# Exercises and problems in Physics

February 2002

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

## Experimental problem |

**M. 231.** With the help of measurements determine what
the dependence of the warming rate of a glass of water in a microwave
oven on the amount of water in the glass, on the size of the glass and
on its position on the center plate is! (6 points)

## Theoretical problems |

**P. 3498.**Fill a graduated cylinder with fresh snow, and put
on the surface of the snow an aluminum cylinder of a mass of
162 g and wait until all the snow melts. (See the *figure*
on the right.) What is the density of the snow? (3 points)

**P.** **3499.** While heating up some water in a pot on
a gas-cooker does the hydrostatic pressure of the water change at the
bottom? (3 points)

**P.** **3500.** A climber sits between two parallel
rock walls so that he presses his boots to one and his back to the
other wall. The friction coefficient between the boots and the wall is
1.2 and between the wall and the climber's back is 0.8. What force
does he need to apply on the wall at least? Draw a figure. (5 points)

**P.** **3501.** In the arrangement seen in the figure,
lying on a horizontal table two parallel, unstretched rubber threads
of spring constant *D* are going through a ring of mass *m*,
which can easily slip along them. We take the ring from its state of
equilibrium to *a*) point A, *b*) point B. What is
the amount of work done and what is the starting acceleration of the
ring in the two cases? The ring can move along the table
fricitionless. (Data: *a*=0.1 m; *b*=1 m;
*D*=150 N/m; *m*=0.1 kg.) (5 points)

**P.** **3502.** 10% of the volume of a floating
submarine is above the water level. In this case 80% of its volume is
filled with air. After an accident the amount of air drops to 10% (in
closed chambers) and the 18 300 m^{3} volume submarine
sinks to a 110 m depth. How much work is needed to salvage the
submarine? (The density of the sea water is
1030 kg/m^{3}.) (4 points)

**P.** **3503.** On a small bridge the road runs along a
circle arc of radius *R* and of 180^{o}-2 angle lying in
a vertical plane. A motorcyclist runs up the bridge with such a
velocity that he flies off the road. What is its velocity at least? At
what velocity would he touch the road again in point B? (Data:
*R*=100 m; \(\displaystyle alpha\)=80^{o}.) (4 points)

**P.** **3504.** We perform the *ABCA* cycle seen
in the * figure* with air as medium in a thermodynamical
machine. Is this machine a heat engine or a refrigerator? What is the
ratio of the absorbed heat in section *AB* and the emitted heat
in section *CA*? (5 points)

**P.** **3505.** At the edge of a plate capacitor there
is an inhomogeneous electric field, which is usually neglected. Taking
this into account as well, would we get a smaller or a greater
capacity value? (5 points)

**P.** **3506.** The electromotive force of a power
source consisting of four serially connected 4.5V batteries is
18 V. A connected consumer carries an electric current of
0.3 A. This current decreases to 0.2 A if an 8 resistance is
connected parallel to the power source. What is the internal
resistance of one 4.5V battery? (4 points)

**P.** **3507.** In what cases does a parallel light
beam incident on a double-convex (``biconvex'') glass lens keep
parallel after leaving the lens? (5 points)

**P.** **3508.** A \(\displaystyle lambda\) wavelength photon collides with an
electron, which can be considered resting and free. In the interaction
the electron recoils and a 2\(\displaystyle lambda\) wavelength photon starts in the
opposite direction of the incident one. Determine the wavelength of
the incident photon. (5 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary