Kvant Physics
Kvant physics problem solutions (193 solved, 80 verified), 1970–1977.
Kvant Physics
Kvant (Квант) is a popular science magazine covering mathematics and physics, published in the Soviet Union and Russia since 1970. This page collects solutions to 193 physics problems from the magazine's problem section, covering the years 1970 to 1977. 80 solutions have been independently verified.
1970
64 problems across Issues 0–2, 56 verified.
Issue 0
| # | Problem | ✓ | Time |
|---|---|---|---|
| 10 The system consists of four resistive coils with resistances $R_1 = 10~\Omega$, $R_2 = 20~\Omega$, $R_3 = 30~\Omega$, and $R_4 = 40~\Omega$, each rated for a maximum power dissipation of $P_\mathrm{ma… | 8m19s | ||
| 12 The only identified defect is the justification of the initial phases and velocity directions. | 26m14s | ||
| 13 Two identical vertical cylinders are connected by a horizontal tube and filled with water. | ✓ | 18m35s | |
| 14 Two pistons of masses $m_1$ and $m_2$ close the ends of two connected tubes whose cross sectional areas are $S_1$ and $S_2$. | ✓ | 2m34s | |
| 15 V. N. Kopylov. The physical system is a refrigerator operating between the refrigerated compartment and the surrounding room. | ✓ | 17m25s | |
| 16 A. T. Drozdov. The physical system is a car moving along a horizontal road. | ✓ | 11m19s | |
| 17 A parallel-plate capacitor has plate separation $d$. | ✓ | 13m41s | |
| 18 G. L. Kotkin. Two transparent combs are superimposed and viewed against a uniform source of light. | ✓ | 11m50s | |
| 19 The system consists of two open vessels connected by a horizontal tube near their bottoms. | 22m42s | ||
| 20 All-Union Correspondence Olympiad (1967). The body is a long homogeneous cylinder of outer radius $R$. | ✓ | 12m55s | |
| 21 III All-Union Physics Olympiad (1969). Two identical DC motors have their armature shafts rigidly connected, so both armatures rotate with the same angular velocity $\omega$. | ✓ | 4m45s | |
| 22 A. M. Budker. Consider a homogeneous piece of iron. | 21m20s | ||
| 23 III All-Union Physics Olympiad (1969). Two identical thin-walled tubes, each of mass $m$ and radius $R$, lie on a horizontal plane. | ✓ | 13m51s | |
| 24 N. I. Goldfarb. A body of mass $M$ is initially resting on a stand and attached to a vertical spring of spring constant $k$. | ✓ | 8m17s | |
| 25 The statement prescribes not only the magnitude of the current but also its direction. | 7m50s | ||
| 26 A small block moves without friction on a smooth surface consisting of two horizontal half-planes separated in height by a vertical distance $h$. | ✓ | 13m24s | |
| 27 The physical system consists of a rigid hemispherical bell of radius $R$ resting on a horizontal table. | ✓ | 12m36s | |
| 28 Two large parallel plates of area $A$ are separated by a distance $L$, with $L$ much smaller than the plate dimensions so edge effects are neglected. | ✓ | 6m25s | |
| 29 The solution correctly addresses the exercise. | ✓ | 9m55s | |
| 30 G. L. Kotkin. A car moves along a straight road with its wheels rolling without slipping. | ✓ | 13m19s | |
| 31 P. L. Kapitsa. Consider a sphere of radius $R$ illuminated by a parallel beam of sunlight. | ✓ | 30m47s | |
| 32 Let the side length of the square cross section be $a$. | ✓ | 22m01s | |
| 33 Two beads of masses $m_1$ and $m_2$ move without friction on a smooth horizontal circular wire ring of circumference $L$. | ✓ | 5m04s | |
| 34 A hollow insulated conducting sphere of radius $R$ is charged by water drops falling from a vertical tube. | ✓ | 22m45s | |
