(\displaystyle \tau\) the acceleration ceases, and the lift continues to move at a constant speed. What is the amplitude of the subsequent motion of the body?
(6 pont)
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