Exercícios Resolvidos cap 4 Mecanica Vetorial Para Engenheiros BEER 5 Ed

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    L r ; = 2 (12S9)+2 {S:5"1,.)-1/,77-11f.s-3 =0("c.hcc.1= )

    ( t1 . - Ld C .D e pni"t of ihtcr.sccJion o rW )j , 'H, S,ound. Hoori-1:onro..! d,,frtnce- f r - , ; n , B + u c r' s

    d.-=(22i")SiY) : '0_ ( iOin.)Co~ 300

    : :- 2.3"+0 ln.

    +~LMB':::D:

    W d - P C 18in.) - : = o(Iso 11 ) (Z.Slfo iY J . ) - P (IBill.) -;;.o

    18in. p= +2.3.~jb P=23 .4 Ib j' ~ Z 'F:: O .: 2B+23.lt Ib -150 If:,=o .. ~ B =+7 .8 .3Ih. o:=78.3Ibt ~ OJ)JJ~~!f j\-) ~qD ~J1' -

    (a.)+J Z"Mk:-=O:

    3 I 45kN (20k,tJ)(s'4m)+(2ktl)(3.Ltm)+(L fSkH) (o .5m)- 2 H (2.5m)::: O

    f/:::+27.!f{,) .jj =27.,u!t~(b),t)' L Mft:::o :(Z O f:: .r< )( 'Z ,3Y ") + (Lkt-iXo.Clrn)

    _ ( l f - 5 ' 1 : N)( 2 rn )+ 2 K (1 . Sr Y I ) :::0K=-I- 6 ,OI f K=6.0ljf:t/1~

    t : ZF . = : 2 (27. l fb)+ 2 (t.otr)-2 0-2:l.f 5"= o (Chd~.s)7

    NI!c.. '8D0'( vJ:= 3000 lI::, ,." El. (I)

    /!.;'J-8.3-jIDI-f.17c"sC (I)- + 5 2 : ' M e, :=0:

    -A(CfU) f P({,ft)-(6k.p s X 2 f)-(6k',p;)(lff t - )=oP - = 1.5 ' fi T 6 k'f-n (z)

    S/me 1 3J\~ 3 O k.;~. j,(I) l/di.:,

    P : : : . J(30)-' r8 P ~ 'fZ kt"Si",,,; ::: A ::-30 k ' fJ , Er (2 ) jicldJ0+ b ~ P ~ /.5(30) + - 6) Gl:lJ:: p ~ SIk0 1 d lfl' w J ~ c b r a r n d il1 P r e l,o lf.8: O . S k ; J : : Q ~ 3.5 k N ~

    39

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    T

    3 ~ 1 1 : 1 / ~ NI I L 1.71t1o . ~ ' : ' ().75~

    T-D

    j ) l

    Q.

    r t E I .1

    '0.75,.,

    30 \~ 200 ti

    +') '2 M ", =0 : (3 kN X O , 'Jn,)- (J kNYO.1SN l ) + 1(2.Z~"')- Q (3 m ) - = OQ= = 0.25 kN + 0.757.. (I).D-1- ) Lf'IJ)'" o: (; k .NXZ . 7 S-,.,,)+ (i

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    L r . 1 9 1 n c. IO!J..;'''rl~ 0 1 - r,,~p l.< ..1-e i

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    L r.Z 9 f, ~LF;=o:10 2JJ" ,4x+(7':n6)Js.2.0-~'2..01b)c.oslD=O_

    r110lb 751b It =1.t7.7/b A =47.7/b_~

    ; t. c ; " " ) 1 - M E = - ( )7 . ' ' ' '

    16m

    1.r>- ; 1 - " l

    - = - ( 3 .b I ) T- 36 o t . . . t J . fY 1

    w ( w A " r I M E I ~ IOOkN.!'>1 Dr'" - IO{)k/l/ ,1"A ::t\_-:/CtJkN./fjc:

    ~ub \h ' iu i - ,y ,J i1J~ -< ,:> < p rc > ss ,c .w ' o b f -c ; . , , , . . , , / f e l" ME:

    -100::; 3 , bT - 3b o::; lO OZ(,o = = 3.GT 5: !f60

    72.2kl'!.::: T-: /2.7.8f:JJ

    +):2. M . .D : : : ; . o:

    p(3o.s;nB) + Q(,wsV- Q (2 a ws e) = ( )3PS;r1 o = Q Cose

    tz u v ,. e -: : Q/3 Pv:::+ CWJ-'(G/3 r)

    Ii

    ~]I- I

    +)'ZMA ~ o :M + (300 ;;)( j f , 3 . 1Zm m ) - ( 30 0N ) ( 18 0 . r l l n )

    =01'1=(:300 tlXIBO-/63. 'l2)m"1 .

    = 4, B 2 )/'m

    L f= o . ' fi...-JOON+(JOCJN)c.ns 3S= oA A - .=' + 1 . ; 0 . 2 J/

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    or ~ "'" Ib 5: '; 0

    1 + -, 3 5 (tJ-) Iric.n~k Af:!:. I~ iso~(~h"W c "'"C-

    CD =(BC)~., e : : . ( c.>~ ~L 1-

    +) 2 : : Me""' o:P({c."se)- W(fur,n:::D5e ttr 'h ::J Co'> l3 = 2 (.,J~' - f - I :

    pe (2c..os'{ -1) - V /e c ..o s f = c)~~ vJ B' - o

    Co;f:

    v l J : .: , s Q - E'P~ s;" Il c.,,,0: - = ( )1 - ~ 2W-l P5in T =0

    e := Z Sin-' (v/lz"p)

    S LJ \F-VJ 02.-'h.lL "" - - - - = . : ; ,z f. P 1 f '.J J .i- = /4,5~ tJ= 21,0'

    .2,

    ti ::-nl O (disc.o.rd)

    C

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    (I ) 3 non-c.o.--c.ur"'~nrJ nO~-for4.I ICL . IflJU Lo, . . " F '1e* " l \ Ull"\s ITa;y ;db . Reo lh ' " " , c1aM;" ,af " ,c. E C I' ,J ii ,b Y " L JW O MAiV\t-a..'h".1

    ~::5k'rd; r:;::b.C7kif>-!'_-8. ;, 3 k , ' / , , " 2. 3G.1"

    C E ? 1 . ltf'\LJ'\- 0 . :;f4/-.irv1cr.(ff\;n:../-t

    c.. 0ru;)'f,r;v...VII" ,...

    rA:"''',),LfV,c..=O: .flJ

    = 5i'\1r .c. . cCf .)lll'brl\,JY't\ ,....-(l ;."...,+o..; .. . .- ( J

    I

    . -= 0, - : ' " E ? ' = = 2 ' - 15: N \

    ('3) lf nO "l-1.D",-vrrr"f,M''I- f " c a l k l rc""t , 'ol l l0.. ?lG.f-c ~plcftl'1 (o~.,ir()..,'vJ.,.,{

    6. k?~Cl.l h\,M\ s r z - /: irdcrq"":"a.f-cC, '4 l . J L I ; b r ' uM M";....~,.,..; c (

    A = 3 b8 1'1- j D = ]68 J.i-- " (A

    Jt'11 = 4~~.S 1'1)

    ' (L i - ) 2 r e t J . c . h - u , " , s

    . C\. Pla . f e rarh\ ~ I.DV\dra;VW'c{

    b. R " " c !'\) n S da .hc . J11 det", , , , ; , , , , , fe . .c. . ~l.Jil,' bc:"'W\ """,;.,t",", d uv,der

