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1、 2004 The McGraw-Hill Companies, Inc. All rights reserved. 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 fl
2、uids (CE, ME 308) 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 2Mechanics Statics (dealing with bodies at rest) and Dynamics (bodies in motion) Assumed to be perfectly rigid for statics and dynamics Fluid mechanics; compressible and incompressible flow (hydraulic, or low velocity ae
3、rodynamics) Mechanics uses mathematics, but applied science for engineering applications 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 31.2 Fundamental Concepts and Principles Study of Mechanics goes back to Aristotle (384-322 B.C.) and Archimedes (287-212 B.C.) Isaac Newton (1642-17
4、27) DAlembert, Lagrange and Hamilton Einstein; theory of relativity (1905) 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 4Aristotle Fourth century B.C.E. Mechanical Problems; collections of questions and answers; in physics, mathematics and engineering Among 35 mechanical problems po
5、sed by Aristotle Why 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? 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 5 Renaissance shipbuilders found that their large timber ships wer
6、e breaking under their own weight Galileo (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 missiles Factor of safety or factor of ignorance? 2004 The McGraw-Hill Companies, Inc. All rights reserve
7、d. 1 - 6Galileos seminal work on strength of materials and dynamicsDialogues Concerning Two New Sciences 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 7Galileos illustration of two failure modesMarble lying on the ground can be soiled, discolored and hard to lift again.Inclined again
8、st wall can cause crack or it may fall.Best way is put on the support. 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 8 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 9Failed Liberty ship, c.1940 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 10 2004 The
9、McGraw-Hill Companies, Inc. All rights reserved. 1 - 11WSGalileos PostulationLSbhWhbhSWL222 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 12Galileo, 1638hbXWLShbXLSbhWbbhSXL2 ,2222 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 13Correcting the Error Can you tell what
10、is wrong? 17th century Hookes law 1729 Bernard Forest de Balidor following the earlier lead of Leibniz and P. Varignon found that LSbhWhbhSWL332 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 14WSForests PostulationLSbhWhbhSWL332 2004 The McGraw-Hill Companies, Inc. All rights reserve
11、d. 1 - 15Edme Mariottes experiments; while designing pipelines to supply water to the palace at Versailles 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 16 Marriotte recognized that there must be linearly varying compression as well as tension acting across the beams section He had e
12、rror in calculating resultant moment, and he used Galileos formula 1713, A. Parent found correct treatment but was ignored because Was not pubished by French Academy Many misprints and poorly edited He was not a clear writer He criticized many others work 2004 The McGraw-Hill Companies, Inc. All rig
13、hts reserved. 1 - 171.2 Continued Basic concepts used in mechanics; space, time, mass and force Space; position of the point P; coordinates of P with reference to the origin In Newtonian mechanics; space, time, and mass are absolute concepts, independent each other (force is not independent) Note; r
14、elativistic mechanics time is not independent 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 181.2 Continued Force is a vector; point of application, magnitude and direction Study the conditions of rest or motion of particles and rigid bodies in terms of the four basic concepts Partic
15、les; a very small amount of matter which may be assumed to occupy a single point in space Rigid bodies; a combination of a large number of particles occupying fixed positions with respect to each other 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 19Six Fundamental Principles All pri
16、nciples are based on experimental evidence, not from mathematical derivations1. Parallelogram law for addition of Forces The two forces acting on a particle may be replaced by a single force; resultant Parallelogram Law 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 202. The Principle
17、 of TransmissibilityThe conditions of equilibrium or of motion of a rigid body will remain 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 3 2004 The Mc
18、Graw-Hill Companies, Inc. All rights reserved. 1 - 213. Newtons First Law; if the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion)TDLW 2004 The McGraw-Hill Companies, I
19、nc. All rights reserved. 1 - 224. Newtons Second Law If 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 the direction of this resultant force F=ma5. Newtons Third Law The force of action and reaction b
20、etween bodies in contact have the same magnitude, same line of action, and opposite senseSee Chapter 6 2004 The McGraw-Hill Companies, Inc. All rights reserved. Photo 1.1 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 246. The Newtons Law of Gravitation2rMmGF 2RMGg R; radius of the ea
21、rthW=mgg; 9.81 m/s2 or 32.2 ft/s2 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 25Units and Dimensions; Objectives Know the difference between units and dimensions Understand the SI, USCS (U.S. Customary System, or British Gravitational System), and AES (American Engineering) systems
22、 of units Know the SI prefixes from nano- to giga- Understand and apply the concept of dimensional homogeneity 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 26Objectives What is the difference between an absolute and a gravitational system of units? What is a coherent system of units
23、? Apply dimensional homogeneity to constants and equations. 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 27Introduction France in 1840 legislated official adoption of the metric system and made its use be mandatory In U.S., in 1866, the metric system was made legal, but its use was
24、not compulsory 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 28Measurement StandardzInch, foot; based on human bodyz4000 B.C. Egypt; Kings Elbow=0.4633 m, 1.5 ft, 2 handspans, 6 hand-widths, 24 finger-thicknesszAD 1101 King Henry I yard (0.9144 m) from his nose to the tip of his thum
25、bz1528 French physician J. Fernel distance between Paris and Amiens 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 29Measurement Standardz1872, Meter (in Greek, metron to measure)- 1/10 of a millionth of the distance between the North Pole and the equatorzPlatinum (90%)-iridium (10%)
26、X-shaped bar kept in controlled condition in Paris39.37 inzIn 1960, 1,650,763.73 wave length in vacuum of the orange light given off by electrically excited krypton 86. 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 30Dimensions & Units Dimension - abstract quantity (e.g. length) Dime
27、nsions are used to describe physical quantities Dimensions are independent of units Unit - a specific definition of a dimension based upon a physical reference (e.g. meter) 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 31What does a “unit” mean?Rod of unknown lengthReference: Three r
28、ods of 1-m lengthThe unknown rod is 3 m long.How long is the rod?unitnumberThe number is meaningless without the unit! 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 32How do dimensions behave in mathematical formulae?Rule 1 - All terms that are added or subtracted must have same dime
29、nsionsCBADAll have identical dimensions 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 33How do dimensions behave in mathematical formulae?Rule 2 - Dimensions obey rules of multiplication and divisionLLMLTTM222CABD 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 34Dimens
30、ionally Homogeneous EquationsAn equation is said to be dimensionally homogeneous if the dimensions on both sides of the equal sign are the same. 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 35Dimensionally Homogeneous Equations22bBbB3hV.LLLLLL322231BbhVolume of the frustrum of a rig
31、ht pyramid with a square base 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 36Dimensional AnalysisgmLpPendulum - What is the period?cbaLgmkp 2/1cb00L2/10201T0000MLTLMTc2acbbaabgLkpLgkmp 2/12/10 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 37Absolute and Gravitational
32、 Unit Systems Absolute system Dimensions used are not affected by gravity Fundamental dimensions L,T,M Gravitational System Widely used used in engineering Fundamental dimensions L,T,F 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 38amF 2TLMF F M L TAbsolute Gravitational = defined u
33、nit = derived unitAbsolute and Gravitational Unit Systems 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 39Coherent Systems - equations can be written without needing additional conversion factorsCoherent and Noncoherent Unit SystemsNoncoherent Systems - equations need additional conv
34、ersion factorsamF cg amF ConversionFactor 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 40Noncoherent Unit Systems One pound-force (lbf) is the effort required to hold a one pound-mass elevated in a gravitational field where the local acceleration of gravity is 32.147 ft/s2 Constant
