# Exercises and problems in Physics

September 2001

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

## Experimental problem |

**M. 226. ** Use a drawing board to make a slope with
a variable angle. Fit the bottom of the drawing board to the edge of
the table so that a sliding body could leave the slope without
collision and fall freely on the floor. Take measurements to find out
what sloping angle a coin sliding from the top of the drawing board
falls furthest. Does the result depend on the length of the drawing
board, on the height of the table or on the coin itself?

## Theoretical problemsIt is allowed to send solutions for any number of problems, but final scores of students of grade 9-12 are computed from the 5 best score in each month. Final scores of students of grade 1-8 are computed from the 3 best scores in each month. |

**P. 3445. ** Julie and Steve live in the same
street, Julie in a 300 m and Steve in a 800 m distance from
the school. In the morning they leave for school at the same
time. Steve goes by bike at a speed of 10 m/s and Julie goes on
foot at a speed of 2 m/s. When they meet, Steve gets off his bike
and they walk on together talking to each other at a speed of
1 m/s. Will they reach the school before the school bell rings if
they started from home 3 minutes before the ring? (3 points)

**P. 3446. ** There is a force of 800 N
exerted on a man standing in a lift due to gravitation. The force
exerted on the lift by the man (his weight) is 820 N. At what
rate does the lift accelerate and in which direction? What can we say
of the velocity of the lift? (3 points)

**P. 3447. ** Let's fill an air-balloon to the
same volume once with hydrogen and once with helium. In which case is
the lifting capacity greater and by what percentage? (In the given
conditions the gas densities in kg/m^{3} units are: hydrogen
-- 0.08, helium -- 0.16, air -- 1.162). The mass of the balloon's
material is negligible compared to the mass of the burden and the
volume of the burden is negligible compared to the volume of the
balloon. (3 points)

**P. 3448. ** Let's push up a crate of a mass of
10 kg slowly on a slope. The work needed to achieve this is
400 J. By pulling the same crate down the slope we use work of
250 J. (The force of both pushing and pulling is parallel to the
direction of the slope.) What is the height of the slope? (4 points)

**P. 3449. ** There are three elastic disks with
masses *m*_{1}=*m*_{3}=0.15 kg,
*m*_{2}=0.2 kg connected with two equal length
strings of negligible mass, on a horizontal air-cushioned table. At
the beginning the three disks are in rest and reside in one line
(according to the *figure*). Then we make the middle disk move
horizontally and perpendicular to the strings with a velocity of
*v*_{0}=6 m/s.

*a*) What is the velocity of the side disks right at the
moment when the disk of mass *m*_{2} stops after the
elastic collision of the two disks in question? What is the angle
formed by the two strings in this position?

*b*) What is the angle formed by the two strings in this
position? (6 points)

**P. 3450. ** There is a ship sailing east along
the Equator with a speed of 45 km/h. How much time does a
pendulum-clock on board lose in 3 hours if it keeps good time when the
ship rests relative to the Earth. (5 points)

**P. 3451. ** A solid piece of metal with a
volume of 50 cm^{3} and a temperature of 20 ^{o}C
can be lifted to a height of 100 m by using 135 J of
work. What would be the temperature of the same object if we
transmitted to it an amount of heat equivalent to the work used in
lifting. (4 points)

**P. 3452. ** The measuring limit of a standard
voltage meter with the resistance of *R*=1 k can be extended to
60 V, 150 V and 300 V as can be seen in the
*figure*. The sum of the three additional resistances is
9 k\(\displaystyle Omega\). What are
the separate resistance values, and how much is the measuring limit of
the basic instrument *U*_{0}? (4 points)

**P. 3453. ** A semicylinder made of a
transparent plastic has a refraction index of *n*=1.41 and a
radius of *R*=5 cm. There is a narrow incident laser beam
perpendicular to the flat side of the semicylinder at d distance from
the axis of symmetry.

*a*) What can the maximum value of *d* be so that the
laser beam can still leave the other side of the semicylinder?

*b*) How can the refraction index be determined if we know
*d*_{max} and *R*?

*c*) By varying distance *d*, in which interval will
distance *OB* shown in the *figure* vary? (4 points)

**P. 3454. ** In 1923 George Hevesy determined
the age of a rock sample with some uranium content based on the
finding that the ratio of the number of ^{238}U atoms to the
number of ^{206}Pb atoms present in the sample was 3:2. What
was the age he determined? (4 points)

**P. 3455. ** The Sun emits electromagnetic
radiation with the power of 3.86x10^{26} W.

*a*) How much energy arrives per second at the top of the
Earth's atmosphere on a 1 m^{2} surface perpendicular to
the radiation coming from the Sun?

*b*) How much is the impulse of the light incident on a
surface of 1 m^{2} in one second?

*c*) What is the pressure exerted by the incoming light on a
surface that is perpendicular to the radiation and absorbs every kind
of light? (4 points)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary