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sol3 - 2.677 21 A gm having aha crass mam mom 13145713...

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Unformatted text preview: 2.677, 21:? A gm: having aha crass mam mom 13145713. 22.6mm an opening 5 it wide and 4 ft {fink in a water mm The sale weighs 3013 it: and in camp «may :31 h m the Mz‘ofAC and? mm 36’. Mac the: WA re‘ m that is dewiépndan them at C. F, ~= H,“ A, um. 42‘, ~ 3mm Wm "‘ “”5” T“ Thus, if"? f; #832,? i, )‘(la H){5.flg x 5‘11») .1 {—3 8‘ 4:8 3 15} um 1% In 7;; fanatic F}, a J: V! 5"? “cv r52, 3’ when a": éffv-zwég 312.9%?! I: F; 2‘ So flat ‘ 3 £1 = W +12.s~i?t Maw—H ’ (x2. thémx art) A15») $645: 734: Wm 73;»- 2g“ (ffiérbft) ‘ ’5“ i [it 3A6 f}: Pt)(#al) 4‘ $2,?g, [1%]{3kxyfl32 “’gaa lg, 5;» £314”: .briéxm , Z M» 3" aw! 5 (3,,“ #l‘) o? w (m) - liféflm) - 5?: 0W) .3 fix! 3?. - t' 1;; “a a )(12. a: 35% mitt) r {Yea Is) (19%)"figz54 ”@413 WWW ..... r ,1; 2’6?- 2.?3 3. 7.3 A thin 4~&~widc. fighmngk: W with mgligible mass mm x 4 n “gelqumahwtafnm‘ ‘ mtggawmnzaasshown ‘ , . in g.m3.mmmflmm mmmai‘fl- ,, , ----- 61mm drain pipe 1% contains six at Maugham Wm~ 8mm“ m .v . _' Dam an: mixdmum mm 6:59:12 3:, at which me gate win pivot B: 831%! mm to flow into an pips. mm Q FiGURE PLZS Far agaih'bmém 2 Ma F}! xfl' a Fé‘xiz (I) I 5r ‘th gm: an 3%: Aeriawéal parfién a}: flu" gain: (Alkali, :5 1.541%:wa pmsure an 597% Ma excepé 44w ’39! am a; m pfpc) Pg; m‘é'mmz :- £2,4fi3y‘1}(¥m¥£3’ : 47.0}: ‘ 7km, From £53.02 Iwfi: flag and {2:342:43 Ozyfi’N-g) .2: @Zbéfli‘fij h $198752 2 “'79 ‘ 2.32 M mums. amen Wamming me same we af fluid rest, an a name tag: as 511.9% in-Fig. P232. "may have 1m: 53% bum“: wtfikf‘ of: lifmé’ 314,9,»wa mm. A but 6mm 33mm When {he mm. )1. of the 1-22un in in: “film"! WM“ the my mm is the 3m. the premix fame. ufzhe quuifls as: me [ l human: iii the ww- Links is use 2mm. Hmver. [be farce that the mm mm on {he-two M: is airmen! became the: weight in web of W tankx is Lfifferw. How d3; yuu imam; fer this appm'm madam ANNA AmamA fl ¥l$ U 8 E 9&33 Far it“!!! 1‘34? («/1774 77k [hall/39d Lyn/1.5) fie 13!!wa an 13%: bag”?! I; dug: fa fit: wry}! 4,5 m [11.29121 In” 77:: enigma 4’ka 12$ka 73:: Man 52.5 than if, fife dafiw Mac: I}! 7'?" fiifme. 731:3 is 71m 54;»: kmij a“ 133% ,Cr ’13:: fimé £0273 ‘31: aw‘nfiglfi‘ 5546. 'flms, «m prawn an my (2.9%” 61:“ We: ‘11:): wt; 1.3 flag may. $737! fidfiMti Mfg/bi 15:33: £17)!sz MW “1339 Ikdmfifll Mail: 13 ikfiferfi’tl 1'7 flu: Inchn’ed M!!!) £5 Illasfmlui 1:? 