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1. Doing Physics

1. Doing Physics. Realms of Physics Measurements & Units Working with Numbers Strategies for Learning Physics. 1.1. Realms of Physics. Realms : Atoms & Molecules Thunderstorms & Rainbows ⁞ Stars, Galaxies, Universe. Technological Applications : Microelectronics

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1. Doing Physics

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  1. 1. Doing Physics Realms of Physics Measurements & Units Working with Numbers Strategies for Learning Physics

  2. 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.

  3. 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, …

  4. 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…

  5. 1.2. Measurements & Units • SI / 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 0C. • 1899: Standard mass (Pt-Ir) in Sevres, France. • Time: Second (s) • 1 / (246060) 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.

  6. Other base units: • Current: Ampere (A) • Temperature: Kelvin (K) • Substance: Mole (mol) • Luminosity: Candela (cd) • Supplementary units: • Angle: Radian (rad) • Solid angle: Steradian (sr)

  7. 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: • English units (ft, lb, s). • CGS units (cm, g, s). Changing Units: See Appendix C

  8. 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.

  9. 1.4. Working with Numbers Scientifc notation: 11015 m 11021m 11026m 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 4,185 = 4.185103 0.00012 = 1.2 104

  10. Tactics 1.1. Using Scientific Notation Addition / Subtraction: Change all terms to the same exponent first. Multiplication / Division: Digits:  /  Exponents: + /  Powers / Roots: Digits: power / root Exponents:  power /  root

  11. Example 1.2. Scientific Notation: Tsunami Warnings Tsunami: entire ocean (top to bottom) participates. Speed = Acceleration due to gravity h = depth of water = 3.0 km

  12. 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 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.

  13. Accuracy & Significant Figures means 2.94 is between 1.6 & 1.8 i.e. or • 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 = 40.0238566106 m Overall # sig. digits = 3  2  RE = 40.0106 m

  14. Error Analysis Let sQ be the uncertainty in quantity Q.   For  

  15. 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.

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

  17. 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.)

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