KöMaL Problems in Physics, May 2009
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Problems with sign 'M'
Deadline expired on June 11, 2009.
M. 297. Glue two battens, which are made of different material, but which have the same size and rectangular cross-section, along their greatest faces. Examine the bending deformation of the battens if the plane of the glued surfaces is
Problems with sign 'P'
Deadline expired on June 11, 2009.
P. 4164. What is the reason that if a stick is put to one of our fingertips, it is easier to balance (to keep it in a vertical position) a longer stick than a shorter one?
P. 4165. Find the mass of that steel wire, which stores elastic potential energy of 10 J when it is expanded. The tensile strength of steal is 900 MPa. Its Young modulus is 210 GPa.
P. 4166. A clever astronaut rotates a necklace in the spaceship, such that it has a circular shape, and turns twice in each second. Calculate the tension in the necklace. The mass of the necklace is 3 grams, and the radius of the circle is 7 cm.
P. 4167. A 1-kg object is placed to an inclined plane of variable slope angle. The object begins to slide down when the slope angle is =20o. If the slope angle is adjusted to =10o, what is the magnitude of the force F which makes the body slide, if force F lies in the plane of the incline and is perpendicular to the direction of the slope. In which direction does the object slide?
P. 4168. A soap bubble is blown above a wet horizontal tabletop. A bubble, which has a diameter of 4 cm sticks to the tabletop. What will the diameter of the soap bubble be?
P. 4169. At what height above a round horizontal table of radius r must a pointlike light source be placed in order that the rim of the table gets the greatest possible light intensity?
P. 4170. Each edge of the steps ``leading to the sky'', shown in the figure, has a resistance of R. Find the equivalent resistance between points A and B.
P. 4171. A generator produces electrical power of 40 kW, when operating at a voltage of 2 kV. The load is connected to the generator through a transmission line of resistance 10 .
a) How much power is dissipated during the transmission of electrical energy?
b) Find the efficiency of the transmission of electrical energy.
c) What are the above asked values if at both ends of the transmission lines an ideal transformer is used to step up or step down the voltage. Both transformers can step up or down the voltage by a factor of 10.
P. 4172. With appropriate washing-up liquids the surface tension of water can be significantly decreased. If a frame is immersed into a mixture of water and washing-up liquid, and then it is carefully taken out, there will be a thin layer of soap film on the frame. Coloured stripes can be observed on the soap film (if it is in front of a black background.)
a) What is the direction of the stripes if the plane of the frame is vertical? Why do they have this direction?
b) What is the colour of the film if its width is only 10-8 m?
P. 4173. Hydrogen atoms of negligible initial speed, being at ground state, are bombarded by protons of speed . What will the speeds of the hydrogen atom and the proton be if the collision is a head-on one along a straight line and the the hydrogen atom will be in its fourth exited state?
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