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1、VectorsWorksheet[AdditionandResolution]WhatisaVector?Vectorsaregraphicrepresentationsofphysicaloccurrences.Weusevectorstovisualizewhatphysicallyhappenstoanobjectundercertainconditions.Vectorsdesignatethemagnitudeanddirectionofthingslikeforces,accelerations,velocities,anddisplacem
2、ents.Theyhelpustodescribemotionthroughacommonsymbology.Magnitude-theamountoftheforce,acceleration,velocity,ordisplacement.Direction-aspecificdirectioninwhichtheforceisapplied,ortheacceleration,velocity,ordisplacementoccur.WhatisVectorAddition?Vectoradditionistheprocessoffindingth
3、eresultantvectorwhengiventhecomponentsofthevector.Inone-dimensionalvectoraddition,youwillbeworkingoneitherthex(horizontal)ory(vertical)axis.Thevectoradditionissimplytheaddition(orsubtractionifthevectorsareinoppositedirections)ofthetwovectors.Iftheyareinoppositedirections,theresul
4、tantdirectionwillbeinthesamedirectionasthevectorwiththegreatestmagnitude.Intwo-dimensionalvectoraddition,youhavebothanx(horizontal)anday(vertical)component.YouaddthevectorsbyusingthePythagoreantheoremsincethetwovectorsareatrightanglestoeachother.Thisvalueisthemagnitudeoftheresult
5、vector.Thedirectionoftheresultvectoristheanglebetweenthehypotenuseofthetriangleandthehorizontal.Tofindthisvalue,youusethetan-1functiononthecalculator.WhatisVectorResolution?Vectorresolutionisusedintwo-dimensionalvectoranalysisandisthereversetovectoraddition.Invectorresolution,you
6、knowthemagnitudeanddirection(angle)oftheresultantvectorandyouaresolvingforthehorizontalandverticalcomponents.Tofindthex(horizontal)component,youusethecosinefunctionandtheformula:;whereRisthemagnitudeoftheresultantTofindthey(vertical)component,youusethesinefunctionandtheformula:;w
7、hereRisthemagnitudeoftheresultantVectorAddition1.Youpullaropetotheleftwith300Nandafriendpullstheropetotherightwith425N.(Don’tforgetaboutrelativesizeofvectors)A.Drawavectordiagramforthetwoforcesactingontherope.B.Use(onedimensional)vectoradditiontofindtheresultvector.(Showwork)C.Wh
8、atisthemagnitudeanddirectionoftheresultv
