Transcript 01._DoingPhysics

1. Doing Physics
1.
2.
3.
4.
Realms of Physics
Measurements & Units
Working with Numbers
Strategies for Learning Physics
1.1. Realms of Physics
Realms:
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Atoms & Moelcules
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Thunderstorms & Rainbows
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⁞
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Stars, Galaxies, Universe.
Technological Applications:
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Microelectronics
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Medical Imaging
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⁞
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Cars, Airplanes, Space Flight
Goal:
Unified description of everything physical.
DVD Player:
Which realms of physics are involved ?
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Spinning disc: Mechanics
• Motion of cars, planets, …
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Stability of bridges, skyscrapers, …
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Sound waves: Oscillatory / Wave Motion
• Ocean waves, Tsunami, Earth quakes, Sonic Boom, …
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DVD-Write: Thermodynamics
• Refrigerators, Heat engines, Energy transfer, …
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Circuitry: Electromagnetism
• Computers, Microwaves, TV, …
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DVD-Read: Optics
• Microscopes, Telescopes, Spectrometers, Optic fibres, …
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Laser: Quantum Physics / Relativity
• Periodic table, nuclear fission / fusion, Black holes, …
1.2. Measurements & Units
SI / MKS units (Systeme International d’Unites)
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Length: Meter (m)
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1 / 10,000,000 of equator-north-pole distance.
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1889: standard meter bar.
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1960: wavelength of light.
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1983: 1 / 299,792,458 of distance traveled by light in 1s in vacuum.
Mass: Kilogram (Kg)
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Standard mass (Pt-Ir) in Sevres, France.
Time: Second (s)
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1 / (246060) of period of Earth rotation (day).
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1956: 1 / 31,556,925.9747 of year 1900.
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1967: 9,192,631,770 periods of radiation from cesium-133.
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Other base units:
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Current: Ampere (A)
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Temperature: Kelvin (K)
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Substance: Mole (mol)
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Luminosity: Candela (cd)
Supplementary units:
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Angle: Radian (rad)
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Solid angle: Steradian (sr)
Size of bacteria ~ 0.00001 m.
10 m.
Distance to 左營 ~ 31,000 m.
31 km.
Derived units:
Newton = N = Kg  m / s2
= Kg  m  s2
Other units:
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English units (ft, lb, s).
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CGS units (cm, g, s).
Changing Units:
See Appendix C
Units Matter: A Bad Day on Mars
1999: Mars Climate Orbiter ($125m) entered Mars atmosphere by mistake & was destroyed.
Root cause: Both English & SI units were used without conversion.
1.4. Working with Numbers
Scientifc notation:
Radius of proton:
Size of Galaxy:
Reach of telescope:
1 / 1,000,000,000,000,000 m
11015 m
1,000,000,000,000,000,000,000 m
11021m
100,000,000,000,000,000,000,000,000 m
11026m
4,185 = 4.185103
0.00012 = 1.2 104
Tactics 1.1. Using Scientific Notation
Addition / Subtraction:
Change all terms to the same exponent first.
3.75 106  5.2 105  3.75 106  0.52 106  4.27 106
Multiplication / Division:
Digits:
 / 
Exponents:
+ / 
 3.0 10 m / s   2.110 s   3.0  2.1 10  m / s   s 
10
8
810
 6.3  10 2 m
Powers / Roots:
Digits:
Exponents:
 3.6110 
4 3

power / root
 power /  root
 3.61
3
104  3 
47.04 1012

47.04 1012/2  6.86 106
Example 1.2. Scientific Notation: Tsunami Warnings
Tsunami: entire ocean (top to bottom) participates.
Speed v 
g  9.8 m / s 2 = Acceleration due to gravity
gh
h = depth of water = 3.0 km
v
9.8 m / s  3.0 10 m
2

