靜力學(xué)基本定理Fundamentaltheoremofst

靜力學(xué)基本定理Fundamentaltheoremofstatics主講人：申瀟概念conception靜力學(xué)公理是靜力學(xué)中已被實(shí)踐反復(fù)證實(shí)并被認(rèn)為無需證明的最基本的原理，正確地反映了客觀規(guī)律，并成為演繹推導(dǎo)整個(gè)靜力學(xué)理論的基礎(chǔ)。Theaxiomofstaticsisthemostfundamentalprincipleinstaticsthathasbeenrepeatedlyproveninpracticeandisconsideredunnecessarytoprove.Itcorrectlyreflectsobjectivelawsandservesasthebasisfordeducingtheentiretheoryofstatics.目錄CONTENTS1234二力平衡條件Equilibriumconditionsoftwoforces加減平衡力系原理Principleofaddingandsubtractingbalanceforcesystem作用與反作用定理Theoremofactionandreaction力的平行四邊形規(guī)則Parallelogramruleofforce1二力平衡條件EquilibriumconditionsoftwoforcesONE一、二力平衡條件Equilibriumconditionsoftwoforces公理1二力平衡公理:作用在同一剛體上的兩個(gè)力，使剛體平衡的必要且充分的條件是，此二力等值、反向、共線。Axiom1:Equilibriumoftwoforces:Thenecessaryandsufficientconditionfortwoforcesactingonthesamerigidbodytobalanceisthatthesetwoforcesareequal,opposite,andcollinear.LocalkeycomponentsPeoplestandingstillAboxthatmovesuniformlyinastraightline一、二力平衡條件Equilibriumconditionsoftwoforces二力構(gòu)件:只受兩個(gè)力作用而處于平衡的物體。Twoforcecomponent:anobjectthatisinequilibriumundertheactionofonlytwoforces.一、二力平衡條件Equilibriumconditionsoftwoforces一、二力平衡條件Equilibriumconditionsoftwoforces二力構(gòu)件的受力特點(diǎn):不論構(gòu)件形狀如何，其所受力必定通過兩點(diǎn)連線。Theforcecharacteristicsofthetwoforcecomponent:regardlessoftheshapeofthecomponent,theforceitissubjectedtomustbeconnectedthroughtwopoints.不是二力構(gòu)件Notasecondarycomponent一、二力平衡條件Equilibriumconditionsoftwoforces例1:如圖所示直桿AD和折桿BC相接觸，在力作用下處于靜止，若不計(jì)自重，分析BC構(gòu)件的受力。Example1:Asshowninthefigure,thestraightrodADandthefoldedrodBCareincontactandareatrestundertheactionofforce.Iftheselfweightisnotconsidered,analyzetheforceontheBCcomponent.2加減平衡力系公理AxiomforaddingandsubtractingequilibriumforcesystemsTWO公理2加減平衡力系公理:在已知力系上加上或減去任意平衡力系，并不改變原力系對剛體的作用。它是力系替換與簡化的等效原理。Axiom2:Addingorsubtractinganyequilibriumforcesystemfromaknownforcesystemdoesnotchangetheeffectoftheoriginalforcesystemonarigidbody.Itistheequivalentprincipleofforcesystemreplacementandsimplification.二、加減平衡力系公理Axiomforaddingandsubtractingequilibriumforcesystems注意:在物體上加減平衡力系，必然引起力對物體內(nèi)效應(yīng)的改變，在涉及內(nèi)力和變形的問題中，公理2不適用。Note:Addingorsubtractingabalancedforcesystemonanobjectwillinevitablycauseachangeintheinternaleffectoftheforceontheobject.Inproblemsinvolvinginternalforcesanddeformations,Axiom2doesnotapply.F1F1’F2F2’加一對平衡力F1和F1’，整體仍舊平衡，卻改變了B處內(nèi)力(桿AD與BC的相互作用力)，也改變了C和A處的作用力。AddingapairofbalancingforcesF1andF1',theoverallbalanceisstillmaintained,butitchangestheinternalforceatB(theinteractionforcebetweenrodADandBC)andalsochangestheforceatCandA.二、加減平衡力系公理Axiomforaddingandsubtractingequilibriumforcesystems推論2力的可傳性原理:Inference2:Theprincipleofforcetransferability:作用于剛體上的力，可沿其作用線任意移動(dòng)而不改變它對剛體的作用效應(yīng)。Theforceactingonarigidbodycanmovearbitrarilyalongitslineofactionwithoutchangingitseffectontherigidbody.二、機(jī)器的組成及特征CompositionandcharacteristicsofthemachineF=F1=F23作用與反作用定理TheoremofactionandreactionTHREE三、作用與反作用定理Theoremofactionandreaction公理3

作用與反作用定理:兩物體間相互作用的力，總是大小相等、方向相反，且沿同一直線，分別作用在這兩個(gè)物體上。Axiom3ActionandReactionTheorem:Theforcesthatinteractbetweentwoobjectsarealwaysequalinmagnitude,oppositeindirection,andactingoneachotheralongthesamestraightline.FT與G是一對平衡力FTandGareapairofequilibriumforcesFT’與FT是一對作用力與反作用力FT'andFTareapairofforcesandreactions三、作用與反作用定理Theoremofactionandreaction作用力與反作用力跟平衡力有什么相同點(diǎn)和不同點(diǎn)呢?Whatarethesimilaritiesanddifferencesbetweenforcesandreactionsandequilibriumforces?相同:兩力大小相同，方向相反，作用在同一直線上。Same:Twoforceswiththesamemagnitudeandoppositedirectionsactonthesamestraightline.不同:Different:作用力與反作用力（異物）燈拉繩的力繩拉燈的力燈的重力作用力與反作用力（異物）平衡力（同物）Equilibriumforce(equivalenttomatter)Forcesandreactions(foreignobjects)TheforceofthelamppullropeTheforceofaropepullinglampTheGravityofaLamp三、作用與反作用定理Theoremofactionandreaction問題2:繩子被剪斷，會(huì)怎樣呢?Question2:Whathappensiftheropeiscut?可見作用力和反作用力具有同時(shí)性，同時(shí)產(chǎn)生、同時(shí)消失。Itcanbeseenthattheforcesandreactionshavesimultaneity,producinganddisappearingsimultaneously.:三、作用與反作用定理Theoremofactionandreaction作用力與反作用力的特點(diǎn)：Characteristicsofforcesandreactions:大小相等，方向相反，作用在一條直線上;Equalinsize,oppositeindirection,actingonastraightline;作用點(diǎn)在不同的物體上;Thepointofactionisondifferentobjects;性質(zhì)相同;同生同滅。

Samenature;.Bornanddiedtogether例2:如圖所示直桿AD和折桿BC相接觸，在力作用下處于靜止，若不計(jì)自重，分析AD構(gòu)件的受力。Example2:Asshowninthefigure,thestraightrodADandthefoldedrodBCareincontactandareatrestundertheactionofforce.Iftheselfweightisnotconsidered,analyzetheforceontheADcomponent.三、課程內(nèi)容ContentFFB’FA4力的平行四邊形規(guī)則ParallelogramruleofforceFOUR一、二力平衡條件Equilibriumconditionsoftwoforces公理4力的平行四邊形規(guī)則:作用于物體上的兩個(gè)力，其合力也作用在該點(diǎn)上，合力的大小和方向則由以這兩個(gè)力為邊所構(gòu)成的平行四邊行的對角線來表示，而該兩個(gè)力稱為合力的分力。Axiom4:Theparallelogramruleforforces:Whentwoforcesactonanobject,theircombinedforcealsoactsonthatpoint.Themagnitudeanddirectionofthecombinedforcearerepresentedbythediagonallinesoftheparallelogramformedbythesetwoforcesasedges,andthesetwoforcesarecalledthecomponentforcesofthecombinedforce.矢量式:FR=F1+F2Vectorformula:FR=F1+F2一、二力平衡條件EquilibriumconditionsoftwoforcesF1F2FRF1力的相加FR=F1+F2F2F1FRF1FR’力的相減FR’=F2-F1ThesumofforcesFR=F1+F2SubtractionofforcesFR'=F2-F1力三角形——力的相加與相減ForceTriangle-AdditionandSubtractionofForcesF1、F2可以合成為一個(gè)合力FR。合力的作用點(diǎn)也在該點(diǎn)，合力的大小和方向用兩分力為鄰邊所構(gòu)成的平行四邊形的對角線表示。F1andF2canbecombinedintoacombinedforceFR.Thepointofactionoftheresultantforceisalsoatthispoint,andthemagnitudeanddirectionoftheresultantforcearerepresentedbythediagonalofaparallelogramformedbytwoadjacentsidesoftheforce.三、課程內(nèi)容Content推論2Inference2:

力平衡匯交定理:作用于剛體上的三個(gè)力相互平衡時(shí)，若其中兩個(gè)力的作用線相交于一點(diǎn)，則此三力必在同一平面內(nèi)，且第三個(gè)力的作用線必通過匯交點(diǎn)。Theoremofforceequilibriumintersection:Whenthreeforcesactingonarigidbodyareinequilibriumwitheachother,ifthelinesofactionoftwoofthemintersectatapoint,thenthesethreeforcesmustbeinthesameplane,andthelinesofactionofthethirdforcemustpassthroughtheintersectionpoint.三、課程內(nèi)容Content該定理說明三個(gè)不平行力平衡的必要條件，容易推廣到更一般的情形:剛體受n個(gè)力作用而平衡，若其中n-1個(gè)力交于同一點(diǎn)，則第n個(gè)力的作用線必過此點(diǎn)。Thistheoremexplainsthenecessaryconditionsforthebalanceofthreenonparallelforcesandcanbeeasilygeneralizedtoamo