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Space, , and

Chapter Outline ENGINEERING PHYSICS I

PHY 303K Coordinates and Reference Frames Units of Length, Mass, and Time Chapter 1: Space, Time, and Mass Derived Units

Maxim Tsoi Significant Figures; Consistency of Units and

Physics Department, The University of Texas at Austin

http://www.ph.utexas.edu/~tsoi/303K.htm

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Standards of Length, Mass, and Time Standards of Length, Mass, and Time

Basic and derived SI standard

•A standard must be defined to communicate results of a • The laws of physics are expressed as mathematical relationships 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 - mass, and time •Time -

• Others: , , ,

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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 – ( from the tip of his nose to the end of his outstretched arm)

•the French  the length of the royal 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 in vacuum = 299 792 458 m/s

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1 Standards of Length, Mass, and Time Standards of Length, Mass, and Time

Mass Time • Before 1960  standard of time = mean solar day in 1900  • 1887  The SI unit of mass, the second = (1/60)(1/60)(1/24) of a mean solar day kilogram (kg), is defined as the mass of a specific platinum-iridium alloy cylinder • 1967  second (s) = 9 192 631 770 the period of kept at the International Bureau 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

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Standards of Length, Mass, and Time Derived Units

Prefixes for Powers of Ten Density

•Density () is a derived • U.S. customary system is still used in the United States •  is defined as mass per • In addition to basic SI units unit of m, kg, s we can also use other units, e.g., mm, ns m • Prefixes denote multiples of   the basic units based on V various powers of ten

•Al vsPb?

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Dimensional Analysis Conversion of Units

Dimension has a special meaning in physics From one measurement system to another

•  denotes the physical nature of a quantity (e.g., of a distance is length) • Equalities between SI and U.S. customary units of length (Appendix A)

• Symbols to specify of length, mass, time are L, M, T 1 = 1 609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm

• Dimensions can be treated as algebraic quantities  dimensional 1 m = 39.37 in. = 3.281 ft 1 in. = 0.0254 m = 2.54 cm analysis is used to derive or check a specific equation

• Quantities can be added or subtracted only if they have the same • Units can be treated as algebraic quantities that can cancel each other: dimensions

• The terms on both sides of an equation must have the same 15 in. = (15.0 in) (2.54 cm/1 in.) = 38.1 cm dimensions (e.g., check x=½at 2 )

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

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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 • the of a label with a meter stick (accuracy  0.1 cm) precise calculation is necessary (5.5 cm)(6.4 cm) = 35.2 cm2 (NSF=2)

• Order of magnitude of a certain quantity  power of ten of the • Zeros may or may not be significant digits number that describes the quantity • Those used to position decimal 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” • When multiplying several quantities  NSF in the result is the same as NSF -2 -3 3 0.0086 ~ 10 0.0021 ~ 10 720 ~ 10 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

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SUMMARY Space, Time, and Mass

• Three basic quantities of mechanics are length, mass, and time, which in the SI system have the units meters (m), (kg), and (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

• 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

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