KöMaL Problems in Physics, April 2023
Please read the rules of the competition.
Show/hide problems of signs:
 |
Problems with sign 'M'Deadline expired on May 15, 2023. |
M. 422. Hold a bar magnet close to a relatively large sheet of iron perpendicular to the sheet. Measure the magnetic force exerted on the bar magnet as a function of the distance from the metal plate.
(6 pont)
 |
Problems with sign 'G'Deadline expired on May 15, 2023. |
G. 813. From the top of a tower block, we took a series of photos of the traffic on the street next to the house. Two selected shots were taken with a time difference of 4/15 seconds, and show cars travelling at a constant speed. Estimate the speed of the cars relative to the roadway if the length of a white line segment of the white, dashed road marking, which divides the lanes of the street, is about 2 metres.
(3 pont)
solution (in Hungarian), statistics
G. 814. A heavy, open (railway) wagon is travelling on a horizontal, straight track at a speed of \(\displaystyle v\). A light toy cannon on the wagon can fire projectiles at a speed of \(\displaystyle 2v\) with respect to the to the cannon. At what angle to the horizontal should the projectile be fired so that it falls back onto the wagon? How long after firing does the projectile fall back onto the wagon? (Neglect air drag.)
(3 pont)
solution (in Hungarian), statistics
G. 815. A lead ball of mass 2 g, and of density \(\displaystyle 11\,300\) \(\displaystyle \frac{\textrm{kg}}{\textrm{m}^3}\) was frozen into a 100 g, \(\displaystyle 0\;{}^\circ\)C piece of ice of density 920 \(\displaystyle \frac{\textrm{kg}}{\textrm{m}^3}\). The ice was put into water of temperature \(\displaystyle 0\;{}^\circ\)C. Due to the room temperature air around the ice-water system, 5 g of ice to melts in every minute. How long will it take for the ice to start sinking?
(4 pont)
solution (in Hungarian), statistics
G. 816. We have three resistors with resistance values of 1 k\(\displaystyle \Omega\), 2 k\(\displaystyle \Omega\) and 4 k\(\displaystyle \Omega\). Two or three of these are connected in series and connected to 230 V voltage supply. In this way how many different values of voltage can we obtain across them, and what are they?
(4 pont)
 |
Problems with sign 'P'Deadline expired on May 15, 2023. |
P. 5481. A vehicle starts from rest and accelerates uniformly. Point \(\displaystyle P\), one of the outermost point on the rim of the vehicle wheel, is initially at its furthest position from the ground. By what factor does the acceleration of point \(\displaystyle P\) increase after \(\displaystyle n\) turns of the wheel?
(4 pont)
solution (in Hungarian), statistics
P. 5482. The thread of a simple pendulum of length \(\displaystyle L\) is stretched horizontally and then released. When the thread of the pendulum becomes vertical, the pendulum bob collides perfectly elastically with another small body, which has the same mass as the pendulum bob, and which is initially on the edge of a table. After the collision, the body on the edge of the table is projected horizontally, i.e. it will move in a parabolic path. Where is the focus and the directrix of this parabola?
(5 pont)
solution (in Hungarian), statistics
P. 5483. Two point-like weights of mass \(\displaystyle m\) and \(\displaystyle M=2m\) are attached to the two endpoints of a diameter of a tire of radius \(\displaystyle R\) and of negligible mass. The tire is placed on a frictionless table such that the plane of the tire is vertical, and initially the two weights are along the same vertical line (the heavier one is on the top). The tire is released from this unstable equilibrium state.
\(\displaystyle a)\) What is the velocity of the centre of the tire when the weight of mass \(\displaystyle M\) reaches the lowest point of its trajectory?
\(\displaystyle b)\) In the case \(\displaystyle a)\), what is the force exerted on the table?
(5 pont)
solution (in Hungarian), statistics
P. 5484. A sample of diatomic gas is taken through the cyclic process which is a circle in the \(\displaystyle p\)–\(\displaystyle V\) diagram, when appropriate units are used, and is shown in the figure.
Using numerical methods, determine the efficiency of the heat engine which executes the above cyclic process.
(5 pont)
solution (in Hungarian), statistics
P. 5485. The vertices of a regular pentagon are connected along the sides by wires which have the same resistance, as shown in the figure. In another regular pentagon, we place wires along the diagonals to form a five-pointed star. (The wires are insulated and there are electrical joints only at the vertices of the pentagon.)
The equivalent resistances measured between adjacent vertices of the two pentagons (\(\displaystyle R_{AB}\) and \(\displaystyle R_{PQ}\)) are the same in the two connections. In which circuit will the equivalent resistance between the vertices of a diagonal (\(\displaystyle R_{AC}\) or \(\displaystyle R_{PR}\)) be greater, and by what factor?
(4 pont)
solution (in Hungarian), statistics
P. 5486. The components of the circuit shown in the figure are ideal. Initially, one of the capacitors is charged to \(\displaystyle q_0\), and the other capacitor is uncharged.
\(\displaystyle a\)) What is the maximum current after closing switch K?
\(\displaystyle b\)) How long after closing the switch does the current first reach its maximum value?
(5 pont)
solution (in Hungarian), statistics
P. 5487. The flat surface of a half-cylinder glass of refractive index \(\displaystyle n\) is tin coated. The half-cylinder is illuminated horizontally with a laser beam as shown in the figure. At what value of \(\displaystyle \alpha\) will the emerging light beam be exactly vertical? What should the minimum value of \(\displaystyle n\) be for such a beam path to be possible?
(5 pont)
solution (in Hungarian), statistics
P. 5488. \(\displaystyle \alpha\)-particles are accelerated through a potential difference of \(\displaystyle 10^6\) V and then the particle beam enters perpendicularly into a region of uniform magnetic field of induction \(\displaystyle B=1.5\) T and of width \(\displaystyle d=7\) cm, as shown in the figure.
\(\displaystyle a)\) At what angle are the particles deflected?
\(\displaystyle b)\) How much time are the particles in the magnetic field?
(4 pont)
solution (in Hungarian), statistics
P. 5489. A rectangular frame was constructed with horizontal sides of length \(\displaystyle a\) made of rigid, straight pieces of wires each of mass \(\displaystyle m\), and vertical sides of length \(\displaystyle b\) made of thin, negligible-mass threads.
The frame was immersed into some dishwashing liquid, holding by one of the wires, and then it was taken out of it. The width of the resulting soap film was reduced to \(\displaystyle d\) at the centre. What is the surface tension of the liquid?
Data: \(\displaystyle a=5\) cm, \(\displaystyle b=8\) cm, \(\displaystyle d=3.6\) cm, \(\displaystyle m=2.6\) g.
(6 pont)
Upload your solutions above.