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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 tenmillionth 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
orangered light emitted from krypton86 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 platinumiridium 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 cesium133 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 OrderofMagnitude 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) “ballpark figures”
0.0086 ~ 102 0.0021 ~ 103 720 ~ 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.
• Orderofmagnitude 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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