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ch1 - Introduction Measurement Estimating Chapter Outline...

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Unformatted text preview: Introduction, Measurement, Estimating Chapter Outline GENERAL PHYSICS PHY 302K The Nature of Science; Physics Measurement and Uncertainty; Significant Figures Chapter 1: Introduction, Measurement, Estimating Units, Standards, and the SI System Converting Units Maxim Tsoi Order of Magnitude: Rapid Estimating Dimensions and Dimensional Analysis Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi/302K.htm 302K - Ch.1 302K - Ch.1 Standards of Length, Mass, and Time Standards of Length, Mass, and Time Basic and derived quantities SI standard • A standard must be defined to communicate results of a • The laws of physics are expressed as mathematical relationships measurement between physical quantities • An international committee established (1960) a set of • Most quantities are derived quantities, i.e., can be expressed standards for the fundamental quantities of science: SI as combinations of a small number of basic quantities • Length - meter • All quantities in mechanics can be expressed in terms of length, • Mass - kilogram mass, and time • Time - second • Others: kelvin, ampere, candela, mole 302K - Ch.1 302K - Ch.1 Standards of Length, Mass, and Time Standards of Length, Mass, and Time Length Approximate Values of Some Measured Lengths • 1120 A.D. king of England standard of length – yard (distance from the tip of his nose to the end of his outstretched arm) • the French the length of the royal foot of King Louis XIV original standard for the foot • 1799 meter (one ten-millionth the distance from the equator to the North Pole along the longitude passing through Paris) platinum- iridium bar stored in France • 1960th and 1970th meter = 1 650 763.73 wavelengths of orange-red light emitted from krypton-86 lamp • Since October 1983 meter (m)= distance traveled by light in vacuum during a time of 1/299 792 458 second (s) establishes the speed of light in vacuum = 299 792 458 m/s 302K - Ch.1 302K - Ch.1 1 Standards of Length, Mass, and Time Standards of Length, Mass, and Time Mass • 1887 The SI unit of mass, the kilogram (kg), is defined as the mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Time • Before 1960 standard of time = mean solar day in 1900 second = (1/60)(1/60)(1/24) of a mean solar day • 1967 second (s) = 9 192 631 770 times the period of vibration of radiation from the cesium-133 atom Weights and Measures at Serves, France • A duplicate of this cylinder is kept at the National Institute of Standards and Technology (NIST) at Gaithersburg, MD 302K - Ch.1 302K - Ch.1 Standards of Length, Mass, and Time Conversion of Units Prefixes for Powers of Ten From one measurement system to another • Equalities between SI and U.S. customary units of length • In addition to basic SI units 1 mile = 1 609 m = 1.609 km other units, e.g., mm, ns • Prefixes denote multiples of 1 ft = 0.3048 m = 30.48 cm 1 m = 39.37 in. = 3.281 ft of m, kg, s we can also use 1 in. = 0.0254 m = 2.54 cm • Units can be treated as algebraic quantities that can cancel each other: the basic units based on various powers of ten 15 in. = (15.0 in) (2.54 cm/1 in.) = 38.1 cm • Another measurement system e.g., U.S. customary system is still used in the United States QUIZ: the distance between two cities is 100 mi. The number of kilometers between the two cities is (a) smaller than 100 (b) larger than 100 (c) equal to 100 302K - Ch.1 302K - Ch.1 Derived Quantities Dimensional Analysis Density Dimension has a special meaning in physics • denotes the physical nature of a quantity (e.g., dimension of a • Density () is a derived quantity • is defined as mass per unit volume distance is length) • Symbols to specify dimensions of length, mass, time are L, M, T • Dimensions can be treated as algebraic quantities dimensional analysis is used to derive or check a specific equation • Quantities can be added or subtracted only if they have the same m V dimensions • The terms on both sides of an equation must have the same dimensions (e.g., check x=½at2 ) • 1m3 of Al vs 1m3 of Pb? 302K - Ch.1 302K - Ch.1 2 Estimates Significant Figures Order-of-Magnitude Calculations Measured quantities are known only to within the limits of experimental uncertainty • Compute an approximate answer to a given physical problem • The number of significant figures is used to express experimental uncertainty • The answer can be used to determine whether or not a more • Measure the area of a label with a meter stick (accuracy 0.1 cm) precise calculation is necessary (5.5 cm)(6.4 cm) = 35.2 cm2 • Order of magnitude of a certain quantity power of ten of the number that describes the quantity (NSF=2) • Zeros may or may not be significant digits • Those used to position decimal point are not significant (e.g., 0.03, 0.0075) • Order of magnitude calculations are reliable to within a factor of 10 • When they come after other digits there is a possibility of misinterpretation (1500 g) • Scientific notation removes this ambiguity (e.g., 1.5x103, 1.500x103) “ball-park figures” 0.0086 ~ 10-2 0.0021 ~ 10-3 720 ~ 103 • When multiplying several quantities NSF in the result is the same as NSF in the quantity with the lowest NSF • When adding or subtracting the number of decimal places in the result should equal the smallest number of decimal places of any term in the sum 302K - Ch.1 302K - Ch.1 SUMMARY Introduction, Measurement, Estimating • Three basic quantities of mechanics are length, mass, and time, which in the SI system have the units meters (m), kilograms (kg), and seconds (s), respectively • Prefixes are used along with the three basic units indicate various powers of ten • The density of a substance is defined as its mass per unit volume • Dimensional analysis is very powerful in solving/checking physics problems. Dimensions are treated as algebraic quantities. • Order-of-magnitude calculations help to answer a problem when there is not enough information available for exact solution • A result from several measured quantities should be given with the correct number of significant figures 302K - Ch.1 3 ...
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