1. Doing Physics

1. Realms of Physics

2. Measurements & Units

3. Working with Numbers

4. Strategies for Learning Physics

1.1. Realms of Physics

Realms:

• Atoms & Molecules

• Thunderstorms & Rainbows

• ⁞

• Stars, Galaxies, Universe.

Technological Applications:

• Microelectronics

• Medical Imaging

• ⁞

• Cars, Airplanes, Space Flight

Goal:

Unified description of everything physical.

DVD Player: Which realms of physics are involved ?

• Spinning disc: Mechanics• Motion of cars, planets, …• Stability of bridges, skyscrapers, …

• Sound waves: Oscillatory / Wave Motion• Ocean waves, Tsunami, Earth quakes, Sonic Boom, …

• DVD-Write: Thermodynamics• Refrigerators, Heat engines, Energy transfer, …

• Circuitry: Electromagnetism• Computers, Microwaves, TV, …

• DVD-Read: Optics• Microscopes, Telescopes, Spectrometers, Optic fibres, …

• Laser: Quantum Physics / Relativity• Periodic table, nuclear fission / fusion, Black holes, …

Conceptual Example 1.1. Bike Physics

Name systems in your motor cycle that exemplify the different realms of physics

Answer:

Mechanics: anything in motion

Oscillation: shock absorbers

Thermodynamics: combustion engine

Electromagnetics: spark plugs

Optics: mirrors, lights

Quantum mechamics : chemistry of combustion, electronics…

1.2. Measurements & UnitsSI / MKS units (Systeme International d’Unites)

• Length: Meter (m)

• 1 / 10,000,000 of equator-north-pole distance.

• 1889: standard meter bar.

• 1960: wavelength of light.

• 1983: 1 / 299,792,458 of distance traveled by light in 1s in vacuum.

• Mass: Kilogram (Kg)

• 1795: 1 gram = mass of 1 cc water at 0C.

• 1899: Standard mass (Pt-Ir) in Sevres, France.

• Time: Second (s)

• 1 / (246060) of period of Earth rotation (day).

• 1956: 1 / 31,556,925.9747 of year 1900.

• 1967: 9,192,631,770 periods of radiation from cesium-133.

• Other base units:

• Current: Ampere (A)

• Temperature: Kelvin (K)

• Substance: Mole (mol)

• Luminosity: Candela (cd)

• Supplementary units:

• Angle: Radian (rad)

• Solid angle: Steradian (sr)

Derived units:

Newton = N = Kg m / s2

= Kg m s2

Other units:

• English units (ft, lb, s).

• CGS units (cm, g, s).

Changing Units:

See Appendix C

Size of bacteria ~ 0.00001 m. 10 m.

Distance to 左營 ~ 31,000 m. 31 km.

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

Radius of proton: 1 / 1,000,000,000,000,000 m

Size of Galaxy: 1,000,000,000,000,000,000,000 m

Reach of telescope: 100,000,000,000,000,000,000,000,000 m

Scientifc notation:

11015 m

11021m

11026m

4,185 = 4.185103

0.00012 = 1.2 104

Tactics 1.1. Using Scientific Notation

Addition / Subtraction: Change all terms to the same exponent first.

6 53.75 10 5.2 10 6 63.75 10 0.52 10 64.27 10

Multiplication / Division:

Digits: /

Exponents: + /

8 103.0 10 / 2.1 10m s s 8 103.0 2.1 10 /m s s 26.3 10 m

Powers / Roots:

Digits: power / root

Exponents: power / root

343.61 10 3 4 33.61 10 1247.04 10 12/247.04 10 66.86 10

Example 1.2. Scientific Notation: Tsunami Warnings

Tsunami: entire ocean (top to bottom) participates.

v g h 29.8 /g m sSpeed = Acceleration due to gravity

h = depth of water = 3.0 km

2 39.8 / 3.0 10v m s m

3 2 229.4 10 /m s

4 2 22.94 10 /m s

22.94 10 /m s

21.7 10 /m s

32

3

1 3.6 101.7 10

10 1

m km s

s m hr

26.1 10 /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, 123.45, 0.0012345, 0.010000

91.0005 10 21.2345 10 31.2345 10 21.0000 10

Caution:

An integer sometimes denotes infinite accuracy ( sig. dig. ).

e.g., 2 in the formulae C = 2 R & A = R2.

Note: 001000500000 may be taken as having 10 sig. dig.

Accuracy & Significant Figures2.94 1.7 means 2.94 is between 1.6 & 1.8

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.Bridge = 1.248 km ( accuracy = 0.001 km )

Ramp = 65.4 m

= 0.0654 km ( acc = 0.0001 km )

Overall length = 1.248 km + 0.0654 km

= 1.3134 km

Overall acc = 0.001 km, error = 0.001 km

Overall length = 1.313 km

= 3.14159 ( # sig. dig. = 6 )

RE = 6.37 106 m ( # sig. dig. = 3 )

2 RE = 40.0238566106 m

Overall # sig. digits = 3

2 RE = 40.0106 m

1.6 2.94 1.8 2.94 1.7 0.1 i.e. or

100. 0.456 100.

Error Analysis

Let sQ be the uncertainty in quantity Q.

x a b c 2 2 2x a b cs s s s

/x a b c 2 2 2

a b cx

s s ss x

a b c

x a b c x as s

/x a b c x a

bs s

c

2 2 2

&a b cs s s

a b c

For

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 ~ 105 m ( Table 1.1 )

Cell vol ~ (105 m)3

= 1015 m3

Number of cells in brain: Brain volN

cell vol

3 3

15 3

10

10

cm

m 33 2 3

15 3

10 10

10

m

m

3 6 1510 1210

Actual data: Average adult brain mass ~ 1.3 Kg, N ~ 1011 .

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.)