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Physical Quantities and Measurement

Quantum Field Theory. Relativistic Mechanics. speed. Quantum Mechanics. Classical Mechanics. size. Physical Quantities and Measurement. What is Physics? Natural Philosophy science of matter and energy fundamental principles of engineering and technology

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Physical Quantities and Measurement

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  1. Quantum Field Theory Relativistic Mechanics speed Quantum Mechanics Classical Mechanics size Physical Quantities and Measurement • What is Physics? • Natural Philosophy • science of matter and energy • fundamental principles of engineering and technology • an experimental science: theoryexperiment • simplified models • range of validity

  2. Quantifying predictions and observations • physical quantities: numbers used to describe physical phenomena • height, weight e.g. • may be defined operationally • standard units: International System (SI aka Metric) • defined units established in terms of a physical quantity • derived units established as algebraic combinations of other units

  3. Scientific Notation: powers of 10 5,820 = 5.82x103 = 5.82E3 .000527 = 5.28x10-4 = 5.28E-4 note: 103 = 1x103 =1E3 not 10E3! Common prefixes How big (in terms of everyday life/other things) is a meter nanometer gram centimeter kilometer kilogram

  4. Dimensional Analysis: consistency of units • Algebraic equations must always be dimensionally consistent. • You can’t add apples and oranges! • converting units • treat units as algebraic quantities • multiplying or dividing a quantity by 1 does not affect its value

  5. Some Useful Conversion factors: • 1 inch = 2.54 cm • 1 m = 3.28 ft • 1 mile = 5280 ft • 1 mile = 1.61 km • Units Conversion Examples • Example 1-1 The world speed record, set in 1983 is 1019.5 km/hr. Express this speed in m/s • Example how man cubic inches are there in a 2 liter engine?

  6. Significant Figures and Uncertainty • Every measurement of a physical quantity involves some error • random error • averages out • small random error  accurate measurement • systematic error • does not average out • small systematic error  precise measurement less precise less accurate

  7. Indicating the accuracy of a number: x ± Dx or x± dx • nominal value: the indicated result of the measurement • numerical uncertainty: how much the “actual value” might be expected to differ from the nominal value • sometimes called the numerical error • 1 standard deviation • A measured length of 20.3 cm ± .5 cm means that the actual length is expected to lie between 19.8 cm and 20.8 cm. It has a nominal value of x = 20.3 cm with an uncertainty of Dx .5 cm. • fractional uncertainty: the fraction of the nominal value corresponding to the numerical uncertainty • percentage uncertainty: the percentage of the nominal value corresponding to the numerical uncertainty

  8. Uncertainties in calculations • Adding and subtracting: add numerical uncertainty • Multiplying or Dividing: add fractional/percentage uncertainty • Powers are “multiple multiplications”

  9. More complex algebraic expressions must be broken down operation by operation a = 3.13±.05 b = 7.14 ±.01 c = 14.44 ±.2%

  10. Significant Figures: common way of implicitly indicating uncertainty • number is only expressed using meaningful digits (sig. figs.) • last digit (the least significant digit = lsd) is uncertain • 3 one digit • 3.0 two digits (two significant figures = 2 sig. figs.) • 3.00 three digits,etc. (300 how many digits?) • Combining numbers with significant digits • Addition and Subtraction: least significant digit determined by decimal places (result is rounded) • .57 + .3 = .87 =.9 11.2 - 17.63 = -6.43 = -6.4 • Multiplication and Division: number of significant figures is the number of sig. figs. of the factor with the fewest sig. figs. • 1.3x7.24 = 9.412 = 9.4 17.5/.3794 = 46.12546 = 46.1 • Integer factors and geometric factors (such as p) have infinite precision • p x 3.762 = 44.4145803 = 44.4

  11. Estimates and Order of magnitude calculations • an order of magnitude is a (rounded) 1 sig fig calculation, whose answer is expressed as the nearest power of 10. • Estimates should be done “in your head” • check against calculator mistakes! • Additional Homework: with • a = 3.13±.05 b = 7.14 ±.01 c = 14.44 ±.2% • evaluate expressions (nominal value and uncertainty expressed as numerical uncertainty and percentage uncertainty)

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