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Published by patcharee01k, 2022-01-06 18:35:36

โมเมนตัมและการชน

ว30202

irrYlg

hu3un''lstsuusn

"A.Dffi o,anlsrsuus Iu r u u o-u ' o i rL o t - n nI r-ia n8.t $..t ?

aBrrr un:riiuarulr trufr+.r n1f n1+ iil urji er r rxv fi t fi u a o t n r : to 6 um ? relu6',}]
LLnsLOnfin'lv\n1:tFtd.oi x{Y'llfl
t atTorn tLdvnr:o ilErn fi ?..r alr.: ar:Tnn Iu
r, d11*,'luL^6'Lo i r) rl,',lfl i r l-l fr &lr''un
T;l.i -l'l\: tLl\3 d1"l in ll L'l dl :-l+.1 yYlt ifirij ullB x r ru r : n r or o fi fl ?,l r {.r'r : t o fi , ufi ,', *.r fi q il I { 1r o {

a nL1 Et flll [.] dir ilun :3l-i 1 1\1 ? Io ? r N tE "[udi n r.] : v.t"r Tu o I ru r : n r-ir o : I e-r 5 rd a.:I i el uoYu
U
rur{ o fi n-1rl}r r }.r uff}rtfi e.t'1A0fi!',tu1t1{nn1:idln, 1{ 6l riltnAu?fl-0'3 vtlae ttur rl

Yro6lo{ oiuru tt6rlfl-111'lau lflu1.l9lyl
1l-)l.r rn"v I 'l r-ri r;u . -lLr -1xl-l
1o.3 1'er 0'luHii'rfr6 yY':rulr ufirir fi'.r r q 6 a ff!Io s zu a qr ru: v 14't r \: l.t 1 n o ?'r x uE -: tt o r: t n

;fi outiu lri6oudx{ u6r:rnr:6oo-) rtrn'ir Irre.ru6'x

L.rrn t r n iLL1"fi 11 rf^i 6^6: r rrlutil

o.r [.] nfl nii ouYnrilar rar ufrrtd

qe1 r @Fffi;*e.6;,; 1;,.p.,6ry,.;

.ii{..' ,#'td*rd,i*;;;;,

lF, ,-

:t

,...$-si

.,J;,g-ll'

5fleJot6to6l[9"ddaAaueJ t. lr.rrsJufiN

u+ n r : turYut o': rTrr n q s t fr o tte.: :J v v ut o tt:': n : v vir : v u'i r',t
I
Le.J LxJi.J6t t J tlrt,..l fl
rffu or r er v n n r o.': rir,: fi3 u r ira r u: t il fr fi i r rdu :n er u6'a o'': ffu
5nu56mnfi5a.0',r[eJ

wjq
-Z-nJ
; - ' v?ftilnU nl:5L{An1*6uv0{nn1??\d\:{rlfUioqnrI:aucuryrfia[:jtu::rJto':ur:':lfiEJoyrruulo;rfis.t

n r r r uffu6',:1 ri r il uh"l or r er n ndqn r : o uYn rin #'r.r r u

Trurruud'er (mornenturn) rfllu:Jierr*{nt,,*.on',:rofioufitatTsrnfifiuearir':ffu Ios
q

lerrxu6'a.rriju:l6xrrurrnrrroSe.r^eiruvirrY:JzuUn9er6u:ru'irtrroffl-Lo-rrert5eto':Tnn d,lfiarnr:
---XLtfl 9t.i o?'t N d$.t?\1.{fi of u

F=mi p 6a Ie.uru6'r16':rfiu a.r^r.rurau{lu filnnYx lLrer:sioiu1fr (kg m/s)
ITI 6a :rrnro':Yon firurauflu flIonirL (kg)

6o o:r s.r r5'r? o'rTon fi r,ir.i,; g rflu lrn:ri oiurfr 1m/s;

yvdr.i rrnronau:rifirao:rxu5:qir',rfiu la.rue.ru6'rto*Trrnfrsveir.]ffu

n'r?ern9N9 [.J?f,1rx{'roL?1rnu

rtiuro^a:fft-LTEqr9nfirodaud6roerr-,u,5rrvirrYu ruqifialrota'rTrrnzuroqir':ffu Ir.lrruqYnto,l

nv uoy :u 6I v
rivnnrf1lds2y' ot'tf
r TnN0rno6:t\1soyr]arN&.J?ntrrnu ,- Au (v. v^)
Lrafl!flo?EJo?18.r13?9r'l.3nu
rt1.+

Eg[d.tl[NL[.Jx{F- t}.JAytFt ]'l{nvu flol1,la\:Ldou?vn1.v[n!:nN0tgr06:\[1fladtr4u!n!Tn!?:?1nrfl:JAf-lo?AuuFt?''l3.Jt:?d
q

ru,irffu r'2V = Vt svfiiuluu6'xfiuonqir.,:rYudru
3',

i1 F,

-------|> i,

2 ---+

-+ 3 d.

t hn rn fr 6. rr u#elt o': To n9uqfi a Tn n fi n lr u lTr lun v r r n rir'l riu

iLr rlLra.LrLLa: 5't

N]SUU;

I

A?Aoyo r'r srn ItarEdro-lrardri-:dfirr.rirarfdlrlu farl Iauilsr:qiafi'rla.r': 6o':ujfiuurliruufdltu ua.ror:qiaiurfidvvulfioftfi'

v- 1OO km _ 100 x 103m
h 3,600 s

. 100,000

3,600

_ 1,000
36

, 27.78 nt/s

q1nflNfl'lT P = mv

= (172)(27.7e)

= 4,778 kg m/s

o- {lY+u :flN0[n0:tfl{4oL<n3Lv:JqNdtaer ]rerilaNu 4--,-7-78 nar[dnv:N [3]fl:91r0?^l.{''lydl t9l6.ii01lyivi ,Lllml{Y^isrfix4io

nrOUl\rn--.: 6.2

ryirlo 6.: s ;fi Iu ru usr-ru ryi r fiu:nut:il n Io a: n x o ro oitqdru' er: a t so fi Ta n fe.r
I

'lfivn qrnfi3-rnr: P=mv

= (2,000x60)

= 120,000

= 1.2 x to5 kg m/s

riru:murn':1err5?ro{:nruormoitfidtfi Ins:nqufrIa.rraru6"xlyirn-:.t 1.2 x 105 kg m/s

Ern fiilnt: P=mv

D

m

- 1.2 x 1A5
150

= 800 m/s

o.:rlu :nxorsroitcidfio,lfiq?rs.Jr5? 800 rruo:sioiurfr 6.:syfiIerreru6'xryirff!:nL::rn

52

*: 2. u:rtuaufllillagulq:t!!:llql'iJ

ru€ofi0raGion16

rtjdeluirrJaoTaJueJud'eJ r- u . Ux e,..-cF d1 4 d uOUr?1dFo${LrLqA
.q,, : I -d a

Un 14 0 n UEJ 1'1 X4\] A O
!t $.J N tn fl Yl N o ?'l t:
t N 1.lA O ? 91 6l 3.1

'*d, rja v d ,{ ^n O ,.1 | u
fi \:
? O nqU el V\ n f {'l U q A 0 1 q t E 1 n n I : L! n U 1,[l :l ?\ O \: \:'l 1l

uonalnlilrnu6'uqydurYru;nuoyorre..rr51fla.':Tqrnqu9 fr'r ur:r:dn:vvirsioTqrnfrfizuooianr:

.i,s

t 0.]lilt! rtlln s.r 1.+ d $ uaLa.r t s-.r N Io u tt:r: s v Yirlfr o r r u r5r o.: Tqr n r:-l fi I u tt:.1
c

Li?.to^?\Er?ilr'r?-e]il-3i-.]?-6- r--n mA qfJlnLr:{vdvd'r6n:;ovirdrrijl]tlnl At voirs'lLYlxe:rxud5lto.':Tvnqu:Jfilu
c

ihlqrn d rflu o-,rnrlnrr? 6.2 loru:rq;rr^suu:':fr'll5fin:vvirdoTqrqlfruilu $-n uqirrfioorru

u xFr..i I r:rs v ur.r t-r t.l tt?{ a 1N 6fi n :vvir si o Tqr n #urfl rvi I riu

il>

------+

)",

nrr.rfi 6.2 Tonqannul:':#lrEn:vilrvirlfrol'rurEtr:l6lutriln':

d 6. 2 i o f^i q I: rur s 1 n n fl n r: ro .i .]. o -i o.l t o': fi ; 6'u q ;'[6'j r
uvr {
a''.lnn1?\Yt rfi fi o fr a

xF=md

= m-Av

Ai

n-ri
= lll.._
AI

:F= mv-mu
At

)Fti4lrAd D =II]u flO Ia.r r e.r udh r; a t Tqr nqrti a un n u:{ ff?\ 5 n :v vir

D = lllV 4

OO

O\:1111 rF=rni-Anrrd = Fr-D,

Ar

IlLlrr'llLLa= i53

tl-ISUU r

F,-F,t$.lo u[] ulx r r u6'l rL 0,,: Tqr n fi irj d u u uil n''rtil ar ar r : n rfi r ua *.r n r etd rfl u
^D=

:F 6o lu:.:o'vrf n^rula uilu fi rfru (N)

,U=* Ap 6o'h rarusie"t o,: -io !,: fr lu'Lrl Nfi1-tl8 Ltll-t fl LAntr.J
nfr irl
9

rufl:eioiurfi ftg m/s)

At !.!
6a hln lYl tililfl x+ t! 8ryl.t JEr Hlx" ?1.r'rvr (s)

qrnfiNnr?d:r.l[6'ir "ri:tffi^r6fin:vvirsioTocrlo q svfiFirrvirfir-rffrr:rnr:r:-]fisrule+nt,l6'sr
cq
v
retinn#u"

\,,sil*,*a
s.d l
,lW, , '+
..r,ltr_
-I,:i,i t-'
,{oR
'*'..i

:-"' -r''

nrv!\ 6.3 nt:rqr;1,'lnlon
I

fiqr:rurnrrnrd 6.3 rfio#nr,q'UJInUr9odoonttr{raraniln!0a virt#nnr.,,lqr:-ronrontroufi

6,,1 .i lu,<6AuX
Ft-ll3-rt::10{mcnjqisloL0d11rfrCI0uYr00n L!Ev3.lo?1Nr:-r3-.nfl11T0uorJ?uoiln!n1io0nLr?fn?y14.t

oioaa9nrnlnron

"[un:ninr:oonrr?\:Y!dny']olaaratriYn:Elrl:yor r,,lmloadr:lofiaufixt6?flo?1NrE'l
qJcqJtc

f^llLraila, r\:nv u Hlnrvuuvtdcuilq1q91til:unvfiCIrnrrfiBonnT,'lst!ant#uao'fi.,Y:#uq;lnrlir ilt:oontL:{;L

n{qnCrJ,q"UlqUrrooluuoiavnrY{ssoCInrL:{tilrvirrYu anilsrronfiroa^oufitr6'lgo?r}rr5?0'':frin:Er

rJtsnqJqqiqvfro.,:oorru?{;!s.Jriln2'rnn}^,laLoddrndouviurfr:sn:rrurErrios 6',,:rffu Lr:{111

nr3?11no1v4a, il9ilqzcufleronrttilfisu' ur.Jo',rTaJrNt,lffil?or;fl61 u:\:fi8..1'tnqsvirlfr'Tnnlfionr:
Lr,i;frsuutr.l,n,,:ile.rrxu6u'r'[i6v15d:n irru5do1o#er)rnr"t[unr: u.]fiuuuril n,tTa-rrrrufr+lrior n irfiuuo',:

)..:/

54

nl:adrrrfi s.s

:nduufi':firu?a 1 .s 6'q rer6a.:au6'ro'::flqc6o.rtfiu:.:ru6'nfidurvirlo rfi41fi:oa',u'rro,"drr*d.ln

fi Auc' tJ t:x 72 fita rNe:oi ofi'rtr.rt lurr ar 10 iurfi
rlo1.h1o1sa'r'r

i6rir crnlsrdq:re.rtE.:fiuu:^o il fieirriluesufi

elme.rr5'1ilnrEr ., _ 72 km -_ Z?l_10tf!

h 3600s

= 20 m/s

rfi a r :r r o':'r :a.r uE r.l a r fl il6 o S ar rut :n rir ur ruu r tl:.:16

q1nfiNn1: :F-AP

At

_ m(v-u)

At

_ m(v-0)

At

- oq:r4c!:q
10

= 3,000 N

d- 'rYrl'u A Eruerdqv69/o { a a n u:': "' f;rXvlu 3, 000 urstu

uer5 o.: zu d'n

oi':atir,rfi o.+

a{ nuaaa{nfid{N?a 2 filanfir rqr6oufifirsoo:r16ro16'r g tilsr:siaiurfi'[uuurtvo-tt rrfrr,oa'oud
y6'':srntulrfirafluoafl:reaunfi'ulutrurnr:rnfiau' fruAo^r.rou:Elo- otrt:dtttl.'rueN
tJsuriruu.:1r*ur*rdo
t

iirir rirviuolfrfierr^qi9,:r{ryrrirulu':fieiruilu:.i:n un;fisil.:oanqrnriruil.:fieirtfllunl

u=Bm/s

v=-8m/s

* n'',r r' 6.+

qlnfiNn'r: Ap = trtv-lrIU

= (2X-8) - (2X8)

-- -32 kg m/s

o$u1{ le.rrruuffa.rrdr:Jfifluuiln,itiltvirffr.l32 fiInnir u:-ro:qioiurfi "turieiry.:oararnrirutl'r':
c

iIuLr.luoilLLa. 55

n-lslJll I

crfoErlJn_-.i 6.5

a!gfluonru?a o.s fitaniar onrovo-oriruil':d:aJn:rr5rdu zo u.rsr:siaiurfi loafia'ir:ru'ir':rr.:

Y;.iiirun,onYouuad?rl^anuaa [Na9au Jrau?'ra{t'11.[ fia{slnuuafluonfltuoouooflN101u80T'lt:lrl1,ttqN q{fi'l
{ t

lruruuoe.rfir:-ldaul:Jtorasns{iloa uaiu:{firiruil.:n:s?irfi'uanraafirirrvirto fimi':.:r'rardanran

n:rmuriruywliiu o.t iurfi

a nlilfr 6.5

i6rir rirvruol#fiFihi.:i{rurriruvrtfipirrilurrn uinyfieiltoansrnriruuil,,:fi€irriJunr
99
fi sr:6mIer ur8.J u6'a.r 6 u fi

P-, =mu

= (0.5x20)
= 10 kg mZs fifieili'trfirurriruvlr

fi qr:rurTer terufi'ert a': nt n:r a am oun:sgr ouo on ertqtnrit uuvr.:

P2=mv

= (0.5x-20)

.10 kg mls fifiei{.:oonqrnrirttvttt

s la-r usr-i-xiv,r-iul a^ €i u'[:J vr r1fi s r n

Lr

Ap = pr-p,

= (-10) - (10)

.20 kg m/s

f," :; :rr[T{ n r L[1^{.i n yir si o n n :..: o n y ru[6q r n a e.r n r
2p=4P

At

_ -20
0.'l

= _200 N
6'rrfu ruroro.:1nrruufi'e.rfinLdaul:.lfreir zo fiIanil re.ro:sia?urfi u^r,,rodri',un,:n:yvirqia

ou$n9r a a rvir fftl 200 fi ': 6'u tufi prr r{fi 6'un n :i o n'[fr rnleo o nsr n rir uril,i

56

3. nrtaauavut{aa

r u Lil 1+!: il r !; !v v :li il 1 ru .i u 6l tt ' u
Ls.t tsl uqt N il{yr tn
EJ ? 1J 0 \: n 0

ru:r vr fftt'r u riJudu 6': fr o[6ir riiuljirr rufi eir dru oi o nr:

o ^fitjLj l'r I tLn r n r o n r : tt+n l r to d a uvt t o'r irr n i: r ar ar r t n rir ur ru
q

r.rrTe.ua.ru6'e.rn:rflu:.:e,':d'tfiqrnTa-rra.ru6'e.rfiu-Jdautr-lqior':nrfi"[fi airunrefiu:.:ff'lrio.,r6":nr:-rr:n

rrl6qrnnr:oa

ru:{oa (impulsive force) 6o u:',:ffir6fin:svirqiaYsrnlutir,rr:ar#u1 ararr:ntfir.lu
9

arunr:16rflu

sLtE-A}t-AA[ p mv_mu

i)nlioa (impulse; 6a e.idon.lto{rL:':oorYrtrnrlutir,:#u.1 ttn;urirrYrlxuxu6'a.rfi

rd! ,1.{:J'a: N o:rviauo t?lqr1 4 v
\: [o u'] n
L! !t,f, , u , tt:\: oFr o \: d il nr?

r:J n er uru:l n
1 rut? n tn

i = >Fnt

i=rF

T = mi-md

v

6"sfiu ar er r:n rr^ u ua il nr:nr:o nt6 rfl u

l=tTlv-mu 6o nr:on fir4r-i:Errilu fiInnYaJ ue.rn:eloiurfr (kg mrsr riio

x{'roxt lx{]11 (Ns)

6o errnro':Tnn fiyururflu filnnYr lkgt
6 o qnr n rErrlora el^rr.irs uilu urm:riaiurfi 1m/s;
6o qrrurS'r6u fivdrrrflu rrn:rioiurfr 1m/s;

1. fl1:oaldatqrntt:{Fr{eT? la.rre-ru6'erro..:Tqnq nsvrilfiuutilfraarfioTorn#u1fiYr

tt:'3CudoIV?v\vfdiq'lnnlUU0nillnTJil1 nlLL:\:O{nn''llOfO? qrnA?1NflN?\1-{ii;11?'l{n'l:9lAnUttT{OA

il t?,i\:t?a1tlu.: arerr:nvtrIa.rua.ru6'a.rfir:-ln^tutr-Jrfio':qrnrt:tfr'uIrd ul:,,ro.:ffrfit':nrlo 1 n:;ri't

vl

n :ff:-L Tsr qq virl#Tn n rrJ n^ s ul u r e.r u6'rr 6,,: u 116 q r n fi ufi 16 n : r v,l rY.: a r n t

sf;- Ad
At

Iutuuriuua: I 57

NISUU !

lt?o nfr = >Flt

qr n fi ilan: rtfl o{o ?r er fi'e.r vVu5:;u'ir,,: fl r?o CI rr?{o d LLay L?dr r:'r fi 'r Nrrn?rrnr:o a

yl

srnfiufilfin:ryl:rujrtu:tfinryvi'r ru r:n'rle, 1 16

z. nlrr^rrlrr:srnu:.r'[ilqrr:6": lunr:riru'rruurn',rr^,dro^.nu:,r1a-in.':6"rsy6o.':

virLrXu:..rfr'Lrin':d'rriunarsriiurrr.:n',:fi'r rfiovirt#ara-n:nvneirzo.,:nr:ea1fi.irEifiu

tik ti tr
It ------>l
^r -----+
(n)
(1)

ntrfi 8.6 n:ril:yuir,: ul:..rfi n:yvirrioTon

,',nn',*d 0.6 (n) syyreirnr:o,n16frr,iorfiovirlfru:',roafieiro.:ffrfi':unr:yleiriaalEr

?o\ru:{oa Fdo*',ulrnrfisun:rr^.]1rri1fi6".:nrltfi o.o (l)Iotfi'ufi16n:rl,,harnrnfi o.o (n)

runy (fl) q;fiturorvirffu srn#u6':vnnr:onsrnfi'ufi"[6n:r1,,]rtiurfis:ffinr?firn'l:on,dr,,ror^

u d0nA?4fifi1-d1{d'lNlrn14'lnlToflfi:aa?\XurL*9tun3tl,i?0, {L?l0n1:il.{}{suYo:uyn1:01.i?1tn:n ro
o,ta? [oEJn1fi]to

"l#tir,.:rrar at fieirriaurfiu.,:wodsvvr'rhlu:.':orn F turrw#uq.,rer-'r aralrril?l12ar?NrLo{

Fot lv "[uti:.:t:nr At IoflqyfieirryirffllTuraru6'ufrr:]6suur:-Jn':h.llutir..:i-:or#u

frtruvsir,,:1

:6',: u ae.rtfi 6'.,r d N n r

i=nF

= dr-i,

= :Fnt

i = ljf>-nat

58

firfirir,':a'vrSfitilrfluet9u9fie.nn:rvirffrlTna s;yirtfrlxlxurr:rlo':TnqurJfruuuu:-ln.:1:l
rforiolsuue-ruoril"lta{inilLild,.Jturr:-lo,t atzunqvtlrturoto{tm\:yl,3l l''lntvrln" Eastila,f^lul tt!a{Lr LJ\4ot?wrJ

q

riourloio€l

I
h

,.{

rnr:r.loag

i 0.-7 fvirrJtat iaaVhl irlq#eono..:e..nq'rnfifl',rlqutdila{fifi$ftnn{:-11-tfiotxir ttny
qJ
E'rnn1y'r?r

4 , A qu X uu qrn:ydu:-Lq-lrxa{t4durfiu qv1',1!'il \rifionn.3!ufiu[fiqvrrnn
6nv'lo.':r.rfr,:"tfionn':lurlu"Lfi

nai:utdfisrn a{Lur^,la'r rlr ss'[ri uror udo{'i1ur''lfi n:vvir ffrl[rids,n n'::-tufi'uteiqv fieir s] I n ni't

ru:',r id n : ; vir rYlhi fi m n n.: I ur',i o.: #r
i^ fiL :r a il q I : il.tl n r : r :-l a^ a uT }.'l L N u 9)-N [r] fr '.: a o': r"l o.r s v

ffufU 1 .1 rrri ti':,,: rr or filfflun I : lrl 6 u uru.l o.: ir ffn nr:n o tt:{ n:r ltr ndr

