งาน กำลัง พลังงาน by วรท ศรีรัตนโช

Irq6auf,affiffqntnn tcRsrflJ:sRrunrrrlsu

f.lu (Worl() lufiinrjrgdrd'urfi atnrhvrufru rTnn,' rdn q trrsn,rruuillr,'o{nurtn 1 lJno.irrflunlrdrlru *eiiuntoannhd'rn'rs r:iu nrri.r uiant,,tiufirrr lnan?,lrJurf,rglo{r'u r{r rhft*fia'ir rflunrrvir'lruun1rrunt'rrJurJ'lrrvn.rilfin{Es.ir nrri,r n*dufiwr rflun*rfimu silun'?ir'rrurirulririlunt:rir*u d'rrfu.rru'r;;;-,;;;;ulut*fifrndqsrfin{utfifidodio finr'lurnrcvirrio{nnudrrirlfi{nrlfinrrnrv{'n lnarj}xrruo.uidri.o"frrfir-;:;;;;;";;. . fiamrnmaCoud -{h

.___rf

?J, uaa:,nlraanurn Fufiinquufunuuayiu*a,t nrqrJ rriio Frfrn,.ronosirdmnz"rirfruinn d rixnrrnrvfqrooiorqtutnn,dn.nu u:r F cvlfr"ji :J?*ruorxduroF ri*cfid*rirfruoragni*u.iro ?rnlnrrBcsro F uo" z N"lol B{nr : nt;f,o i uaoin q d.rri uutiluar nrrldfr,:d

Lri-:-]

r1)

lns W 6a {'lu?,o{n?.: F iflurJitrrunrnnrffiur,j,ruti,u firfru_rlorr(N m) u?a rrsn?'lgn (Joule) 'J' frrt*'tnr;t'noio{nq1ritfr'a.uluuu",fiulfiuffunrrrn6oudrs.r{nq rriu ,dasanur.:.F

uudurc 6'u1 uuu*hrrr 0 fi'uuu"r r; ri'urhti6'n q,-;; ;;

ff #H:fi

iluuo,c d.u1*

&or t

z usai,nt?aonutrdtiaqluuucitque fruuucntnndaui

ianrirs,nuriail

{1uuas!rd{{1u

q{rou

r.fin aifnulg _

urfr

mnngrl t ur.rFdnrvrhoioinq triagluuun#ur F oanrilu e uuclasuunudsl#rurufiun:lrmdo uddnuu.rud.rlfiaglr.ur.o d.tu.nfiruurrrnq iadouilmnErJunluuucfr.rornriurnrr"daudfinurnFsino urslr.uu,l-rutlfluuu,rrr-',r,daud fiturn F cos.0fimrrur.nuilrfianrnurorio z uucnufi un F sin0 lririahirfinvrurnns'hlrifintrndoudnruuururs , un F.cos0 rioXrirha-rru rxn;,hiinrnndaudnuuutunlfir , JI qrufrfiniu

Fcosgxs

W = Fscos0

uro

(2)

rdo F f,o rurnundnrcri,rlrio{nqnnonrrnrdiirnr,ndoud

s inoru'ran*{ad{nqrndgut'tfr 0 f,a rllrvu.itfi nurqo.rui.rnrsriri'uuu.rnt,odaud -1

---

.l-

w -na,inuiltnRnun{uila q1n W * Fscos g 4

tNo

rrJo .a ItlO 01tl

0 r9 O o

coso rflu6uri(O ).rruffi)tdrfin

eoo< e < 160o cosg rflunu (-) .nu (W) fitflunu (_) (w) rflnurn (+) umafi{ mudrfinornur.ru?arflrd:snsuraonrodrfin

nlllg f,rul31durfrr1 n.","dgrd Try1rul i' :'o"i-('iryf ,ilr."u(-)''umafii"orr*drfico-rrro*.r*rJrnouuoou:odfin oriirnrunnuroaflnu$?i?$morYu nr:rndond nrrrlamndtftnornut n:cd1flnr suroililsinqfi nurJd s$fiRnr.t lumriid{nqgnur.rnr:ri, unlrrlrn ufiefinrrndaud uioinqfiunnrvrirrft e{ur.t rf,ur ufrrfirnruJCsufi amrrnnadaud iia6n-rnrrmulfid'.rd r . fr'rfrarrnru'l{r1uro{un1aunud.rrfi a.ru^6s"J lfil{nilnrr 2' W - Fscos0 . tnsuyrur ff.ruur.rrfu 1 2. firfro.rrnru1{r,luron$?oriouna fin6rh1frz n6 2-t hnlrudoffi o{udncur.rtnslinilnrrw F scoseufi.rrirltqrtrTu 0afl f,nmia.ruuruowrufrcu; 2.2ur'murcI uia.rrudnf,ldrnsln arnrur ur.rdnf (>r ) uns m rnr;in firrf riou udrur$udnrilns1{$rnt W = E Fs c os 0

:F 6a ur.rfrnf

s fia ntnr;{nfinf,

0-{ Fo 4urvu'h.:uu'rur.rdnfnr,ln'rnrs{niinf

doilri:snuliuu

{jurnsilfi{{il

nX{cau

urfr*__3*_

or ud rfiori'uisrndft rJdro'lriuriuou 'luur.rni.:{nqriiuqnr;.,nr:rirufirfinrrrnfioufilnfl$rinyn',}uuri.::ro.:inqfinrr rn6oufrtdvn.:lri rvi'i'u rriunt4 urir nr*n6oudto.:1dlun'ra*r ucl nnl rduf,r uie r*ru lunrrrn6oudto.r&ifif.rctnrn'l{?}Jn1r w= Fscos0 laras fionmnrv{pr,uorln4utinnr.r u.,oro.r,i'l,tn; hirawr;drufifinrln6aufit:Jrvi'niu nr:uroTrlt*n'ltguti. rhraun'hiri'rluriofiucn r qn4u{utJrirfr.:rfiurhd'.rgrJ 3 p6aur.rdlflr.nrr6uri.cuililnila1r.frdf,u*g rdo -:n f-/

)*i.r

fu# ll

s fiontnrs{nrarli.rc'rnrjarir{u{n'.tvirfiu i

l- a--

e6or$r,rvu'jr.r F fiusludrftoo"

mn W

F sco s0

ld'.irW

mgh

(w) =mgtr 6"rrf*orudtf,tun."guf.

_tt_ fl

s udn$nnguitmnila{ulthfiuluri,t

nr:urorr'lnnrr6iofii riruunl#tdm,)t fit'ra m #oaoglud'nrru;dlgrJ l,i6T gnfi.:1#o{d',rgrj a (r) |)

T l-q

l_ (n)

(t)

rdann,Hor,,.n1u*,fl ; jff ilffiiffiu#-1g;;f#rnuzduna.:rudrffi ---J--

e{uuu (}V.,) unvnudl{fi.rldcieuri"r.:

'{rn ldrlr.l lfr.i1 tds.ra unc triem t -a fiu,tn.

m ( ' . - it : ' .tL,

iomiranr:firu

{.ru$ffififi{{rrr

JtV

ofdsou

ur?r__E_

mga

F rfluurqfrlilunl?f,$liricuuu : F, ,l r

mH_(t ifl)

F rfluuniitilunrrfi$rir{.rudt.r :h '2 2 ld.ir lrulun,trfi.rhi

W +W

'It

F'ts +F s 1

mg a (2 J, -a) 27

w= u

mga x 3 * m e 0 t - q ) x a L2 L

mg a (21 -a) 2k

&r a dbr&+ornfr1f,t*nr:60&i 1W;=

n1?r,i101 rrdr sti6i'l $z mornCr.rdtdnrr v{ q1nn'JrilfrN nrrur ri'ufnru*tnr? z,ufi'rtTqfi lunrrurmuralurrdnr;r"rda{nq u?afioldrlttnap?o{trrlnrcdrlu {lutoitnr.uonr;urodntrriroqliruurrdanfi'un,trnrc{n d'1t' ruucrdarfi'unrrnrv{rrtorun.rulo'tnduiitfinnv{rvu'ir.lur.rfi'unrenrs{or r urt(F) ntrirn.rd sr fi'u urfiunr'rlurruqrd rdofiur"rn.rdnrvrirda{nqufrrrhlfrinqrndaudrfl runfinr;rir crlfrnn v'lr;ra'jtur.rnluntnrv{nd'ld s qrnfigruta.r.:rulfr'ir W

â&#x201A;Ź

Fscos0

(o= o'l .,.r,.........(') l

o -+ s , lfi'ir o.ndtdlfinnv{turirl duflfrnnr{ - F s

.............(z)

(r) - (e) ucnr"i't

trils ut.unrsitntilc

,{ e}

r .' r a fruf,lsin:rdrurrirl F, s fia ir'tunotnritF lurhcnrrir:vfn s

z uro (r) rrlduwnlnoodrodrhr,rrro e

h .

..ve

, <-y-.-..

--rFoIur$rinrfrnrlrhtu?nqnnouvltuuu*fiunnrriu tdaoanuna{tnqvl

tY v

rfroaonund- $fl til rirnhaufi r,ru.h frTffa'rnrrhi{nq A & t.avJ

mnountnailln

na{CIonuf{Fr{il1nn2s$u{1tJ1tn

rigunnr'{nr'rilfiilv{udrcu.ir.rur6.r(nfi'unrrmc{n 7 q'lnug1lJ1lo.l{1u 1s)'ro.r{rrq1frd'.:grJ

e uaant t 6.t{nqi fiatrun!?t

FscosO

.(0= 0")

ndl---l-

F do.rriJuur.rfinrfi uia rfluuxdrodfl qrnnnyl F rSiri{us dtn rh rnxa q;lfr.ir F +F 12 2

(F)

uruo6s

= o +F 2

( F) x s Fs

cln W $1tfrua Xil zuttnll;itfrrutnfiix{ual.tnta

rylnrirul4lnn !

flur4lnn'1Y{

= =

(t) = (z) unnvir

F,S

;

xFxs

Fs 2

..................'..(z) RO

s url (F) rrfduuurlmori'rolrititana rdofiur.rna;rir ria{Ern1fr rndauiirflurfiunrr I nsrur araqur{njdeuuiln.r otiT.rtrjnrirrnrio rdattsunfl?,lr;u.jt ur.lnrvrir(F)frunrrnrv{n(s)nvtfrd'.rgrJ e (n)

&, &r ' &.

gtt a rctfrtutauJdauwlavluntn;via mngrJ g(n) nu'ircirud.rdudline.r.loonlfiut{rrrdoayftgrl s(r) fi111rm

tr.vrufrulald.nn a$ror**fft dunur6n1 rutirrfu#i*riqrfluunulf;rfinurnrrirln mufiur t tv

- - .l mq]nnflil msz6uc;gtlgnna{x1nxu

r?oafl

rdoftntrlhvlra'ro F riu s nrmrnurirrlaooruldo.ndr.tdnmr{tndro

..a{dqau

nuun;r'rdwu

ioni:anrrrlsu ..

u.urn#inulr

urlr---*g-.*

rirdo (power) rfu hirds? $ssnlrnrsinrviT mnn"r'uriria{.nunu,i.orud,finq;ds'r{arrTuurq rTrnjirr'rsuduniulrirdrlr{orrTur.rnrusirftfiGmrudrdaef,arr{umuun;rco-rdlitun.tfinmu6n niu vrudrirlircnrriasrnnc{rc'hnsfirird.rmnn'hri"rfr.rluri'xorudrirlurcnrduann'jr fi srr rirfio 6a dnrr m:rirornut oorndrfiadr'r1r,ru*rri'rnt?a'l riruualfi w f,a .nudrilf, fiuriTarflqa. (J) t fia ,rnrdlilt ntrhnu'fiuri'rsrfluiuT fi (s) P fia rirdr qrnfi tn ut a.rriT d.:ri gutfluntnrrlfi'ir

P=T

(g)

uri?ffiaqrirftfio Jzsu?ar?sn'irwaa ({nd) 'w' nT:nr drfio?raoiorqdrira-o rndond#esdnfl r5?v p' = cy.rn U F: usi w -

fr.rrfup -

E t

(ria v-

l'l9t

ttrn

uil,lsrurl

r. 2.

qrn P Fv arqbi'ir r roda r'Fv rods r frn-rrit (IIP) fliu or'i^6 rirnil.r

nf,o.tru (EnergY) , rnlr;mvroi'rl1 rt"o *a;i{nnfr'r'rT rXa1nril#etn6'wru '- -:.J^,.*"--'rl rin6uuv1nRu6cslnafiurTn lurur rin6sufinqqsnaufi'ultJnir's ngifirnryi'rttfrtmuf,aaglr nuu1u1{rnorur"rnilrs,{r{u nfrootuflnanu-fiorhorodosoo:tuudrioiisiln tufl&ndldriruunnrytNr4rJ,ls?a{tilfi.rsru.ir rld'{nufioqiunro nr1ilil1$1:o1*nrrrirmn yrfriqrura.r{nq4l{nldmnlrunodnqdrirlfr fr.:.nunaiil d rflufru ufi t rn6$f r^r ulv'lfir vrdr.rr grJuuu niu nd.rmunn lrd'lvruinfi r,r6.r.:'r e

uuudirs 1 rioufio rqfrwrunndoltttto urnrfinrnr,r6"s.rrulugrJ 1u{ur?sudq;ril s nfr.r{lucnfunvfid{'lrufrnd fi Rnd,{rnunnfii{nunnaantflu Z rjrsrnvrfi

no 1fid'ru6'nuni

mfr-J.-

firod1nil?'lu'irinrldrird'rrn6audadfind'.r.rruqnrirnnu?oriosrfisfln fiarqr,tr l!

16'lnsl#iqqdd.fro,ndatrd a;irfulrttirnuodroufitFt.*ortrdntrl##rrn" ur.nrrrfo t- i . u v a u g

2nn?run$00!1n1 nu ila!it'l$oarauo0?oq$$

rl,uunhi{nq ,Jrn m rir6'.rrn6at firr.drrsd'ufrca6'nnr5e v d',rpJ c frolnt a

ulyta{{1ucnuxo.{til1nm

i.'---t

..1

I - 4a e enqmnounuunuftnunuu?ntdilnn1u

q'rnnlrnlrmnndoufiluuutfiuon.r 2

u +2 a s

,d a noo,u=v

t'*ru 2

a!+

, r {l ^ r - - ti- - - - v a aFritflunu urtnl.irnmui$ifinnr{{tilrTu nmurirfru

,i1n

>F -

2 -f = m tfr )

's2

uia

1*ut

%s 2 -"' fl n il?mil'rrt drLlfrrilurncsrrirfi'undsvrunnri te*) n{ilu

.Ja

rfro

q. = L^t'

(s)

kg m Fo rtnrorinq firarieurflu fiurirsrflu mts , v fio d'nnri'raa.:{nq fiuricarflut/*?ri? uiu (tg .rr')* EK fio nfr.Hruqnrf ..',

'...,.

t'.

..,

,.."

ti?u rqt ti3o"J ,

"' E* tlnu v lfrd'.rgr.l finniln1? (5) etrillrnriirJunmr',lnlufrrrr{'udto.r

flonri:srnfim

{ruua!ilfirrxr

nt{rou

nr?r_g_

nJ ro nrtiluant amu{u fiuin ixt uqaiffu{n n 6o fi urstilE

n #rqruoarirflurJ?urorarnarfl riirfi 16.rfi snr.rlnuduaqiriu{2auat vdag

onf'|l??ril'tuu

n,ttrmn?1ufrnrT*d:cf iro o1$usvndo{trt ar{

ri,uunti {nnl.r"rn* ,ndatdfrcfldnnri'r u udqfiurl F d.riiturna.rd

s ri,tifid'nnri'rrildsurfluvri'.qr! rr mnxrirluuulrfisrfiun.rnndaidrflurvscmr u

2 u +2as

2. Ve F rv , lilO a = :t0 t' ]

m 2 v

12 :mv

u -+2 (-l) s m !mu" + Fs 2 !o

Fs = L,^"' -l-u' a

uro

R{UU

W=A E l

-E

(6)

(t)

Courieunrrfiuu

nuuosuf,q{Tr

til0

rrh_g__

-nldcou

6o .:rurfiolqrnuer F

fio vrd'r.:runnriro$'nqdufiu (fid'nnti,:u)

(fidnnri.l v) fio nd1:.nunnrira.rdnqilnrs â&#x201A;Ź

r-i

AE nO il n{.11 uqnuyltuafl U lil1o{renn k

nfootrdnri leotential energy) qrntio{ilfi{{'lucnlinu'irinqdnhti'.:rndaudiind'r.r,ru rds.rcrndnrtirrra.r{nq t ano.nfr'uiorqur.rrlr;rnntfionnernd4o s{urrnyi''r.lru1fir:iuri'u rriuntc{6.nh,lfl,rlrrsorfi'a n{rrirlfnnnTndg:luan.:{fin'r raionrrnonrcrr.fiNlnulfiriudu r.rsalunrfifirrrEnrari.:n6'n nu'jrfl'l{rru:6nnurnrirvrulficrnd'?adr.rdndr"rurnonqrltf rfia0.r{nqoonhJ i'r i'nqdoqi .r:rnr;6noonnrrrrnrirnulfr r,unn.:"h{nrqdoqi1ru?os.lflorrfinfir^rfrir"rurfi^{r, {-tu?oaT u0anild.rvludnnru;d'ir nfioorndnri luficiodrnry fintnxd.rtrr ui'nti z rlrsrnyrd'etrfi'u fio rryd.r.rrui'n rihil ri,).}unvyrd{{rufin?i6nutiu r nfioo'rnfindlfiriz.t (Gravitational potentialenergy) _ .t

