Conceptual Physics Final Exam Notes PDF

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Chapt er3–Li nearMot i on  Speed o Di st ancecover edperuni toft i me o Speed =

Di s t anc e Ti me

o I nst ant aneousSpeed  Thespeedatanyi nst ant o Aver ageSpeed  Thet ot al di st ancecov er eddi vi dedbyt het i mei nt er v al 

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Av er ageSpeed =

Tot al Di s t anceCov er ed Ti meI nt er v al

Vel oc i t y o Whenwek nowbot ht hespeedanddi r ect i onofanobj ect ,wear eabl et o cal c ul at et hevel oci t y o Vect orQuant i t y  Quant i t yt hathasbot hmagni t udeanddi r ect i on o Scal arQuant i t y  Quant i t yt hatcanbedescr i bedbymagni t udewi t houtdi r ect i on o Const antVel oc i t y  Const antspeedandconst antdi r ect i on o Changi ngVel oci t y  I fei t hert hes peedordi r ect i onchangest hent hev el oci t ydoest o

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Accel er at i on o Howqui ckl yv el oci t ychanges  ‘ Howqui ckl ydoesf astchange” o Accel er at i on =

ChangeofVel oc i t y Ti meI nt er v al

o Decel er at i on  Thedecr easei nv el oci t y o Si ncewear econsi der i ngmot i onal ongast r ai ghtl i net het er msspeed, andv el oci t ycanbeusedi nt er c hangeabl y

o Whendi r ect i ondoesn’ tchange,accel er at i onmaybeexpr essedast her at e

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aswhi chspeedchanges o Rat eofar at e Fr eeFal l o Whenaf al l i ngobj ecti sf al l i ngf r eeofal lr est r ai nt s( nof r i ct i on,orai r r esi st ance)andf al l sundert hei nfluenceofgr avi t yal one o Dur i ngeachsecondoff al l ,t heobj ectgai nsaspeedof10met er sper second  =10m/ s2 o gi susedt or epr esentaccel er at i on,becauset heaccel er at i oni sduet o gr avi t y  Gr avi t y=9. 8m/ s2  Wer oundt hi st o10m/ s2 o Vel oc i t y = Ac cel er at i onxTi me  v=gt o Howf aranobj ectf al l si sal t oget herdi ffer entf r om how f as ti tf al l s o Thedi st ancet r av el edbyauni f or ml yaccel er at i ngobj ect sst ar t i ngf r om r est i s  

Di st anceTr avel ed =  ( Accel er at i onxTi mexTi me) 2 d= gt

o Al l t hi ngsf al lwi t hequal accel er at i on  Duet oai rr esi st ance,orwhatnot ,t heyappeart of al lunequal l y  Howeveri fbot hobj ect swer epl acedi navacuum t heywoul dhave equal accel er at i on Chapt er4–Newt on’ sSecondLawofMot i on  For ceCausesAccel er at i on o NetFor ce  Thecombi nat i onoff or cesact i ngonanobj ect 

Accel er at i ondependsonnetf or ce  Accel er at i on~NetFor ce o ~means“ i sdi r ect l ypr opor t i onalt o”

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Fr i ct i on o Thedi r ect i onoft hef r i ct i onf or cei sal way si nadi r ect i onopposi ngmot i on

o Foranobj ectt omov eaconst antv el oci t y ,af or ceequal t ot heopposi ng f or c eoff r i ct i onmustbeappl i edsot hatt het wof or cesex act l ycancel each ot herout o Sl i di ngFr i ct i on  Cont actf or cepr oducedbyt her ubbi ngt oget heroft hesur f aceofa movi ngobj ectwi t ht hemat er i al ov erwhi chi tsl i des o St at i cFr i ct i on  For cebet weent woobj ect satr el at i v er estbyvi r t ueofcont actt hat

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t endst oopposes l i di ng o Ai rResi st ance( Ai rDr ag)  Acommonex ampl ei sflui df r i ct i on  Ai rr esi st ancei ncr easeswi t hi ncr easi ngspeed MassandWei ght o Mass  Thequant i t yofmat t eri nanobj ect ,I ti sal sot hemeasur eoft he i ner t i aorsl uggi shnesst hatanobj ectexhi bi t si nr esponset oany

