## Exercises and problems in Physics |

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

## New experimental problem:

**M. 212. **Determine the frequency of the fundamental
tone created by clinking two empty goblets.

## New problems:

**P. 3304 **Two metal
rods of identical cross section but different length and material
properties are glued together. The rod obtained this way is hung up by
two long and vertical ropes fixed to its end points. In which
direction will the point of contact of the two rods be displaced upon
increasing the temperature?

**P. 3305 **Determine the average spacing between cars
of a row proceeding at 60 km/h, if the driver of a car travelling
at 80 km/h in the opposite direction passes by 14 cars of the row
per kilometre. (The average length of the cars is 5 m.)

**P. 3306 **Going downhill on a long 30^{o} slope, a skier of mass 80 kg reaches a
terminal speed of 30 m/s, i.e.\ after a while he travels at this
constant speed. He did not use his sticks to accelerate, thus the
first 2 metres took him 1 second. How much snow would melt under his
skis per minute if all the heat produced by friction were used to melt
the snow? What forces act on the skier, and how large are they?

**P. 3307 **A simple pendulum swings with an initial
angular amplitude . How does the
period of swinging change if two elastic walls making an angle are introduced in the system in a
symmetrical way as shown in the figure?

**P. 3308 **A four-wheel drive car arrives at the
bottom of an icy slope of angle
with a speed *v*. How high can it go up if the coefficient of
friction is ?

**P. 3309 **Two bodies
connected vertically by a length of rope are attached to the free end
of a vertical coiled spring as shown in the figure. If the rope snaps,
the body staying on the spring starts to oscillate. If the two bodies
are interchanged and then the rope snaps, the body staying on the
spring starts to oscillate again. The difference of the two periods of
oscillation is 0.3 sec. Determine the period of oscillation in
each case if the two bodies together oscillate with a period of
1.5 sec on the same spring.

**P. 3310 **A battery is
connected to a linear variable resistor between one end and the
sliding contact of which a load resistor is placed. *a*) What is
the maximum attainable power across the load resistor? *b*)
Determine the position of the sliding contact if the power across the
load resistor is half of the maximum value.

*Use the following data: U*=12 V, *R*_{b}=1 , *R*=120 , *r*=25 .

**P. 3311 **Will the
total electrostatic energy of the capacitors in the figure increase,
decrease, or stay unchanged if switch *K *is closed?

**P. 3312 **Each edge of
an infinite grid has resistance *R*. One edge between two
adjacent grid points is removed. Determine the resultant resistance
between these two points.

**P. 3313 **Part of the series of isotopes produced by
the decay of thorium-232, together with the corresponding half-lives,
is given below.

Thorium-232 and thorium-228 in equilibrium are extracted from an
ore and purified by a chemical process. Sketch the form of the
variation in the number of atoms of radon-220 you would expect to be
present in 10^{-3} kg of this
material over a (logarithmic) range from 10^{-3} years to 10^{3}
years.

**P. 3314. **A metal
disc of radius *r *can rotate with negligible friction inside a
long, straight coil, about a shaft parallel to the symmetry axis of
the coil. One end of the wire of the coil is connected with a sliding
contact to the edge of the disc and the other one to the shaft. The
ohmic resistance of the coil is *R *and there are *n *turns
on a unit length of it. The coil is placed so that its axis is
parallel to the induction vector **B**_{0} of the Earth. What current flows through the
ammeter if the disc rotates with angular frequency ? Plot the current as a function of
for both directions of the
rotation. Prove that the work necessary to spin the disc is identical
to the Joule heat released on the ohmic resistance of the coil.