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Problems in Physics, February 2009

Please read the rules of the competition.


Problems with sign 'M'

Deadline expired on 11 March 2009.

M. 294. Measure the ratio at which the different washing-up liquids decrease the surface tension of water.

Does this ratio depend on the concentration of the liquid?

(6 points)

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Problems with sign 'P'

Deadline expired on 11 March 2009.

P. 4134. There is an iron load of mass 10 kg at the end of one of the arms of a balance and at the end of the other arm there is a wooden load of mass also 10 kg. Which end of the lever will tilt downward? To which arm and what size of iron weight must be hanged onto the scale in order to balance it?

(The density of iron is 7800 kg/m3, the density of wood is 600 kg/m3 and the density of air is 1,3 kg/m3.)

(3 points)

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P. 4135. Why does the second hand of a clock have a ``tail''?

(3 points)

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P. 4136. The power in the resistor R2 shown in the figure is 250 W. What are the resistances of the resistors R1 and R2? What is the reading on the third meter? What is the voltage across the power supply?

(3 points)

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P. 4137. A small ball is pushed along a horizontal tabletop, and totally elastically bounces off an inclined plane placed in the way of the ball. Moving upwards, how many times will the ball bounce on the incline? (Neglect the rotation of the ball.)

(5 points)

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P. 4138. A disc of radius 25 cm and of uniform density can swing (with a small amplitude) about a horizontal axle which is perpendicular to the plane of the base of the disc.

a) What is its period in seconds if the axle is 25 cm from the centre of the disc?

b) Where must the axle be placed in order that the period is to be 1 s?

c) Where must the axle be placed in order that the period is to be the minimum?

(5 points)

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P. 4139. In a spherical container of radius R there is a sample of ideal gas containing N molecules each having a mass of m. Supposing that they move randomly in all directions at the same speed of v derive the basic equation of the kinetic theory gases, so determine the pressure of the gas.

(5 points)

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P. 4140. The centres of two small metal balls, whose radii are equal, are initially at a distance of r. If both balls are given different magnitude and opposite charges, and then they are released, they begin to move towards each other. They touch each other and then they move away from each other again. When the distance between their centres is 4r, then the force exerted between them is one-twentieth of the initial force exerted between them. The initial charge of one of the balls was 2.10-7 C. Calculate the initial charge of the other ball.

(4 points)

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P. 4141. A rechargeable battery of 12 V is connected to a coil of self inductance 20 H and of resistance 30 \Omega. What is the rate of change of the current when the current through the coil is 200 mA? How much energy is stored in the coil when the equilibrium is established?

(4 points)

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P. 4142. An object is at a distance of d from a screen. The convex lens, placed between them, forms the sharp image of the object at the screen at two different positions, the distance between these positions is s.

a) Find the focal length, f, of the lens.

b) Suppose that d is known very precisely. When will the uncertainty in the measurement of s cause a greater error in the calculation of f if the value of s is greater or if it is smaller?

(4 points)

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P. 4143. The large hadron accelerator in CERN accelerates protons of initial energy 450 GeV to a final energy of 7 TeV, according to the plans. During the acceleration what is the increase of the speed of the protons in m/s? (Round the result to integers.)

(4 points)

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