| 35 The physical system consists of a satellite in low Earth orbit photographing the surface of the Earth. | ✓ | 12m03s | |
| 37 Two vertical cylinders of cross-sectional areas $S_1$ and $S_2$ are open to the atmosphere at their upper ends. | ✓ | 20m39s | |
| 39 Moscow State University Physics Olympiad (1967). Consider a planet of radius $R$ and mass $M$ surrounded by an atmosphere of uniform density $\rho$. | ✓ | 17m59s | |
| 40 A neon-filled discharge tube is placed between two large parallel plate electrodes separated by a distance | ✓ | 8m52s | |
| 41 The physical system consists of sunlight incident on the Moon and the light scattered by the illuminated lunar hemisphere toward the Earth. | ✓ | 4m53s | |
| 42 A flexible rope passes over an ideal pulley. | ✓ | 10m01s | |
| 43 All-Union Physics Olympiad (1969). A planet is modeled as a sphere of radius $R$ filled with an incompressible liquid of constant density $\rho$. | ✓ | 5m48s | |
| 44 All-Union Physics Olympiad, 1968.. The physical system consists of two dolphins moving through water along the same straight line toward one another. | ✓ | 5m46s | |
| 45 A spherical capacitor consists of two concentric conducting spheres of radii $a$ and $b$, with $a<b$. | ✓ | 5m52s | |
| 47 Solution to patch | ✓ | 13m11s | |
| 48 G. I. Kosourov. A mass $m$ is attached to a rope wound around the shaft of a dynamo armature. | ✓ | 15m37s | |
| 49 B. B. Bukhovtsev. A U-shaped tube contains water. | ✓ | 1h27m | |
| 50 The system consists of two identical cubes, each of mass $m$, placed on a smooth horizontal table. | ✓ | 10m54s | |
| 51 A. L. Stasenko. A camera obscura is modeled as a rectangular box of length $L$ with a small circular aperture of diameter $d = 1,\text{mm} = 1\times 10^{-3},\text{m}$. | ✓ | 3m32s | |
| 52 A ball is thrown vertically upward from a point that will also be taken as the point to which it later returns. | ✓ | 11m12s | |
| 54 A. R. Zilberman. The circuit contains an ideal source of electromotive force with voltage $U$, several ideal resistors, and an ammeter with negligible resistance placed in one branch of the network. | ✓ | 13m19s | |
| 55 An arrow of mass | ✓ | 2m41s | |
| 56 A flag is modeled as a thin flexible sheet of characteristic length $L$ and mass per unit area $\sigma$, clamped along one edge to a rigid pole. | 15m41s | ||
| 57 Two identical balls, each of mass $m$, are connected by a massless spring of stiffness $k$. | ✓ | 4m53s | |
| 58 The system consists of a thin metallic ring of mass $m$ and resistance $R$, with diameter $d$, falling vertically in a magnetic field that points along the vertical direction. | ✓ | 10m19s | |
| 60 A candle is placed in front of an ideal plane mirror. | ✓ | 11m50s | |
| 63 The physical system consists of a person moving on an icy slope inclined at an angle $\alpha$ to the horizontal. | ✓ | 8m57s | |
| 64 The system consists of a vessel, the water contained in it, and a wooden ball. | ✓ | 17m26s | |
| 65 L. G. Aslamazov. The system consists of two conducting plates and the ground. | ✓ | 5m09s | |
| 66 The circuit consists of a battery with electromotive force | ✓ | 8m51s | |
| 67 A ball of mass $M$ moves along the axis of a buffer device and strikes the end of a massless rod attached to a massless spring of stiffness $k$. | ✓ | 23m07s | |
| 68 The physical system consists of a rigid container containing an ideal gas whose bulk temperature is $T_1$, while the walls are maintained at temperature $T$. | ✓ | 14m48s | |
| 69 The fragment “NOT_FOUN_” contains no equations, constraints, or target quantity, so the problem cannot be instantiated as a well-posed Kvant task. | 8m34s | ||
| 70 Moscow Institute of Electronic Engineering (MIEM) Physics and Mathematics Olympiad, 1969.. The physical system is a cyclist moving along a road. | ✓ | 8m15s | |
| 71 MIPT Physics and Mathematics Olympiad, 1970.. Consider a straight line segment $AB$ carrying a uniform linear charge density $\lambda$. | 11m50s |
Issue 1
| # | Problem | ✓ | Time |
|---|---|---|---|
| 1 Three communicating vessels contain water and are covered by pistons made of the same material and having the same thickness. | ✓ | 16m10s | |
| 2 Two balls of masses $m_1$ and $m_2$ are placed on a smooth horizontal plane and connected by a spring of stiffness $c$. | ✓ | 7m53s | |
| 3 Two helical springs are made from identical pieces of steel wire. | ✓ | 3m07s | |
| 4 III All-Union Physics Olympiad. A sample of an unknown purified gas is contained in a cylinder. | ✓ | 2m47s | |
| 5 The circuit consists of ideal voltage sources and resistors connected as depicted in Figure 4. | ✓ | 24m35s | |
| 6 2nd All-Union Physics Olympiad. A conducting sphere of radius $r$ is connected to ground. | ✓ | 8m38s |
Issue 2
| # | Problem | ✓ | Time |
|---|---|---|---|
| 7 We consider a horizontal rod of length $l$ that rotates about a vertical axis passing through the point $O_1$. | ✓ | 9m57s | |
| 8 MIEM Physics and Mathematics Olympiad. The system consists of a long rigid rod of length $L$ and mass $m$. | ✓ | 8m36s | |
| 9 All-Union Correspondence Physics and Mathematics Olympiad (1967). A small mass moves on a horizontal table attached to a fixed point by a spring. | ✓ | 10m40s | |
| 11 The system consists of three open barrels containing water. | ✓ | 2m56s |
1971
3 problems across Issue 0, 1 verified.
Issue 0
| # | Problem | ✓ | Time |
|---|---|---|---|
| 72 The solution correctly identifies that each ball undergoes uniform circular motion about its respective pivot, with angular velocities $\omega_1 = v/l$ and $\omega_2 = 2v/(2l) = v/l$, so the angular s… | 15m07s | ||
| 77 A rectangular block of height $H$ and base dimensions $a \times b$ stands on a horizontal rigid surface. | ✓ | 5m52s | |
| 85 An ideal gas in equilibrium is described by states $(p,V)$ with $p>0$, $V>0$ and equation of state $pV=\nu RT$. | 9m00s |
1972
23 problems across Issue 0, 17 verified.
Issue 0
| # | Problem | ✓ | Time |
|---|---|---|---|
| 137 S. M. Kozel. The radiation of a fixed infrared wavelength propagates through methane according to the exponential attenuation law. | 7m08s | ||
| 139 A football is launched from a fixed point on level ground with initial speed $v$ at an angle $\alpha=30^\circ$ to the horizontal. | ✓ | 3m08s | |
| 154 P. L. Kapitsa. The physical system is a layer of fog consisting of identical spherical water droplets suspended in air. | 7m50s | ||
| 166 E. I. Butikov, A. A. Bykov, A. S. Kondratyev. A horizontal cylinder contains $n=1$ mole of an ideal gas. | ✓ | 15m47s | |
| 170 V. G. Averin. A homogeneous plasma initially occupies a slab of thickness $x$ and contains a uniform density $n$ of positive ions and an equal density $n$ of electrons, where $n$ is the number of particles of each… | ✓ | 2m26s | |
| 171 A. R. Zilberman. The system consists of two identical point masses, each of mass $m$, fixed at the ends of a massless rigid rod of length $l$. | ✓ | 4m01s | |
| 172 V. V. Svetozarov. A rigid conducting rod of length $l = 0. | ✓ | 6m20s | |
| 173 V. D. Krivchenkov. A solid sphere of radius $R$ carries a uniform volume charge density $\sigma$ with units $\mathrm{C/m^3}$. | ✓ | 6m30s | |
| 174 An ideal gas containing $n$ moles undergoes a quasistatic thermodynamic process in which the temperature $T$ is prescribed as a function of the volume $V$. | 11m23s | ||
| 175 G. L. Kotkin. Two identical solid elastic spheres of radius $R = 1~\text{cm} = 1. | ✓ | 5m39s | |
| 176 A. G. Kosourov. The system consists of a rigid tool, such as an awl, nail, or knife, interacting with a deformable material. | ✓ | 11m22s | |
| 177 I. A. Zaitsev. A stretched string performs small transverse vibrations. | ✓ | 6m51s | |
| 178 A. A. Borovoy. A cubic vessel of edge length $a = 1~\text{cm} = 10^{-2}~\text{m}$ contains $n$ gas molecules at room temperature. | 23m14s | ||
| 179 A submarine moves vertically downward with constant speed $u$ in still water where sound propagates with speed $V$. | ✓ | 4m30s | |
| 180 Yu. A. Dreizin. A perfectly conducting isolated metal sphere of radius $R$ is placed in a uniform external electric field of magnitude $E$ directed along a fixed axis. | ✓ | 5m14s | |
| 181 A satellite of mass $m$ moves around the Earth of mass $M$ in a nearly circular orbit of radius $r$ with orbital speed $v$. | 27m40s | ||
| 182 A person jumps vertically upward from the surface of the Moon. | ✓ | 6m46s | |
| 183 G. L. Kotkin. The problem involves a dynamometer sliding along a smooth horizontal table, pulled by a constant horizontal force $F=4~\text{N}$, with the mass of its spring equal to the mass of its casing. | 16m00s | ||
| 184 The physical system is a television image transmission channel. | ✓ | 9m13s | |
| 186 A passenger of mass $m$ moves along a curved path of radius $R$ with speed $v$ during a turn. | ✓ | 2m22s | |
| 187 V. D. Krivchenkov. Consider a thin metal plate of area $s$ coated with a layer of liquid dielectric of density $\rho$ and relative permittivity $\varepsilon$, where the thickness of the layer is much smaller than the li… | ✓ | 13m15s | |
| 188 A refrigerator operates for a time interval $\tau$ while consuming electrical power $W$. | ✓ | 2m20s | |
| 189 V. G. Svetozarov. A point charge $q = 10^{-8},\text{C}$ is uniformly distributed along a circular arc of radius $R = 1,\text{cm} = 10^{-2},\text{m}$. | ✓ | 2m32s |
1973
5 problems across Issue 0, 3 verified.
Issue 0
| # | Problem | ✓ | Time |
|---|---|---|---|
| 193 Two infinite sequences of thin lenses are placed along a common optical axis $z$. | 12m24s | ||
| 197 A. V. Ustinova. A body of mass $m$ lies on a fixed horizontal rough surface. | ✓ | 14m37s | |
| 198 G. L. Kotkin. A skater moves on horizontal ice with both skate blades in contact with the surface. | ✓ | 8m09s | |
| 199 P. L. Kapitsa. The physical system consists of a neutron entering a layer of material. | ✓ | 2m28s | |
| 201 The circuit consists of one or more batteries connected to a fixed external resistor. | 15m13s |
1975
4 problems across Issue 0, 2 verified.
Issue 0
| # | Problem | ✓ | Time |
|---|---|---|---|
| 315 A wire spiral is connected to an ideal constant-voltage mains source with voltage $V$. | ✓ | 7m31s | |
| 318 B. B. Bukhovtsev. The circuit in Fig. | 15m31s | ||
| 319 V. E. Belonuchkin. A luminous object is placed on the optical axis of a thin converging lens $\text{Л}_1$ with focal length $F$. | ✓ | 9m12s | |
| 324 The optical element is a thin converging lens with focal length $f = 50\ \text{cm}$ and diameter $d = 5\ \text{cm}$. | 17m24s |
1977
1 problems across Issue 0, 1 verified.
Issue 0
| # | Problem | ✓ | Time |
|---|---|---|---|
| 471 The system consists of a thermally insulated cavity of negligible volume compared to the connected vessels, linked via small identical openings to two large volumes of gaseous helium. | ✓ | 5m17s |
Unknown Issue
| # | Problem | ✓ | Time |
|---|---|---|---|
| 1 Three identical communicating vessels contain water of density $\rho$ in a uniform gravitational field $g$. | 1m22s | ||
| 2 Two point masses $m_1$ and $m_2$, with units kilograms, lie on a horizontal frictionless plane and are connected by a light spring with stiffness $c$ measured in $\mathrm{N,m^{-1}}$. | 5m25s | ||
| 3 Two helical springs are made from identical steel wire segments of equal total wire length $L_w$ and identical wire diameter. | 58s | ||
| 4 III All-Union Physics Olympiad. A fixed mass $m = 1,\mathrm{kg}$ of an unknown gas is considered under two thermodynamic processes: heating at constant pressure and heating at constant volume. | 54s | ||
| 5 The solution depends entirely on the topology of the circuit in Figure 4, since the potential difference between points $C$ and $D$ is determined by the specific arrangement of sources and resistors. | 57s | ||
| 6 II All-Union Physics Olympiad. A grounded conducting sphere of radius $r$ is fixed in vacuum. | 7m14s | ||
| 7 A rigid horizontal rod $O_1A$ of length $l$ rotates with constant angular velocity $\Omega$ about a fixed vertical axis through $O_1$. | 1m11s | ||
| 8 MIEM Physico-Mathematical Olympiad. A long rigid rod $AB$ is connected at end $A$ to a vertical screw by a threaded hole. | 1m08s | ||
| 9 All-Union Correspondence Physics and Mathematics Olympiad (1967). A small mass $m$ is attached to a fixed point on a horizontal table by a spring of stiffness $k$. | 1m00s | ||
| 10 The system consists of a real voltage source with electromotive force $\mathcal{E} = 20,\text{V}$ and internal resistance $r = 20,\Omega$, connected to an external heater assembled from four thin wire… | 1m19s | ||
| 11 Three large open barrels contain water and have free surfaces located at fixed heights $H_1$, $H_2$, $H_3$ above a common reference level, with $H_1 > H_2 > H_3$, measured in meters. | 1m02s | ||
| 12 G. L. Kotkin. Two identical steel balls of mass $m$ move on rigid, massless rods that constrain motion to circular trajectories of fixed radii $l$ and $2l$. | 1m11s | ||
| 13 Two identical vertical cylinders contain water and are connected by a horizontal tube filled with the same incompressible fluid of density $\rho$. | 1m14s | ||
| 14 Two pistons of masses $m_1$ and $m_2$ move inside two rigid tubes of cross-sections $S_1$ and $S_2$. | 1m08s | ||
| 15 V. N. Kopylov. A refrigerator maintains its internal air at temperature $T_1 = 5^\circ\text{C}$ while it is placed in a room at temperature $T_2 = 20^\circ\text{C}$. | 1m00s | ||
| 16 A. T. Drozdov. A car moves on a horizontal road from rest under the action of an engine delivering constant power $W$ in watts. | 1m12s | ||
| 17 A parallel-plate capacitor with large identical plates of area $A$ is short-circuited, so both plates are connected by an external conducting wire and always remain at the same electric potential. | 1m04s | ||
| 18 G. L. Kotkin. Two one-dimensional periodic structures represent the combs. | 57s | ||
| 19 The system consists of two open vessels connected at the bottom by a narrow horizontal tube filled with water. | 1m06s | ||
| 20 All-Union Correspondence Olympiad (1967). A long cylinder of radius $R$ and uniform material density contains a cylindrical hole parallel to its axis. | 1m12s | ||