LN 'lrl1#1un r : o a il rt 1,1 :.: 6': r\-':
rN lier N 11 1r r er t?r
:naud iocrl#lfi i'r nr"lun::
ffu olri r a.r u6'a.r s v qi r.,: tl ,: , i
n oi r r 6 u': a r filfilun r: rr.l d I u rr:-l a':
n EJutt:l 6r \: t$.J rN 1la 3-l 3- I n
It I uilI e.r r a-r usr'el o':'[ri fi o n n rr virlfr u:.r o n fi
#t io.s q s e.r r n n rirlvY ur:,: n: v u ir n fi o I ri o s

l orfitfidrI v u rd u I U4:dArvJttl{OnNO rUA€l l1"l0
d o u:.: n:v tt?r nlut ru:d rfin
o r uo EJ tlr E { La.r rtn fl t gi o n:vyr rl 1^,1 o.:
luvrr.s n a rYur: ori6ruor

t I rlun t {Ir rr] cll cr u i u rJ n cr t e-t uqTe-r o.:1ri fi n n o',: udutai s v 1io u n'i

oqe tt:\: O n dI N u 14 tt9lfl AX
11'l 114
Nql 1n tflq\: ta'lOn:rr:-ll'lUtei

fuLludi.lLLa. i 59

D'ISUU I

_ .dffi& _..!

mg:_a_E*!y_Lq9_

gU iar fiertdruuNsurn6oufi

trlluuur:sounr a'[un ar 0.0 1 iurfi q{fi 'r fl 'r:o a uave:r rJ rErr o.: qn n a $r^l

i6vir riruuol#fi ervrr'rr?r fi o fi eir rijur.L: n uarfi err{#r u fi o fi eir rijunr

piru:ruvlnr:ontfi srnasrnr: = (:F)Ar

= (5X0.01)
:0.05Ns

r:rir u: ql
rxy re1l al r5r r a': n n n o dr,{lfr n fi a.r n

q,

I=Ap

I = mv-mu

0.05 = O.2v - (0.2X0)

., _ 0.05

0.2

v = 0.25 m/s

6'rfiu a{ nnodv'lsvfinr:oarvirffi 0.05 fir6'u iurfi uravfio,lrrr5r 0.25 re.rqr:sioiurfi tufiemr'l

4

fl?1NA

6l3aU'l\rn-! 6.7

anlaaru?a o.+ fiInnfel ,"d.r*r'dromrrurEr 35 r&rq:eiaiurfi luuu::;orr#rrrrirr,*o ,u',

n:smuriruli.:ufi:anuaadcfiaunff:raanrurtuuur:s6'ud'lErfl'rsuEr z5 rusr:sioiurfi stfirnr:ola
U

Ydlolu;{n?3il1aonqnuoa -a'l

I
I

)

riruuolfifipiili{oonsrnr;ruv,r.:fipiruilurrn un;fr-er,!.:u{rrirul,'r'rfiri'ruilunr

E1nflNil't: I = mv-mu

= (0.4x25) - (0.4X-35)

(0 4)[25 - (-35)]

e{l,[u nrrflnrdu:.:n:;yir.rionnU9ronryirfi]v] = (0 4)(60)

I = 24 kg m/s

Z, + fairlonfa] uern:qiaoiuldfi f4i^%fl1,r,:oonsrnnrul {

60

_-!

cl3Au',tun 6.8

0rfludrsu:r 80 fir6'u frranflu*r^rura 0.02 filanie.r uasrfla^auyr'd:somsrrS: so rxsr:siaiurfi

iil^rnorglunvu a, i .

R$sflTJ fr ntc?ir
u6r{rur u
nrro n ua r ra ar ei o a nfl

i6vir rirvruol#fiefihiroonsrnn:rronflufirirrflur:n unyfreyi{rfirn:;ronflufieirriJunr
lq

reiru-:n+rrnr:ootfi sr n as.r nl: = (:F)At

=Ap

= II]V - lIlU

= (0 02x50) - (0.02x0)
I = 1.0 kg m/s

qitu:rxrr r-:nr'16 srn ailn'r:- r = (>F)Ar

1.0 = (80) Ar

Ar=a
80

At = 9.9.125 t
6'.:riu na9nfluErfinr:on t fiInnYe-r rilrsr:eioiurfi tufiehiroonsrnn:r:.Jonflu rLnyrxflrfiui{n:ryi-r

siannfl urvirffu 0.01 25 iurfi
U

n3A8'l\rn-..: 6.9

turirjrqsans9il$a9uanru?a o.z fiInnYru rirlfianv{ouaaro6oufidru6'q:r#r zs rruo:sioiurfi rflrsu
p,[email protected]:1uuur6Y'.:qrn ud- aasfiounfi':.raans{l"6[ilul.ra1a6ildau6'n:r#:d zs rero:dr oiurfi frranylsruoa

n:vvrurlrruri,ouru 0.03 iurfi q.:nrnr:ea9o'iany{ouoa

Uq

i6dr rir lruel#fr eiliq9r rfi r nr r..lr zu #.: uiluyrn urn rfi euir a o n qrn rlr zu #t rflun u

E-rndNnl: I = (>F)Ar

=Ap

= Illv - lIlU

= (0 7)(-25) - (0 7)(25)

= -17.5 - 17.5

I = -35 kg ni/s

e,$fiu nl:e,nrlo\:nnylm:J0rlrvirff:.l 3s fiInnYr re.ln:qioiurfi fifierhi':oonqrnz]rzu#'r
{q9

IlLuunuLLa. X6l

N1SUU 1

nbodrud o.to .--"--J.#saf,GmFi{{tr

or.lrnrdanrmufiarurn 60 niru firirfi'.:aosrfirnrmrirtfirvrufialuuur:sd'ufrraol,lt5? 20 tilell

sioiurfi t#acfrauna'uhjtuuuarfirufirsnms.rr5'r +0 ruo:sioiurfi turia':ura1 0.002 iurfi s'0fir

a nrufi 6.9

i6rir rirrluo"l#fieuflryrurirlfiuvrufiafiri-rriluurn unvfisui',:oonsrn.lrfirtfiuvrufiafirirtiJunl

qlnfillnt: Ap
XF

At

SE mv - mll

At

- =SE

LI
(0.06x-40) (0.06)(20) _.1.800 N

0.002

9{ tvtrn:-l 1,800 fr:6'u fi fi Pirli.:oonqrnurirteirrufra

d':fiu ut:.:ootadulo':anuruua

ioqfruvrfi'rnnrt:tn:srir fin:rr{uao.:narrufi'uviu$fi'ut:ar o-':nrufi 6.10 q{fi1nl:qauau$:\:od

s nrvrfi 6.to

i6rir nr:oarr\fiqrnfiNn1: r = (>F)At

I X Aa-

= ?\}I'Yl [on:lY]

t = 1 = 450 kg rnrs

;(3)(3oo)

Iriru:ruvr uu:.1ofl Etfl dNnl: = (>F)Ar

vo=!
At

#1>F = = rsoN

o-.:rfu nr:onuvirffu 450 filnnYe.r lro:sioiurfi trarur:':onivirrYu 1 50 fir6'u

AA __4,mflu

fl16lAaOL[Yt?JOOA6?O

rraun156uL06l 1.{onqln 5- v ) u 0{nvLlJ:rNa '1rl.[04u 6] y-
L)Lnvur\22zoofluou10[5 LNra.JuFrilqsLnu?1 Ltn?