1M 55am. 2‘99 2.3? A plug in me balm of a pmasuriami tank is conical in shape:- as swam in Fig. P237. The air prcssura is 1?» id’s anti rim tiquid in tin: tank has a Wific W‘gficf‘fi? kN/m‘. Determine (3w magnitudc‘ direction, and line of action cf the farce exerted (m the curved gamma m” the can: witfiin the tank due to the ‘18 KPa pmssure and tin: liquid. MURE 933? £11,?” I}: _ . ‘ . I For eguc/dmmn, '2’ eréaul “‘30 law 5:: find: ; Fe; : fin» A “P M v T when F; £5 The Lari: he Cam ends 1 04: The 1” aid. Al“, F at, ”fl at} A a (“FMLK )(Ig‘yd‘) (a so” "é g I g 45,- VE‘ Jgg a 41.? If (42:: &)(,)(i M) k d: zfigaa':1.}5§m K I I ! I ‘5. mu! 0w” V [ 1%" mam.) «- wfiw 1] W 4 Wu 3 and“ [2? - LE 5' [47%)(w)(1¥155m)1(§m) 2 75"" AN Thus, ’ Fa“ 47.“? JAN ., 752wa -‘~' ”7493/ and flu. Lat“, cm 1712 Came ha a majnmtad‘e: at; ”7‘12” and 13 dlrnfevf Hakka/l a’mnyqrr! :31»: 739: 2‘86: 2,35 magmas 3f negfigibike weigh: am and :0 MM back warm: flannel 9f whim has MW}: in fig. W mifm of the gm: agutxm 1M black Fm gm (1:) is R. thinc (in am am mime against it): bucks fur an: mixer m: 333% Fo‘r man.) I FSGURE P2515 mg”: Mxm; w 6/} 5? Case {a} an M-Mncfiqm» sigma: fig: {192-} (gram 415%?) if»! ya " “a? i If {Wm 7M £35: 3%“? (£373) Fm»: 67. a; m m, ”as“ Fe: flu/7"? 5%“ we (4')] 4%» {‘51: (“five—W?” 0’54er0: mw) 7%: It”: 12: cm 7376‘ GEN/ll iaténén fangs“ mWh he 34m“ 69m! Mmfiiz dats an?! warfnéqée h ’7»: Mvwmt‘ drum; £1. 0n Mia»: pm a; 544, a; w = flaw/M : gm flair 1 5mm F320) 9‘5’435?’ ‘f‘hafi .. 7 .. 1%- yg- £375}? 2) Regardless of the complicated expressions for p(z)and P(z), note that P(z) is still the weight/area of fluid above 2. Let PNew be the pressure after the 2"d fluid is added and P34 be the original pressure. We know: AL F=—ry= [AiPal(2)—Pou)-[—y]dA and I}; ~—- “PM —Pw,)z§ dA. By symmetry, the z — component of PC is zero and the y component is zero because I‘c is perpendicular to F. For convenience, I chose z=0 at C(or 2c :0). The new pressure inside the tank is PNEW P34 + mg/a. This is independent of the details of p2(z). - What is Fuew ? PM = [(an —Pom)[-9]dA. Pour is unchanged, so FNEW =F+ LMga [—y] dA A A FNEW = F—y M9(;] The new torque at C is r3" 4A (PM —pm)z§dA A =l‘c +13%?— szx =r +§firAsz c a 0 by symmetry 50 1“ng =1“c NEW Fe rgfiw = ra + WMgAfiJrLZLZdMgA)? 