# Exercises and problems in Physics

April 2002

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

## Experimental problem |

**M.** **233.** Put a small sized glass filled with
water on a matchbox lying on a table. Use a ruler to knock the
matchbox out from under the glass. Take simple measurements (for
example among others measure the displacement of the glass), and with
the help of these estimate how much time it took to knock the matchbox
out. (6 points)

## Theoretical problems |

**P.** **3520.** Two trains are running along two
parallel tracks. One of them covers 90 km an hour the other 10
meters a second. A passenger sitting in one of the trains
observes that the other train passes in 8 seconds. How long is
the other train? (3 points)

**P.** **3521.** Pour 10 cm^{3} of water
into an empty cube with 1,01 dm long edges, and then put an oak
cube of a mass of 0,7 kg into it. Does the oak cube float? (4
points)

**P.** **3522.** There is a 0,8 m long homogeneous
stick attached with a hinge to the rim of a big tank partially filled
with water. The density of the material of the stick is
5 kg/dm^{3}. If a 650 cm^{3} sphere of
density of 0,4 kg/dm^{3} is fixed at the other end of the
stick, then the sphere submerges in the water and so does three
quarters of the stick.

*a*) What is the cross section of the
stick.

*b*) How much is the force and what is its direction
exerted by the hinge on the stick? (4 points)

**P.** **3523.** The *figure* (see on page 251)
shows the velocity and the acceleration of a point-like body at the
initial moment of its motion. The direction and the absolute value of
the acceleration remain constant.

*b*) When does the velocity reach its minimum value?

*c*) What is the minimal curvature of the orbit of the
body?

(*Data:* *a*=6 m/s^{2},
*v*_{0}=24 m/s, \(\displaystyle varphi\)=120^{o}.) (5 points)

**P.** **3524.** The medium (ammonia, freon) in a
compression refrigerator and heater (heat pump) goes through the same
thermodynamic process in each cycle. What does it depend on whether it
works as a refrigerator or a heater? (4 points)

**P.** **3525.** There is a *d* distance between
the big sized plates of a plate capacitor charged up to voltage
*U*. From the negative plate a particle of charge *Q* and
mass *m* is detached without an initial velocity. At what
velocity will this negative charge hit the positive plate? What is the
*U* voltage where this velocity is minimal? (5 points)

**P.** **3526.** At the two ends of an electric
insulator pipe the ends of which are bent at right angles there are
soap bubbles of radius *r* and *R*, respectively. How much
electric charge is to be added to one of the bubbles to ensure that
the size of the other bubble does not change after opening the tap at
the middle of the pipe? (Neglect the effect of the electrostatic
induction!) (5 points)

**P.** **3527.** A magnetic rod is dropped into a very
long vertical short-circuited coil as seen in the *figure.* Make
a schematic drawing of the currents in the coil and the acceleration
of the magnetic rod as a function of time.

(5 points)

**P.** **3528.** The boundary surface of the media of
refractive indices *n*_{1} and *n*_{2} in
the optical system that can be seen in the * figure* is a sphere
of radius *R*. Is there a point on axis *t* where light
beams starting from (closing only a small angle with axis *t*)
are running parallel to axis *t* in the other medium? (5 points)

**P.** **3529.** At the beginning of the 20^{th}
century the Sun was considered a 6000 K hot glowing homogeneous
gas sphere consisting of H_{2} molecules, and slowly cooling
down by its radiation. The current intensity of the Sun's radiation at
the distance of the Earth is 1400 W/m^{2}. Estimate how
long it would take for the Sun to darken, that is to cool down to
about 1000 K? (According to our present knowledge, the Sun
- similarly to other stars - maintains its radiation from
the energy released in fusion processes of atomic nuclei and will
probably shine for about 5 billion years from now on.) (5 points)

**P.** **3530.** What is the apparent resistance of the
endless chain seen in the *figure* in alternating
voltage at circular frequency (between terminals *A* and
*B*? Can the result be two different values? (6 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary