# Exercises and problems in Physics

May 1998

## New experimental problem:

**m. 198.**
Determine the number of carbon atoms per millimetre on lines drawn with pencils containing graphite leads of various hardness.

## New exercises:

**FGy. 3160.**
The height of a brick is 15 cm, its density is 2.5 g/cm^{3}.
What is the maximum possible height of a wall built out of such bricks of the
pressure at the base is not to exceed 0.5 MPa? The thickness of the
mortar layer between the bricks is 1.5 cm and its density of
1.5 g/cm^{3}.

**FGy. 3161.** The temperature of some plants rises considerably
when they are in blossom. A plant of that kind is put in a thermally insulated
vessel with a heat capacity of 18 J/K. Initially, the temperature of the
air enclosed is 20 ^{o}C, and it rises to
25 ^{o}C in 40 seconds. Then, after a quick airing, it only
takes 30 seconds to raise the temperature from 20 ^{o}C to
25 ^{o}C again. Find the heat generating power of the plant.

**FGy. 3162.** A series combination of three voltmeters is
connected across the poles of a battery with relatively large internal
resistance and an electromotive force of 9 V. One voltmeter reads
2.4 V, the other reads 2.9 V and the third one reads
3.6 V. What will the same voltmeters read if they are connected to the
battery in parallel?

**FGy. 3163.** A pendulum swings in front of a scale between the
divisions marked 10 and 30. In photograph of the pendulum, the blurred image
covers the region between the marks of 18 and 25. Find the time of exposition
if the period of the pendulum is 1.73 seconds.

**FGy. 3164.** The initial speed of the centre of a ping pong ball
spinning ``backwards'' on a level tabletop is 3 \rm m/s, and the
tangential speed of its rotation os 9 m/s initially. The
coefficient of friction is 0.2.

- a) Find the time it takes the ball to get back to its starting
position.

- b) For that speeds will the ball come to rest on the table instead of coming back?

^{2}.

## New problems:

**FF. 3165.** A direct-vision prism is made out of three prisms,
each with a refracting angle of
=60^{o}, attached to each
other as shown in the figure. Light of a certain wavelength is incident on the
first prism. The angle of incidence is 30^{o} and the ray leaves the
third prism parallel to the direction of incidence. The refractive index of
the glass of the first and third prisms is 1.44. Find the refractive index of
the material of the middle prism.

**FF. 3166.** The magnetic field shown in the figure consists of
two uniform regions. The width of the first part is 5 cm, and the
magnetic induction here is 0.001 T. The width of the other part is also
5 cm, with the direction of the induction being opposite in direction and
0.002 T in magnitude. What should be the minimum speed of the electron
arriving from the direction indicated in the figure so that it can pass
through the magnetic field? How much time does such an electron spend in the
magnetic field?

**FF. 3167.** Find the average power drawn out of an object
oscillating
at a frequency f with an amplitude *A* by a taut string attached
to it, in which the speed of elastic waves is c and its mass
per unit length is \mu.

**FF. 3168.** A 2-kg block is placed in an inclined plane enclosing a
30^{o} angle with the horizontal, and a 1-kg block is placed on top
of it. The two of them are connected by a thread wrapped over a pulley as
shown in the figure. The coefficient of friction between the blocks in 0.1 and
0.2 between the lower block and the slope. Find the acceleration of each block
and the tension in the thread.

**FF. 3169.** A person of height *h*_{0}=2 m
is doing bungy jumping from a tower of *h*=25 m over the lake
Balaton. One end of an
elastic rope is attached to his foot and the other end is fixed in the
tower. He starts falling from rest in vertical position. The length and
elastic properties of the rope are chosen so that the speed of the descending
person should decrease to zero at the instant when his head reaches the
surface of the water. At the end the person is hanging from the rope with his
head 8 m over the water.

- a) Find the unstretched length of the rope.

- b) Find the maximum speed and the maximum acceleration during the
jump.

## New advanced problem:

**FN. 3170.** Consider the following well-known experiment: There
is an object suspended from a thread and having an identical string attached
to the bottom. If the lower string is pulled slowly, the upper one will
break. If it is jerked abruptly, it is the lower string that will break. Let
the mass of the object be *m*=0.2 kg.
Let the force constant of the strings
be *D*=1000 N/m and let the maximum tension they can withstand be
*F*_{max}=6mg.
Which string will break if the lower end is pulled with a speed
of

- a) 0.15 m/s,

- b) 0.28 m/s,

- c) 0.40 m/s,

- d) 0.80 m/s.