# Exercises and problems in Physics

May 2002

## Please read The Conditions of the Problem Solving Competition.

## Experimental problem |

**M. 234.** The viscosity of fruit juices
with fibre increases with cooling and decreases whith diluting. Take
some measurements to decide which effect is ``stronger''. What happens
to viscosity when the absolute temperature and the concentration
decrease by the same percentage (e.g. 5, 10 and 15 percents)?
Find a method, where it is easy to measure viscosity ratios. (6
points)

## Theoretical problems |

**P. 3531.** Some hikers hired a boat for 3
hours. The river flows at a speed of 2.5 km/h, and the speed of
the boat is 7.5 km/h relative to the water. How far can they get
from the port if they want to be back in 3 hours? (3 points)

**P. 3532.** We fix an inextensible thread
to the ceiling and tie a body of mass *m* to the lower end of the
thread as it is seen in the *figure.* To the bottom of the body
we fix a spring and on it hangs a body of mass 2*m*. The system
is in equilibrium. The dilation of the spring is 30 cm. Now burn
the thread!

*a*) What is the acceleration of the
bodies right after the thread is burnt?

*b*) How long will it take the spring to
reach its unstretched state first and what is the velocity of the
bodies at that moment? (5 points)

**P. 3533.** It is hailing on a flat area
of 10 000 m^{2} uniformly in time for 41 seconds in
a uniformly random areal distribution. The hailstones, which can be
considered as uniform spheres, fall on a soil which they only slightly
indent. Only those move further from their place of impact that fall
on their comrades. Among the 20 000 hailstones that fell in the last
second there were 200 which fell on those that landed in the previous
40 seconds. *a*) What is the percentage of the ice covered
area? *b*) What is the area of the great circle of an ice
sphere? (5 points)

**P. 3534.** What thickness layer of a
snow-blanket of 20 cm depth, 0 ^{o}C
temperature and 0.25 kg/dm^{3} density melts after
5 hours of sunshine when the radiation includes an angle of
25^{o} with the snow layer on average? At the top of
the atmosphere at every surface element of 1 m^{2} which
is perpendicular to the radiation of the Sun the incoming radiation
power is 1350 W. 50% of this is absorbed in the atmosphere, and
the snow reflects 90% of the energy incoming. (4 points)

**P. 3535.** The tube of cross section
*A* seen in the *figure* is closed at one end, bent twice in
right angles and resides in a vertical plane. The *L*=38 cm
long air column of temperature *T*_{0} in the vertical
part of the tube is closed off by a 2*L* long mercury column. The
length of the horizontal part of the tube is *L*. The
*p*_{0} air pressure outside equals with the hydrostatic
pressure of the 2*L* high mercury column. Let
*L*^{.}*A* be
termed *V*_{0}.

*a*) Give in
*p*_{0}*V*_{0} units the work done by the
expanding air while the mercury flows to the upper vertical tube.

*b*) What percentage of the heat
transmitted to the air increases the internal energy?

*c*) Plot the air temperature against its
volume. (5 points)

**P. 3536.** A slightly divergent electron
beam of 5 keV energy arrives at a homogeneous magnetic field. The
velocity of the particles include only small angles with
**B**. What magnetic induction is needed to ensure that the
electrons meet again at a 10 cm distance? (5 points)

**P. 3537.** In a Compton scattering (the
elastic collision of an electron and a photon) event the momentum of
an initially resting electron became greater than that of the incident
photon of frequency *f* was. At least at what angle did the
photon scatter? (5 points)

**P. 3538.** The kinetic energy of an
electron is the *n*th of that of a photon and its momentum is
*n* times as much as the momentum of the photon. At what *n*
values are photons like this visible? (4 points)

**P. 3539.** We are holding with our arm
outstretched a collector lens of focal distance of
*f*=12 cm, and observing a 24 meter high tower at a
60 meter distance. Using estimated data determine the size of the
image on the retina of our eye. At what enlargement or reduction do we
see the tower through the lens compared to the naked eye? How much is
the dioptre of our eye in the two cases? (5 points)

**P. 3540.** The SOHO satellite observing
the Sun's eruptions is always on the line connecting the Sun and the
Earth. How far is SOHO from the Earth? (Take Earth's orbit as a
circle.) (6 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary