Transcript Physics for Science and Engineering I (PHY 240)

1.
Physics
- Part of science that describes (not
"explains") the behavior of matter and its
interactions at the most fundamental level.
Physics
is
based
on
experimental
observations.
Geology,
chemistry,
engineering,
astronomy, biology, psychology and medicine
all 'require' an understanding of the principles
of physics.
classical physics
a) classical mechanics: the study of motion
b) thermodynamics: the study of energy
transfer
c) electromagnetism: electricity, magnetism,
optics
modern physics
a) relativity: a theory of the behavior of
particles at high speeds
b) quantum mechanics: a theory of the
submicroscopic world
Structure of physics
• Physics describes (!), in an approximate
way, the natural phenomena taking place in
the universe.
• An abstract model, using imaginable
elements and mathematical relations is
created to analyze the phenomena.
Example (mixing of liquids)
pepsi
water
pepsi
pepsi
water pepsi
water
pepsi
0
pepsi  0
water
 1
1
0
0
0
1
0
1
Because of their simplicity and accuracy,
mathematical models are used to represent
nature. The most common mathematical
concepts used for this purpose are:
numbers
vectors
tensors
functions
operators
xx xy xz
55 km/h
yx yy yz
zx zy zz
y(t)
=
A
sin (t)
[5,4,3] N

pˆ x  i
x
120 kJ
3. Measurement
The procedure, which assigns
a mathematical quantity to a
physical quantity is called a
measurement. A measurement
is based on a comparison of
the given element of the
quantity with a chosen
element called a standard.
units
The most commonly used SI (metric) system
is based on m, kg, s, mole. In some cases it is
convenient to introduce other units by adding
prefixes.
femto- 10-15
micro- 10-6
pico- 10-12
mili- 10-3
nano- 10-9
centi- 10-2
kilo- 103
mega- 106
giga- 109
Conversion of units.
In principle the choice of units for a certain
quantity is arbitrary. Different numbers can
be assigned to a single quantity! Therefore, it
is always necessary to indicate the units. The
numbers are related by conversion factors.
4.
a)
b)
c)
d)
Concepts, axioms, theorems...
A concept is an idea that is used to analyze natural
phenomena. It can be either a primitive concept
(undefined) or a concept defined in terms of other
concepts.
An axiom is a relationship between concepts assumed to
be valid (postulates, laws).
A theorem is a relationship between concepts, which can
be derived from other relationships (laws, principles).
A model is a convenient representation of a system (a
theory).
5.
Scalars
The character of a physical quantity is
determined by the rules of combination of that
quantity.
A scalar quantity obeys the same rules
of combination as numbers. Each scalar
quantity can be represented by a number.
3+2=5
Time
- a scalar quantity associated with changes
in the universe.
(The SI unit is one second defined as a time interval in which
a specific spectral line of cesium-133 (Cs133) performs a
defined number of oscillations.)
Example 1. Time-interval
(do not confuse with time-instant)
A repetitive process is used as a time
counter (a clock). The number of
repetitions is the value assigned to the
time-interval.
Distance
- a scalar quantity associated
with the relative arrangements
of two points.
(The SI unit one meter defined as the length
of the path traveled by light in a vacuum
during a time interval of 1/299,792,458 of a
second.)
s0
Mass
- a scalar quantity assigned to the principal
inertial property of a body, i.e. its
'resistance' to a change in motion.
(The SI unit is one kilogram defined as the mass of the
platinum-iridium cylinder kept at the International Bureau of
Weights and Measures.)
Length
- a scalar quantity associated
with the size of objects and
figures.
l

ds 
curve
lim  si
s i 0 i
example: length (circumference) of a circle
l  2
y
dl
R
2
2




dx

dy


R
 2
R

R
dy
dx
x
 2
R

R
 2
2
 dy 
1    dx 
 dx 


 2x  
 dx 
1   
2
2 
 2 R x 
2
R
R
R
R x

2
2
dx 
R
y  R2  x2
x
 2R  arcsin

R R
  
 2R   
  2R
2 2 
example: area of a circle
y
A
R

2
R x
y  R2  x2
2
 dy dx 
R  R 2 x 2

R
R 2 x2
y  R 2 x2
R

dx
dy
dx 
x
R
  2 R 2  x 2 dx 
R
R
1
x
 2   x R 2  x 2  R 2 arcsin  
2
R  R
R 
R

2
  R R 2  R 2  R 2 arcsin     R R 2  R 2  R 2 arcsin
  R
R 
R 

example: area of a circle
y
A
R 2
  rddr 
0 0

R

dr
2
r  0 dr
0
R
 2  rdr 
0
2 R
r
 2
2
0
 R 2
rd
x
Density
The (differential) mass dm of a
(differential) volume dV of a
substance is proportional to the
volume.
dm    dV
The proportionality coefficient is called the
density of the substance.
example: (non-uniform density)
mass of a differential shell




dm  dV   0 1  r 2  4r 2  dr  4 0 r 2  r 4  dr
dr
r
total mass

 =  0(1 – r2)
M
 dm  4 0   r
R
object

 r 4 dr
0
R
r
2
 r3 r5 
 R3 R5 

 4 0      4 0  

5 
 3 5 0
 3
example: (uniform density)
mass of a differential fragment
dm  0dV
total mass
M
 0dV  0   dV  0V
object
object