KöMaL Problems in Physics, May 2026
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Problems with sign 'M'Deadline expired on June 15, 2026. |
M. 450. Smartphones are equipped with sensors capable of measuring magnetic induction. Find in the school laboratory, or construct yourself, a coil large enough to place the phone inside. Compare the magnitude of the magnetic induction measured at the centre of a current-carrying coil with the theoretical expectation. Measure and map the magnetic field along the axis of the coil.
(6 pont)
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Problems with sign 'G'Deadline expired on June 15, 2026. |
G. 925. We ride a bicycle down a long slope and intend to stop at the bottom. Under which conditions, and why, does the brake pad wear less: if we accelerate to a high speed and brake strongly at the end, or if we brake continuously and do not allow the bicycle to accelerate? (Assume braking without wheel lock, and that brake wear is directly proportional to the work done by friction and independent of speed.)
(4 pont)
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G. 926. Two identical bar magnets each have a weight of 0.5 N. If the magnets, placed in contact with each other, are set on a horizontal frictionless table, they can be separated by a horizontal force of 1.5 N (see figure 1).
figure 1
The magnets are suspended as shown in figure 2.
figure 2
a) Determine the tension in the string and the contact force between the magnets.
b) Solve the problem also for the case in which one magnet has a weight of 0.5 N and the other 1 N, while the attractive force between them remains 1.5 N.
(3 pont)
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G. 927. When a person wearing glasses enters a warm room from the cold in winter, the glasses usually fog up. However, if the glasses are wiped immediately, they usually do not fog up again. Explain this phenomenon!
(4 pont)
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G. 928. When looking into a plane mirror, we see our mirror image, which is not the same as how other people see us. How can we use two plane mirrors to see our face as others would see it?
(3 pont)
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Problems with sign 'P'Deadline expired on June 15, 2026. |
P. 5733. A boy practices free throws on a basketball court. The basket is located horizontally at a distance of \(\displaystyle d=4~\mathrm{m}\) and vertically \(\displaystyle H=1~\mathrm{m}\) higher than the release point. The initial velocity of the thrown ball is \(\displaystyle v_0=10~\mathrm{m}/\mathrm{s}\).
a) At what angle should the boy throw the ball so that it goes cleanly into the basket?
b) What are the minimum and maximum values of \(\displaystyle v_0\) for which the shot is possible, taking into account that the ceiling is located 6 m above the release position of the ball? Assume that the ball and the basket (i.e. the centres of the ball and the rim) are point-like, and neglect air resistance.
(5 pont)
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P. 5734. A point-like ball of mass \(\displaystyle m\) can move without friction along a long horizontal rod. A string attached to the ball passes through a small ring situated at a depth \(\displaystyle h\) below the rod, and a weight of mass also \(\displaystyle m\) is attached to its free end. When the inclined segment of the string makes an angle \(\displaystyle \alpha=60^\circ\) with the vertical, the ball is released from rest.
a) By what factor is the tension in the string greater as the ball passes above the ring than at the instant immediately after release?
b) What is the period of small oscillations of the ball about its equilibrium position?
(5 pont)
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P. 5735. What is the minimum time interval, as observed from the Earth, between Mars being in opposition and subsequently in quadrature? As seen from the Earth, Mars is in opposition when it lies in the direction opposite to the Sun, and in quadrature when its angular separation from the Sun is \(\displaystyle 90^\circ\). Assume that the Earth and Mars move in circular orbits of radii 1 AU and 1.5 AU, respectively, about the Sun, in the same direction and in the plane of the ecliptic.
(4 pont)
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P. 5736. A research spacecraft of the small green Titan-eating creatures has discovered a spherical asteroid with the following properties:
– it has no atmosphere,
– it always keeps the same face towards its star,
– the solar constant at the asteroid's surface is equal to that on Earth, \(\displaystyle 1360~\mathrm{W}/\mathrm{m}^2\),
– the absorption coefficient of its surface is \(\displaystyle 0.5\).
a) Determine the temperature of the asteroid, assuming that, due to the good thermal conductivity of titanium, the temperature is uniform throughout the asteroid.
b) The small green Titan-eating creatures began surface mining the material of the asteroid over one quarter of its surface. The ``worked'' area may be regarded as a perfectly black body. How does the temperature of the asteroid change depending on whether the mine is located on the dark side or on the illuminated side of the asteroid?
(It may be assumed that, in the case of the illuminated side, the worked area also covers one half of the illuminated hemisphere, when projected perpendicular to the direction of the incoming radiation.)
(5 pont)
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P. 5737. A point charge of mass \(\displaystyle m\) and charge \(\displaystyle Q\) is situated at a distance \(\displaystyle d\) above a well-conducting plane metal sheet. It is given an initial velocity \(\displaystyle v_0\) in a direction parallel to the plane of the sheet. After what time, and at what point, does the charge strike the metal sheet? (Gravitational force is negligible compared to electrical forces.)
(5 pont)
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P. 5738. A circular wire loop of radius \(\displaystyle d\) is formed from a thin wire. A small conducting ring of radius \(\displaystyle r\) (with \(\displaystyle r \ll d\)) and resistance \(\displaystyle R\) is placed at its centre, with their axes coinciding. A steady current of magnitude \(\displaystyle I\) flows in the loop. What total charge passes through a given cross-section of the small ring as it is moved very far away from the loop? (Self-inductive effects may be neglected.)
(4 pont)
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P. 5739. In the past, during cataract surgery, the natural lens removed from the patient's eye was not replaced by an artificial lens. A patient operated on in this way could see distant objects clearly with spectacles of power \(\displaystyle +12\) dioptres. What power of spectacles would be required for the patient to read a book at a distance of 30 cm?
(4 pont)
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P. 5740. In air at room temperature and atmospheric pressure, the mean free path of nitrogen molecules is approximately 65 nm. Estimate the average displacement of a nitrogen molecule from its initial position in 1 hour.
(5 pont)
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P. 5741. The \(\displaystyle I(U)\) characteristic of an incandescent lamp is shown in the figure.
a) Plot the temperature of the filament as a function of the power dissipated. Assume that the resistance of the filament is proportional to the absolute temperature, and that the ambient temperature is \(\displaystyle 27~{}^\circ\mathrm{C}\).
b) The filament loses heat by two mechanisms: thermal conduction and thermal radiation. Determine the effective radiating surface area of the filament.
Assume that the filament behaves as a black body.
(6 pont)
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