Page of High School Student
In this section we present problems in physics for students of high school.
You can send your solutions to Alexey Savin to SavinA@info.sgu.ru, and then your work will be
checked and you will receive a mark or a referee report.
For those who starts to learn physics
Here are the problems for beginners in physics that introduce you into a spirit,
stile, and approaches of this science. The first impression that is often emphasized
in school lessons is that physics is an exact science, somewhat like
application of mathematics to a study of nature. It is true that mathematics
is important for physics, but this is in fact a very distinct discipline deeply
connected with the Universe, having its own approaches and criteria of effectiveness.
We hope that the suggested problems will help you to catch and understand some
important and interesting peculiarities of physics.
- Compare pressures of man and cat onto the Earth surface.
- In ancient ages some people thought that the Earth is placed on the back
of a giant whale swimming in the Ocean. Ectimate characteristic size of the
whale. Assume that the Earth has a form of semi-sphere of radius R=6400
km, the mean density of it is ,
density of the whale .
Approximate the whale by a cylinder of diameter 10 times less than its length.
- What is larger - a ratio of the Sun mass to the mass of Earth, or ratio
of mass of the oxygen molecule to the mass of electron?
- A cylinder vessel of height H with cross-section area S is
filled by water up to level h. Then, a body of volume V and
thrown into the vessel. What are possible qualitatively distinct situations.
What are parameter intervals necessary for these situations to arise?
Olympiad problems in physics
For those who are familiar with the school level physics we present here several
problems from physical Olympiads.
- Estimate relative compression of planet Jupiter near its poles,
( is difference
of equatorial and polar radii). The mean radius of the planet is r=70000
km, gravitational acceleration near the surface g = 20 m/s2,
period of revolution T is equal to 10 hours. Assume for simplicity
that the overwhelming part of the whole mass is concentrated in a compact
central nuclear of the planet.
- There are two springs made of the same material twisted in such way that
neighbor coils of each spring touch each other. Diameters of the springs are
3 and 9 mm, lengths 1 and 7 sm, diameters of the wire, respectively, 0.2 and
0.6 мм. Spring coefficient for the first is 15 N/m2. Find the coefficient
for the second spring.
- There is a circuit of connected successively a capacitor C and an
inductance L, and a voltage is supplied varying in time according to
an expression .
Determine current in the circuit.
Problems of research character
Here we suggest you to try problems of nature different from those you deal
at lessons or Olympiads. Lesson or Olympiad are short time, and you can spare
not so much time to each problem because need to solve as many of them as possible.
Among the following problems you may prefer to select one, that you like more.
It may take not an hour and not a day to elaborate a solution. Significant is
not number of the solved problem, but the depth of understanding
and development of the solution. Such problems help you to understand better
science as a profession that consists in obtaining novel results by your own
A feature of these problems is that they do not have one definite solution,
each of them allows multiplicity of approaches as well as subsequent development.
Arsenal of your tools is not fixed. You may use theoretical reasoning, experiments,
computer simulation, following your own preferences, experience, consultations,
literature, internet, discussion with friends, any other available ways. Discuss
the problem with friends.
If your investigation will be successful, you can present results to a school-conference
"Nonlinear days for youth in Saratov". You must account, however, that preparation
of the report on your work is itself a serious work even if the results are
ready, true, and relevant. This is one more step to the profession of a scientist.
The authors of the best solutions will be awarded with special diploma.
- A distorsion of the ocean surface. P.L.Kapitza suggested
such a problem: Upside the ocean surface let us place a massive particle of
mass m, at the height h up the unperturbed water surface. Study a form of
the surface perturbed by the gravitational field of the particle. Depict the
corresponding profiles using computer. Is it possible to observe all found
forms in realistic experiments on the Earth? Consider possible modifications
of the problem (particle under water, case of two comparable gravitational
- Optical caustics in a cylinder cup. Inside a cylindrical
vessel (say, a cup with milk) illuminated by incident light you can observe
a bright curve with yet more bright spike (cusp point). The curve is called
caustic, and it represents envelope curve of the family of rays reflected
from the cylindrical surface. Undertake experimental, theoretical, and computer
investigation of the caustic.
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