    ". :t;v< '\ loc.d ," " ' . sC=D==21.1':;N\

    I(5) 3 ()lY\-CO,,\lVf'l'1"vl+, r,o"'-por Il ~ I rc o L l-'C iA

    0... P\?k CoJnple~l'1 (O'o'l\i'rn,'","'; fb. RE'~ '~"Q"'~s hd - ; ( c . )~ d~ f-r . . .; :' ~+e ' c. = 7 v,'I , 'br- ,\) W\ m a , ' n rt , V / . . -d

    , = 36 '5 t{ --; ?=bI3 N~5'3f

    (6 ) Z " '~o . ,ho . ..sC i . . Plt..h:. F ef i . li, c .o"" .f - r4 . . ;" ,~db. Re,,~h'o""\ ol.'''''''~,.l- f t . . . . . d'1o '1Clfr\ , ' . c :>

    C, No e1u;U,,/u""\ (L.~ = f O)

    (7)3 W...ll,/('o{'("'r rc c c c l-, , , , , ,sC + ;,rw :;t oD )0... 'PG h- lvvo.P" - "P" ' " l ~J'\,Ir""~"d Ib. Reacf,'o"'l tlre rI'z;r. ,r ., { e r . , . . " " " ';O" t e ..,c. N o .('Cjvl\;l.;,r/uw. (2 :'I '-1j) 7 o)

    (8 ) Lf (0" l",rn"r r"~o..tf-,'t",( (furuVjh:0)rJ-. F 1Jt ( i""p-up-'l' c..:o",drtl.i'''t'Jp . R.~...o r , " " " s ewL stz:..t.ir,J~rcr"';"'Atc::

    C, N o ~",ilc"'"'''-''''' ( : ? : : . M.D 'lo)

    ( '1) Li ~u,,-c..)I\lVrrcl'\r, M V \-psrd ld r~et ,O>1.s(L. P IA re i, co "" ' r J< + ' / 1 wv.tl

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    A '.'-=3CON~

    B

    A = 3001\1 = 2.2)0 NSJf\T.5.

    . .8=223 0(1),..7.73.

    B= 3 CN = Z2 10 N B~ 221 0N """" ~t1?7r -

    Fn:e.-tod\ J)io.S'-o.YVI. As ir is rv.i~~cl,f"c t -K,"'OI)~ h C ".}'n

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    . L /ne dc..r.nOh J f r-~c..{- ;on

    0(- A !Y1u,i p'dS ~hc.) Wh ' . ! PI-/ 2 Lfr)",,,,,

    (!J - = 22.62"

    r

    \.f- A Mu-m-.---r--JOil1.---I (3- force bod'j)

    r i K Ree.ch'onar C fY Ju sf po-!.. ' 0 S i . ., Ju~ = - 7S mW fF D =C D - C F = = 2()() '" 75'" = - IZ)'mll-t

    rru"1 Tr;aYl'f/~ EFD/ctnr;l 5'''''''(1:' 4J)==.3c/:f=F::: (F])) m n 30~= 12S-fa.., 30-" " , 72./7 tYI " - t

    F rd 'Y h f r 1c . "1 ! j / < . . E FC :t em c

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    B

    1 7 D N Y

    Frce- bod J J~ jl lS ~ (3 - r or u bOdj)

    The "-coch'oY1 ",r fi mv~r r :~ '{iHUUj J - , D wh"'c. f AY1 -< ,< :17 () - N fu r'~ i fi I- e ($ {'cI- .

    f';:tn M = - 160m,.", c(::::28.07~300,.,""

    W e r1vk 11""r tr-,""n::)~ A-BDi< . iSr/,u:!..-s (S,r!L(. fie=- ec)

    t2rJ. /V I U'Cfrrrc1:CAD =- c'lO-ei. C rJ",j tAl< "'A ve

    c < - fi = = - /70 JI. C=- 2 . { !7Dti )S in c< = - j60.0t!

