# Exercises and problems in Physics

April 1998

## New experimental problem:

**m. 197.** Examine how the electric power output of the dynamo of
a bicycle through different constant resistances depends on the number of
revolutions of the rotor.

## New exercises:

**FGy. 3150.** A row-boat travels downstream on a
river at a speed of 8 m/s with respect to the shore. A
motor-boat comes from the opposite direction at a speed of 10 m/s
with respect to the water. 10 seconds after meeting each other they
are at 160 metres from each other. At what speed does the river flow?

**FGy. 3151.** After disassembling a new type energy sparing
light source one can see a 0.25 watt, 27 ohm resistor and a complicated
circuit (including the part that emits the light) connected in series inside
it. The new light source gives out as much light as a 60 watt filament lamp.
By at least how many percents is its power consumption reduced?

**FGy. 3152.** When a tank vehicle half filled with some liquid
is in uniform acceleration what is the direction of the upthrust inside it?

**FGy. 3153.** A piece of -10 ^{o}C ice is heated to
-1 ^{o}C using a certain quantity of energy. Then
another 20 times as much energy is necessary to finally obtain
water. Using that the specific heat of ice is half of the specific heat of
4.2 kJ/(kg ^{o}C) of water,
determine the heat of fusion of ice from the above measurement data.

**FGy. 3154.** A pair of compasses hangs on a thread fastened to
one of its ends. At what angle should the compasses be open so that their
joint is at the highest possible position? What is the position of the lower
leg then? (The legs should be approximated as homogeneous rods.)

## New problems:

**FF. 3155.** Estimate the radius of a drop of water
in which the density of the water has increased by one per mil due to the
pressure of curvature. (The compressibility of water is
5^{.}10^{-10} Pa^{-1}).

**FF. 3156.** A satellite is launched from a spherical planet in
such a way that its velocity vector at its return to the planet is parallel to
its velocity vector at launching. The angular distance between the launching
and the landing point is . How much time
does the satellite spend
in space if the period of a satellite on a circular orbit near the surface of
the planet is *T*_{0}? What is the maximum distance of the
satellite from the surface of the planet if the radius of the planet is
*R*? Examine the limiting case when
.

**FF. 3157.** There are diodes that do not conduct under
2.5 V, while at 2.5 V only the internal resistance of the
current supply limits the current flowing through them, and they emit
light (LEDs). Design a simple circuit with the following properties
using two of these diodes and different ohmic resistors: when a
voltage between 4.25 V and 5.5 V is connected to the circuit
then only one of the diodes lights up, when a voltage between 5.5 V
and 6 V is connected to the circuit then both diodes light up, and
when a voltage under 4.25 V is connected to the circuit then none
of the LEDs lights up. The current flowing through the diodes must not
be higher than 25 mA.

**FF. 3158.** The end of an optical fibre is cut perpendicularly
to the fibre. What is the minimum required refractive index so that light
inciding from any direction at the end of the fibre can enter the fibre but it
cannot leave the fibre on the side?

## New advanced problem:

**FN. 3159.** A spring with *N* turns, radius *R*,
length *l*_{0} and force constant *D* is made from a thin,
insulated steel wire. The turns of the spring do not touch each other, i.e.
it cannot only be expanded but also compressed. What is the new equilibrium
length of the spring if current *I* is conducted through it?