chapt01_Introduction理論力學第一章英文課件

1、1 - 11.1. What is Mechanics? The science which describes and predicts the conditions of rest or motion of bodies under the action of forces1. Mechanics of rigid bodies (GE 204, 205)2. Mechanics of deformable bodies (GE 206)3. Mechanics of fluids (CE, ME 308)1 - 2MechanicsStatics (dealing with bodies

2、 at rest) and Dynamics (bodies in motion)Assumed to be perfectly rigid for statics and dynamicsFluid mechanics; compressible and incompressible flow (hydraulic, or low velocity aerodynamics)Mechanics uses mathematics, but applied science for engineering applications1 - 31.2 Fundamental Concepts and

3、PrinciplesStudy of Mechanics goes back to Aristotle (384-322 B.C.) and Archimedes (287-212 B.C.)Isaac Newton (1642-1727)DAlembert, Lagrange and HamiltonEinstein; theory of relativity (1905)1 - 4AristotleFourth century B.C.E.Mechanical Problems; collections of questions and answers; in physics, mathe

4、matics and engineeringAmong 35 mechanical problems posed by AristotleWhy are larger balancesmore accurate than smaller ones?Why are pieces of timber weaker the longer they are, and why do they bend more easily when raised?1 - 5Renaissance shipbuilders found that their large timber ships were breakin

5、g under their own weightGalileo (1638) prefaced his seminal study of strength of material by reciting the breakup of ships, etc.Still there are failures of heavy steel ships and large missilesFactor of safety or factor of ignorance?1 - 6Galileos seminal work on strength of materials and dynamicsDial

6、ogues Concerning Two New Sciences1 - 7Galileos illustration of two failure modesMarble lying on the ground can be soiled, discolored and hard to lift again.Inclined against wall can cause crack or it may fall.Best way is put on the support.1 - 81 - 9Failed Liberty ship, c.19401 - 101 - 11WSGalileos

7、Postulation1 - 12Galileo, 16381 - 13Correcting the ErrorCan you tell what is wrong?17th century Hookes law1729 Bernard Forest de Balidor following the earlier lead of Leibniz and P. Varignon found that 1 - 14WSForests Postulation1 - 15Edme Mariottes experiments; while designing pipelines to supply w

8、ater to the palace at Versailles1 - 16Marriotte recognized that there must be linearly varying compression as well as tension acting across the beams sectionHe had error in calculating resultant moment, and he used Galileos formula1713, A. Parent found correct treatment but was ignored becauseWas no

9、t pubished by French AcademyMany misprints and poorly editedHe was not a clear writerHe criticized many others work1 - 171.2 ContinuedBasic concepts used in mechanics; space, time, mass and forceSpace; position of the point P; coordinates of P with reference to the origin In Newtonian mechanics; spa

10、ce, time, and mass are absolute concepts, independent each other (force is not independent)Note; relativistic mechanics time is not independent1 - 181.2 ContinuedForce is a vector; point of application, magnitude and directionStudy the conditions of rest or motion of particles and rigid bodies in te

11、rms of the four basic conceptsParticles; a very small amount of matter which may be assumed to occupy a single point in spaceRigid bodies; a combination of a large number of particles occupying fixed positions with respect to each other1 - 19Six Fundamental PrinciplesAll principles are based on expe

12、rimental evidence, not from mathematical derivations1. Parallelogram law for addition of ForcesThe two forces acting on a particle may be replaced by a single force; resultantParallelogram Law1 - 202. The Principle of TransmissibilityThe conditions of equilibrium or of motion of a rigid body will re

13、main unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different pointFFThe same line of actionSee Chapter 31 - 213. Newtons First Law; if the resultant force acting on a particle is zero, the particle will

14、 remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion)TDLW1 - 224. Newtons Second LawIf the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magintude of the resultant and in th

15、e direction of this resultant forceF=ma5. Newtons Third LawThe force of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite senseSee Chapter 6Photo 1.11 - 246. The Newtons Law of GravitationR; radius of the earthW=mgg; 9.81 m/s2 or 32.2 ft/s2 1 -

16、25Units and Dimensions; ObjectivesKnow the difference between units and dimensionsUnderstand the SI, USCS (U.S. Customary System, or British Gravitational System), and AES (American Engineering) systems of unitsKnow the SI prefixes from nano- to giga-Understand and apply the concept of dimensional h

17、omogeneity1 - 26ObjectivesWhat is the difference between an absolute and a gravitational system of units?What is a coherent system of units? Apply dimensional homogeneity to constants and equations.1 - 27IntroductionFrance in 1840 legislated official adoption of the metric system and made its use be

18、 mandatoryIn U.S., in 1866, the metric system was made legal, but its use was not compulsory 1 - 28Measurement StandardInch, foot; based on human body4000 B.C. Egypt; Kings Elbow=0.4633 m, 1.5 ft, 2 handspans, 6 hand-widths, 24 finger-thicknessAD 1101 King Henry I yard (0.9144 m) from his nose to th

19、e tip of his thumb1528 French physician J. Fernel distance between Paris and Amiens1 - 29Measurement Standard1872, Meter (in Greek, metron to measure)- 1/10 of a millionth of the distance between the North Pole and the equatorPlatinum (90%)-iridium (10%) X-shaped bar kept in controlled condition in

20、Paris39.37 inIn 1960, 1,650,763.73 wave length in vacuum of the orange light given off by electrically excited krypton 86.1 - 30Dimensions & Units Dimension - abstract quantity (e.g. length)Dimensions are used to describe physical quantitiesDimensions are independent of unitsUnit - a specific defini

21、tion of a dimension based upon a physical reference (e.g. meter)1 - 31What does a “unit” mean?Rod of unknown lengthReference: Three rods of 1-m lengthThe unknown rod is 3 m long.How long is the rod?unitnumberThe number is meaningless without the unit!1 - 32How do dimensions behave in mathematical fo

22、rmulae?Rule 1 - All terms that are added or subtracted must have same dimensionsAll have identical dimensions1 - 33How do dimensions behave in mathematical formulae?Rule 2 - Dimensions obey rules of multiplication and division1 - 34Dimensionally Homogeneous EquationsAn equation is said to be dimensi

23、onally homogeneous if the dimensions on both sides of the equal sign are the same.1 - 35Dimensionally Homogeneous EquationsBbhVolume of the frustrum of a right pyramid with a square base1 - 36Dimensional AnalysisgmLpPendulum - What is the period?1 - 37Absolute and Gravitational Unit SystemsAbsolute

24、system Dimensions used are not affected by gravityFundamental dimensions L,T,MGravitational SystemWidely used used in engineeringFundamental dimensions L,T,F1 - 38F M L TAbsolute Gravitational = defined unit = derived unitAbsolute and Gravitational Unit Systems1 - 39Coherent Systems - equations can

25、be written without needing additional conversion factorsCoherent and Noncoherent Unit SystemsNoncoherent Systems - equations need additional conversion factorsConversionFactor 1 - 40Noncoherent Unit SystemsOne pound-force (lbf) is the effort required to hold a one pound-mass elevated in a gravitatio

26、nal field where the local acceleration of gravity is 32.147 ft/s2Constant of proportionality gc should be used if slug is not used for massgc=32.147 lbm.ft/lbf.s21 - 41Example of Noncoherent Unit SystemsIf a child weighs 50 pounds, we normally say its weight is 50.0 lbm1 - 42Example of Noncoherent U

27、nit SystemsIf a child weighs 50 pounds, on a planet where the local acceleration of gravity is 8.72 ft/s21 - 43F M L TNoncoherent = defined unit = derived unitNoncoherent SystemsThe noncoherent system results when all four quantities are defined in a way that is not internally consistent (both mass

28、and weight are defined historically)1 - 44Coherent SystemF=ma/gc; if we use slug for massgc= 1.0 slug/lbf*1.0 ft/s21 slug=32.147 lbm1 slug times 1 ft/ s2 gives 1 lbf1 lbm times 32.147 ft/ s2 gives 1 lbf1 kg times 1 m/ s2 gives 1 Ngc= 1.0 kg/N*1.0 m/s21 - 45The International System of Units (SI)Funda

29、mental Dimension Base Unitlength Lmass Mtime Telectric current Aabsolute temperature q luminous intensity lamount of substance nmeter (m)kilogram (kg)second (s)ampere (A)kelvin (K)candela (cd)mole (mol)1 - 46Fundamental Units (SI)Mass: “a cylinder of platinum-iridium (kilogram) alloy maintained unde

30、r vacuum conditions by the International Bureau of Weights and Measures in Paris”1 - 47Fundamental Units (SI)Time: “the duration of 9,192,631,770 periods (second) of the radiation corresponding to the transition between the two hyperfine levelsof the ground state of the cesium-133 atom”1 - 48Length

31、or “the length of the path traveled Distance: by light in vacuum during a time (meter) interval of 1/299792458 seconds”Fundamental Units (SI)Laser1 mphotont = 0 st = 1/299792458 s1 - 49The International System of Units (SI)PrefixDecimal MultiplierSymbolAttoFemtopiconanomicromillicentideci10-1810-151

32、0-1210-910-610-310-210-1afpnmmcd1 - 50The International System of Units (SI)PrefixDecimal MultiplierSymboldekahectokilomegaGigaTeraPetaexa10+110+210+310+610+910+1210+1510+18dahkMGTPE1 - 51(SI)Force = (mass) (acceleration)1 - 52U.S. Customary System of Units (USCS)Fundamenal DimensionBase Unitlength

33、Lforce Ftime Tfoot (ft)pound (lb)second (s)Derived DimensionUnitDefinitionmass FT2/L slug1 - 53(USCS)Force = (mass) (acceleration)1 - 54American Engineering System of Units (AES)Fundamenal DimensionBase Unitlength Lmass mforce Ftime Telectric change Qabsolute temperature qluminous intensity lamount

34、of substance nfoot (ft)pound (lbm)pound (lbf)second (sec)coulomb (C)degree Rankine (oR)candela (cd)mole (mol)1 - 55(AES)Force = (mass) (acceleration)ft/s2lbmlbf1 - 56Rules for Using SI UnitsPeriods are never used after symbols Unless at the end of the sentenceSI symbols are not abbreviationsIn lower

35、case letter unless the symbol derives from a proper namem, kg, s, mol, cd (candela)A, K, Hz, Pa (Pascal), C (Celsius)1 - 57Rules for Using SI UnitsSymbols rather than self-styles abbreviations always should be usedA (not amp), s (not sec)An s is never added to the symbol to denote pluralA space is a

36、lways left between the numerical value and the unit symbol43.7 km (not 43.7km)0.25 Pa (not 0.25Pa)Exception; 50C, 5 6”1 - 58Rules for Using SI UnitsThere should be no space between the prefix and the unit symbolsKm (not k m)mF (not m F)When writing unit names, lowercase all letters except at the beg

37、inning of a sentence, even if the unit is derived from a proper namefarad, hertz, ampere1 - 59Rules for Using SI UnitsPlurals are used as required when writing unit nameshenries (H; henry)Exceptions; lux, hertz, siemensNo hyphen or space should be left between a prefix and the unit nameMegapascal (n

38、ot mega-pascal)Exceptions; megohm, kilohm, hectare1 - 60Rules for Using SI UnitsThe symbol should be used in preference to the unit name because unit symbols are standardizedExceptions; ten meters (not ten m)10 m (not 10 meters)1 - 61Rules for Using SI UnitsWhen writing unit names as a product, alwa

39、ys use a space (preferred) or a hyphennewton meter or newton-meterWhen expressing a quotient using unit names, always use the word per and not a solidus (slash mark /), which is reserved for use with symbolsmeter per second (not meter/second) 1 - 62Rules for Using SI UnitsWhen writing a unit name th

40、at requires a power, use a modifier, such as squared or cubed, after the unit namemillimeter squared (not square millimeter)When expressing products using unit symbols, the center dot is preferredN.m for newton meter1 - 63Rules for Using SI UnitsWhen denoting a quotient by unit symbols, any of the f

41、ollow methods are accepted formm/sm.s-1orM/s2 is good but m/s/s is notKg.m2/(s3.A) or kg.m2.s-3.A-1 is good, not kg.m2/s3/A1 - 64Rules for Using SI UnitsTo denote a decimal point, use a period on the line. When expressing numbers less than 1, a zero should be written before the decimal15.60.931 - 65

42、Rules for Using SI UnitsSeparate the digits into groups of three, counting from the decimal to the left or right, and using a small space to separate the groups6.513 82476 8517 4340.187 621 - 66Rules for Using SI UnitsWhen a derived unit is obtained by dividing a base unit by another base unit, a pr

43、efix may be used in the numerator of the derived unit but not in its denominatorExample; k a rate of a spring which stretches 20 mm under a load of 100 NK=100 N/20 mm=5000 N/m or 5KN/mnever use k=5 N/mm1 - 67Conversions Between Systems of Units1 - 68Significant DigitsSignificant figures are extremel

44、y important when reporting a numerical value.The number of significant figures used indicates the confidence (certainty) of that value.1 - 69Significant DigitsHow many?Number known to:Number of sig. figures1234etc.1 part per 101 part per 1001 part per 10001 part per 10000etc.1 - 70Significant Digits

45、A significant figure is an accurate digit although the last digit is accepted to have some error.If length = 7.58 cmThe number of significant figures does not include zeros required to place decimal points.Slight errorexactexact1 - 71Significant DigitsSignificant digits allow us to systematically ex

46、press a degree of confidence in a number.A significant digit or figure is any digit used in a number except:Zeros that are used to locate the decimal point, such as:0.050.00030.002300Zeros that do not have any nonzero digits on their left, such as:0.50.5150.251 - 72Significant DigitsDo the numbers 5

47、000 and 5000. imply the same significance?5000. contains four significant digits.5000 is an ambiguous number. It contains either one, two, three, or four significant digits.How do you write 5000 to two significant digits?Use scientific notation: 5.0 X 1031 - 73Significant DigitsHow many significant

48、figures should you use?The number of significant digits used implies a certain maximum error range.1 - 74Significant DigitsExample:The number 101 has three significant figures and means a number between 100.5 and 101.5. Theerror range is 1 ( 0.5) or about 1% of 101.Three significant figures implies

49、a maximum error range of 1%.Four significant figures implies a maximum error range of 0.1%.Only in exceptional cases will precision better that 0.1% (four significant figures) be necessary in engineering problems.1 - 75Rules for Significant Digits In multiplication and division - use as many signifi

50、cant digits as the number that has the fewest (excluding exact conversion factors)(4.00 kg) (5 m/s2) = 20 kg m/s2(2.43)*(17.675)= ? 42.95025 Ans. 43.0 4.30*101(2.479 h) (60 min/h) =? 148.74 min Ans. 148.7 1.487*103Exact conversion factor1 - 76Rules for Significant DigitsIn multiplication and divisio

51、n(4.00*102) (2.2046 lbm/kg) =? 881.84lb Ans. 881 lbConversion factor is not exact; cannot increase precisionUse one or more significant figure for your conversion factor1 - 77Rules for Significant DigitsIn addition and subtraction - line up the decimals and retain the least significant place.897.0-

52、0.0922896.9078896.9 (Answer)1 - 78Rules for Significant DigitsCombined operations:If products or quotients are to be added orsubtracted, perform the multiplication anddivision first, establish the correct number ofsignificant figures in the subanswer, performthe addition and subtraction, then round

53、tothe proper number of significant figures.1 - 79Rules for Significant DigitsCombined operations:When using calculator, it is normal practice to perform entire calculation and then report a reasonable number of significant figuresNote; 39.7/(772.3-772.26)=992.5But if 772.3-772.26=0, then it becomes impossibleUse common sense1 - 80Rules for Significant DigitsRounding827.48 rounds to 827.5 or 82723.650 rounds to 23.7 (3 significant figures)0.0143 rounds to 0.014 (2