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q

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9qqjd

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qJ ',:

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lr9cJ

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i

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q

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9dq

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?18.lFl'l18.JtT?Fl1l '1
n:J

Tornea2r2r9ncrn fifi..'.ru15:6urilu d ieslrifinr?ila.rr,l vir"[#o-:rxrEru#,:nr:turLo':TonvY.:ao':

12q fi rfi o du:v u'i r': Trr n vY'.r a o':

fXrofro'rirrdiJ, urr:{n'rquluiyrr u ':

6'.:riu Ie.rlruufrir:':er?o{:rL!qv6a,,rfiniro.,:6'r

utq1 n nfdl9n 1:o vdf xdI ndlttl" =:d-
'vfli"ru
n :9 t8.J te.J 1t9l N

m 1IdI-+m^22ti^=m-'1i-'1+m^2i^2

m 1r1i -mi11 = In2V2 -md22

m,(d,-V,) = mr(ir-ilr) (1)

ur d o',: q r n uiJ un l r t% u:J :J fi o fi si lnr fi''':': r us n fi fl o { ; v :J :J 6.0 fi ei r n''r 6":

qlnnfln1?0%vd:dn:9?\d{{1ilEAU ,Uon.uru = tEor^_,ou

Z1n211,u2r 1*2T1m2ru, = Znlrvr *,n1ru,

m1.(u2r - u21). = mz\Y22- 2.

u2)

m,(u, - v,)(u, + v,) = mr(vr- ur)(vr+ ur) (2)
(3)
draernr: (2)/(1) e;td d, + i, = d, + i,

6''.:#u nr:ruLL!:-lfiofid9udru, onElnqrlfinnnr:au:hr$le-rrrun-rt6urfir a'.:are-rr:nlfimarnr:

(3) arndruru ti:u1unr:rirurru166n6':u lqtraslnr: (3) ufiJuae.rnr:filfiurvrums]nr?n6nrr

uv d v dAqlt ar I Y. a o r : rir ur r*16

o ur n 1*?\ n { f I uq a r : n o o rYuqr wtun

9{AidladtnlAoqlnnl:t1lLLULJElOfi U1l O 0
q

ffi In' ,noutu In'

= .-

llil\l:xl1

ffi

ffXi Eki n,r"n=n:E kufft:ru

,a nrnfi 6. t z nnfi rlrl rru6'u uilunr:ruriuuu:rlfisrv ri u
,99C
d dt v
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6i4

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rm,rnruuanrrn:;vi'r lerirufi'e-rro'r:;:-L:Jsvfio'to.':fr:taara rtoarqnail':'[fi'ir "n''l:rilLL:J:J

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da Vl 14 I4
il n?t tnoql n n 1:t11tL1l1-l t&.luo11ut{ o 0
q

>rnnou:rl.{=)D' -l4f,{uu

>Ekriaur,+uXE kvfi'ttu
t;tli

:. n11^1fi 6.13,{dn:ir6rnour^nrrrrdu t[]unt:tuiiuttl:-t

iir ! Ir1 ili fl er sl ufr il n-.:,:'r u s o a,t : ; fi Ei I I ri n.: frr

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rruutrifioueiqugaeirr:aruu:ni rflunr:tudlrn,0.:ruaofito.::v:-r:-rssCIoo\:Ld[.Jo q^rrtririlu[:-]nta.t

yt

n""dnJn"'"r*':qa'""u- Ynr$lrfr'trruqnri Iosnrsvro':nr:tu' TornvqY.tao.:svGeffulil uuarrofiaufiriluTsrn
e

to=t'lri-u luolls't:6Hr:u!1Jr Le.tNtt:'tnluuoniltn?gyn tilt8.t119lN1o{l;lj]-JEYo\:91? LtflStlnl?}..]

vl nvdrr:truq nUn OUnl:t1,{E33l1n ldv O

n-11zu fl:?N?\n{{'11-{q d11U f,$n1?11.[tflN

r..J dr,Jr^n oq r n n 1:t1iu1J lr[il 6 ou d u
q

rd4

0EJ't{d3..lu:61.[ oo
qJ

:6I noutl-t =:d' -fin{tu

:Ekriau:>nu:E.kufr'ttu

.* n.*d 6. 1 4 :n sru6'turYuurfi a6o n-ut:l uiiunr:turiuurl :.t

LNBot,tu91$.rou'r,xfl ell:rudarufi.:,:ruqofilo.::vlufi riltrio.:o-r

ailyflvlnt.:-'tuqn1.[1r1Afiruuaas i4L:rJqrnnr?tu rtx{ nr:tnotfdlu{ fi4:atnaon?rNv:ou fi'l}.11:tl

rirurrxlfiqln zunqirt:yy-it.':lln-t':'tuqnririoutuff!vlo':.:rusorivrfi'.,rtu 6'.:aunr:

sLLt,r - s=-ttr"n, uutt^-ttur-t ''14d'1"Iu

"m[xL6tu

iIuLuun.-uLra. 65
N]SUU i

NONSSU . nITAOnTIYI LloYd0n?l3..1fi i.l'lB

n 1 s u u nlu u o u f,lo nlu lr u f, I A u n s\, fl0lJn

iaoo:Jnrni 5. urriurrfrnar.lS.: 6ointrrsraorS

t. :r'rlai b_ :nyl9rnOr! 2 Fl'U . erarxauleb.l5
7. Hilattil0{ st?ilg'r,o1tt
2. ou1.{t}ru o 0g?l1,{
3. rrnln:ror:g A-
4. n:ror:csrr5!au r l01lO01l
8. t9l:0 \: tFll 3fi m ry1ilt? n'l

ffiisil6ra
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ll,68t:,

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cFl

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lhu6 o a r r r : n u t^ EJ ulu: o,rh r ar u6'a.r16 6',,r {1
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ut

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CJ

noryo-.,:u{ ura{ eyrtdluirt6nflu4,oanu:..:fi3arvirl#o nqtvv:-Lonflu4frio.',:aonu:..t:-Jfrrafaraitr't:Jvvl rrr ':6rue

\:H a uo d9eUyyn u I : 6u ru ro rm\: n r u uo n n:;vit ri o :: 1 ' fr 6 on 4r ; n :r :-l o dl u#u r o.:
!!n
n1ri16 fi 16'': nfl uttn nfl

nr:ruai':ulrqjrilunr:tuurr'[riCoueju riu6o vrfi'.:':rutilaqrfier[rJuuoiorsrfionr:lild€ru

:urclqyjrffr'.rrub]riJulnrffr..:'rurfis',:vrtol',rnt',:ruoerarSou 6'rfizunvirl#Tnnrfionrtrrlduu:rlir,,:

nD n 1 s o t{ 5n rilu r u u n-u nju nr s E rr-U u

n''-dn'''-n-,ir- :ou:nvdf:e--r' rueruoixalarr:noBLlunr:fi',:flu'|fi lsrEjriouO'ilutuu6'alta.:fluttnuo{n

n:-risa{9usflluryi'rriLFiufl zrw0.:onnryauflu^rrodouviaonsrn6i'rnfio,rflu lelueluo-alta':0nn:uqtt
6d .:fdrAyr=eraonsrnairn6o.d:t,lu d- '{rYiu svr-4ritlu64 .:uo)fiaufAirflurvrrri0':fr-:sr.rurola.ru*.ru6'e.rtvirfliluror

Iru ra..ru6'a.rs o.t on n:r aufl u
{9

fiuLluoTuLLa= 69
N1SUU i

nrasl0n-.! 6.12

:nsud'aorduri.:rfrrrun-uuuuer:t 1 Ioa6'ufiuorfiru:a t,zoo fitanie.r airu:nau6'6'ufirirriuruaa
1,0oo fiIaniru d':r.ndrsnarrur5ruvirri'ufi'rfirirrvirnr.r zs rcrsr:oiaiurfi f,r:n#.raatruufirdqri'u

r\-\-,

mz = 1,ooo kg

nrr,.rfi o. t B

i6tirad. tfaroT- srn?r, i'.:ao':tfionr:tufiu'[ri'jrsvn:nilofrn]er arrr:nl#n6nr:ouYndlarraru6'e.rt6

Xp = 2o.

'l 'f

,nr'o*aoor*,rfir6on-utrj dra.r'r;nlr'rFr?rau5:il#rsrnruror:nruo5vY,:aa,:tfiqrnfi3rnr:

tl - ffirVri + ffizvzi

m +m

aarnr:o-tnoir;riJuaarnr:r':nrqo{ qvrffuil:n#.:ao,:riourusyfifiemr{fl:,ifiu{1er IoEi

rirfi uot#fi synf or N un u x'[:Jrrr: r:.r rilu * hJvn,:fir us rfl] -

r'lfi :tuffurn r r ar rE : tl a-': s I n
o,,r : n #.: a o.: r E -l n fi N n.)

\'/f -_ m1v.1+1 m(-v.2)1'
mr + %

_ m,v + mr(_v)

m1+m2

m1v - m2v
ffit*ffi,

(m, - mr)v
ffi', * fl,

(1,200 - 1 ,000)(25)

1,200 + 1,000

200 x 25

2,200

vt- = 2.27 mls z.zt rilrn:sioiurfr fifiet:hr,:s:r
d-Y'ttru o:rrr5a.lra.::nfr?'tao'rrff:qrnruufirfioffu'hjritily

144a:4ovrq[ou?n]JN?a m1

70

nf,Og1\rn-.! 5.13

a{ nuaall?a z filaniu rodoufifirsox'rilr5? e rsJer:siaiurfi rfirsunsn::aaura 4 fitani* 6.:i.r

axuyll$lllfr?ser?1Nr5? t o rruo:sioiurfi tuururrirusurinartilra :J:rng'jrnnuoavts':aa':6orTu1:J

-u| =8m/s u, = 10 m/\
2

(n) ria-utu

,e n]flfi 6.19

n qf il10?1N[:a?Z?af aflilaail{da,i
$

A?dflmo 1 o O e^ d d r <' ttn;?a1q?1't\v]frIu4Nadilot 'lt:dltunL
n'lu1.{o[']1?1qfll{1Jl1N0e.to'lt:l1.{:.iIn

q r nfiN n1:nfln r:au;ndTer rNueT?-.r

=Xn-)Pri"uru
a fiil,1tu

ffi1u1 * ffiru, = ffitV., + m2Yz

ffi',u', * ffiru, = (m, + mr)v

(z)(8) + (4X-10) = (2+4)v

16-40 = 6v

-24 =6v

v = -4 m/s

o-Y{r1{1.[ a n' + raror:sioiurfi lufisirGa.rlofnnLOds]?n fiInnix

e?'r?]r:??la\:UflnALonfr\:aa'':uvirffi

rl q\:fi 'tv{a-{r:rusa{dr'ral:Jtunr:zu

'loYl'l ErnflNnl: AE*=Uu,-U*,

rr E, tfiarn u*, = **,"1 *l^r"i

uo,= tr(2)(8)2+ telrof

Ek = 2641

,. -E, = *e+\()2
"or'lfisrn
lz
uJau6o
E, = 48J
Nf

AE. = 264 - 48
k

AE. = 216 J
k

o-Y.tuu ln-rntrruqatAufrillfltillunr:rurvirffu z1 o sn

IuLuunuLLa. i 7l

ntsut.t i

nfaEr,l0n-.! 5.14

ion A xra 4 fiIaniru roajoufifraso?1eJrE? e u.ro:sioiurfi rfirsuion B ru:n z fiIaniru fiod
9q$

fi':uudufi u frr riiunr:tuuru 6om tqiuUae.ru:ni

a nrflll! 6.20

q{fi l'irio n R ro 6 oufi dr c n1r u rE: ryirlon ff r nr:sqrYu
q

1Adfivo l't o qva d 4 I dr a V d d t dl
nt14x{o tl4vrsyt'tf fl?'tN0ilo'tt:J1.+:t?n
ttnvrflrt\:6r'tu3-.l0No'tt!1,{n:..1

qrnn4nl:ouYn:$Ia-rra-ruo''a.r lnAuA + rrrrun = mAvA + mBvB

-o(ro - vo) = mu(vu - uu) (1)
(2)
arnnflnr:ouYn:ifla-':.:'rusoli l*,r'^ * |rur'u : **^"', * ]*uui (3)
1z -uo2), 1z
= - 2,
7m+(ue ZlnB(vB uB)

mo(uo - vo)(uo + vo) = *o(u" - ur)(vu + uu)

U"'1fi1Jn1(52'\ : Ur*Vo = Ug*ug
(1)

rilurcuur vu [fratn uo * ,o = r.lu + v.

2+vo = Q+vg

vu = vo+2

E1nilffnnr:ra\:nr:t1.{ zun:rarfarrnum-rriouturvirrTrzua:ra.rlertarufrerun-.:tu

lnAur\ + ffigue = ffil.ve * ilgvg

4(2)+0=4vo+2vu

4v,r+2(vo+2)=8

4vo+4 +2vo = B
6vo=4

vr = 0'67 m/s

o-Y-t,tiu ua':nr:tu;on A ! .lu, 4 0.67 re.rsl:sioiutfr
rqfioufitilvr'r.l?r?1fi0fi?rlo?'rs.rt5?

I q{fi 'r'i1;oa B rn6aufi 6?sn:rer 16r rvirlou6'.:nr:suri'u
I

eadoorir ErnfiNnl: (.-3. ) v'tvor?1 vt-sA= v. + 2

=0.67+2=2.67mls

o-Y$-{l.1lr,-4[vdv-n- \:flr:%l.{?nn B refroufr'[r]rr':trrfro6:EiFl:'rNt5: 2.67 tero:oo:urvt
I

72

nf,Og1\r-n.! 6.15

?fluZilffa\:or-{?ruor1ilflu3r'r sIou:nfIud-.'iufi Z suiurdErn'tirdv':aaa-o:rr5dr 20 du, [ilm1{fl?1

u.roroo?1.r'ryr

a,irurnrirgud'-uvri t a vv 6 to rruo:riaiurfdru',[ilvrrtsrrrriuri'u rirtfr6'ufi z sufrrufrufi 1

rTunrdaad'n:rrEr

firfi a'irnr:tudrfl unr:suuilufi ofi du :n#':aa'r oYuurrodoudoe.ir':'[: zre.r'a'lfr:a6'ufi fi ruea
!

t250 filanie.r :n6'ufi firura zoo fiIanir.r

-u-1-=--1+0 m/s

* n',*d o.zt

qrrtli t f lJ ? 1 3-t 0 N€t t 1L11.[! 1 tta
rilo n vrqr?oYt'tad.oOuaAdrG'a t \:ry] 8 N 0 ]]o't r:l 1.{nL
nt

eiru:rxvr v,'[6arn (1)

Ur*V, = tJr+Y,
10+v, = 20+Yz

v', = v2+-1 0

qrnilffnnr:r0\:nr:11.r,.rn:?NIN[e.Jil6'e.rriouturvirrYrzun:rnlerreru6'errfi'.rtu

2Pi - >Pr

ffi,U,*ffirU, = ffitVr*frrY,

(200X10) +(250)(20) = 200v1 +250v,

2,000+5,000 = 200(Y2+10) +250v,

7,000 = 200vr+ 2,000+250v,

7,000 = 450v2+2,000

=5,000 450Y
z

.'z, _- 5,000
450

Y, = 11'1 m/s

riru:r*vrr v1 q1fldelfl'r: 1t1 ar'Ifi'jr

V, = Vz+10

= 11.1 + 10

v = 21.1 m/s
1

o-Y,:Zf-iAul.l:,n,:a-Twav-*rq^&,uafi-t qyrodoufr'trlrr.:rrrfro6:roqr:r15?rfierfiul[]u 2i.1 rero:oioiurfi urar:n:ia.l

F- r'uAfi z s--.r€r'r ro i o ufri,,'Lilr l.: t rr au v rd5': t 11 . txqr:oi oiurvr
fi u o sr:r
fr o 6r

IIuLr.;uoi'uLia. 73,

nrsuu i

4.3 n1i$uOluaadatri6

nr:tuluaa.'rfi6 6o nr:tuffurLo..:Trr9nCfifi*r*rn',r,udrufir:4.:Toqriourinsvfi":tu
nr:f-rAin9-q, t-u-4-n-'uLuout nquAuunad.l{N?a?o{?CIAervltqaAno^4u^m^.^L-1Al'lutl'[
or u4ioorqnoi|rr'v1ty6'Ijr

virae.rtoiariu

trir]rusurcdfunsnr{3.r?oflo'3Tsrndnnru rdu:nuur{tuffufivrr.:ttun Qnfintdaotufi'u riiufiu

n1:tuluflo,,rfiOfi#.':nr:trlttt-l!fiou9{9uula;\rifieuqu rflutrlorra'rn4nr:oqYnr$

krru6'r fi,:s;16'ir "lfiotrifiu:.:6'vrf;nrsuonNlnii?i1sio:v:r! nlrtuluao'rfi6s;fi?ld5?31

ffi l I tu"r a tI u t *.r uor-x ri o u n r : r u i vi r
:':zu o e.r o',rI u a-r uqYl u 6't n r :

oF,.' e

n0ual:tu \F,\r

Yfr':nr:tu

',. nrnd 6.22 nr:ind oud.i.rrnlrru,t^vr#':nr:tiul o':4nfl o u6uo

qcui'-u-dnd^- l.{,t-n.-l?n-n-.d*udnd4ror.oz{zvll8rI.dJIor.aqtln.uitfqi uadurfni cnrol{fNi u---lontofnun:A:+muro.ril6uatnTfui a rdsoft#r uGu tLu?nr:L"d.t*dr.o

u

Ydr/-.-l-n-- 1:tutrfirqnflalfiuofr'':ao'lrfio
u

n1: ttu n 0 0 nq'l n n-fu,afsivG\: Nrr L3.l L}.lt{91 3..] t:Ju p, .lt,. LtnS p^l
'zt

fl1:L'rr.r0:?N?6\:INrpx{6'rro.':nnflnl6uov#.lnr?tuflu urlfisrnl}rtslu6'rl d' l,l" ttnv

dT2I^Iouzuo::a.lrlo\:INtN1.r6'triouturyirfftLzua:relta':Ia.rulurYuufi'tru 6":nrvld O.Zg

., ntrfi 6.23 le.r uxu#unr:sut a.:o nfl o udloluao': fr 6

74 nrttu"luaalfrfr

nf,O81\r-n.! 6.16

Ia${nufiatfiao i':6rsfrn:rr6r 10 rno:siaiurfi rfirsuri'unnfiardao B fiocid':Bacfiilaarvirri'u A
af,,if,
fia$q1fltrilnuua? aqqftlualaso7h1ffo{[flaoilytrlsflaonqrnfi'r4tsru A ririlx 37 0\:et1 uas B ?i'lr{il

53 a{fl1 rTuuur16ru fr'rnrr^rfi 6.24 firnr:tura\:an{tfiarssorijunrrruuuufiqfidud':lri6oHacrn
n1:fiNqrs{{$asnrrrufloror:#un-uanfiardao 6'q:rr5rrtatanfiardgorf,:aaresriluryirlo

(n) riounr:tiu ils = omls

@

(r) rn-tnr:tu
nrvrfi 6.2+

1A<6o rir qlflild-vnnr:?o'inr?tl.unlrJCeu4 dufi',irfri'":Ieiraru6'ar:;arr[ay?\fl-r$'rr-{:x}.rryi']ro}r rusirilunl:
u d2%11tHlL ilsl s^': fi o': ff r u? fl.l ttu n a 1 a.t [t1.{? trn 6',,:

LINU X; muA = mvACOSoo + mvuCOS0B
10 = vocos3T'+ vucoso53'

1o = vn*. rr3

4vA+3vR = 50 (1)

ttnu y; movo sin 0o = muvu sin 0u er

vAAsBinB e = v sinO
-vosin 37 " vB sin 53'

3u = 4u
58
5A

,u = ?ro

tuYrl.{&Nn1: (2) n':luaunr: (1) avlfi

4vA+3(*uo) : so

16vo+9vo = 2gg

25vo = 2gg

va= f9- = a *r'

rul11.rri'r vA n\:tuarufl'r: (Z) a;'[fi

" ='B - 1/n\3)(8) -= 6v m'lrrrrsJ

o- {uY il naan:aJnt4ouo \4/\v/
E3tntirlOilYAry9r?uv09t:trd:? d a4 qyronA0uyAlou?u
A 8 rHatgt0?1.{111 -B
trfl3nnilfr[6i€io

6's):ru5: o lersr:sioiurfi

iIuLuumrLLa: 75

nrsru i

OIOU'l\r_n-.i 6.17

{ornt9uura zm rndaufid?ero?irurEx 5 rruo:sioiurzr- r{rruiqn}.r?a m 6.:odfittosrilunr:ruuuu

80fi ailailutfl.dl Y, a orrNrEd arvrisrl:nramatfl lrsunu
9g
e]2afl {6{o{ecfi

?nfi'l Elflda-ifl'r: U1 +V1 = rJ2+Y2

5+v, = Q+v2 (1)
2mu, +m(0) = 2mv, +mv, (2)

ruyl1.{fl8rn'r: (1) n':luae.rnr: (2) ar1fi

2mu,=2mv, +m(5+v,)

2mu, =3mv,+5m
2m(5) -5m = 3mv.

E3 tO l'r v, = $mrs

vr=fmis

I po-rrfu ra-rn'r:tt-la.r?fl 2m fin:rarrE: ra.rn:riaiurfi udvil?n m fiorra.ruEr tero:rioiurfi
JJ

ffi

Hffi?* nr-rodr,rfi G.1B

M*@

ion A il?d 4 fitaniru rndaufidran?is{rE? + r$ro:siaiurfi ufirsu{nn B N?a z fiIanfir od
9{

f.r!,tuufXruf"ri u fvirnr:sudrXil*u, n'rr%1{ruu64oudur aeru:nid ivoq B uni A qsroa.oi uyri-vd?urrx1rut5d?

odr':1:nfi',rernrurYu

?ovl't qlnflNnr: 'u*, = :E
kf

Uo+Vo = uB+vB

4+vo = R (r )

s r n n fl n r : o %Yn :$Iai ra.r uO''ru

ffiAur\ + ffieue = ffi,qve * ffinVs

(a)(a) + 0 = 4vo + 2vu

4vo+8+2vo= 16

ve= 1.33 m/s

tuYrl-{eir vA n{"I%ds-Jnr: (1) a:16

v. = 4 + 1.33 = 5.33 nt/s
IJ

6'.rriu Ton A uro; B rn-.:tufiuufiesvrefioufifi?uqr:rarr5': 1.33 itnv 5.33 ;e.rm:sioiurfi snrn'r6'l
9

76

nf OUlrrn-.! 6.19

ri.rurirlilvrr.:fiermlio d:u:n6'ufiuo.:ri.:urirl:Jvrr'lfisoyiuon :nau6'#,taa.:susfi:6ofi'u}Jtuficr

lq

37 a.:errriufisrfifia fqrt-r:n6'ufiuo.:16"[rlnr:'ir:n6'ufitr:r-urnil]6xsFrxlerr5rfirfiun'irrirmusr

il:smrx zz rilq:eiaiurfi eiru6'rr:nriufli:nrurufr:ru:n:afrrururnr'[r,,] uff:6.:aano'rrdauiu

h.l rr'sr c':fi aa{q{fi rn:r ilsi.:'irrirl#nr:to': firTu:o6'ufi uo.: rilu"iontrtri

* o',*r' o.zs

i6rir slnIqyrSalil'r;tr[6flufrqrrr:nr:ron]oud1o.::n€iu6.yrv.:ao.:ffurioutur[0utlfi":ru'lfi 6":nrw

Yt 6.26
v

, nrl,ltr' 6.26

nr:tu6'':nair':riJunr:tuurrr'la.idouduaHr:16,dro^.nrnouoi#':ao':ruufi:6orYu1il
9{

0-\:1Y-{u n?rilr:<?1{da {ErnturYuarul:nrl:3ilrilq?rN[:']fdlo\::flu1.t9lfdiot uturi'u[fi

qln 6lNnrT -v.f=- m1v.1+1mv 221

m12+m-

srn:ai9l"itdo.rrymnr:ninr:tuffurLa',::nrud slrfiuir:nrYrao.':run-r*lunn:ga+rso..:a0.,:fi6

nl:eirurruk rlu6'ei6.:fro.: ursn riluaa',: uu? unu

ttnu x; .',rr = m1vm.1lx-+rl,1l2v2tx

iIuLuum-uLra: 77
N-lSlJL];

qrn!ilqrrfiu'jra.r:n m. 1:nffufiarrl rjouturYr m, {:nffuduo':; nare.ru5:"luuu,lunu x

q'1

u rd 0u{1Y41-[v = 0^ uv r
11X
[3.,1N aU[g?'l

m '2i
\''l=x2r-' m12+m

unil y; 'r',12= -m1vf.r|+fmlrv

q1na?2ilqyrfiu'jr*.raa m^ (:n6'ufiuo.:) riouruffrl m, (:nffufitrr) er:rruu5:t%$u?unr,l y
v rd oqfuVu
!N$l v-. = u- sYI t6'ir
21v
m
v'i.y =- mr + m2 \'/1i

-l--

fisr:flarsrnfierr'rta':o?1Nr5?dofrrEJfifi't:ntf,{aorffuturYuufraoofful:l qyufiu'ir
9

6's):r6iruto':Fl?'ru[5xdofitilarN[[1r?[Lnu y oioer:rxr5':aofirusnrrtuil1fli.{ x 6oeir tan 0
c

1'l0f3e.'l13A..J%:YflYlffi0{^OO-un'X{tll ! a v^ 6a m Ov ft[AOfhq.{f]'l?\Yil
LN0tylULnLrFIflO\:n?13.1t:?tO}.l1lO{N?A

6.26 firu:lu

VI 'f*

lsns = ul \-l,,,
fi \ ---]

firn0 = I ln1m*2nL2l/1',,,i \

I\
,'m
t \J., 'i

111 **

ra.o = {rl"T'lz r"1rV1t,;ii ' ,,. nryit e.zl
'4, \

v

tan 37" = 21
V
1l

0]5 V

= 21

\rl
i

vr, = 0.75 v,

o''triu aa.rnr:fir':fiuuao.tlfiufiuir o-fl:rr5:ra'rer?a ln2 firjrriornire.r?d m1 urao'r'iTrirl#nr:

tl vd rlo':fir:rui'ro, uro\:u-:J s.]16?u o-er:l r5rriarnirriuuiluqr1]rs6':

o\,:rrd'ud

78

4.4 nt;;vufia

nrttsufi ora5a nr:6oore (recoil) 6 a nr:t^Tsr n u6 o:s:-rrTor o LLU fl o a fl qr n fi'u ar r n:r r.t

?a{Tr!!qyfio.ro.r6': Iouer.;a:rxrot:rrrriou:yrfioqyryirfr'r.rerrn:arro.::v:-rrufi'.::vtflo

Em. = Imf

firtria.r^rr:.:nlEJuonNrn?;vir'ffi:vruleruerum-erro'::;r.L::fieiro':sr-: firrfllu[:-Jnrrn6nr:

ouinr{Txre.runH

E4=14

{S

@

nrufi 6.28 nr:ruernFl'loonarnfiuro.x:;rfi o

nr::v rfloq; rfio nr: r:J du u:rlt a',:vrff..:.,:r uqr nvrff.,:rru &ffidt *@a!adq M& MM-
U &q, B" Be.

}l Irn fi ril ul^r ff i,i r us a { u n ; vl n-t r: r u3:l ur-r d u .1 rtiu n ff,t r r u rirnruhlhlUnlSnOAUd{
t U
duuvdtI

{ {tfl El ?\ A { \:'l UO 1 1 Nl A U ?\ n { \: I U ttfi tll 1.[9] U

inn1 -! -.! 5hi 0 n s:a n ifu n a:u
s r R e o u oo
6u

nr:refioufirto'rrfinsvlfrufi'nnr:lriurdarrYrnr:oio6':H6onr::srfiqto':iurfilfin# 6.:
vf4rn!!sqvrvrXnfroufrlounr:fioo:tatndrrruocl'-ror r^iur-[roana]rsrnlrv"lou lsiphon; fiodrr.:6ru

air.':to':aieufr'rvirl#sr-rr^i':'hl{r':vrirlufievrrtidn:.:{ra.rfitifierrrro.r#r orrerrE:lr*n',r,rd.ur'
c

qYXl}{AEJnLO?-lN[t?f1J0\:nl:4:l11v9l-]14{n, nlNtXU0nln? d u4 d r v v .i
[tn3143]nflfN9l::JOU?1'l\:O'l1.l1llfnl9]?[1^,10
UU
,o eav J
ti : a"Lun r : vr :,: d':"trl ro fr o ufi trjlufi er r'r fi ru ar r v a :-.r

iluLr.luoTuLLa, 79

nrsru i

nroulun-.! 6.20
flulmqjn::uanvfi.:firura 2,000 filanfir uasanflufir.r?a 15 filanir.r vd'.:fi.:fluluqjufrrnu"jr

asunilufiomrurS:50 rero:sioiurfi asrnm:ru'irorfluluaiesnaafifitfi:ao:rsrr5rrvir'lou6'':nr:fit

i6rir ar nlq% flar err:n ufi Erunrv{ uao': n'r:0':fl ulu nilfi 6'':fi i,

V ---+ ;,t

(n) riouO': (r) r.iA'tfi.:

.s nrnfi 6.29

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