ࡱ>  G8bjbj Hoo !hZZ++1+1+1+4e+m.m.m.h.tI/de+D~22(223333˜d*1+333333+ %+ 2333331+31+33333zHt/1+1+?|Krm.3wxj[|0Dx^3?|31+?|333e+e+dɯ~e+e+ɯZ ):   Table 17.1 Multiple units to express the same quantities QuantitySI base unitsother units distance meterscentimeters, nanometers, miles, inches, feet, fathoms, ngstroms, microns, kilometers, yards, light-years, femtometers, mils, astronomical units mass kilogramsgrams, centigrams, kilograms , milligrams, micrograms, atomic mass units, carats, ounces, slugs, tons, metric tons time secondshours, days, minutes, centuries, decades, millennia, nanoseconds, milliseconds  temperature kelvindegrees centigrade, degrees Celsius, degrees Fahrenheit, degrees Rankine  volume cubic metersmilliliters, cubic centimeters, liters, bushels, gallons, cups, pints, quarts, pecks, tablespoons, teaspoons, cubic yards, barrels, board feet density kilograms per cubic metergrams per milliliter, grams per cubic centimeter, grams per liter, pounds per cubic foot, ounces per gallon pressure newtons per square meterpascals, kilopascals , bars, millibars , dynes/cm2 , baryes, torrs, millimeters Hg, centimeters H2O, atmospheres (atm), pounds per square inch (PSI) energy jouleskilojoules, ergs, dynes, Calories, kilocalories, kilowatt-hours, British thermal units, therms, electron volts  Table 17.2 CGS and MKS unitscgs unitmeasuringSI (mks) equivalentbarye (ba)pressure0.1 pascal (Pa)biot (Bi)electric current10 amperes (A)calorie (cal)heat energy4.1868 joule (J)dyne (dyn)force10-5 newton (N)erg (erg)work, energy10-7 joule (J)franklin (Fr)electric charge3.3356 x 10-10 coulomb (C)galileo (Gal)acceleration0.01 meter per second squared (ms-2)gauss (G)magnetic flux density10-4 tesla (T)gilbert (Gi)magnetomotive force0.795 775 ampere-turns (A)lambert (Lb)illumination104 lux (lx)langley (Ly)heat transmission41.84 kilojoules per square meter (kJm-2)maxwell (Mx)magnetic flux10-8 weber (Wb)rsted (Oe)magnetic field strength79.577 472 ampere-turns per meter (Atm-1)poise (P)dynamic viscosity0.1 pascal second (Pas) Activity 17.1.2 Units in Everyday Life In the statements that follow you will find a variety of interesting facts, but each is missing a crucial piece of information the units (dimensions)! All the statements are meaningless until supplied with the appropriate units. Complete the following statements using whatever resources you wish. In most you will need to draw logical inferences. Table 17.3 Units for activity 17.1.2acre centimeters degrees Celsius degrees Fahrenheit feet G grams/ml hectareinches kcal (Cal) kelvin kilograms kilometers kilometers/hour kilowatt-hours light-yearsliters megatons meters miles miles per hour milligrams milliliters millimetersounces pounds square miles square km stories tons yard (1) Coldest Place In The Known Universe The Boomerang Nebula, a cloud of dust and gas dispensed by "white dwarf", is one of the coldest places in the known universe, with an estimated temperature of -521.6 ______. (2) Deepest Lake The deepest lake in the world is Lake Baikal, in Siberia, Russia. The lake has a depth of 15,371 _____, of which 3,875 ____ are below sea level. Baikal contains one-fifth of all the worlds fresh surface water! The lake has a surface area of 12,200 square ______.) (3) Highest G-Force Endured By An Animal The click beetle (Athous haemorrhoidalis) moves its body in a snapping fashion to generate lift at a record-breaking acceleration of 400 ____. The beetle jumps this way to avoid predators, and can leap up to 15 _____ high. By comparison, humans can endure brief periods of up to 6 _______. (4) Fastest Dive By a Bird A peregrine falcon can reach a velocity of 350 ______ when diving towards its prey. (5) Driest Place on Earth The meteorological station in Quillagua, in the Atacama Desert, Chile records an average annual rainfall at just 0.5 _________. (6) Greatest Temperature Range On Earth The greatest recorded temperature variation is in Verkhoyansk, Siberia. The temperature is as high as 105 _______ in the summer and as low as -68 deg C ______ to 37 ______ in the winter. (7) Fastest Avalanche The volcanic explosion of Washington States Mount St Helens on May 18, 1980, triggered an avalanche with a velocity of 250 ______). (8) Farthest Object Visible By The Unaided Eye The remotest object visible with the unaided eye is the Great Galaxy in the constellation of Andromeda. The Great Galaxy is composed of approximately 200,000,000,000 stars and is 2,200,000 ____________ from Earth. (9) Most Powerful Nuclear Explosion The most powerful thermonuclear device ever tested was the Soviets "Tsar Bomba, with an explosive force equivalent to that of 57 ________ of TNT. The shockwaves from the 1961 blast circled the earth three times! (10) Tallest Living Tree The tallest tree currently standing is the Mendocino Tree, a coast redwood (Sequoia sempervirens) at Montgomery State Reserve, in California. When measured , its height was determined to be 112.014_______. (11) Wood and Paper Usage The average amount of wood and paper consumed per person each year in America is equivalent to a tree ______ tall and 16______ diameter. (12) Largest Forest The boreal forests of northern Russia, lying between Lat. 55N and the Arctic Circle, cover a total area of 2.7 billion _________. (13)Longest Venomous Snake The king cobra (Ophiophagus hannah) from Southeast Asia and India grows to an average length of 3.6-4.5 m (12-15 ft)! It is estimated that two fluid _________ of a king cobra's venom can kill 20 people! (14) Largest Bird The largest bird is the North African ostrich. It can grow to 2.75 ________ tall and weigh 156.5 _______ The ostrich is also the fastest bird on land, reaching speeds of 72_______. (15) Greatest Snowfall For A Snowstorm In February 1959, a single snowstorm dropped 480 _______ of snow at Mount Shasta Ski Bowl, California, USA. Table 17.4 Physical Quantities and Their SI Units (fundamental units are in bold)quantity symbolSI measurement unitssymbolunit dimensionsdistancedmetermmmassmkilogramkgkgtimetsecondsselectric currentIampereAAtemperatureTkelvinKKamount of substancenmolemolmolluminous intensityIcandelacdcdaccelerationameter per second squaredm/s2m/s2areaAsquare meterm2m2capacitanceCfaradFA2.s4/kg.m2concentration[C]molarMmol/m3densityDkilogram per cubic meterkg/m3kg/m3electric chargeQcoulombCA.selectric field intensityEnewton per coulombN/Ckg.m/A.s3electric resistanceRohm(kg.m2/A2.s3emf(voltVkg.m2/A.s3energyEjouleJkg.m2/s2forceFnewtonNkg.m/s2frequencyfhertzHzs-1heatQjouleJkg.m2/s2illuminationElux (lumen per square meter)lx cd/m2inductanceLhenryHkg.m2/A2.s2magnetic flux (weberWbkg.m2/A.s2potential differenceVvoltVkg.m2/A.s3powerPwattWkg.m2/s3pressureppascal (newton per square meter)Pakg/m.s2velocityvmeter per secondm/sm/svolumeVcubic meterm3m3workWjouleJkg.m2/s2 Table 17.5 Definitions of the units of the seven fundamental quantities QuantitySI unitDefinition of unitdistancemeter (m)The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.masskilogram (kg)The kilogram is equal to the mass of the international prototype of the kilogram.timesecond (s)The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.electric currentampere (A)The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 ~ 10-7 newton per meter of length.temperaturekelvin (K)The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.amount of substancemole (mol)The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. intensity of lightcandela (cd)The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 ~ 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. 