| 21 III All-Union Physics Olympiad (1969). Two identical direct current motors are rigidly connected by their shafts, so they share the same angular velocity $\omega$ and produce torques that add algebraically. | 1m03s | ||
| 22 A. M. Budker. A piece of iron of mass $M$ is acted upon by two blacksmiths. | 1m11s | ||
| 23 III All-Union Physics Olympiad (1969). Two identical thin-walled cylindrical tubes of mass $m$ and radius $R$ move on a horizontal rough plane. | 1m15s | ||
| 24 N. I. Goldfarb. A body of mass $M$ is attached to an ideal spring of stiffness $k$, whose upper end is fixed. | 1m09s | ||
| 25 The system consists of a set of DC circuits containing batteries, resistors with given resistances in kilohms, and photoelements. | 1m10s | ||
| 26 A small block of mass $m$ moves without friction on a rigid surface consisting of two horizontal half-planes connected by a smooth spatial transition. | 1m02s | ||
| 27 A rigid hemispherical bell of radius $R$ rests on a horizontal table with its rim in tight contact with the table, preventing fluid flow under the rim until lift-off. | 1m02s | ||
| 28 Two large parallel plates of area $S$ are separated by distance $L$, with $L$ much smaller than the lateral dimensions so edge effects are neglected. | 7m01s | ||
| 29 A flat water surface at temperature $T = 20^\circ\text{C} = 293,\text{K}$ evaporates into a vacuum. | 1m12s | ||
| 30 G. L. Kotkin. The system consists of a car moving with rolling wheels of diameter $D = 1,\text{m}$, filmed by a camera and projected onto a screen at a rate of $f = 8,\text{frames/s}$. | 1m47s | ||
| 31 P. L. Kapitsa. A rigid spherical spacecraft of radius $R$ and mass $m$ is placed in a uniform поток of solar radiation. | 1m14s | ||
| 32 A prismatic wooden block of constant square cross-section of side $a$ and length $L$ floats on the surface of water of density $\rho_w$. | 7m12s | ||
| 33 Two beads of masses $m_1$ and $m_2$ move without friction on a fixed rigid circular wire of circumference $L$. | 1m20s | ||
| 34 A stream of water forms identical spherical droplets of radius $a$ and density $\rho$. | 1m11s | ||
| 35 A satellite moves in a circular low Earth orbit at altitude $h = 300,\text{km} = 3. | 1m05s | ||
| 36 The scan of Kvant problem F36 is missing, so the physical system, numerical data, and even the problem statement are not available. | 40m27s | ||
| 37 Two vertical cylinders of cross-sectional areas $S_1$ and $S_2$ are filled with water between two weightless, frictionless pistons. | 6m56s | ||
| 39 Physics Olympiad of Moscow State University (1967). A planet of mass $M$ and radius $R$ is surrounded by an atmosphere of height $H$. | 1m12s | ||
| 40 A neon lamp consists of two large parallel plate electrodes separated by a distance $d = 3 \times 10^{-3},\text{m}$. | 1m13s | ||
| 41 The system consists of the Sun, the Moon, and an observer on Earth. | 1m11s | ||
| 42 A uniform rope of linear mass density $\lambda$ (kg/m) passes over a frictionless pulley. | 1m30s | ||
| 43 All-Union Physics Olympiad (1969). A spherical planet of radius $R$ is filled with an incompressible жидкость of constant density $\rho$ in hydrostatic equilibrium under its own gravitational field. | 1m23s | ||
| 47 Moscow City Physics Olympiad (1970). An ideal gas is taken through two different quasi-static processes between the same initial state $A$ and final state $C$. | 1m22s | ||
| 49 B. B. Bukhovtsev. A U-shaped tube of constant cross-sectional area $A$ is completely filled with water of density $\rho$. | 1m36s | ||
| 51 A. L. Stasenko. A pinhole camera obscura of linear size $L$ forms a real inverted image of a tiger located at distance $u \le 20,\text{m}$. | 1m08s | ||
