A_-_Units___Significant_Figures

A_-_Units___Significant_Figures - Units of Measurement...

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Unformatted text preview: Units of Measurement Units LEARNING OBJECTIVES LEARNING Be able to identify the basic quantities. Be Be able to differentiate between the SI and FPS systems of unit. FPS Be Be able to convert quantities from one unit system to another. system Be able to define dimensional homogeneity LEARNING RESOURCES LEARNING Text book Lecture notes Classroom discussion Concept questions Homework assignment Practice problems (text book) INTERNATIONAL SYSTEM OF UNITS (SI) OF Basic Quantities Length is measured in meter (m) Length Time is measured in second (s) Time Mass is measured in kilogram (kg) Mass Force is measured in Newton (N) SI UNITS SI Unit Force In the SI system, the unit force is measured In in Newton (N), which is defined as: in 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 SI 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 µ n In addition, multiple of ten terms (kilo, hecto, In deca, deci, centi and milli) are often used. deca, U.S. CUSTOMARY SYSTEM OF UNITS (FPS) OF 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 CONVERSION FPS Units 1 mile = 5280 ft; 1 ft = 12 in; 1 in = 1000 mil; 1 kip = 1000 lb; 1 ton = 2 kip = 2000 lb, kip FPS and SI Units FPS 1 lb = 4.4482 N lb 1 slug = 14.5938 kg 1 ft = 0.3048 m Force Force Mass Length FPS UNITS FPS Unit Mass In the FPS system, the unit mass is In measured in slug and is defined as: measured F = m.a If F = 1 lb and a = 1 ft/s2 Then m = 1 slug = 1 lbs /ft SIGNIFICANT FIGURS SIGNIFICANT A significant figure is any digit from 0 to 9 of a significant 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 For 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 The number of significant figures it contains. Exponential notation (in multiple of 3) is Exponential typically used to facilitate conversion of SI units. units. SIGNIFICANT FIGURS SIGNIFICANT The numbers 450245, 256, 31207, and The 0.003467 can be expressed in three significant figures as follows: significant 450245 = 450(10)3 256 = 256 31207 = 31.2(10)3 0.003467 = 3.47(10)-3 ROUNDING OFF NUMBERS ROUNDING The number of significant figures in an The answer should be equal to or less than the number of significant figures of the data. The answer should be rounded off. answer 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 DIMENSIONAL In a given equation, all terms must be In Expressed in the same unit system, for example, in the equation example, S = vt + 0.5 at S = distance in m; v = velocity in m/s; distance velocity m/s t = time in s; and a = acceleration in m/s time and acceleration m/s DIMENSIONAL HOMOGENEITY DIMENSIONAL In the equation S = vt + 0.5 at whether hether All terms must maintain their All dimensional homogeneity QUESTIONS QUESTIONS 1. Which of the following units are the unit of Which mass? mass? A) Lb B) N C) Kg D) Kg-m/s2 QUESTIONS QUESTIONS 2. Which of the following units are the unit of force? A) Kips B) Kg-m/s2 C) Both D) Neither QUESTIONS QUESTIONS 3. The unit m/s2 is the unit of? A) Force B) Velocity C) Acceleration D) Energy QUESTIONS QUESTIONS 4. The unit lb-s2/ft is the unit of? A) Force B) Acceleration C) Mass D) Moment ...
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This note was uploaded on 10/31/2010 for the course CEE CE 221 taught by Professor Baladi during the Fall '10 term at Michigan State University.

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