# Exercises and problems in Physics

December 1997

## New experimental problem:

**m. 193.** Determine the directions in which pictures of objects can
be seen through a binocle and the magnifications. Does the magnification
depend on the distance of the object?

## New exercises:

**FGy. 3110.**
Two candles of identical lengths and different thicknesses were lit at
Christmas. Half of the thin candle and one third of the thick candle could
be seen to burn down in 15 minutes. How long after the candles had been lit
was the ratio of their lengths 4?

**FGy. 3111.**
The tramway control lights show red when lights 1, 2 and 3 are on, and it
shows green when lights 2 and 4 are on. What circuit makes it possible to
turn the lights from green to red or from red to green with a single
switching?

**FGy. 3112.** Hanging a 3 dkg body on each of a 12 cm and a 9 cm spring
makes both springs extend by one third of their original lengths. Half
of the long spring and two thirds of the short spring are cut off,
therefore fastening the ends of the remaining springs together gives a
9 cm-long spring. At what frequency will a 6 dkg body oscillate on this
spring?

**FGy. 3113.**
There are two pistons of negligible thickness and of mass
*m* each in a vertically standing cylindrical container as shown in
the figure. The upper piston is slowly pushed down until it arrives
at the initial position of the lower piston. Where is the lower piston at
this moment? The area of the cross-section of the cylinder is *A*,
the atmospheric pressure is *p*_{0}. (Both pistons can
move without friction; consider the temperature as constant.)

## New problems:

**FF. 3114.**
Astronauts land on an asteroid of radius *R* and homogeneous mass
distribution. A physicist astronaut makes a simple pendulum and measures
its period to be 1 second. As precious ores can be found in the asteroid,
a sphere of radius *R*/2 is exploited and removed from the asteroid
(see the figure). What will the period of the pendulum be in points
*A*, *B*, *C* and *D* shown in the figure?

**FF. 3115.**
The bottom one of two horizontal metal plates of area *A* and mass
*m* is fixed and the top one hangs on a spring of force constant
*D*. Connecting voltage *U* between the plates the equilibrium
distance between the plates is *d*. What is the frequency of the
small amplitude oscillations that the top plate can do when

- a) the battery is switched off,

- b) the battery remains switched on during the oscillations of the
plate?

**FF. 3116.**
On 6 November, 1997, Venus could be seen at a maximum deviation of
47^{o} East of the Sun. The previous time Venus was in such a
position was on 1 April, 1996, when it could be seen at an angle of
46^{o} from the Sun. (The reason for the slight difference
between the angles is that the planets move on elliptical orbits.)
Determine the period of Venus. When will Venus next be at its maximum
deviation to the West?

**FF. 3117.**
An airplane moves at a uniform speed in a horizontal plane. What is the
curve of its track if there is a point that the sound of the plane reaches
at the same time from any point of the track?

## New advanced problem:

**FN. 3118.**
The 22nd of December is said to be the shortest day of the year. According
to the data of a pocket calendar, the earliest sunset is on the 11th of
December (at 15 h 53 in Budapest) and the latest sunrise is on the 2nd of
January (at 7 h 32 in Budapest). Explain the phenomenon.