# Exercises and problems in Physics

March 2002

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

## Correction |

Problem **P. 3486.** in December, 2001 contained a mistake. Now
the problem is issued again. You can send your solution for the
corrected problem together with the problems in March. (Your score will
be counted in December.)

**P.** **3486.** The binding energy of the
^{14}N nucleus is 16.76 pJ and the ^{14}C nucleus
is 16.86 pJ. Which nucleus is the decay product of the other, and
why? (5 points)

## Experimental problem |

**M. 232.** Hang a homogeneous metal bar symmetrically using two
strong threads as seen in the *figure.* How does the period of
this somewhat distorted system depend on distances *l* and
*b*. (6 points)

## Theoretical problems |

**P. 3509.** Is it possible that a freely falling body covers
twice the distance in the last second of the fall than in the previous
second? (3 points)

**P. 3510.** A 150 kg piston closes 32 g of oxygen gas
of a temperature of 0 ^{o}C in a vertical cylinder of
base area of 4 dm^{2}. The air pressure outside is
1.01^{.}10^{5} Pa. The axis of the cylinder is
vertical, and the piston can move in it without friction. At what
height is the piston in rest? How much heat is to be transferred to
the gas to raise the piston 20 cm? (4 points)

**P. 3511.** There is a line pendulum of length *l* hanging
from a nail sticking out of a vertical wall. Release the pendulum from
the horizontal position. When its angular separation from the
horizontal is \(\displaystyle alpha\) the line hits another nail and from here the small body
at the end of the line moves along an arc around this second nail. How
far can the second nail be from the first one if the body goes all
along this new circular path? (4 points)

**P. 3512.** One side of a building is exposed to heavy
sunshine. What is the direction of the draft inside the building if we
open one window on both the sunlit and the shady side? (3 points)

**P. 3513.** Estimate the resistance caused by rain under no
wind conditions for a running car. Suppose, that in half an hour there
has been 10 mm of precipitation, the diameter of a rain drop is
2 mm, the frontal area of the car is 1.5 m^{2}, and
its velocity is 90 km/h. What is the ratio of the rain and air
densities? (5 points)

**P. 3514.** Examine the motion of a solid cylinder of mass
*m*=4 kg moving down a long \(\displaystyle alpha\)=30^{o} angle slope having two
different surfaces. The initial velocity of the cylinder is zero. The
first section of the slope is very smooth, the friction coefficient is
\(\displaystyle mu\)_{1}=0
here, while on the second section it is \(\displaystyle mu\)_{2}=tan. The cylinder
arrives on this second section after it has descended
*h*=1.8 m in the vertical direction.

*a*) How long after starting will the cylinder roll cleanly?

*b*) How much mechanical energy is lost during the motion of
the cylinder? (5 points)

**P. 3515.** In a parallel-plate capacitor the area of each
plate are 1500 cm^{2}, and the distance of the plates is
20 mm. After switching on a 250 V power supply we push a
5 mm thick metal plate and a 5 mm thick glass plate (_{rel}=5) between the plates. How much work
is done while pushing in the plates? (5 points)

**P. 3516.** One half of the square cross-section ring seen in
the *figure* is made of aluminium and the other of copper. The
inner radius of the ring is 8 cm and the outer is 10 cm. It
is in a homogeneous magnetic field perpendicular to its plane, where
the magnetic induction is 0.1 T. How much electric charge
accumulates at the joints if the magnetic induction is linearly
decreased to zero within 2 seconds? (6 points)

**P. 3517.** The decay half-time of a radioactive source is
*T*, and initially it resides in *r*_{0} distance of
our radiation counter. Then it starts moving towards us in a way that
the count number does not change on the counter. Give the distance of
the source and the counter as a function of time. What was the initial
velocity of the radioactive source (The absorption in the air is
neglected here.)? (5 points)

**P. 3518.** In the 19th century people thought that the Sun is
a burning block of coal, which loses its energy through radiation. On
the Earth the intensity of the radiation of the Sun is
1400 W/m^{2}. Let us suppose that the intensity will not
change in the future. The mass of the Sun is
2^{.}10^{30} kg, its distance from the Earth is
1.5^{.}10^{11} m and the caloric value of coal is
30 MJ/kg. How long would the Sun shine, if it really were a
burning coal block? (The result of this calculation surprised the
scientists at that time as well.) (4 points)

**P. 3519.** In the assembly seen in the *figure,* the
piston of the lower cylinder is initially at a height of
10 cm. Under the cylinder there is 20 ^{o}C nitrogen
and above it there is mercury which fills in the rubber hose and has
its free surface in the upper vessel 2 meters above the
piston. The base area of the cylinder is 100 cm^{2}, the
piston is weightless and the nitrogen can expand to a 30 cm
height. The air pressure outside is 10^{5} Pa. While
heating the nitrogen the piston rises and we make the upper vessel
sink continuously so that while the piston rises 1 mm, the upper
level of the mercury drops 9 mm. Continue this while the nitrogen
absorbs heat. How much is the absorbed heat? How much is the top
temperature of the nitrogen? (6 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary