Space, Time, and Mass 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 Conversion of Units Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi/303K.htm 303K: Ch.1 303K: 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 303K: Ch.1 303K: 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 303K: Ch.1 303K: Ch.1 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 times 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 303K: Ch.1 303K: Ch.1 Standards of Length, Mass, and Time Derived Units Prefixes for Powers of Ten Density •Density () is a derived • U.S. customary system is quantity still used in the United States • is defined as mass per • In addition to basic SI units unit volume 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? 303K: Ch.1 303K: Ch.1 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., dimension of a distance is length) • Equalities between SI and U.S. customary units of length (Appendix A) • Symbols to specify dimensions of length, mass, time are L, M, T 1 mile = 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 303K: Ch.1 303K: 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 (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 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” • 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 303K: Ch.1 303K: Ch.1 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), 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 303K: Ch.1 3.