    .8:/70N~33.1~j f= /bD!YL2!J,Ic ~

    4- .5 2 > IH'u. -bod'1 J),4QJOt!j

    (3 -6ne bJdj)

    fi

    '71- - II Ib Om", ,7i--rr

    I 150lMJ

    nCI . I O ""'"

    Ls I7DN

    lhe r((/c fr'v'n aI f!fY1rr ; ; - f?D fhr""-'j h D/ 'V~"'" c w -d /70-fllvrce /11 fus

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    F : c e - b od'1 'D i0. '1S0h 1 . ,. ( ~ rnvst beConc.

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    (4CSinbO'.-IOCU,(,D')j + (-S8~-t,C)j + -{S B y-I C < J)j.:: oE(ftJ"/-i"::,, {I " c".. . .{ f ic.;,,,rJ c r - !~(_ u,,;/-vutv.!. f"

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    .37

    VW =(20'k:61'1,'/njS0

    = ;16.2 H

    V;rY101~/on!:.

    in 11lTJ1'

    L"H =0: ~n/ X T j. f"-t xl l' + 1: )( (-I'1UH\,'::O-13 '/6 A_ -C./6 c . . ! . . -G/B '!j

    500~X7,;;J. +(-SoVj+J7S.~)X ~i+(-2sDi';-2SiJ!:)x(-I?'.2j. - =0

    . - 500.~!:.'- 5 "o l.J I!-3 7 S [ .i . + .lf1.05";

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    52 (

    (

    i

    (

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    ~5 = ~ F - = : I. /21.fh.N

    A ). + /,570 - I - t(!.7{,)fI.1Z 1) ':: O\f.5 . .4 = -Z.15kN

    : < . .

    z ~=0 ; f + ; j - I .Q [ ,L-O, '181 ' : "1 . /77-2(3 ,30) : 1 . I24) = O, + , ' )

    ! ' t ( J : : + 5. 77 kt!

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    'D= 3.10'5 rY1

    BE=3.' !o S" 1

    TBD:: " -r ;D ~ = 78.0 (- Q. ' ) 12 j - Q,76B_d +0 ,38 '1 !!)

    7 5 ", =T R= T -8J-O.SI2.i -Q.7b3j-O,38Y~)

    ~ B~ BE t - _

    i ::= A. = (3m)wUo'cn,.p i +(3m).s, , ,30'J't(3rn)co53c.is'n1'k-C/A - _ -

    ::: (2.bm )eos 1 '. : . ' + (IS",)/ - ; - (2.60m)5"'1 4'!!.

    L M = 0:.10

    'T. T t'"l- X T - + - ~ Ix (- Wl' ) ::: Q-A Y/ A -eo C/r- -B -_cp.:!.. ([) -8J)Sin'J+/6Z0cosc

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    W e n o re f+,~I - s h'Li:.F +:::~.

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    V/-=(200 kg )(q .8Ir n/'): :: - ( 9 6 2 r Y

    \t Je htd~ 6 uf"lKY'owf1 T, A , A B 8~ B, O'1.I>- J' -"-1 v' CI

    e . ;u t> .r ; ' : ! : . , OK.CE.:::- - (1,2m} .I : + (1.8m) J -(O.7Z.rn ) - t iDE.= - (U..m)j + (1,80

    1+ (I , e ' f rn H

    T - = = Ta = l < (_ 1.2 !. + - ( . 6 ;. - O .72 + )- C C!C E Z . Z Il 12-

    - '"T =/ .DE - = T::J( - J . 2~ T 1.8; +I.e\tk)-De D[ Df. 2,84 - 4 -

    "EM ::-0: !C"/nXJc- t"-; XT +1: I ;

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    ;

    ~ '6S CoNTIN UED I Reec.11ins E15. (I ) C {M d U ) o~ Prub. J.;,BZ:r . - = o: Bx T50':'.1 - J . , 2 , . . . (1126.1) -.i.L (JL,iS:I) - = o

    ;J . l.2i) 2.i3't

    , E;r.-= /50,1 N

    ~r=0: 1 3 T..!- . -~ (l12D.I),...!:.!!.- (NO . I) -I"I~Z = - oJ . 'f 2.2.8 2J)'f '.B = = 18I r - Jd

    r:-= ,D : B - 0,72 ( 1 1 2 6 . 1 ) j- ~ (145, I) = - o 8- = 2.[,2. tic ~ 2..2tl 2..B'I c -

    Q = - (/50, qt i ) , ; , + {981l'I)j + - (2bi'-tlH ~

    8 Q S e-e "3o/vf,'o.-. ?r o h, lf.80 f,r A~ r ' r " " " " " f, o~ (Jfa",?/~ o( f:,A.t sh"ck CIJ hn"'~ , , ; /1-1. f1 . . iro'1l-n/:

    .5in ~:= I0;::: 11 .5 ' ( '

    5ft:

    1

    , ' 3J + ~D 5ino:. - 15':: oBJ + 3 (f) -/5";: o

    =0: B~= o~itlb)j +(1lf, ! .fO/},)1;IjB- = -(20.7 Ib . f L - ) j -(8,82 Ib'~j

    , ~ = /IIAD /i J

    5ec S~ivhl>l a r- Prol,. lt,8:) for d",r-a"";",r'o", o rQI'I~k c< -rhAr shi:k CD S,rms w, 'K , ho(irorj-,,(:

    Si,., c < ' - = 7 ' c < ;: li: 5 7i- 4

    Sft-

    br

    - c . = . DC __ ,

    (Y= Ji.SV

    VJe hAVe S(},.,k,.,ok,/~S, ~D~ ALI A:;lHA)"Jl-fA)J) P.nd. b

    e , v,Fbr, 'voYt c:rw..h',p,L Tl.e S..r - . , . . . "';",{av fI fr~ lu ,.-no\rC il1n,e i':,direcf,~. ~, e.;UI'/,hr"VH.1lt YY1a."hi't>.inl',( vnd:-rr n ~~/V't"" /Dl!iin~ I Sinc! :z : :- O,

    L,tIA =0: :r::4'1/(-fn-f!:G-//lX(-/~)-r(/'f~~i+(fLf,,~j =0

    .-.s-j. X (r GJ~.;(" + F si,., c(J)- (D - C.lJ

    +(2.f;';>12C(j - 2.;'-CMJcj- I. 5"~)x (-15.1) + (11/!,U T(M,J:;} = . O)

    5F ;D Cc5 c < - 37.5 s ., - , ., 2 c : : : : : -o

    F -:=J7.S(2sino:.casc< ) =155/f]cI=/5(~)c :o :?COSC( .

    - 72.5' + ( /vj~); , = o

    l' (Mf'~=0

    F - = 300 l .bCD '

    (/'1 ) = - 2 L,5 16,ftf i - ; l . .

    '2F :::o: fi -i - F w~::;(= o.2 ;2 , C!)

    , 4 ; . : . + 3 c.a, jISlf"=-O

    ~ := JL r,7 o Jb

    . =- (2 .q~ I b) i + (Iif. l fD /b ), i j ~=(22 ,5 Ib !d i ~

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    w ~ (200g ) : '1 .81 r r / s ~: : : - /Q6l. . rV

    VJ~ Ir.o.ve.

    T =/ := TCE J)E

    w { htlv~, 6 "K>-1OWVd, T; B>., Bl, Bb,CN, s ) .L ' (f'IE);)' e; , , . . , ! f

    6 "1vl'II~'Vf~ e7uo f iuV'; - O,i-'(,CE=-(/,2M).i +(i,Brv,ji-(O,7201)-!!

    . . D : : : . -(r'2M);

    +(/ ,g" 'Ji -l- (i,8lff.,! ~a

    T = T CE. -=.I- (- I.2; +/,8;' -(),72 f!)-CE CE Z,W - ~

    T - = T:D E = -.I- (_/, 'Li. +1.8)+ /,81f:!)-])1: DE 2.8lJ -

    L M-:=,o: 1. x T + - t x T +."l. X (- J ",,. . ,J. ~ - ~ / E. A - -6/8 - -

    usins d~f("'r.-.r1"anf-sl \l,Jc hp.ve

    i - / ; . 1 T I ~ i ~ i~~T O 1:-3 /.b + m D 1.8 I.b +1%2. 0,6 () 1,0'1

    2.1.5 -1.2 I,B -{),72 -1.1. /,8 UJ~ o -1 D

    .1-(M \ i + (f- '. \ ; - O, " E l;c - \ '81 i -

    _ I_ : ( - 4, J 7 b i - /,C il . i ;-'2, I G ! : : ) + ZT ( 0 . 1 +3 I. i -/.1 I. i+-2.1b -!s )2,21' .SLi - -

    +2.040. 'I13i - 117 7 . 2 . - : ! : + rM)). + (fv\13\, j = O

    '" - o /8 " s ( (,8 ' 1 . 8 ) /tlbZ-OL(1:::0: v ;; + b ' 1 . L . 2.,28 'js'l - 7 -

    ."" 1:',.;:: O: f < J-8925(- 0,72 + ! . : !J . ! : ! . ) =0c .. I: Ui;' 2.28 2,8~

    B .J = 1 8 1 /'I

    B =-ZZ1t1r

    E= (65lj/f)j +(981 !'{,~.-(221 N)-/! , ) ~

    t\= - (883 N .m )j + ( / D '1 -6 fi,"')1

    L~::-O: !J J + G81,ZS(~ + - E-) -/%2 =0

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    w = ) 2 /b ._Ij!=-wj ::-(l2fb)j

    /1~ fnes CJ.LNf1"( i.ln roer 48 ""r8=: .-t! v

    F = : E.)- .,;).,UC /l is i Jn i r wC+or..L ABand(D.::: -:) -[.

    i : : : : A ,. -; + Fiel.i + 1 \ 1 :'! : : ! = - (22,511)1W e . ~ '/~ 5 u .Kroown, S , E J A,..) 1 '+1

    1J1 "') C .CD ::--(IOin.)j,,+(6;"')..-(lf.5/!l.~ C,}):IZ,5";V).

    T:: T C D = T(-IO; + b)' - lt.N):::- T(-o.8L -i-O.1;Si-{)'~f)- C D Il.S - _ -

    M = D: -1, ; , x. B" + . i , . . / x. T + 1. .x ( -_w - t ) = o-A 7)1 - "()1 - -C/A . . ' !

    ol;'n5 {' ,..""f 2fl/k=-(lDin.)i -i-(J2'-n.)j+(tlin.)-}

    1C/A =-(IOi n.),:' + {6 i1 '1 )j + (4. ' ; ' - \01.)1

    -;~ to "b:'( 'J ih

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    4- .93 Sei! Soi"t;oO'\ d i- ?, . .o 'o. Y..'1L f,n F6 J..0~r","'" ,T~t f tr ,IC:: ' Cith'"q 0'0'\ f'~( Cc,}"""'.(",",.,-r11'I1S S= 300 rI ;'i tv l-k",( {'"h'v" ,Jv:.r c l i : : : / ,p,'",,,,,/ vJc vrril-i t""'- r -

    a ~22

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    ~Lr. 9 L f

    0 = -M i tf= -F_ }~ -!;r.i:

    D

    ) -2

    lfc I d_ .! c r . ( ) . Vt 6 uI'knvwt1S B;r. B, c C .D D --..~J rp~ I J"C) 7 ' J.., )1.1 11L-1" b

    ilt'6n'U"" e7v41-,'Oh~ - Ok.

    0;::'O: :f6 x(~+E )+ -:?:c X ~ +-.! : 'n XP+0 = u

    ~oh"3 f i. .a . r : :' -'-81 I ~ I,;' rM Y,(/Vr:or -'-'l iV ' lro (2 :8{-7.5~)- t:;D:;. - , I - - f =0

    /5''D,. .j- b O DJ = c - M

    hil)/'7''''J ,,/1 hr ", , in (3) b~ 1f0:

    .) 8 0 D:L + (, o D , - = - 320 F (8)r re- , r ' ' ' ' J (7) f- :- . ,r r " , (3):

    ( ; 5 ' J)x. = - 1 ' - -' 1 - ~ 2 . o Fe . ' " ,D,;;:k: r= ~sIh, M = Q7,,. 16fl:-

    sh'rvh'nS ; , - ,1 -0 (1):S']):., ::-Cl7,-320(b.)

    1,'>1~ ;11 r o (7):' IS(-30,S) -r6o'D)=-17." D,,-=+&'00/1o

    " " (5): c ;; = = F-~.:: 6, ')- 6 = = 0.5'00 /6"~ (I): C< , - = 7, 5 " (b. 00) = J . f , o /6U"' f (lf ).' 8".= - D"..=- + - 30. ') Ih

    ' ' ' ' ' '('G): E!" :=- c~ -= - 45,0 /bZ) . ~ ( 30 .5 /6 ); " - (45.0 / b ) - j J )

    c ;:-(o. 51/,) J -I- (L I5. () li ) t. ),~ I ? = - (30.5 Ib)i: + (b l.b)j ,~

    ft)

    4,95 Scc 5,,(Llh'oV\ o r P,.-oS.L[,Q4 hr F cJ~'o..vcldu,v"h'oV\ o~ 9" (I) t:"rt.V~!A (~). -

    GivU'. D",i-.~ F=:o, M:: Cf7,5/b.ft,

    SJl:Jsh'tuh'"s i " , tu (1): 65'J) :=.17.'; .J ) =: 1.5 /b(' (. .r :r.\--c;rr'1i"'~ i"ro l): 80(1.:;) 'i-6oD =0 ]]J -::-2 Ibr ; -D~ ' (5): C" " -2 =0 d i C, ==2 / 6 r ru Y>1 (I): t~= 7.5(-2) = - / ) ' /b (Jrl"~"I (!t): B;r. = - J)). := -: /, 5 " /6F r< J"\o 1 (6 ): B 'l ;:- - c= = + 15'/b

    -r 9::--(I.5'lb)J+(I

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    ~

    ~4-,9 L r I;; tL: - Mi t

    F~-F}~ - B-i A__ ;r._> B

    v -2

    ) 1F t : I d_. .

    ! C r.().Vt 6 Ul"kn0Nt1S B;r. B. C- C .D D /'.."J rp~ I J -; / -o (1).o

    65v:.. = = Cl7,-310(b.c:)

    r l "Y l~ ir, lu(7): .IS(-3D,S) -/-6CJDJ==-17." D,,-=+&.0011o

    )'Y) (5): C;;::: F-~.:: 6. ')- 6 = = 0.5'00 /6"~(I): C .c.-C;rrJiV':i i"ro lB): 80(1.:;) -I-6oD =:0 .])Jc v . ! , , r e . .

    ~ 1 ~ i: ~I I J i ! - l l f : . j ~- f . 2 b O O .% ~D +

    o o o . q b IT e r ; + o ()O1b T]f

    + -a . i 50 .% =0

    o o . b -0.5 -tu 0.12 -0.%, 1.7'1 M 0-0.(, o -2,4 D

    Eluah''' '~ + u ",ai) H -, cuni-ic;cY

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    4.'77 e~ SO iVf,ry, D I- P~uO . 4.~b r o r fB i,,-sr"rt1 o.....dd(r;vo..h'1 of- E.rf. (I], (2.), c.h0h( t;.re S-h: fic-,-.," (2) of -/-t1~ So!"I-)f.)~ f fhh. /.f.1B rcNinaJ

    L{ ' - i rtE= = - o: 2 A-E' (i8/1! X. ) -I-2A -E [ i .LYEX ( - 6j~ =0

    1 0 (; -I';) la G -/5lo O o + O o 7.5 =0o B O o -60 O

    -1508 + 4'5'00= O B= + )u

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    l!= - - ( 1 00 I b ) !.? ~(4iJ;nJi -(30inJ-t

    CE ~ 50i".

    T-:T- C EI= T ( 0.8i - . ~)

    ? _ A B _ (24;".)'; :(IOin.Ji-AB - /te - 26 ;n .

    2pe, = I~ (12}.- 5~ )

    'y{;"a~ ~=/B = ilO} (1n) ~6/,4=121:-5/1 -I - JS-~U5(n5 deram;",,,,,,!$. ClM rnvli/fJj""S 60ft., TU""lV'(c wrJ ~ Ef (I) (f!. hIl o.., ;r :

    12 . -5 o ]2 -5 Oo 110 O T + 12 -5 15 - = OO 0.8-0.6 o - 100 O

    - 28[;T + 18, (;00 = = O

    "' S a."" c 'o Iv h\J>1 0 . "+ - o r Prob. 4.107,c:.)C~rr f'~ now

    T= T DE- : D E

    T - = T 2'/J +30';-30~'- W. 7 it1-

    f. (I) ir :;ft!J vai/ti,h t/ f E'f.(2) r;ow ro:h

    ~ ~ ! ~ I = o-/00 O

    T=609/6 ~.

    12. -5 O 1 1 2u 40 O -..I- + 12.

    ZLi 3D -30 lf8.7Y'f O

    Ilf)'-/DO T+ /8 O rJD =0liB.71./'-I J

    '{ O O te ( :::110.%

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    (o-)~Z: r : : =0 :PC.O \ 60 - Tw 56o - = O

    T - = P

    (b) = r -, ~ M e = o :(T C-O) 30.)(20) - (B 5 i (1 3

    o ')tt = = O

    8= 2Tc.o/-30o::: 1Pif38==zIf3PL6o'

    +) Zl-'15

    = o:(/CDSJO)a. -(CSi;-do") ~

    C=Tcot30-= pif3

    f ":::f3 p 760.

    TM=o:'" xA +-7.- ; - -c -O-ix (RJi + - ' \ 1)+ b J X C B z ~+ Bx.~)

    -f Ctx (C", i i- c:J d ') - = O

    o . . AJ

    1 : : - a A ~ i -I- b 1\i - b B . > -~ + c C ; x . . . . i - c Cfi. : ::O

    qvc.f,"~ r J 'tU-u t"e. c6dfic;(~rJ of r~( vn;r vCc!-J- rs ' C D b B " -cS = = O CJ-:.(b/c) E ): (I)G ) -a l1 / : + c C ; : : : : O A< : : (c/o) C ". (2.)C D ttA

    J- b 8~ - = O P'J::: ~b/o)3" (3)

    L 5 ; : D : RJ + (1- P= O HJ + c . t - = f'L'F ,. : : : O : I t } - tB " / - = = O r + te := - D .

    5"vbrirv f,'",,:o f - , r C ) " . . tr( T 'Y I (1 . ] ) iY l fo (2): / ' Iz .=-(c/~)!3:1d,,,~ o - - ~ (

    t'1'ii 11(n",'0'1 S,

    (r) :

    (7) (t):

    (2 1 . -

    (8) (It):

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    F = - - k 5F=*'(f-e)

    VV c no ( - ( lkd t r , , , , ,S !-J)V~ Xf ' -1

    B" , " o )

    1 3 v r ~ fV\vrt Ix dr'r~cr't('c ,l a v o: ] CD

    JS,"Y1(C CD

    i~ a. t,,;.)-furiC 01Cl

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