KöMaL Problems in Physics, March 2023
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Problems with sign 'M'Deadline expired on April 17, 2023. |
M. 421. Draw lines on a piece of paper with a soft black graphite pencil. We can assume that the graphite is ``smeared'' in atomic layers, and that the distance between adjacent atomic layers is 0.34 nm. Determine the height of a line in terms of number of carbon atoms above each other.
(6 pont)
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Problems with sign 'G'Deadline expired on April 17, 2023. |
G. 809. We rub a small object with a light file in a horizontal plane. The line of action of the sum of the forces exerted by our two hands passes through the centre of the filed surface of the object, and this line of action makes an angle of \(\displaystyle 30^\circ\) with the vertical. What is the coefficient of friction between the file and the object?
(3 pont)
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G. 810. When a penalty kick is shot, the average speed of the ball can reach a speed of 150 km/h. How much time does the goalkeeper have to save the penalty if he is in the middle of the goal at the instant when the ball is kicked and the ball is moving towards one of the bottom corners of the goal? Is the following statement true: ``You can't defend a penalty kick well, they can only kick it badly.''\(\displaystyle \,\)?
(3 pont)
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G. 811. Three rectangular blocks are pulled along a horizontal sheet, with a constant force \(\displaystyle F\), as shown in the figure. The blocks are moving along a straight line all the time, and their instantaneous velocity is \(\displaystyle v_0\). How does the tension in the threads connecting the blocks depend on the value of the coefficient of kinetic friction \(\displaystyle \mu\) between the blocks and the sheet?
(4 pont)
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G. 812. A body immersed into water can be kept in equilibrium with a force of 1.5 N, and with a force 1 N when it is immersed into glycerine. What is the volume and density of the body?
(3 pont)
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Problems with sign 'P'Deadline expired on April 17, 2023. |
P. 5472. How long does it take the James Webb space telescope to orbit the Sun once?
(3 pont)
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P. 5473. A projectile of mass \(\displaystyle M = 3\) kg is fired vertically at a speed of \(\displaystyle v = 50\) m/s, and it explodes into two parts after \(\displaystyle t = 3\) s. The piece with mass \(\displaystyle m_1 = 1\) kg will land in \(\displaystyle t_1 = 1\) s.
\(\displaystyle a)\) How long after the explosion will the other piece hit the ground?
\(\displaystyle b)\) If the first piece has landed 40 m from the firing position, how far apart will the two pieces be after the other piece has also landed?
(4 pont)
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P. 5474. One end of a uniform density, thin stick of mass \(\displaystyle m\) and of length \(\displaystyle \ell\) is fixed with a hinge on a horizontal surface. The other end is struck by a brief horizontal force of magnitude \(\displaystyle F\), which is perpendicular to the rod. At this instant what is the acceleration of the centre of the stick, what is its angular acceleration and what is the force exerted by the hinge on the stick?
(4 pont)
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P. 5475. A container with mass \(\displaystyle M=32\) kg and volume \(\displaystyle V=4~\mathrm{dm}^3\) can move frictionlessly on a horizontal table. It is divided into two parts by a piston of mass \(\displaystyle m=16\) kg. On the left side of the piston there is a mixture of gases of volume \(\displaystyle V_0=1~\mathrm{dm}^3\), at a pressure of \(\displaystyle p_0=0.3\) MPa, and of adiabatic exponent \(\displaystyle \kappa=1.5\). On the right side of the piston there is vacuum. What is the relative velocity at which the piston will hit the wall of the cylinder if the piston is released? Assume that the gas is in thermal equilibrium for all the time.
(5 pont)
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P. 5476. Three alike metal plates of area \(\displaystyle A\) are placed parallel to each other. The distance between the plates is small compared to the size of the plates.
\(\displaystyle a)\) What is the electric field strength between the plates if the charge of the plate on the left is \(\displaystyle +Q\), the charge of the middle plate is \(\displaystyle +2Q\) and that of the right plate is \(\displaystyle +3Q\)?
\(\displaystyle b)\) What is the electric field strength between the plates if the charge of the plate on the left is \(\displaystyle +Q\), the charge of the middle plate is \(\displaystyle -2Q\) and that of the right plate is \(\displaystyle +3Q\)?
(4 pont)
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P. 5477. An ideal battery of emf \(\displaystyle U=24\) V, resistors of resistance values \(\displaystyle R_1=500~\Omega\) and \(\displaystyle R_2=300~\Omega\), a switch and an ideal transformer were used to construct the circuit shown in the figure. The primary coil of the transformer has a number of turns of \(\displaystyle N_1=800\) and the secondary coil has \(\displaystyle N_2=1000\) turns. The switch, which had been open for a long time, was once closed. What were the values of the current in the primary and secondary coils immediately after the switch was closed?
(5 pont)
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P. 5478. A plano convex glass lens is bounded by water on its flat side and by air on its convex side.
\(\displaystyle a)\) What is the ratio of the two focal lengths corresponding to the two sides of the lens?
\(\displaystyle b)\) What will this ratio be if the two media at the sides of the lens are reversed?
The lens is thin and has a small aperture angle. The refractive index of glass is \(\displaystyle 3/2\) and that of water is \(\displaystyle 4/3\).
(5 pont)
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P. 5479. According to the classical electron model, the electron is a uniformly charged insulating spherical shell whose electrostatic energy is equal to the rest energy of the electron \(\displaystyle mc^2\). Using the laws of classical mechanics, determine the kinetic energy that should be given to the electron if it is to collide with another initially stationary electron such that they ``touch'' each other?
(5 pont)
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P. 5480. Through a given point \(\displaystyle P\) of a vertical plane, slopes with different angles of inclination are laid (perpendicularly to the plane), and point-like objects, which were released from rest, slide down the planes. What is the locus of points which are reached by the sliding objects in a given time of \(\displaystyle t\)? The coefficient of friction between the slopes and the objects is \(\displaystyle \mu\).
(6 pont)
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