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A - Units & Significant Figures Angel

A - Units & Significant Figures Angel - Units of...

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Unformatted text preview: Units of Measurement LEARNING OBJECTIVES Be able to identify the basic quantities. Be able to differentiate between the SI and FPS systems of unit. Be able to convert quantities from one unit system to another. Be able to define dimensional homogeneity LEARNING RESOURCES Text book Lecture notes Classroom discussion Concept questions Homework assignment Practice problems (text book) INTERNATIONAL SYSTEM OF UNITS (SI) Basic Quantities Length is measured in meter (m) Time is measured in second (s) Mass is measured in kilogram (kg) Force is measured in Newton (N) SI UNITS Unit Force In the SI system, the unit force is measured in Newton (N), which is defined as: F = m a If a = 1 m/s2 and m = 1 kg then F = 1 N Hence; 1 N = 1 kg . m/s2 SI UNITS Prefix Giga Mega Kilo Milli Micro Nano Multiple 1,000,000,000 1,000,000 1,000 0.001 0.000 000 1 0.000 000 000 1 Exponential Symbol 109 106 103 10-3 10-6 10-9 G M k m n In addition, multiple of ten terms (kilo, hecto, deca, deci, centi and milli) are often used. U.S. CUSTOMARY SYSTEM OF UNITS (FPS) Basic Quantities Length is measured in foot (ft) Time is measured in second (s) Force is measured in pound (lb) Mass is measured in slug CONVERSION FACTORS FPS Units 1 mile = 5280 ft; 1 ft = 12 in; 1 in = 1000 mil; 1 kip = 1000 lb; 1 ton = 2 kip = 2000 lb, FPS and SI Units 1 lb = 4.4482 N 1 slug = 14.5938 kg 1 ft = 0.3048 m Force Mass Length FPS UNITS Unit Mass In the FPS system, the unit mass is measured in slug and is defined as: F = m.a If F = 1 lb and a = 1 ft/s2 Then m = 1 slug = 1 lb-s2/ft SIGNIFICANT FIGURS A significant figure is any digit from 0 to 9 of a given number. The zero is counted as a significant figure if it does not specify the location of the decimal point. For example each of the numbers 4072 and 0.04072 has 4 significant figures, whereas the number 0.0025 has only 2 significant figures. The accuracy of a number is specified by the number of significant figures it contains. Exponential notation (in multiple of 3) is typically used to facilitate conversion of SI units. SIGNIFICANT FIGURS The numbers 450245, 256, 31207, and 0.003467 can be expressed in three significant figures as follows: 450245 = 450(10)3 256 = 256 31207 = 31.2(10)3 0.003467 = 3.47(10)-3 ROUNDING OFF NUMBERS The number of significant figures in an answer should be equal to or less than the number of significant figures of the data. The answer should be rounded off. Rounding to 3 significant figures 0.005689 = 5.69(10)-3 2657.243 = 2.66 (10)3 1.345557 = 1.35 244.4399 = 244 DIMENSIONAL HOMOGENEITY In a given equation, all terms must be Expressed in the same unit system, for example, in the equation S = vt + 0.5 at2 S = distance in m; v = velocity in m/s; t = time in s; and a = acceleration in m/s2 So, the quantities (S, vt, and at2) have exactly the same dimension, meter. DIMENSIONAL HOMOGENEITY In the equation S = vt + 0.5 at2 whether we are solving for S = vt + 0.5 at2 or solving for a = (s/0.5t2 vt/0.5t2) or solving for v = (s/t 0.5at2/t) All terms must maintain their dimensional homogeneity ...
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