Transcript PHY101
PHY101 CHAPTER 1 Measurement Unit Significant Figures Dimensional Analysis 1.1. Measurement Units • SI - International Metric System • US - Customary System • Basic Metric Units Quantity Length Mass Unit meter kilogram Symbol m kg Time second s El. Current Ampere A Temperature Kelvin K SI Prefixes Power 10-18 10-15 10-12 10-9 10-6 10-3 103 106 109 1012 1015 1018 Prefix atto femto pico nano micro milli kilo mega giga tera peta exa Symbol a f p n m k M G T P E Metric Line METRIC LINE Tm Tg Tl Gm Gg Gl T - tera G - giga M - mega k - kilo m - milli u - micro n - nano p - pico f - femto Mm Mg Ml km kg kl m g l Center m - meter g - gram l - liter mm mg ml um ug ul nm ng nl pm pg pl fm fg fl am ag al Length Mass Capacity Conversion Table METRIC TO ENGLISH ENGLISH TO METRIC From Metric To English Multiply by From English To Metric Multiply by meters meters centimeters kilometers grams kilograms liters liters yards feet inches miles ounces pounds quarts gallons 1.09 3.28 0.39 0.62 0.035 2.20 1.06 0.26 yards feet inches miles ounces pounds quarts gallons meters meters centimeters kilometers grams kilograms liters liters 0.91 0.30 2.54 1.61 28.35 0.45 0.95 3.78 Temperature Conversion Converting Fahrenheit to Celsius 5( F 32) C 9 Converting Celsius to Fahrenheit F 9C 32 5 Conversion in Metric system • Example 1: Convert 50 mph to m/s. From 1 mile = 1609 m: 50m 1609m 1h 22m / s h m 3600s • Example 2: A hall bulletin board has an area of 2.5 m2. What is this area in cm2? Because 1m=100cm it is sometimes assumed that 1 m2 = 100 cm2, which is WRONG. The correct conversion is: 2.5m2 2.5m m 2.5 100cm 100cm 25000cm2 2.5 104 1.2. Significant Figures The number of significant figures of a numerical quantity is the number of reliably known digits it contains. • Zeros at the beginning of a number are not significant. They merely locate the decimal point. – 0.254 m - three significant figures (2, 5, 4) • Zeros within a number are significant – 104.6 m - four significant figures (1, 0, 4, 6) • Zeros at the end of a number after the decimal point are significant: – 2705.0 m - five significant figures (2, 7, 0, 5, 0) Significant Figures - Conclusion • The FINAL result of a multiplication or division should have the same number of significant figures as the quantity with the least number of significant figures that was used in the calculation. • The FINAL result of the addition or subtraction of numbers should have the same number of decimal places as the quantity with the least number of decimal places that was used in the calculation. Significant Figures - Practice • Example 1: Find the area of a room 2.4 m by 3.65 m: 2.4m x 3.65m = 8.76m2=8.8m2 Rounded to 2 sf - because 2 is least # of sf • Example 2: Given the numbers 23.25, 0.546, and 1.058 – add the first two – subtract the least number from the first 1.3. Dimensional Analysis • The two sides of an equation must be equal not only in numerical value, but also in dimensions (BOTH SIDES OF THE EQUATION ARE NUMERICALLY AND DIMENSIONALLY EQUAL). And dimensions can be treated as algebraic quantities. • [L] - Length • [M] - Mass • [T] - Time Dimensional Analysis - Practice • Example 1: Is an equation x = v t a correct equation? • Example 1: Is an equation x = a t2 a correct equation? – x - is the distance in m – v = is the velocity in m/s – t - is the time in s – a is acceleration in m/s2 Dimensionally the equation is: [ L] [ L] [T ] [ L] [T ] [ L] [ L] 2 [ T ] [ L] 2 [T ] Practice • Show that the equation x = xo + vt, where v is velocity, x and xo are lengths, ant t is time, is dimensionally correct • A Boeing 777 jet has a length of 209 ft. 1 inch, and wingspan of 199 ft and 11 inches. What are these dimensions in meters? • Determine the number of significant figures: – – – – 1.007 m 8.03 m 16.272 kg 0.015 µs • The two sides of right triangle are 8.7 cm (two significant figures) and 10.5 cm (three significant figures). What is the area of the triangle?