29.4 103 m2 / s 2

2.94 104 m2 / s 2

2.94 102 m / s
 1.7 102 m / s
3
3
 m   1 km   3.6 10 s 
 1.7 10    3  

 s   10 m  1 hr 
2
 6.1 102 km / hr
 610 km / hr
Significant Figures
Significant figures (digits)
• of an integer: all digits between the leftmost & rightmost non-zero digits.
Trailing zeros are ambiguous.
• of a real number: all digits except leading zeros.
Examples:
Numbers with 5 sig. dig. :
001000500000,
1.0005  109
123.45,
0.0012345,
0.010000
1.2345  10 2
1.2345 103
1.0000 102
Note: 001000500000 may be taken as having 10 sig. dig.
Caution:
An integer sometimes denotes infinite accuracy (  sig. dig. ).
e.g., 2 in the formulae C = 2  R & A =  R2.
Accuracy & Significant Figures
2.94  1.7
means 2.94 is between 1.6 & 1.8
1.6 
i.e.
2.94  1.8
2.94  1.7  0.1
or
2.94  1.7146428199482247
Accuracy worsens after each calculation.
Result has accuracy of the least accurate member.
 /  : Number of significant digits = that of the least accurate member.
+ /  : result is rounded off to the rightmost common digit.
100.  0.456  100.
Bridge = 1.248 km
( accuracy = 0.001 km )
Ramp = 65.4 m
 = 3.14159
( # sig. dig. = 6 )
RE = 6.37 106 m ( # sig. dig. = 3 )
2  RE = 40.0238566106 m
= 0.0654 km
( acc = 0.0001 km )
Overall length = 1.248 km + 0.0654 km
= 1.3134 km
Overall # sig. digits = 3
Overall acc = 0.001 km, error =  0.001 km
 2  RE = 40.0106 m
 Overall length = 1.313 km
Error Analysis
Let sQ be the uncertainty in quantity Q.
x  a bc
For
2
sa2  sb2  sc2
2
x  a b / c
 sa 
 
a
sx 


sx  x
2
 sb 
 sc 
&
 
 
b
c
x  a bc
x  a b / c


2
sx  sa
sx 
b
sa
c
2
 sa   sb   sc 
     
a b c
2
Example 1.3. Uranium fuel rod in nuclear reactor
Before insertion, rod length = 3.241 m
After insertion,
rod length = 3.249 m
Q: What is the increase in length?
A:
3.249 m  3.241 m = 0.008 m = 8 mm
Accuracy = 1 mm
Error =  0.001 m =  1 mm
 Increase in length is 8 mm ( 1 sig. dig. )
Any intermediate results must have at least 1 extra sig. dig. to avoid rounding errors.
Caclulator: apply round-off & truncation only at the end.
Estimation
Example 1.4. Counting Brain Cells
Q: Estimate the mass of your brain & the number of cells it contains.
A:
Head is ~15 cm wide.
Discounting bones: ~10 cm wide.
Assuming cube shape, vol ~ ( 10 cm )3 = 1000 cm3 .
Mostly water  density = 1 g / cm3 .
 Brain mass ~ 1000 g = 1 Kg.
Brain cell size ~ red blood cell size ~ 105 m ( Table 1.1 )

Cell vol ~ (105 m)3
= 1015 m3
Number of cells in brain:
Brain vol
N
cell vol
3
10 cm
 15 3
10 m
10  10
3
3

1015 m3
 103615  1012
Actual data: Average adult brain mass ~ 1.3 Kg,

2 3
N ~ 1011 .
m3
1.4. Strategies for Learning Physics
Challenge:
Must be equally adept in both concepts & mathematics.
Simplicity:
A few basic principles govern everything.
Problem Solving: An IDEA Strategy
Interpret :
Intrepret & understand problem.
Identify applicable concepts & principles.
Identify players involved.
Develop:
Draw diagram & label objects.
Determine relevant formulas & values.
Evaluate:
Evaluate / execute the formulas.
Assess:
Assess correctnes of result (use common sense, consider special cases, etc.)