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Problems in Physics, March 2008

Please read the rules of the competition.


Problems with sign 'M'

Deadline expired on 11 April 2008.

M. 286. Measure the vacuum which is made by a vacuum-cleaner.

(6 points)

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Problems with sign 'P'

Deadline expired on 11 April 2008.

P. 4053. A train goes through a 1100 m long tunnel with a speed of 72 km/h, in one minute. What is the length of the train?

(3 points)

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P. 4054. In winter moist can often be seen on the traditional window panes of houses. The moist, or fern frost appears on the inside pane of some windows, or on the outside pane of some others.

What do the extent and the position of the condensation or deposition of water vapour depend on?

(4 points)

Statistics

P. 4055. One end of a long, thin elastic sheet of negligible mass is attached to the rim of a horizontal table, and a 3-kg object is fixed to its other end. At the equilibrium position the end of the sheet descends by 6 cm below the horizontal. Then the object is raised by 4 cm above the horizontal.

How much work is done while the object is raised?

(4 points)

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P. 4056. An object of mass m is projected vertically up with a speed of v0. At the same moment another object of mass M, which is initially above the projected one, is dropped from a height of h. The two pointlike objects collide totally inelastically, and they stick to each other.

With what speed will they hit the ground?

(Data: m=1.25 kg, v0=19 m/s, M=2 kg, h=20 m.)

(4 points)

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P. 4057. What percent of the surface of the Moon can be seen from that chinesse Moon-probe, which orbits about the Moon with a period of 127 minutes along a circular path. The shape of the Moon can be considered as a sphere.

(5 points)

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P. 4058. On the first part of a horizontal path of length L friction is negligible. The coefficient of friction of the other long enough part of the path is \mu.

a) What should be the initial speed of a pointlike object if the time of its motion along the path is the shortest?

b) What is the covered distance in this case?

(Data: L=18 m, \mu=0.2.)

(4 points)

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P. 4059. The Little Prince (the main character of the novel written by Antoine de Saint-Exupéry) lives on the spherical planet named B-612, the density of which is 5200 kg/m3. The Little Prince noticed that if he quickens his pace, he feels himself lighter. When he reached the speed of 2 m/s he became weightless, and began to orbit about the planet as a satellite.

a) Suppose that the asteroid does not rotate. What is the radius of the planet?

b) What is the escape speed on this planet?

c) Suppose that the asteroid rotates about its axis, and one day is twelve hours. What is the least speed of the little Prince at which he should run in order to orbit about the asteroid?

(4 points)

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P. 4060. The figure shows a disc and a trolley. The mass of the disc is m=5 kg, its radius is R=0.2 m, the mass of the trolley is M=8 kg, and its length is L=1 m. The trolley can move easily, and the disc does not slide on the trolley. The string which rolls down from the massless pulley attached to the disc is horizontal and the mass of the weight attached to its other end is also m. How long does it take for the disc to roll down from the trolley if it was released from rest at the middle of the trolley. The radius of the pulley is r=R/2? How much distance does the weight descend?

(5 points)

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P. 4061. How can you heat 1 kg mineral water which is at a temperature of 0 oC, to at least 60 oC with using 1 kg water at a temperature of 100 oC?

(5 points)

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P. 4062. A cloud of average temperature 5 oC consists of water drops of average radius 25 nm. These small drops continuously coalesce to greater spheres of average radius 1 mm. What is the temperature of the raindrops formed?

(5 points)

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P. 4063. What should be the least frequency of the gamma-ray which is able to split a deuteron of negligible initial speed? What can be the speed of the released proton and neutron?

(5 points)

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