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effor tmadet ost ar t ,orst opi t ,orchangei t sst at eofmot i oni nany way Thegr eat ert hemassofanobj ect ,t hegr eat eri t si ner t i a Massi sameasur eoft hei ner t i aofamat er i alobj ect

o Wei ght  Thef or ceuponanobj ectduet ogr avi t y o I nt heabsenceofaccel er at i on,massandwei ghtar edi r ect l ypr opor t i onal t oeachot her o Massi saf undament alquant i t y o Gr avi t yont hemooni s1/ 6ofwhati ti sher eonear t h 

MassResi st sAccel er at i on o Theamountofaccel er at i ondependsnotonl yont hef or cebutont hemass bei ngpushed o Accel er at i on ~

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1 Mass

Newt on’ sSecondLawofMot i on

o Theaccel er at i onofanobj ecti sdi r ect l ypr opor t i onal t ot henetf or ceact i ng ont heobj ect ,i si nt hedi r ect i onoft henetf or ce,andi si nv er sel y pr opor t i onal t ot hemassoft heobj ect

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Accel er at i on ~

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Fnet m

a=

o Accel er at i onofanobj ecti sal waysi nt hedi r ect i onoft henetf or ce WhenAc cel er at i ngg–Fr eeFal l

m

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NetFor ce Mass

F =g m

2m

2F =g 2m

WhenAc cel er at i ngi sLessThang–Nonf r eeFal l o Newt on’ sl awsappl yf oral l obj ect s,whet herf r eel yf al l i ngorf al l i ngi nt he pr esenceofr esi st i v ef or ces o Accel er at i onar edi ffer entbet weent het wot hough  I nv acuum ori ncasesi nwhi chai rr esi st ancecanbenegl ect edt he 

netf or cei st hewei ghtbecausei ti st heonl yf or ce I nt hepr esenceofai tr esi st ancet henetf or cei sl esst hant he wei ght  I ti st hewei ghtmi nusai rdr ag,t hef or cear i si ngf r om ai r

r esi st ance o For ceofAi rDr ag

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Fi r st ,i tdependsont hef r ont alar eaoft hef al l i ngobj ect ,t hati s,on

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t heamountofai rt heobj ectmustpl owt hr oughasi tf al l s Second.I tdependsont hespeedoft hef al l i ngobj ect :t hegr eat er t hespeed,t hegr eat ert henumberofai rmol ecul esanobj ect

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encount er spersecondandt hegr eat ert hef or ceofmol ecul ar i mpact Ai rdr agdependsont hesi z eandspeedofaf al l i ngobj ect s

o Ter mi nal Speed  Whenanobj ect saccel er at i ont er mi nat es  I fwear econcer nedwi t hdi r ect i on,downf orf al l i ngobj ect s wesayt heobj ecthasr eac hedi t st er mi nal v el oci t y

Chapt er5–Newt on’ sThi r dLawofMot i on  For cesandI nt er act i ons o For cei ni t ssi mpl estsensei sapushorpul l  Ev er yf or cei sani nt er act i onbet weenonet hi ngandanot her  Newt on’ sThi r dLawofMot i on o Whenev eroneobj ectex er t saf or ceonasecondobj ect ,t hesecondobj ect

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ex er t sandequal andopposi t ef or ceont hefir st o Toever yact i ont her ei sal waysanequalandopposi t er eact i on o For cesoccuri nf or cepai r s Li f t o I nappl i cat i onofBer noul l i ’ spr i nc i pl e,t henetupwar df or cepr oducedbyt he di ffer encebet weenupwar danddownwar dpr essur es  Whenl i f tequal swei ght ,hor i z ont alfli ghti spossi bl e

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Vect or s o Vect orQuant i t y  Requi r esbot hmagni t udeanddi r ect i on  Ex ampl es:   