- arTnur.rhilrir.runznluuilflor{aqnruvd'u no fl8{t{'lu finvruog1u{aqrfi o:ru Inr

.:rufi1dtrn6'nq=

t|t! xnlrnrs{a mgh

12 u?t r undnq{ugtntniuflutcas h

unvrdarJrioa{nq{.:4.rr.nCt rr rndaudnna{il.Inu,jlrfin.rrurdorqrnnril ra S

d.t

euifi{nqfiN?n m'r-r.ro{uufru ,iuu"nff F" undnqduq.ro.nd, I d'rgrJrz ld,jr , "f

tnnna.lnn iln1til1nu mgh

unn.:.lT {nqdaqlqrnrndu h firnrd'rvru r

risn'jr ndr.:rufi'ntilriuritl (E_) drfirirrrirfru mgh'riuro.rri sunr nrlf;dr p Eo

mgh

{ a)

m 6o mnaor{nQuri'rarflukg g 6o noutilrdo.rc"lnur.:tilrirqo.rlnnltdrstilu mus2 rail':utilum h f,o nmuq.:crntiruuilrdT.16.: nrie s?ro.rrrno.rT ndn rltrir rirorfl*g n (J )

lonrimnrrrlw

fluragilfrwru

{'rIlrtllril? Ep

u.r:n rfi,Ynult

. fti{cou

....

, ufir-*$--

mgh urarqndmilsrilrlaln6.r.r'rufi'ntihhrirl ru lhuur.i$rr1

i 6aorudttt*nr:r?rsr'oqornairuuriodr,r6.rhJd.roi*ruriorfnI'iu'i frTe rflusiriiviri.rdr.r6.r lumrfrra{nqnrnA trJn 6'ogtJrg fro$friu wo, (nunrnA,+ B) . ' .

Fx.s

mgh

gr] rs nttitsinq{uaduuuchv

d'.:riud B fir{fr{{rufinfifilrir.:mghuoidrn rilu n'1ur.r drdr{fulunrrfira{nqnrn niil e fia.rlft.ru (.nuntn B -+ A)

\o W" o

Fscos0

wr^

mgh(-r )

-mgh

(0 = t 8 o o )

d.rriuiie fi nd'.r.rrun nriLilrir.r - mgh uil1t 1il91

,. ,iolridrcdudrodofinfioo.rnfinrilrfudrqrfrugrri (h = o) iorqdaqigon.jr:cayu drl 6oiin fiiatrdn til-riru rir.rrfl$u2n 1*1 inqd o{ oirn,ir:re'ud.o# firr#oo.r. : #nril-rfudrorflrau (-) e. eiruud{dio6orflHacl:fi1# rdr,rCrrfirrCtfgr niasiruudotua-rnffi ru qeln.1 frldnfioolrfinritritrirtrfi*nfro.rruddr.ra{rYust'inurioleiautonror6u6olfln rjlilrnrrrnnr{

orurYu rnr uJdsrruila{r dootrdn fif*drl fiirfir.ririqadfrf" A gsnnduh' ud.run{nq{r.fiou rur.r F (ui,rrTumg) {nqtndoudtrtdln u d.rq.rmndu h, ri'.qil' la frarrir{1ulunrrsnlfi,jr W =Fs

l. 6,' n r.

ffiu." Et,

&-_

m â&#x201A;Ź( h2_hl)

*S,

- mghr

gil t4 mtsni{nq{ugten e ltl n

= Ep(s)

fourirsnrrfiau

_ rrurnsilfiiuu_

fildssru

nrl1____tl_

o'rnstnnrtdlduano'iroruatn:n nl dsnrfiHnfiiorr,rf,n rifriusieoldTa ?ror*dtf unioql#g.rrrirfiunfioorndnrilfririrodrr.lda$Iil niaa.ro4nnfiuld.ir rr#ooru#nri IrindradrilT:lmldungrlrinolrrorinqld ''

. .: ,d

8 it]il1tar1uunfliltrnx|tililu6io{

flndlrnt

?|atv

ItJ

E ua3 h na{$r

t,s nr,iludatntriaitlriuâ&#x201A;Źxitnuiniiuamug,t

e nftqlrifnrf6elir (urqt potcnffdcmrEr) r. uralnrr.h rhuualffirdi*urduudrmuudunurndtHrjnrsstud{f,afi'uarriri.r d.r6an.irirundril{Qa r{fr ertiqfiaoonmruiruurfurf,u ilJ ro rJnrs6nfl.tud.rfiurofu rflur;ss s rdsrirftutflr F fi'ur;a;das rrtisunnr{r:u'ix F rTus dtfiftgd 17

N t z nn il unfuuazt sacEat avrr/?.r V' *rnnnr{ncufixr{ufrcu'ir{ F, s la'n

fll to ntdat6dffiaaan

F'cs a

ilto

F = ks

....-.-.-.( to)

t tilurgwdoJ?lunfi": nrnrr r0,fi{i1f,lun$id r rflruurana.rurodl{nartrFrung klururnr ro rfludraricrisn.hirnofizto.1fittt d+rennnr'lRslugrl rz'dt k fif,orir ntuf,n (stope)mmnr,lriio*'lnrnriruqsu k - E *iotnalir k rflu fi'lfiuu trtnr (N/m)

u.a:vrdinult

-nr?r-*J2--

s. mrrilil{lo:uaorcrf,io

f,O i.rl z uuufr'lsti'u rdorhnrJ?lmdoi,:rfiutn(Ttlfi,nrirfiqrQuomrji{f, e.r nrriatrJiiouuusntr f,ornnhtuFlurdafi'ui'lpl I I

_(wtatWl-t, r, gtJ rs nttiastfrauuwul,u

nrngrJ

F +F

F-

ks'r + k s 22 r

t.llt

k :lN1 =k2+k _ z.z nT:daarji{$uuoqntl

f,anrrilrnrJi.rmoiefr'ud"lpJl ?

Il.]n-Fr-F ckg =*"2 p. = F

--m\*" rc nrrdofirjil*uuounnt

qrnril

s +s

tQll

'E ,

/:l t

.J+2

k"cr

1 kr.u

1+ ' k1

1 k,

ionri:rrnr:risu -

sruun;ilfiqqru

. .l.r:n #inu1t

-_q{rou

nrft---:t-

s. rl$1$nr:6oarjil'lffi naoR naann'rgrl 2a ri"ni.rlra m lrfi nriurjnr sArlar udcoonut'tfi'rinqrir'[riA1|?l6

fiulrhmr.n

l.I

$...i I

gtl zo nttdtinqifratruatli,'t

F I xS lonu 1O+F

w a

E p

tuatqln

Eo = *rt

tt.:uu

lz jF s

(l l )

ruo{c1n

a1'v

olqtn't'l

6:Jn1t

Eo = lurn

( r2) ..................

r r rav r z ri.r1i'1fi'Lunrrfifi F rfluaurprroruxfrlt'npr(il?.r rns s rflur;-tr$

ytg{ljlit1,rft9t?

nriTgtoonfion*dnrffiourjn. rflu gn (J)

.l.urr r:'inu1t -

rlt{cau

{tiluasilf;r{ru

iorrirunr:ilgu

nrh-*-t4--

tfiorriiaarlio iinr:rrlfisuurJao'lrJ alJnfioorudnri6ouriuluarJSo(uiaioqi{fiouriuloi; or nsiruuriostrrqn 6a ii ooan ui ouorr,rirsirgosn ir'oorud'ndfiou riuurldor n

Eo = trr

uis

Eo = }tt'

,d" k daeirfiosooarjso s 6a:;ucliou3onoorna{ruurfudilqn H 6orrroluarjioriiaarjtofioHsauo

{lniufnt

12 l'irramriaunnr{rrmnrTrtriufi*Enuss s lf,f,{iJ

a azfrauiiau #J 2| n ril'l ar1u{ufiufn ftmuinti6autlun1nz ngfnrs{;nJnfrootr

(Law of conservationof energr}

rndrGunnfr.rmurilnavhnf,oornns

C^ "^-o

riruunlfi{nqr.tmm nriq'lnlne dlaiiEnn.ndr.h nlvt adtdnrcluuucfu d'lgrJ zzlaflfinefltfur?r.rfruwi1fi'u 6udmrinqnnahup n d.:oqidrnrnlaA rriTriu x u?o

o"J'"

. e 3 , 4' ' - - - - 9tv" unvtrul{rrq e{1lnrnf;u trirfi'u -h-x fincrutS'l

nnnfiilu dunofi fin'J-uricv" nrrfintnxdwulo'rinq

d1nA,B,c1frrra6'rd d I ttfroo"uuasinqE^

. a"J,"

E* A

E= A

E P mgh

.(1)

ir.

ioxrirsnr:rinu-.

r1uufisild{{rl

?J 22 n1?rldaainau?am

rlldsou

Tfinnunnai

u.?rnfriisuls

nrlr___lj_

E" "froor*so.rinq EE

E +E. pk .'r2

mg(h-x) *

-ns + 2gx) mgh - mgx + |* tu' m gh- m gx+m gx mgh

..............(z)

E" d c r,fioo.uro.rinq E=

k l2

-mv 2C

1 m ( u2 +

2 l t= U

mgh

zgh)

..( s)

c1n$Nn'l?(t ) , (z) uns (s) ttu'ir A

::_ ,r l.^ r z_ .-f^-.-r-_t_-

rixtrhrlu fi a inqfirarnrrvlrd.:.:rufinti}fu lnfldrild.l{nu#ndhirri?rnnliosnl rnril6'$1ufrnd1fitsin.r d n {nqfiri.rn6'r.nuqnd *sifind'{muqnd,fin{ud{r'tfr{{nuqotidrnn{unfioyrdl.rrufinrihil.rri"r.ldnnnornrt

B rrirri'u1nA nfr.r.rrufi1n c tnngn"rtrE':fiqn d c {nqilvrft.r"rucnfsdr"lr6o.Jndr$ufinrihir.rric.:firilflu6uti (C rflupdr.r6{)tnsndllrucnfdc firitrirfi'undl.:rui'nfiri:.lti'l.l rrirrTuquri c uilnnafi e nJduuErJrfluild:rmucnrid d1, ei o^,itrfiwrufr'nrlhirricrdln qrnd'lodrln,l?nnadr;dugrar.:lfirfiu,irndwrucnriun;n6'.r'rrufr'nrihiilric{trlvlrnrrJda frulfr uanc1ndtiofi fi"radr{t ocnmrilduuplndl'rTu6n lriu

v rirtuail?l ft1J ' rnleff* rnfiordd..rsdmmtSr s zs rh1#*rJ?.ruacrnn'ruurilnr.rqnri'rhl'' rudr nrlid d'uhimrndouiifrounduaanmffrs d"nnri"l v nutfi lfiualnttrJfiuugrJrolrnrd'.r .l'luylury] .-. 31 C ---t-, -^--J' na+inuqnu' ngga- uqu-+ . r'rdr'nuqnil -+ fi n.lvlufi

dlfrrhifi ur.:tf,saflrunlsuo n td.t.t"tuqnrI n6'lsrufintiEnu{ulunrJ}lqsqn toso fio*riTrTu 7tJ n uf,a:,tnxildaugilndwru

nfi'r---tg-e

t I'

(E, . E ) nnt ndlqunn frlarTu a'lnnqoEr]itilnn'l?1{'tufrc1u#o.rto.r.:rufiuttdqinunn p k ilildrorrrlt,trntarrfdsu3rh$unfioit,rrnn (Eo, Eo)

nfroounffir nrrnrrtdrrngrlrfluoru ugrJdn1 nfioor*erurmuldangrlrsnnfro.rT ft alJrflu nlltultio.:rurfu' r6urr ud.rlri finrrqrg nrnddau3rhaufrwunnvsr 9Jv

ngnr:aqintrrdoor* lfi'jr Jl rra .

tll o tltr utittfi Bnil1 uN.tn?gvt'l .,1

tln{N'lu?et{ytlauu.: Eos Jt-o

erla

iln{,q1u??lJvlanlnuu{ E

u.toltut{ tnuAvrluNlntJvtl j u :.t r, -!. -^--^--.C . nfr.r.rrufi lndilfru - it'luta{$t{tfignm}r : ndtqrurclfilnrlnra

Eo - Wo_" I

rllo

E^ .A

6s nfrclrurcilft"e

: ri "B

f,o udrlluroilfig n

A fiq B f,o nutotttt{t6unfl'lutrll'i1'qmrtndaudcrrn

wo*" I

lntoilna

,.{aon" f,a mia.rfisd1i?sehun:ru?sri?dti'tucuatlrld;nlnluntrh'uu *nt*d g 1firi.rud'nmrao{rg{qnro{ur{rastuuudrrotrndtdflefiulnr*h{il'l{tfifrung n6mu unsthdlx'loGurflnlfli1 #aonaur$lrgmil urrluun6sudtsrirud'nrnrro{sl1u nuno{ffiio{tnnrn{tilrln?ltdu ?on, mu ,,fisunctnnr, fut6gq ' f,ng ui.ot qvarfi'aufrnrntlioit{1tl;':d6o lunrraGursudnnmrir.nuroirri?uon^ o.udri.Tnsuroils.ts.rrl = .rrudriu$R'lrs * nrt*d6rgrilsldtiunmr,lrilsnn1s a'rclfr'ir tiruiurc - uur# o.rnndfi rtr.rtduavrlurioflilrn *"drirlnsn:,tils1tnil .l.rv

uJotu

a t

F I

= fl$dd1u$R'lts

uxd nrsrhu?our{ns"ltl'ltJ

u:lffruu?aurodlfr

nrrnrc{nt?.Fr,,

S= 2

nlrnrc{nlol F,

nrlr----tg-

r tu-ritii'.tw=FS nio r= -i -

p = Igu io p v 't drfl.r {{nrf) P f = l?n'l (iil1fi) v = nmutir lurnr/lurfl)

W = .rru (ga) F = r!t.t (fidu) S = rsusyrr.t(ruerr) E*

vrri'.r.nu

|^r2 Eplrlurial = mBh

ildq't'tiloarf {qa)

(1a) Eplriurir1= ndlqrudntllrirurirt m

= u?o (filnn:"u )

drJi'r P=kS r) Epdorxtju = 2'ks-

*ot

lg = froaili.: (fi16'u/rrun: ) = (rurrr :cug6nfiio?ro ) $ u:.:1uaili.:(f,ld'u) F

uii'nnr: n.rdr or rrdrrt u, riolririu:l rduprvrru = tr * Epr,uuurn Ek * Epnauud.t ,{ < 1

ruouu:ruflugnIrulrio dili.t to(r) = E k(l) * wr * 2 d w \\w \* \p . w

u rlq o t f lu* u:{tduqrlruf, rflu ilo': mg sin o (L) do E* d.rrilu mgtr arji.r

ioilri1rnmritnr

rrurrngild{{u

nl{aau

l.rrn #iault

rfir--tg-

arv

ttuuHnutl

e0 fudu rfiun*iutnqr4 urnroou.orud^,t.rlorfiTtfilunrfficnr;$lr '.r.florrfiu#onryrfl.rurin

z. truuuud.,anfnqr':ns filnnir.r{uqo z uJtlt s{1t.{'luto{!l?{sn

zo wnr d':snltnit o.s wnrfiurfi' s fitanirJudrueioun.lqrndg s. firrdandilr6n 1 4n{mqilen c{uxluno{ $t :6.:lurdurisnrdaudouinqnlilrlffrse;TN 10 H rrr

0.2firrx zo fird'ufisimqlu$u'rruru 4. il.in a fitanir.r...uudur.utirfimr:Jrc8ilf,tornrrlldenulu durdotnqrnrduudr.ruutu.i20 fitd'u tdvrrl to rilfirts.iu1.i'riltfiowrn n' urtdrnrf I' urstdsnr'lu n. uN 20fi?d'u

4 rlrnt 1o c o-dlurruc n rri'rrYu A u,os{.ts'tn A ln e aqirufloln s. {nqurinzo ilcd'uc'rmquududqn B rflurser 3 Htlt qqu'xTufirirlunrron{nqmnn tl e $d"Jt'ilc s r,m;r,ir,is1n esdurdacfiurTuln

s iuTfi zo filnnfuliluufrurndmtuuu"lrvd'ltflutanruru o. uronldnuln40 fi"rd'unryvtrriuu.rn ds oourr.udri.ldlud$riurfi

ionriesnrrfi?,u--

{lunfisilfr{{ru

r.r:n nâ&#x201A;Źfnult

-a3{aotr

ufir--az.--

*n udnn'rh.:rutol tnioonntnl'nri sutilunxnrrlfr'jT

?tto

rfiow=

F IsI

..2

.rTufitfrurirti$aonn .rrufirn6arnn1#oanu'r

(Eff ) rJ:=RvrSnrn nnriu1 I orflri'luunlfr 'rar rn5o.: rjrvfivrGntr

rilunrruonn?1lrt{'rxmn'lunr:rirulour,iSourJnrnJvrd.rmu

j&s

t4:o

EfT

@x' r ooo/o

o.t filniri'u,16ornn =

*x1 o o y; lv

?rto

ianri.unufiau

fiuuffinftrru

qdaou

u..un dinuls

rnh--20-

z' {nqr,nin zo fi':fu aqiuudurrdurqtr; *fiflnJr;svrf,rarnlrrdanrrudrrTu o.sqnqad.raund.rri.r4u 3z riuuu?rcdu firirrqrndoufid'lanmr#lnod,flurrurn.l 'r00uJn?qrutrulunrrqn{nqii

8. len lo fitnnil crouudu,duorir4ru so ornrffuuurr:d'u furJrvdvrf,to{nmilrdsanrurvu.;r{nqriu furdalnirri'u0.2e.llt'r.r'lilnaurr':qor{nqhuu"rrururTudur6a$rl{nqrndaud{ud',lsnlrr.rrfun.rd rflursam.: 10 uJnt

g. l'tt,nuudooonur.:6lfnqil'ro 100filnnil 'luuu"rru'urTufrurda.itlmn.rilfrur6rl.rdd14u 30 mnrrfu uu'lrcd'udnanmlr5rnlf, rYT firJr;Evrf,ta{n.rrrJdflnyrrur:u.hr{nqr{udurde{rflu .61 z uor..,.u ts.:ur.rdrrdainqmdoudn{ilrtdrcavyrl,r 40 urn?

ro. ilqdrdrudtl{rlina,rdrun!. 2 lrJn?6n s runrftrir6n3 uJnrd'a.:ntquirnrnriotriti.rfi.lr;fur1rnrio qrurorudltlun.r{utl.(ncrruuruduroql,rrf, u rooofitanirlqnmrrriwnr)

Coniranrliulr

{1uuosildr{ru -

-nt{aau

u.?:il #inx.lr

nrh---ar-

rr. trrrlrdrudouqnurRriarodrunr q{ut1u 2 !ilerr#.roqjuugruq{ s !iln?o{iu*lnaasClfiritfiunh.: lun,tqlrhe"rnnnor{utrJqurfi rri.rnad |e2|n-'

t z. rdailurqnrvriraiodnqtlr"daudn.*,uurue': lna*xdnrvvirdr.n{'ufrlunrrnrg{rrd'rnnr,l csursrurda{nq r"doudldvno20 rilnr F( N) a I

t t l- - - - ; v l - /l

+Y ' I l

t 20

,S cmt

ts. tdol{$Nr f,r{nqlfirndaudtttuudurcriu nnvlio.rnnF un; rarurrdanfllut unord'rpJ rda{nq rnfioufildvrr.: 20 $n? s{u1 n. .!1ulal$tr F

n. {1uto{tt?.l6gflyr,ruf

n. nurawrdnf

ra. riudufiotnQrrrn 1000fitnnfi.r{umnfruldq{p0 urrrrlunnr to iurfi 6"renm:rdtnod com n. R,l't:.td-:to.f{nqfi s. rnraRm.:flu{u n. .rrud:ludufrrtd r. rird.rmrfru{u !

ibnriunr:riou

{luutwtfi{{ru

qfuu

il.2:ndinult

nrlr-*-:Z-

rs. rnfruudrltn?oraudd,rilrirril'q s itninf *tnrnruiutdrhqrEos6 fitnrilnrl*?1il{t c{u1ur{qnq{qn m{niasauri

16.rnn'rn1ril.rnto fiu {ufrur6ar30ornrfiiuuar;d'uldlnn600 Hnr lur"ror to urfi d"ranerurien.id

tl^F q.rurfirdrrnn'rn1rfi1uuri,:ahtn{prd firmr:Jrc8v#?olnmilrdsnilrm;u.jrrdur6a.rriu.q.r

tz. nrnpJinqaqjuufrulvd'u qnnr;ri,dlanNF fr1{il 3zorRrduuurr;a-uau1fira{B$r F nJdauurJnrntr nrrnr;{nluuucrcd'un-{nn?,{ c{urrirn-.i1unrrfir{nqrndoufilfinTr 40 liln? lur,]nr to iurfi F(N)

'ol--r-\ l,/ |

! \ 30

,sttnl

tg. lunrr& 100$n? mr$qfi nu'itndird.ran?rild.rnrd idlnrnln*orrfidesnnrur5'ldurflu6u$ rdoftrdui'a{unnrld'to iurfi nafi fi'rmrf,fitJtn4s fiInnil mdfirirftwi'r1n

iafirhanmrlsu

r',,.rasild{{il

nl{rau

'.r:n

sSinuh

urlr--33--

30 o{Rrfi! tooofitnnil dulrlnrr.rdurdel 19. rniaqaurfq;daraanrird.rd{noilunrai'urndournauriilcn uuctin-rdlsdnntfunld t s $nrfiurfi firtrifirr$Nfianmu

fisnrrnxfirluuucrdaldu zo u.rnrhurfi o.orfilnnir ri.rd'.rrndoudf,ean.lufc zo.oria.nudrfir.no n'*daudri.lfinnuriu.rd6 wnrnurfi'osrnrru"jrnlaluto iuTfi orin,nfiqvfivrdl'lruqnriwirln unsfin n1lrurildau$ilnlodr{1r

gmfid'nmr5c av qviindwuqnrfw{r1n zr. {nqrrn m finnrurirv finduruqnrir fir{nq6nfiouvd{fil"Jn

22. 6nqZ fiInnfu nnqrnnrnflr{{ 20 $Jn?rzu;nrvrudufindllruqarigirln

nui'ururnhluqnld zo wnr6urfi mdfirfini.rri'nurir zs. rnfiuudrfiil.larooofitnnil.rru{ud.:sd'nrrrFr n lur;svvrr.t20 urttt qwrsr.:drudnr;rirriornfiul

{llluntild{{ru

Conrhsnufiuu

nl{cou

l'rrn rrtfnulr

tfii-:e-

o.+d"lancu#ca z+.ndrqniofisnil?no.zfilnnir trJudunuudrfirird:rrJryRnf,taln'rrurdaAillu unr6urfi oarnnnu'lrqninrdennd{tilt#tnnrvirtr

to runrAurfiszuv;unufurudaud'urd'l rooofilnnir.rrird'rrndouddcsd'flrTr5r zs. rnaudduud.:fil"rn rirlfilofidnnfc zo snrAurfi nralutral 10aulfi s{il'l rFrdlolrn n. o.ufiflun.rrfiudnrT 1.

tt?'iotrllo.lln?g.iflurl

filndnFi rnio.lauollullrhfl R. rird.:ss.r

zo. d'nlrirtadnqudlriir{urflu z nirrortol6r ofl'tnmril'jrfld.lnuqariqvrflufinirmsn-l6u

3 urtlt dnqfindllrufinri z fitonir.tnrnfiqrro nnrlfinnlluulfi{trustdo{nq4mrndu zz.rjdoa{nqr.r"rn Bl fruwirb fih ri"rrnirb rrnsfifidllrufrnfnnn.rqrn

t0m

ieilrir?rorrrirnr-

. . ln+rngild{{il

-. .

{aau

-rl.3:X.f6inulr

ufir--2:.-

S rxnt ud"rcrn{:Iudufius {1, qlurnnfftuvrrma.:frufiu 28.{nqtta t filnni:.rrrno.nd4o

'T'

I 5m

tirum to filnnit t:lritd :lnra{Nufirirtrjgtcul{fiumnru zg.nrl}.rfriufifirirfiqrooofi"rriwurne tri{r rdafnqoqiiir rJnradni'r{udr nilirq;finasnqrnthu

rix{rrq 30.rtili.rz iltfrafrucrl?rd'rdrfirirfiq t00 firdrlwmrnrlird'"rd2iltiliiq zooird'wu.rne t rrn;ftdz e qw'r*s;dnls.lttil?':d'ld il?n 0.5fiInnfur{rrTuiln,e6'tl?ld":d

too &ns200fitfwwnr 10{}1.ltnr z0 rlr. rrudrd':.tlnafiririlqm.ra:J]r nililctoqdufiRt1ilsr.rfiil nrr.rdrd'u rdafitjnradruud.ua{n:INrrrdor.roiofi'uudo{urlnrsutinc${udruda6.:aonl:Jfiorriuanisdcdr{ 40 r1r.qlurnilSrsria;dufinosnuirtr

iF-4oon--_--*

{auriunmris$

{luuo!ilfi{{ru

El{aor'.

,-r:n tâ&#x201A;Źlnult

ufir--:g-

d.rfidr{lrlr;frnf,aoqnlr:J 3 $n? udcrr,daudtilrudut., sz. rJdodnqurez fitnniu nrndurderduq{

fi enmuo,s{nqnvrndouduufrurrulilnad4arrirtr

ouut#udEn0.2nrnr arJ}tftrirfiqtoo ss. fiou{nq1rnr fitnnfu*daudr{rruc{r$tdm.rluuulr.u 0.2qlurdnnfltat{rrqtrusnrsnudil}{fiad fi.rfwwnruovdufirirdu:lrs?vrfrou,:rlfisnnru

t urnr :Jrn3'itdo{nq :+. dr{oainqiltn0.5 fifnnir tinnnluuarJir tas:Jnrsuulolrt:J}taqjdrn'lrinq qlulrirfiqla{nili{ nnnrslludilS{nrJ}lun#ud4n10 {1.t.rloudodnqndu

ufrtrir{san'ilunrFld':N#'l 2 $nr rfilaqiil.ruu'Jtt{utiano{1uuum;du 3s.ilrin t filnnfutnfi"rflrianarn ndr4nlalrdanftXr.lnrJilt;untud4nrirlr i r.=1000fiefu/tilnt) 1uuu":rtd'ud1

Colrrirunr:risu

lruunsildr{u

al{aou

ur:vr dgnulr

nfii-zl---

toofi"rd'wrunr d.rfirirfiq 30 uon.drJu.udruritfiarl?'r o.+fiInnir.ruufrur6aodufi1qrr eo.rJr{aa{nq .r'Nilrl0.8u.r t{rtill'nii4''iT tr nrd'.lg:Jqlu'jrctil?sqvu^

to rilnrhu,fi lrucd zoofirdwu.rnrdradnarrfo 37.,nrnno{ilin 0.s filnnil fur{,uunrJ?ldfirt.fiu rirdfi"rdu ntalunduluc{il?1fi rir tflu4ud:rur ornoriidnn rnvr

n trJti.:a nY'rgrl uderk{oeti{nqrndauds.n 2.s runr finrTurunru 38.{nql"rnz filnnir.r4nrfronsm stiond e c{vrd'nn6'lunvrrr.lfi

37 arnrfiuuu*sd! ss. nrnpl oonrfllzo ficd'uqn{nqrnoe filnniu {ufiu.,6sodo;'r*il qrurilrvfivrGnrlrtaldur6a'ld

q!Be?q1..