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1. Doing Physics 1.Realms of Physics 2.Measurements & Units 3.Working with Numbers 4.Strategies for Learning Physics
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1.1. Realms of Physics Realms: Atoms & Moelcules Thunderstorms & Rainbows Stars, Galaxies, Universe. Technological Applications: Microelectronics Medical Imaging Cars, Airplanes, Space Flight Goal: Unified description of everything physical.
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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, …
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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) 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.
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Other base units: Current: Ampere (A) Temperature: Kelvin (K) Substance: Mole (mol) Luminosity: Candela (cd) Supplementary units: Angle: Radian (rad) Solid angle: Steradian (sr)
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Derived units: Newton = N = Kg m / s 2 = Kg m s 2 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.
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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.
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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: 1 10 15 m 1 10 21 m 1 10 26 m 4,185 = 4.185 10 3 0.00012 = 1.2 10 4
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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
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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
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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 Caution: An integer sometimes denotes infinite accuracy ( sig. dig. ). e.g., 2 in the formulae C = 2 R & A = R 2. Note: 001000500000 may be taken as having 10 sig. dig.
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Accuracy & Significant Figures means 2.94 is between 1.6 & 1.8 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 ) R E = 6.37 10 6 m ( # sig. dig. = 3 ) 2 R E = 40.0238566 10 6 m Overall # sig. digits = 3 2 R E = 40.0 10 6 m i.e.or
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Error Analysis Let s Q be the uncertainty in quantity Q. For
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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.
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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 cm 3. Mostly water density = 1 g / cm 3. 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 m 3 Number of cells in brain: Actual data: Average adult brain mass ~ 1.3 Kg, N ~ 10 11.
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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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