For ce,v el oci t y ,andaccel er at i on

Repr esent edwi t hanar r ow Whent hel engt hoft hear r owi ss cal edt or epr esentt hequant i t y’ s magni t ude,anddi r ect i onoft hear r owshowst hedi r ect i onoft he

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quant i t y ,t hear r owi sr egar dedasav ect or Addi ngVect or s

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I ft heyactal ongpar al l el di r ect i ons,andi nt hesame

di r ect i on,t heyadd Subt r act i ngVect or s  I ft heyactal ongpar al l el di r ect i ons,buti ndi ffer entdi r ect i ons, t heysubt r act Thesum oft woormor ev ect or si scal l edt hei rr esul t ant

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For ceVect or  Hav eawei ght ,ormassass oci at edwi t ht hem

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Vel oc i t yVect or  Hasaspeedass oci at edwi t hi t

o Scal arQuant i t y  Requi r esonl yamagni t ude  Ex ampl es:  Mass ,v ol ume,andspeed o Component sofVect or s  Justast wovect or scanbecombi nedatr i ghtangl est ocr eat eone r esul t antv ect or ,anyv ect orcanber esol vedi nt ot wocomponent s v ect or sper pendi cul art oeachot her  Theset wov ect or sar eknownast hecomponent soft he 

gi v env ect ort heyr epl ace Thi spr ocessofdet er mi ni ngt hecomponent sofav ect ori scal l ed r esol ut i on  Anyv ect orcanber esol v ed( br ok endown)i nt oav er t i cal and hor i z ont alcomponent

Summar yofNewt on’ sThr eeLaws 1.TheLawofI ner t i a

o Anobj ectatr estt endst or emai natr est ;anobj ecti nmot i ont endst ost ay i nmot i onatconst antspeedal ongast r ai ght l i nepat h o Thepr oper t yofobj ect sr esi st i ngchangei nmot i oni scal l edi ner t i a o Massi sameasur eofi ner t i a o Obj ect swi l l under gochangesi nmot i ononl yi nt hepr esenceofanetf or ce 2.TheLawofAccel er at i on o Whenanetf or ceact sonanobj ect ,t heobj ectwi l l accel er at e.The accel er at i oni sdi r ect l ypr opor t i onal t ot henetf or ce,andi nv er sel y pr opor t i onal t ot hemass o Sy mbol i cal l y ,a=F/ m o Accel er at i oni sal way si nt hedi r ect i onoft henetf or ce o Whenobj ect sf al l i navacuum,t henetf or cei ss i mpl yt hewei ght ,t hepul l ofgr avi t yg o Whenobj ect sf al l i nai r ,t henetf or cei sequalt ot hewei ghtmi nust hef or ce ofai rr esi st ance,andt heaccel er at i oni sl esst hang o I fandwhent hef or ceofai rr esi st anceequal st hewi ghtofaf al l i ngobj ect , accel er at i ont er mi nat es,andt heobj ectf al l sataconst ants peed,t er mi nal speed 3.TheLawofAct i onReact i on o Whenev eroneobj ectex er t saf or ceonasecondobj ect ,t hesecondobj ect exper t sandequal andopposi t ef or ceont hefir st o For cesoccuri npai r s,oneact i onandt heot herr eact i on,whi cht oget her const i t ut et hei nt er act i onbet weenoneobj ectandt heot her o Act i onandr eact i onal way soccursi mul t aneousl yandactondi ffer ent obj ect s o Nei t herf or ceexi st swi t houtt heot her Chapt er6–Moment um  Moment um o Thepr oductoft hemassofanobj ectandi t sv el oci t y o Moment um =massxv el oci t y  Moment um =mv  Ori fdi r ect i oni snoti mpor t antf act or  Moment um =massxs peed o Amovi ngobj ectcanhav eal ar gemoment um i fei t heri t smassori s v el oc i t yar el ar ge