2007 John Wiley Publishers - Norman Herr author Chapter 17 Dimensional Analysis -  PAGE 1 2007 John Wiley Publishers - Norman Herr author Chapter 17 Dimensional Analysis -  PAGE 3  22nd General Conference on Weights and Measures, (2003). The International System of Units (SI). Paris: Organisation Intergouvernementale de la Convention du Mtre. Table 17.6 Different units for the same quantitymasslengthtimetemperatureluminous intensityelectric charge quantitymasslengthtimetemperatureluminous intensityelectric charge quantityA (ampere)houramuinchbiotK (kelvin)bolt (of cloth)kilogram Cd (candela)leaguecubitmeterdaymoledecadeneutron mass (Coz (ounce)F paceR (Rankine)pica Re (Reaumur)pound ap dozenpounddram ap second earth mass, sidereal dayfootball fieldsidereal monthfortnightslugGrossUK mile handweekhefner candle. yr (year) Table 17.7 Different units for the same quantitiesQuantitySI base unitsother unitsdistancemeters (m)masskilograms (kg)timeseconds (s)temperaturekelvin (K)volumecubic centimeters (cm3)densitykg/m3pressurenewtons per square meter (n/m2)energyjoules Table 17.8 Variety of units for the same quantities distance, mass, time, temperature, volume, density, pressure and energy ngstroms () astronomical units (au) atmospheres (atm) atomic mass units (amu) bars (bar) barrels (bbl) barye (ba) board-feet (bd ft) British thermal units (Btu) bushels (bu) calories (cal) carats (ct) centigrade (C) centigrams (cg) centimeters (cm) centuries centimeters water (cm H2O) cubic centimeters (cm3) cubic yards (yd3) cups (c) days (d) decades degrees Celsius (C) degrees Fahrenheit (F) degrees Rankine (R) dynes (dyn)  dyne per square meter (dyn/m2) electron volts (ev) ergs (erg) fathoms (fth) feet (ft) femtometers (fm) gallons (gal) grams per cubic cm (g/cm3) grams per liter (g/l) grams per milliliter (m/ml) grams (g) hours (h) inches (in) joules (J) kilocalories (kCal) kilograms (kg) kilojoule (kJ) kilometers (km) kilopascals (kPa) kilowatt-hours (kWh) light-years (ly) liters (l) metric tons (mt) micrograms (g) microns (m) mils (mm)  miles (mi) milligrams (mg) millennia millibar (mb) milliliters (ml) milliseconds (ms) minutes (min) mmHg nanometers (nm) nanoseconds (ns) ounces (oz) ounces per gallon (oz/gal) pascals (Pa) pecks (pk) pints (pt) pounds per cubic foot (lb/ft3) pounds per square inch (lb/in2) quarts (qt) slugs (slug) tablespoons (tbsp) teaspoons (tsp) therms (therm) tons (T) torrs (torr) yards (yd)  Table 17.10 Discovering key equations with dimensional analysisderived unitQuantityexpressed as fundamental unitscomplete the equationin terms of volt (potential diff., V) EMBED Equation.3 V=IRcurrent (I) resistance (R)watt (power, P) EMBED Equation.3 P=current (I) potential difference (V)watt (power, P) EMBED Equation.3 P=current (I) resistance (R)watt (power, P) EMBED Equation.3 P=work (W) time (t)joule (energy, E) EMBED Equation.3 E=force (F) distance (d)joule (energy, E) EMBED Equation.3 E=work (W)joule (energy, E) EMBED Equation.3 E=mass (m) velocity (v)joule (energy, E) EMBED Equation.3 E=mass (m) acceleration (a) distance (d)N(s (impulse) EMBED Equation.3 Impulse=force (F) time (t)farad (capacitance, C) EMBED Equation.3 C = potential difference (V) charge (Q)Pa(pressure, p) EMBED Equation.3 p=force (N) distance (d) <=>ab  L M > ? 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