35、of proportionality gc should be used if slug is not used for mass gc=32.147 lbm.ft/lbf.s2 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 41Example of Noncoherent Unit Systems If a child weighs 50 pounds, we normally say its weight is 50.0 lbmlbfftlbmslbfsftlbmgmFL0 .50*174.32*174.320
36、.50g 22c 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 42Example of Noncoherent Unit SystemszIf a child weighs 50 pounds, on a planet where the local acceleration of gravity is 8.72 ft/s2lbfftlbmslbfsftlbmgmFL6 .13*174.32*72. 80 .50g 22c 2004 The McGraw-Hill Companies, Inc. All right
37、s reserved. 1 - 43F M L TNoncoherent = defined unit = derived unitamF 2TLMF Noncoherent SystemsThe noncoherent system results when all four quantities are defined in a way that is not internally consistent (both mass and weight are defined historically) 2004 The McGraw-Hill Companies, Inc. All right
38、s reserved. 1 - 44Coherent System F=ma/gc; if we use slug for mass gc= 1.0 slug/lbf*1.0 ft/s2 1 slug=32.147 lbm 1 slug times 1 ft/ s2 gives 1 lbf 1 lbm times 32.147 ft/ s2 gives 1 lbf 1 kg times 1 m/ s2 gives 1 N gc= 1.0 kg/N*1.0 m/s2 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 45T
39、he International System of Units (SI)Fundamental 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) 2004 The McGraw-Hill Companies, Inc. All rights reserve
40、d. 1 - 46Fundamental Units (SI)Mass: “a cylinder of platinum-iridium (kilogram) alloy maintained under vacuum conditions by the International Bureau of Weights and Measures in Paris” 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 47Fundamental Units (SI)Time: “the duration of 9,192,63
41、1,770 periods (second) of the radiation corresponding to the transition between the two hyperfine levelsof the ground state of the cesium-133 atom” 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 48Length or “the length of the path traveled Distance: by light in vacuum during a time (m
42、eter) interval of 1/299792458 seconds”Fundamental Units (SI)Laser1 mphotont = 0 st = 1/299792458 s 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 49The International System of Units (SI)PrefixDecimal MultiplierSymbolAttoFemtopiconanomicromillicentideci10-1810-1510-1210-910-610-310-210
43、-1afpnm mmcd 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 50The International System of Units (SI)PrefixDecimal MultiplierSymboldekahectokilomegaGigaTeraPetaexa10+110+210+310+610+910+1210+1510+18dahkMGTPE 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 51(SI)Force = (m
44、ass) (acceleration)2sm kg 1 N 1 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 52U.S. Customary System of Units (USCS)Fundamenal DimensionBase Unitlength Lforce Ftime Tfoot (ft)pound (lb)second (s)Derived DimensionUnitDefinitionmass FT2/L slug/ftslb2f 2004 The McGraw-Hill Companies, I
45、nc. All rights reserved. 1 - 53(USCS)Force = (mass) (acceleration)2fft/sslug1lb1 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 54American Engineering System of Units (AES)Fundamenal DimensionBase Unitlength Lmass mforce Ftime Telectric change Qabsolute temperature qluminous intensity
46、 lamount of substance nfoot (ft)pound (lbm)pound (lbf)second (sec)coulomb (C)degree Rankine (oR)candela (cd)mole (mol) 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 55(AES)Force = (mass) (acceleration)2mfft/slb1lb1cmagF2fmslbftlb32.174ft/s2lbmlbf 2004 The McGraw-Hill Companies, Inc.
47、All rights reserved. 1 - 56Rules for Using SI Units Periods are never used after symbols Unless at the end of the sentence SI symbols are not abbreviations In lowercase letter unless the symbol derives from a proper name m, kg, s, mol, cd (candela) A, K, Hz, Pa (Pascal), C (Celsius) 2004 The McGraw-
48、Hill Companies, Inc. All rights reserved. 1 - 57Rules for Using SI Units Symbols rather than self-styles abbreviations always should be used A (not amp), s (not sec) An s is never added to the symbol to denote plural A space is always left between the numerical value and the unit symbol 43.7 km (not
49、 43.7km) 0.25 Pa (not 0.25Pa) Exception; 50C, 5 6” 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 58Rules for Using SI Units There should be no space between the prefix and the unit symbols Km (not k m) mF (not m F) When writing unit names, lowercase all letters except at the beginnin
50、g of a sentence, even if the unit is derived from a proper name farad, hertz, ampere 2004 The McGraw-Hill Companies, Inc. All rights reserved. 1 - 59Rules for Using SI Units Plurals are used as required when writing unit names henries (H; henry) Exceptions; lux, hertz, siemens No hyphen or space sho