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I mpul se o Thepr oductoft hef or ceact i ngonanobj ectandt het i mewhi chi tact s o I ft hemoment um ofanobj ectchanges,t heei t hert hemassort hev el oci t y , orbot hchange o Thegr eat erf or ceact i ngonanobj ect ,t hegr eat eri t schangei nv el oci t y , and,hence,t hegr eat eri t schangei nmoment um o Ti mei si mpor t anti nchangi ngmoment um,t i me–howl ongat i met he f or ceact s o Af or cesust ai nedf oral ongt i mepr oducesmor echangei nmoment um t handoest hesamef or ceappl i edbr i efly o Hencewhybot hf or ce,andt i mei nt er v alar ei mpor t anti nchangi ng moment um  Thequant i t yf or cext i mei nt er v ali scal l edi mpul se  I mpul se=Ft

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I mpul seChangesMoment um o Thegr eat ert hei mpul s eex er t edonsomet hi ng,t hegr eat erwi l l bet he changei nmoment um  I mpul se=changei nmoment um  Ft=( mv)

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o I mpul seandc hangeofmoment um ar eal way sl i nk ed I ncr easi ngMoment um o Toi ncr easet hemoment um ofanobj ect ,i tmak essenset oappl yt he gr eat estf or cepossi bl ef orasl ongaspossi bl e o Thef or cesi ni mpul sesusual l yv ar yf r om i nst antt oi nst ant o Gol fEx ampl e  Thecl ubheadt hatst r i k est hebal lex er t sz er of or ceont hebal l unt i l

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i tcomesi ncont r act ,t hent hef or cei ncr easesr api dl yast hebal l comesupt ospeedandr et ur nst oi t sor i gi nalshape  Suchf or cesar er egar dedt oasav er agef or ce Decr easi ngMoment um ov eral ongt i me o I nt hecaseofhi t t i ngabr i ckwal l ,orahayst ackandcomi ngt ost op,i t t ak est hesamei mpul set odecr easey ourmoment um t oz er o o Thesamei mpul sedoesnotmeant hesameamountoff or ceort hesame amountoft i me,r at heri tmeanst hesamepr oductoff or ceandt i me  Byhi t t i ngt hehay st ack,i nst eadoft hewal l ,y ouext endt het i me dur i ngwhi chy ourmoment um i sbr oughtt oz er o

o Al ongert i mei nt er v al r educest hef or ceanddecr easest her esul t i ng 

decel er at i on Decr easi ngMoment um ov erashor tt i me o Remembert hat ,f oranobj ectt obebr oughtt or est ,t hei mpul sei st he same,nomat t erhowi ti sst opped  But ,i ft hatt i mei sshor t ,t hef or cewi l l bel ar ge o Kar at eEx ampl e  Shebr i ngsherar m andhands wi f t l yagai nstt hebr i ckswi t h 

consi der abl emoment um Thi smoment um i squi ckl yr educedwhenshedel i v er sani mpul set o

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t hebr i cks Thei mpul sei st hef or ceofherhandagai nstt hebr i cksmul t i pl i edby

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t het i medur i ngwhi chherhandmakescont actwi t ht hebr i cks Byswi f tex ecut i on,shemak est het i meofcont actv er ybr i efand cor r espondi ngl ymak est hef or ceofi mpacthuge  I fherhandi smadet obounceuponi mpact ,t hef or cei sev en gr eat er

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Bounc i ng o I mpul sei sgr eat erwhenanobj ectbounces o Thei mpul ser equi r edt obr i nganobj ectt oast opt hent o“ t hr owi tback agai n”i sgr eat ert hant hei mpul ser equi r edmer el yt obr i ngt heobj ectt oa st op  Ex ampl e  I fy oucat c haf al l i ngflowerpotwi t hy ourhands,y oupr ovi de

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ani mpul set or educei t smoment um t oz er o Buti fy out hr owt hepotupwar dagai n,y ouhav et opr ovi de

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addi t i onali mpul se Thi si ncr easedamountofi mpul sei st hesamet haty ourhead

suppl i esi ft heflowerpotbouncesf r om i t Conser v at i onofMoment um o Fr om Newt on’ ss econdl aw,y ouknowt hatt oaccel er at eanobj ect ,anet f or cemustbeappl i ed o Onl yani mpul seext er nal t oas y st em canchanget hemoment um oft he s y st em o I nt er nal f or cesandi mpul seswon’ twor k  Ex ampl e

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Themol ecul arf or ceswi t hi nbasebal lhav enoeffectont he moment um oft hebasebal l ,j ustasapushagai nstt he

dashboar dofacary ou’ r esi t t i ngi ndoesnotaffectt he moment um oft hecar o Theycomei nbal ancedpai r st hatcancelt oz er owi t hi nt heobj ect o Tochanget hemoment um oft hebal lort hecar ,anext er nal pushorpul li s r equi r ed  I fnoext er nal f or cei spr esent ,t hennoext er nalpul sei spr esent ,and nochangei nmoment um i spossi bl e o Cannonbal l Ex ampl e  Thef or ceont hecannonbal li nsi det hecannonbar r eli sequal and 

opposi t et ot hef or cecausi ngt hecannont or ecoi l Si ncet hesef or cesactf ort hesamet i me,t hei mpul sesar eal so

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equal andopposi t e Recal lNewt on’ st hi r dl awaboutact i onandr eact i onf or ces,asi t

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appl i est oi mpul s est oo Thesei mpul sesar ei nt er nal t ot hes y st em compr i si ngt hecannon

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andt hecannonbal l ,sot heydon’ tchanget hemoment um oft he cannoncannonbal ls y st em Bef or et hefir i ng,t hes ys t em i satr estandt hemoment um i sz er o Af t ert hefir i ng,t henetmoment um,ort ot al moment um,i ss t i l l z er o  Netmoment um i snei t hergai nedorl ost Moment um i ssi mi l art ov el oci t y ,andf or cei nt hesens et hatt hey bot hhav eadi r ect i onandamagni t ude  Li k ev el oci t yandf or ce,moment um canbecancel l ed

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Moment um i sav ect orquant i t y So,al t hought hecannonbal li nt hepr ecedi ngex ampl egai ns moment um whenfir edandt her ecoi l i ngcannongai nsmoment um

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i nt heopposi t edi r ect i on,t her ei snogai ni nt hecannoncannonbal l s y st em Themoment aoft hecannonbal l andcannonar eequali n magni t udeandopposi t ei ndi r ect i on  Ther ef or ecancel i ngt oz er of ort hes y st em asawhol e

o Whenmoment um,oranyquant i t yi nphy si cs ,doesnotchange,wesayi ti s conser v ed o TheLawofConser v at i onofMoment um

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I nt heabsenceofanext er nalf or ce,t hemoment um ofas y st em r emai nsunchanged

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Col l i si ons o Moment um i sconser v edi ncol l i si ons  Thati s ,t henetmoment um ofas y st em col l i di ngobj ect si s 

unchangedbef or e,dur i ng,andaf t ert hecol l i s i on Netmoment um bef or ecol l i si on=netmoment um af t ercol l i si on

o El ast i cCol l i s i on  Acol l i si oni nwhi c hcol l i di ngobj ect sr eboundwi t houtl ast i ng def or mat i onort hegener at i onofheat o I nel as t i cCol l i s i on  Acol l i si oni nwhi c ht hecol l i di ngobj ect sbecomedi st or t ed,gener at e heat ,andpossi bl ys t i ckt oget her o Conser v at i onofmoment um  ( netmv) netmv) bef or e =( af t er Chapt er7–Ener gy  Wor k o Wor ki st heeffor tex er t edonsomet hi ngt hatwi l lchangei t sener gy o Wor k=f or cexdi st ance o W =Fd o Whenwel i f tsomet hi ngagai nstear t h’ sgr avi t y ,wor ki sdone.Theheavi er t hel oadt hemor ewor ki sdone o Twot hi ngsoccurwhenwor ki sdone 1.Appl i cat i onofaf or ce 2.Themov ementofsomet hi ngbyt hatf or ce o Wor kf al l si nt ot wocat egor i es 1.Wor kdoneagai nstanot herf or ce 2.Wor kdonet ochanget hespeedofanobj ect o Theuni tofmeasur ementf orwor kcombi nesauni toff or ce( N)wi t hauni t ofdi st ance( m) ;t heuni tofwor ki st heNewt onmet er( N·m) ,al socal l eda j oul e( J) o Onej oul eofwor ki sdonewhenaf or ceof1Newt oni sex er t edov era 

di st anceof1met er Power o Power

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I sequal t ot heamountofwor kdonepert i mei tt ak est odoi t Wor kDone Ti meI nt er v al

