# Exercises and problems in Physics

October 2002

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

## Experimental problem |

**M. 236.** In the vinification process new wine
is drawn from an upper barrel into a lower one through a rubber
hose. Model this process with water. Examine the dependence of the
water stream velocity on the level difference and on the length of the
hose. (6 points)

## Theoretical problemsIt is allowed to send solutions for any number of problems, but final scores of students of grades 9-12 are computed from the 5 best score in each month. Final scores of students of grades 1-8 are computed from the 3 best scores in each month. |

**P. 3551.** A crane driven by a toy DC
electromotor is lifting a load of a mass of 200 g with
0.2 m/s velocity. What is the power of the crane's electromotor
if 10% of the overall power goes against the friction? How much is the
current drain of the 9 V electromotor if its efficiency is 80%?
(4 points)

**P. 3552.** We try to measure the depth of
a well on the basis of the delay of the splash of a stone we have
dropped in. What is the error of the depth measurement if the error of
our time measurement is *p *%? Neglect the aerodynamic drag and
the time of sound propagation. When is it allowable to discard these
data? (4 points)

**P. 3553.** Add forces of magnitude
*F* and *kF* including an \(\displaystyle \alpha\) angle with each other (*k*1). At what angle ,
the angle of the resultant force and component *kF*, will be the
greatest? What is this angle? (5 points)

**P. 3554.** We release a solid ball and a
cylinder from the top of a slope at the same time. Can they reach the
bottom at the same time as well? (4 points)

**P. 3555.** We stand in front of a
wall. Between us and the wall, at the height of our ears, there is a
whistle blowing, at a frequency of 600 Hz. How fast must the
whistle go towards the wall so that we can hear 3 beats a second? (4
points)

**P. 3556.** Inside the air-gap of a
toroidal coil the magnetic field has a circular cross section and it
can be considered homogeneous. If charged particles are coming in a
radial direction perpendicular to the magnetic field lines, do the
slower or the faster ones leave the magnetic field in a shorter time?
(5 points)

**P. 3557.** A light beam is falling on the
hypotenuse of a rectangular symmetric glass prism from the air. Choose
the \(\displaystyle \alpha\)
angle of incidence so that total reflection will occur at both
opposing sides (*n*=1.5). *a*) Determine the angle
included by the beams incoming and leaving the
prism. *b*) What maximum value can we choose for angle , so that
total reflections still occur? (5 points)

**P. 3558.** In an atomic reactor the slow,
thermal neutrons cause atomic fissions with a greater probability than
the faster ones. Therefore, the neutrons emerging from fission
processes must be decelerated (moderated) with deuterium oxide or
graphite. Determine what fraction of its energy does a neutron lose in
a straight elastic collision with a ^{2}_{1}H and a
\(\displaystyle {}^{12}_{\phantom{1}6}\rm C\) atomic nucleus. (4 points)

**P. 3559.** Estimate what percentage of
the area of Hungary has to be covered with modern (50% efficiency)
solar panels if the current electric power need of the country
(7 GW on average) is to be supplied by them. (5 points)

**P. 3560.** There is a 1 m long
horizontal rod. One of its ends is fixed and on the other a body of a
mass of 1 kg is hung causing a 1 cm deflection. Estimate the
force *F* under which the same, vertically placed rod
collapses. (Hint: the elastic energy of a bent rod is proportional to
its length and inversely proportional to the square of the radius of
curvature.) (6 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary