《大學物理簡明教程》 課件 6-1 Torque

TorquerotationforcebalanceStaticequilibriumWehaveconsideredforcesactingonasinglepoint.-point-massmodeltheobjectmovesasapointmass–atranslationalmotion.ForcesandTorquesNowweconsidertheobjecthavingcertainshapeandsize.Whatiftheforcesactondifferentpointsoftheobject?Atorqueisaphysicalquantitythatis:aproduct

ofaforceandadistance.ATorqueisalsoknownasthe“MomentofForce”.Itoperatesatsomedistancefromthepivotpoint.It’sactionrotatesanobject.Torque/MomentofForceFdpivot

TheSIunitisN·m,butitisNOTjoule(J)!Fd

dF

F

Thedirectionsoftorqueare“clockwise”or“anti-clockwise”ForceCoupleTwooppositeandequalforcesthatactondifferentpointsofanobjectareknownasa“couple”.Acouplewillrotatetheobject-itexertsatorque.*FFNocontributiontothenetforcecontributetothenettorque*FF*l/2l/2

clockwisecenterofrotationExampleAmechanicexertsaforceof100Nperpendiculartotheendofawrench300mmlong.Whatisthetorqueappliedtothescrewnut?

Clockwise–tofastenthescrewAnti-clockwise–toloosenthescrewAchildofweight150Nsitsontheendofasee-sawoftotallength3m.Herfatherstands0.5mfromthemiddleofthesee-sawandpushesdown.Whatforcemustheexerttobalancehisdaughter?Ifherolderbrother(weight200N)getsonthesee-saw,whereshouldhesittobalancehissister?150N3mF=?0.5ma)Anti-clockwisetorque=positiveClockwisetorque=negativeTobalance,thesumofthemomentsmustbezero.(150Nx1.5m)+(-Fx0.5m)=0Example:balanceoftorquesF=(150x1.5)/0.5=450NF1d1+F2d2=0d2=-(F1d1)/F2

=-(-1.5mx150N)/200N150N3md2=?200Nd2=1.125mfromthecenter(or1.5–1.125=0.375mfromend)LeversWecanusetheconceptoftorque/momentstoexplainhowasimpleleverworks:Momentduetoweight=+l1·MgMomentduetoperson=-l2·WMaximummasswhenthesecancel-(totalmomentiszero)l1Mg=l2WM=(l2/

l1)·W/gWMg?kgl1l2W+MgWhatisthemaximummassthepersoncanlift?(l2/

l1)isthemechanicaladvantageofthelever,thelargeritis,thelargerthemassthatthepersoncanliftThebarisbalanced.WhatisthevalueofF?F?50N10N5N10N20N-10-8-4+30+8+10WedonotknowthedirectionofF,soweassumeitisup

ANTIANTIANTICLOCKCLOCKCLOCKCLOCKWISEANTI-CLOCKWISEExample

Fisactually15NinthedownwarddirectionF?50N10N5N10N20N-10-8-4+30+8+10ANTIANTIANTICLOCKCLOCKCLOCK-100-20–160+400+30+10F=0F=-15N

Balance→

StaticEquilibriumAnobjectisinstaticequilibriumif:ThesumofallexternalforcesiszeroThesumofallexternaltorquesiszeroANDIthasnotranslationalmotionIthasnorotationalmotionandConditionsofstaticequilibrium15N50N10N5N10N20N-10-8-4+30+8+10ANTIANTICLOCKCLOCKCLOCKCLOCKIfthebarhasaweightof20Nandisinstaticequilibrium,whatistheforcefromthefulcrum(pivot)?F=?W=20N

√10+5+F+10-50–20–20–15=0F=80NExampleA5kgmassisplaced0.3mfromleftendofa1mlongplankthatissupportedateachendbyapairofscales.Whatweightdoeseachscaleread?