# Exercises and problems in Physics

September 2002

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

## Experimental problem |

**M.** **235.** Determine the direction of the magnetic
induction around a disk shaped magnet. First use some iron dust then a
compass. (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.** **3541.** In a vessel filled with water to its
half there is a closed, thin walled glass sphere. On the same table
there also stand two glasses of equal size entirely filled with
water. Pouring the contents of one of them into the vessel we see that
the glass sphere sinks a bit deeper. If we pour the contents of the
other glass into the vessel the glass sphere floats higher. How can
that happen? (3 points)

**P.** **3542.** How can the mass of a test tube be
estimated with the help of a graduated cylinder and the side-piped
vessel shown in the *figure.* (3 points)

**P.** **3543.** Eve, the 176 cm tall model is
looking at herself in a mirror hanging on the wall. The mirror is
vertical and its height is 75 cm. Eve stands straight, her eyes
are at a height of 168 cm from the floor. Can she see her eyes if
she can just see her shoes? (3 points)

**P.** **3544.** From the vessel shown in the
*figure* the air is pumped out. The upper sphere is filled with
water. If the lower sphere is cooled with liquid nitrogen, the water
in the upper vessel freezes after some time. How can this phenomenon
be explained? Is it possible for the water to freeze while boiling? (4
points)

**P.** **3545.** Two spherical shaped equal sized glass
fishbowls filled with water are standing on the table. In the middle
of each fishbowl a small fish is swimming. How large and in what
distance can they see each other? The refraction index of water is
1.33. (5 points)

**P.** **3546.** A 1000 kg space ship with a
100 kg astronaut inside and a 100 kg satellite are floating
in space at a 20 m distance from each other. The pilot kicks
himself off the space ship to adjust an element of an aerial on the
satellite. His velocity relative to the space ship is 1.1 m/s. He
concludes the job in 130 seconds, and then he wants to return to the
space ship in 100 seconds. At what velocity should he kick himself off
the satellite to achieve this? (4 points)

**P.** **3547.** Geostationary satellites are put into
orbit as follows: first the satellite is in a low, Earth parking
orbit, then by firing its engines for a short period an elliptic orbit
is achieved with its close Earth point (perigee) on the parking orbit
and the farthest from the Earth point(apogee) on the stationary
orbit. When the satellite reaches the furthest point, it is put into a
circular orbit by firing the engines again. Let us assume that the
parking orbit is a circular orbit of an altitude of 200 km above
Earth's surface. How long does it take for the satellite to reach the
distance of the geostationary orbit? (5 points)

**P.** **3548.** The resistance of the current consumers
in the electric network seen in the figure is
*R*_{1}=300 \(\displaystyle Omega\) and *R*_{2}=700 . The
electromotive force of the power source is
*U*_{0}=50 V, and its internal resistance is
negligible. The capacity of the capacitor is *C*=50 F. Connecting the
voltmeter between points *A* and *B* it shows an
*U*_{1}=14.5 V voltage.

*a*) What is the
resistance of the voltmeter? How many electrons leave the negative
coating of the capacitor during the measurement?

*b*) What
would the voltmeter show connecting it between points *B* and
*D*? What is the absolute and the relative error of this
measurement?

*c*) At least how much the resistance of the
voltmeter should be that connecting it between points *B* and
*D* the relative error of the measurement is 1%. (5 points)

**P.** **3549.** An optical grating is lit with parallel
light beams of 589 nm wavelength. On a screen at a 3 meter
distance of the grating the distance of the zero order and first order
diffraction maxima is 20 cm.

*a*) How many lines are
there in the grating in one cm?

*b*) How far is the second
order diffraction maximum from the first order one? (4 points)

**P.** **3550.** In an Earth orbiting spaceship a
floating laser pen of mass 50 g suddenly switches on, and emits
light of 500 nm wavelength with a power of 3 mW for one
hour.

*a*) How many photons are emitted during this period?

*b*) Estimate the velocity gained and the distance covered
by the pen in the spaceship during this time. (5 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary