This book contains some of the problems and solutions in the past domestic theoretical and experimental competitions in Japan for the International Physics Olympiad. Through the exercises, we aim at introducing the appeal and interest of modern physics to high-school students. In particular, the problems for the second-round of competition are like long journey of physics, beginning with fundamental physics of junior-high-school level, and ending with the forefronts of updated physics and technology.
Contents:
Part I: Theory:
General Physics
Mechanics
Oscillations and Waves
Electromagnetism
Thermodynamics
Modern Physics
Part II: Experiments:
How to Measure and Analyze Data
Practical Exercises
Appendices: Mathematical Physics
Readership: High school students and high school teachers, as well as undergraduates.
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The units of fundamental physical quantities, such as length, mass and time, are called the fundamental units, from which the units of other physical quantities are derived.
In the International System of Units (SI), the unit of length is the meter (m), that of mass is the kilogram (kg) and that of time is the second (s). Other units can be composed of these fundamental units. For example, the unit of mass density is kg/m3, because the unit of volume is m × m × m = m3.
On the other hand, there are units composed of the gram (g), the unit of mass; the centimeter (cm), the unit of length; and the second (s), the unit of time. This system of units is called the cgs system of units. In the cgs system, the unit of volume is cm3 and the unit of mass density is g/cm3.
The unit size in the SI is not the same as that in the cgs system. For example, 1 m3 in the SI unit is 106 cm3 in the cgs unit.
How many times larger is the unit size in the SI as compared with the unit size in the cgs system for each of the following physical quantities?
Enter the appropriate numbers in the blanks below.
the unit of volume:
10a times a =
(1) the unit of speed:
10i times i =
(2) the unit of acceleration:
10j times j =
(3) the unit of force:
10k times k =
(4) the unit of energy:
10l times l =
(5) the unit of pressure:
10m times m =
(the 1st Challenge)
Answeri = 2, j = 2, k = 5, l = 7, m = 1
Solution
(1) The unit of speed in the SI is m/s. The unit size of speed in the SI is 1 m/s = 1 × 102 cm/s (because 1 m = 1 × 102 cm). Therefore, it is 102 times the unit size of speed in the cgs system.
(2) The unit of the acceleration in the SI is m/s2. 1m/s2 =1 × 102 cm/s2. Therefore, the answer is 102 times.
(3) Force is “(mass) × (acceleration)”, therefore the unit of force in the SI is N = kg⋅m/s2. 1N=1 × 103 g × 102 cm/s2 =105 g⋅cm/s2=105 dyn (because 1 kg = 103 g). Therefore, the answer is 105times.
(4) Energy is “(force) × (distance)”, therefore the unit of energy in the SI is J = N⋅m. 1 J = 105 dyn × 102 cm = 107 erg. Therefore, the answer is 107 times.
(5) Pressure is “(force)/(area)”, therefore the unit of pressure in the SI is Pa = N/m2. 1Pa=105 dyn/104 cm2 =10dyn/cm2. Therefore, the answer is 10 times.
Problem 1.2. The pressure due to high heels and elephants
Suppose the total weight of a person who wears high heels is 50 kg and is carried only on the ends of both heels equally (assume the cross section at the end of one heel to be 5 cm2). Also, suppose the total weight of an elephant is 4000 kg and is carried equally on the four soles (assume the cross section of one sole to be 0.2 m2). How many times larger is the pressure exerted on one sole of the elephant compared with the pressure exerted on the end of one heel of the high heels?
Choose the best answer from (a) through (f).
(the 1st Challenge)
Answer (e)
Solution
It is important to express the units of physical quantities in the SI. Let the gravitational acceleration be g. The person’s weight, 50 g, is carried on the ends of both heels equally. Hence, the pressure exerted on the end of one heel is pH =