| 54 A. R. Zilberman. The circuit in Figure 2 consists of an ideal DC source, a network of resistors, and a single ammeter inserted in one branch. | 1m07s | ||
| 65 L. G. Aslamazov. Two conducting plates form a parallel-plate capacitor with mutual capacitance $C$. | 1m01s | ||
| 137 S. M. Kozel. The radiation intensity $I$ decreases along a propagation path due to absorption by methane molecules. | 1m11s | ||
| 139 A ball is launched from a fixed point with speed $v$ at angle $\alpha = 30^\circ$ above the horizontal. | 1m09s | ||
| 154 P. L. Kapitsa. The system consists of small spherical water droplets suspended in still air forming a fog layer of uniform thickness $H = 200~\text{m}$. | 1m09s | ||
| 166 E. I. Butikov, A. A. Bykov, A. S. Kondratyev. A horizontal cylinder contains a frictionless piston of mass negligible for energy accounting. | 1m14s | ||
| 170 V. G. Averin. A homogeneous plasma contains electrons and ions with equal number density $n$ in $\text{cm}^{-3}$. | 1m13s | ||
| 171 A. R. Zilberman. The system consists of two identical point masses of mass $m$ connected by a rigid, massless rod of length $l$, forming a dumbbell initially oriented vertically. | 1m17s | ||
| 172 V. V. Svetozarov. A rigid conducting rod of length $l = 0. | 1m16s | ||
| 173 V. D. Krivchenkov. A uniformly charged solid sphere of radius $R$ carries a constant volume charge density $\sigma$ with SI units $\mathrm{C,m^{-3}}$. | 1m04s | ||
| 174 An ideal gas containing $n$ moles undergoes a quasistatic process in which pressure, volume, and temperature are always well defined and related by the equation of state $pV=nRT$. | 1m12s | ||
| 175 G. L. Kotkin. Two identical spheres of radius $R=1. | 1m22s | ||
| 176 A. G. Kosourov. The physical system consists of a cutting or piercing tool, such as an awl, nail, or knife, interacting with a solid material. | 1m09s | ||
| 177 I. A. Zaitsev. A stretched string of length $L$ carries transverse oscillations under constant tension $T$ and has linear mass density $\mu$, measured in $\mathrm{kg,m^{-1}}$. | 55s | ||
| 178 A. A. Borovoy. A closed cubic vessel of edge $L = 1~\text{cm} = 1 \cdot 10^{-2} |
1m09s | ||
| 179 A submarine moves vertically downward in a homogeneous, motionless fluid where sound propagates with constant speed $V$ relative to the water. | 1m11s | ||
| 180 Yu. A. Dreizin. A perfectly conducting sphere of radius $R$ is placed in an initially uniform electrostatic field of magnitude $E$, directed along a fixed axis. | 1m19s | ||
| 181 A satellite of mass $m$ moves around the Earth of mass $M$ in a nearly circular orbit of radius $r$ with orbital speed $v$. | 1m30s | ||
| 182 A person performs a vertical jump from the surface of the Moon, reaching a maximum height $h_{\mathrm{M}}$. | 1m16s | ||
| 183 G. L. Kotkin. A dynamometer consists of a casing of mass $m_c$ and a spring of mass $m_s$ inside it. | 1m08s | ||
| 184 A single television frame is transmitted as a finite amount of information with total size $S$ measured in bits. | 1m30s | ||
| 186 A passenger is modeled as a point mass $m$ moving along a curved trajectory of radius $R$ at speed $v$ in a horizontal plane for a car or bus, and along a banked circular path for an airplane. | 1m26s | ||
| 187 V. D. Krivchenkov. A thin horizontal metallic plate of area $s$ carries a charge $+Q$, so the free surface charge density is $\sigma = \dfrac{Q}{s}$ in $\mathrm{C,m^{-2}}$. | 1m27s | ||
| 188 The system consists of a refrigerator operating over a time interval $\tau$, consuming electrical power $W$, and a mass of water initially contained in a vessel at temperature $t^\circ\text{C}$ that i… | 1m11s | ||
| 189 V. G. Svetozarov. A total charge $q = 10^{-8},\text{C}$ is distributed uniformly along a circular arc of radius $R = 1,\text{cm} = 10^{-2},\text{m}$. | 1m23s | ||
| 193 Two one-dimensional paraxial optical systems are considered, both composed of thin lenses with identical focal length magnitude $f$ measured in meters. | 1m15s | ||
| 197 A. V. Ustinova. A body of mass $m$ lies on a horizontal rough surface with coefficient of kinetic friction $k$. | 1m08s | ||
| 198 G. L. Kotkin. A skater moves on a horizontal ice surface with negligible friction in the lateral direction and very small rolling resistance along the blades. | 1m34s | ||
| 199 P. L. Kapitsa. A neutron of mass $m$ and kinetic energy $E_0$ enters a material consisting either of heavy nuclei (lead, mass $M_{\mathrm{Pb}}$) or hydrogen-rich nuclei such as protons in paraffin or water (mass $M_… | 11m38s | ||
| 201 The statement of Kvant problem F201 is missing, so the solution cannot be constructed. | 2m04s | ||
| 318 B. B. Bukhovtsev. A system of ideal capacitors is connected as shown in Fig. | 1m12s | ||
| 319 V. E. Belonuchkin. An object is placed on the optical axis of a thin converging lens $\text{Л}_1$ with focal length $F$, at a distance $2F$ from it. | 1m18s | ||
| 366 A. V. Mitrofanov. A sealed spherical flask has volume $V = 1~\text{L} = 1. | 1m08s | ||
| 373 Two identical billiard balls of mass $m$ move on a horizontal frictionless table. | 2m52s | ||
| 375 Two blocks of masses $m_1$ and $m_2$ rest on a horizontal rough surface with coefficient of friction $k$, which acts as the coefficient of static friction limiting the onset of motion. | 1m10s | ||
| 377 The system consists of a distant pointlike lamp emitting monochromatic light of wavelength $\lambda$ in the visible range, typically $\lambda \sim 5. | 1m11s | ||
| 480 A ship moves in still water with speed $v$ in the laboratory frame. | 1m27s | ||
| 553 A heavy board of mass $M$ rests horizontally on two thin walled rollers. | 2m25s | ||
| 555 Part (a) concerns a light rigid rod of length $l$ hinged at its lower end. | 2m45s | ||
| 557 I cannot write a correct solution to Kvant problem F557 from the text alone, because the problem statement refers to \ | 2m04s | ||
| 558 A small heavy ball of mass $m$ enters a hollow smooth spherical shell of radius $R$ and mass $m$. | 2m49s | ||
| 559 The physical system is the carbon cycle of thermonuclear reactions in a star. | 3m01s | ||
| 566 An atom moves in the laboratory frame with velocity $v$, where | 2m10s | ||
| 567 The solution depends critically on the two missing elements: the $I$–$U$ characteristic of the bulb (Figure 3) and the circuit configuration (Figure 4). | 2m01s | ||
| 594 A heated bathhouse contains air saturated with water vapor at temperature $T_{\text{in}}$ and pressure $p_{\text{in}}$, while the outdoor air is at temperature $T_{\text{out}}$ with $T_{\text{out}} <… | 1m05s | ||
| 619 Leningrad City Physics Olympiad (1979). A thin diverging lens with focal length $F = -10~\text{cm}$ is fixed in space, and a luminous point source is initially located on the principal optical axis at distance $d = 40~\text{cm}$ from the le… | 1m04s | ||
| 620 A rigid square table of side $2a$ is supported by four identical legs located at its corners, modeled as point supports. | 1m11s | ||
| 1000 M. M. Tsypin. A cube of edge length $a$ carries a steady current $I$ along a closed contour formed by its edges. | 1m13s |
Kvant Physics Problem 555
Part (a) concerns a light rigid rod of length $l$ hinged at its lower end.