## Exercises and problems in Physics |

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

## New experimental problem:

**M. 217. **Measure the density of a pebble with the help of two identical measuring cylinders, a pair of scales (without weights) and water. Find the error of your measurement. Perform your measurement using 2-3 other pieces of stone, too.

## New problems:

**P. 3353. ** There is 16 m^{3} of water in the container of a watering-cart. Thus the
compression of spring structure holding the container is 8 cm. The vehicle
travels 250 meters away in 10 minutes at constant velocity, while it sprinkles
16 litres of water every second on the road. At that moment rain begins falling
so the vehicle stops sprinkling and turns back to its initial position at
uniform motion, while a pushing force of 3.0 kN is exerted on it.

*a) *Find the compression of spring structure when the vehicle is
coming back.

*b) *At least how much work does the vehicle do back and forth, if
the required force for traction is 2.5 % of gross weight. (4 points)

**P. 3354. ** A SUZUKI SWIFT car of 1300 cm^{3} consumes 5.4 litres of petrol in 100 km at a
constant speed of 90 km/h. When the car travels at 160 km/h the power
of its engine is 48.3 kW. The efficiency of the engine is 30 %, the
density of the petrol is 700 kg/m^{3}, its
heat of combustion is 46 000 kJ/m^{3}. *a) *How many litres of petrol does this car
consume at 100 km? *b) *What is the power of the car at
90 km/h? (3 points)

**P. 3355. **
At a tennis tournament the second place winner has got a medal made of
silver. The medal has been made such a way that the material, initially at a
temperature of 20 ^{o}C, was melted at its
melting point and then it was cast into the mould. How long did the quantity of
silver for 20 medals (5 dkg each) melt, if the melting furnace has a power
supply of 230 V, the resistance of the filament of the furnace is
46 and its efficiency is 40 %? (The
melting point of silver is 960 ^{o}C, its
specific heat is 0.2 kJ/(kg ^{o}C) and
its heat of fusion is 100 kJ/kg.) (3 points)

**P. 3356. ** On how steep an inclined plane (maximum angle)
can a homogeneous solid hemisphere be placed on its convex side to remain at
rest? What coefficient of friction is required for this? (The centre of mass of
the hemisphere is at 3/8 of the radius.) (4 points)

**P. 3357. **
It is a well-known experience that an open plastic litter bag filled with hot
air and turned up-side-down (its opening is below) lifts up like a real hot air
balloon. Why false is the following argument? "The opening of the bag is free,
so the air pressure inside and outside is the same. This is why the closed
bottom of the bag (at the top) is pushed upward by the inner air with the same
force as the outer pressure downward. Thus these forces cancel each other and
the bag falls down because of gravitational force exerting on the material of
the bag." (4 points)

**P. 3358. **
Make the plan of a road bend with the following conditions: "When the road is
icy (the coefficient of static friction is 0.08) a car at rest cannot slip down
to the centre of the bend, and the car at a speed of less than 60 km/h
cannot skid off the road." What is the minimum radius the trajectory? Find the
angle respected to the horizontal at which the roadway should be tilted in the
minimum radius case. (4 points)

**P. 3359. ** A steel and a copper cylinder with the same size
and painted white both are warmed up to the same temperature, and then are
placed to cool down on a table (not right next to each other). According to our
experience the copper cylinder cools down faster. What could be the
explanation? (The specific heat of copper and steel are nearly identical as
well as their density.) (5 points)

**P. 3360. **
From what minimum height did a spherical mercury drop with a diameter of
1 mm fall onto a glass plate, if it has disintegrated to 1000 identical
spheres. (4 points)

**P. 3361. **
A direct current motor is operated at 100 V. When the motor is first
turned on, the current in the coils connected in series is 16 A. When the
motor has reached maximum speed, the current decreases to 4 A. This motor
is used as a generator at the same revolutions per minute. Find the external
resistance to connect between the terminals of the generator, if the current of
the generator is also 4 A. What is the useful power of the generator in
this case dissipated on the external resistor? (4 points)

**P. 3362. ** It has been detected that a nucleus at negligible speed radiates an particle with a kinetic energy of 5.5 MeV when it
decays. *a) *Find the speed of the particle and the recoil speed of the nucleus which has been formed in the
decay. *b) *Find the released energy in the decay of the nucleus. *c) *Find the released energy
in the decay of a 1 mg pure sample of radon during 3.82 days, if the
half-life of the radon-222 isotope is just 3.82 days. (4 points)

**P. 3363. ** What maximum temperature can a small, spherical,
black body reach using sun light with the help of a thin lens, if its focal
length equals to the double of its diameter? Does the result depend on the
radius of the small sphere? (5 points)