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Power=

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Ex ampl e  Ahi ghpowerengi nedoeswor kr api dl y .Anaut omobi l e engi net hatdel i v er st wi cet hepowerofanot heraut omobi l e

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engi nedoesnotnecessar i l ypr oducet wi ceasmuchwor kor mak eacargot wi ceasf astast hel esspower f ul engi ne Twi cet hepowermeanst heengi necandot wi cet hewor ki n

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t hesamet i meordot hesameamountofwor ki nhal ft he t i me Amor epower f ul engi necangetanaut omobi l eupt ogi v en speedi nl esst i met hanal esspower f ulengi ne

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Mechani cal Ener gy o Ener gy  Thepr oper t yofas y st em t hatenabl esi tt odowor k o Mechani cal Ener gy  Ener gyduet ot heposi t i onofsomet hi ngort hemov ementof somet hi ng  Canbei nf or m ofpot ent i alener gy ,ki net i cener gy ,ort hesum oft het wo o Pot ent i alEner gy  Theener gyt hatsomet hi ngpossessesbecauseofi t sposi t i on  Ast r et chedorcompr essedspr i nghast hepot ent i alf ordoi ngwor k  Chemi calener gyi nf uel si sal sopot ent i al ener gy  

I ti sact ual l yposi t i onatt hesubmi cr oscopi cl evel Thi sener gyi sav ai l abl ewhent hepos i t i onsofel ect r i c char geswi t hi nandbet weenmol ecul esar eal t er ed–t hati s,

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whenachemi calchangeoccur s Thepot ent i alener gyduet oel ev at edposi t i onsi scal l edgr av i t at i onal

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pot ent i alener gy Theamountofgr avi t at i onalpot ent i alener gypossessedbyan el ev at edobj ecti sequalt ot hewor kdoneagai nstgr avi t yi nl i f t i ngi t  Gr avi t at i onal Pot ent i al Ener gy=Wei ghtxHei ght  PE=mgh

o Ki net i cEner gy  Ener gyofmot i on,quant i fiedbyt her el at i onshi p 2  Ki net i cEner gy= MassxSpeed  Wheny out hr owabal l ,y oudowor koni tt ogi v ei tspeedasi t l eavesy ourhand.Themovi ngbal l cant henhi tsomet hi ngandpush i t ,doi ngwor konwhati thi t s.Theki net i cener gyofamovi ngobj ect i sequal t ot hewor kr equi r edt obr i ngi tf r om r estt ot hatspeed,or t hewor kt heobj ectcandowhi l ebei ngbr oughtt or est :  Ki net i cEner gy=NetFor cexDi st ance 2  KE= m ·v o Wor k–Ener gyTheor em  Whenacarspeedsup,i t sgai ni nki net i cener gycomesf r om t he wor kdoneoni t .Or ,whenamov i ngcaral l ows,wor ki sdonet o r educei t ski net i cener gy .Wecansay:  Wor k=KE o Der i vedasf ol l ows:  Mul t i pl ybot hsi desofF=mabyd  

WegetFd=mad Const antaccel er at i onf r om r est 2  d=at

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Sowecansay 2 2 2  Fd=ma( at ) maat at ) )=( =m(

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Subst i t ut i ngv=at 2 WegetFd=mv

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Whi chi s ,Wor k=KEgai ned

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Wor kequal t hechangei nki net i cener gy ,t hi si st hewor k–ener gy

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t heor em Thewor ki nt hi sequat i oni st henetwor k,t hati st hewor kbasedon

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t henetf or ce Th...