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## 1. Doing Physics Realms of Physics Measurements & Units Working with Numbers Str

Carolipio, Redmond, Features Reporter & Gaming Columnist has reference to this Academic Journal, PHwiki organized this Journal 1. Doing Physics Realms of Physics Measurements & Units Working with Numbers Strategies as long as 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,

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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 & Units SI / MKS units (Systeme International dUnites) Length: Meter (m) 1 / 10,000,000 of equator-north-pole distance. 1889: st in addition to ard 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: St in addition to ard 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: C in addition to ela (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 ~ 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. Multiplication / Division: Digits: / Exponents: + / Powers / Roots: Digits: power / root Exponents: power / root 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

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 as long as mulae C = 2 R & A = R2. Note: 001000500000 may be taken as having 10 sig. dig. 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 ) RE = 6.37 106 m ( sig. dig. = 3 ) 2 RE = 40.0238566106 m Overall sig. digits = 3 2 RE = 40.0106 m i.e. or Error Analysis Let sQ be the uncertainty in quantity Q. For

Example 1.3. Uranium fuel rod in nuclear reactor Be as long as e 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: Actual data: Average adult brain mass ~ 1.3 Kg, N ~ 1011 . 1.4. Strategies as long as 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 & underst in addition to problem. Identify applicable concepts & principles. Identify players involved. Develop: Draw diagram & label objects. Determine relevant as long as mulas & values. Evaluate: Evaluate / execute the as long as mulas. Assess: Assess correctnes of result (use common sense, consider special cases, etc.)

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