1“ng i[(xG — xc)i+(YG —YC)Y + a 35500 I 02.3) 13d F +11 pla’re- 1.54423 rate F: f P414 are P resswe PH'SM 1 _ p restore {s (2 km, H’ Z‘M- (and: +11 Ibex. TL»; garage. \: P(Zu) A: P(Zu) LgJ—z oae +L m4 any ’I (ids .. on , ”C. (area of reek”): 1) 2 , PVessure is O YeSu H’ 09 +L; fluid between 2U C(ncl ZL . l‘h SN: ‘Hve box . a = 1% ©1224) =P<2ufl L744.“ Th3 firce ads on [:31— PKZ) ih +Lesei 7—81w91‘ms [st (area o 19 +rtbvrglc 2) above ZL- No": 1H1" ob‘kdneo‘ {h Pours:- (b)- Do fry ‘HV 90 me mgr F3 0 rd Fl... “S by P(Z) Ou-MAQ H4. box, We Cam find _ F; FULFZ—F, ”:1 0d" arc: : , Fq Ht 149“» Sole H: you infer} Ht <i§v<pressians 12W P( z“) and pm.) ingidc He but \N ‘M‘UL gNe; A; Vfi9=Ffl+ FL=‘[F0\+M —’ON\920 ~l0~9 (EB-EEL- -Z°)] {‘1‘ng w chL canes W174» #1 Op’ormcls ac‘VaHed by H: book *4er F; qretax premm (1+ #1 Cenlméd PM} EMF F4 Pd /o 2M +ZL LxL " l (3 “K: 3+ .. -:[ M" m9 {fl} 1 j W _, if: [War-"92° +/ow920 .15 (ow‘fm)9 (Zufl')] LhLZ figf;f3<l0~’lom) (Zn -— ZUH‘ZL)LM L7. 9 L Suck a farce SAPLJCJ b: app/ea? 4:: Peep +9.1, plaid. A: «expechd, Fnd :9 t"? fog“ : (0w . C1) 7 TL: ms f *9 fl-opcrs‘wvc WM) 1-» fine} F about“ ‘Hk +wo CWH‘IS )5 +12 1% Ma Q 0mg ‘Hu w e ‘H‘ ‘eflUQJfl/M 9W4" 4"“ ‘H—< no‘TS ‘31. $041 ‘1 ghoul" u TLe gen em! M) be flour, [2 Is +0 inlrefiYasrC Bur} :rpw VHNE PYO‘PRW‘I we CM" UR “" +LC PYejjUY¢ prisM‘ CA90HIH- Fz I. L2’3 T2 on 'H4 Cten+roi0| 30 C! Hana W< 5064' (‘H—trc I} (\0 % Gwrm ‘I’ b€CquJc "e Sjmhj V 3° Pa: ( L—Lfl (“F1+F4)=L¢%(--L'(P(2L)-/f(2«))+‘7(f’u)4u] L} / erEEYen =1” EEELEP m — 264.43% .) —%.+m+pwg(zL.zo) 35500- 35500 ' when/e E: LL 9L _ .12 Z I. 30 F 5 7K 3 +6»ch 5L“: N- L). o o Ful- ,L' ‘ A L “ 5.1, PM = ——§—L;—9(/’~—A)x+ Fm ——- Fw E:- wkm PM: 900.. - M) (Z0 — Zuft) LxLz TL¢ Sane approacL Ray Egan 4d,” WhWC Y‘ : '— LA- ): .f. .L—l— 2 Z L A Z P(?—) = PO+M — ‘35 Z < 23 b) so»: 615‘ Lifer: «er 9 S Z S 26 Pa) = Pom 7. , l ‘ Z. C ’ 2'1 2.7 H ) =i’0 Z Zok—OL— =-,0, ,:.7..\u<Z l P9< (HR) 2); 9331 + R _.o( 2 ]+C P (29) 3 PGJIM =9 P0+m : C < :9 PR) ; —-P. 9 (2—20) [(H’dza — °‘ ZZZ“ :1 + Pom deck: RB oLzo, “HM fiuu‘HOn SkuH Lt +1; Sane Cu {'Lfi equqfiau :11 02.3 (b).\/ $3” 35500 $13»: 35500 C) To final F W 'che on +L \ewa 330‘: (which H‘ Box) [S Simp‘j ankle ._.._ P6; Pq'l’m LxL-Z 9 Fa r 'H-v» exec {A $0.0“ Hie ‘oox , VVC (En Mi” We ‘Hve PM 550 I: PYiS M Since Pg) }; nd’ “near. 30 )NTEGRATE' 9 PM; -Patm 141.19 —p.9L.Lz< (y+«zg)(z;+22_u__ )_ 02k (MEL. £9 _ ansfale _ j A5 {xyed—e‘! , Fwd: = w)?! “0 aka. 9,0... 02.? (c) A750 01‘ ‘e‘erc M , HQ "Ecru RS». “13 £0". PM» , Cant! \S on" 0“ EAL $640 . 30 F051,: -P09L,LZ (Quin) (Z‘fa in) »—9§(L‘f*l;z“*z“z — ))9 35500 . $3 To flog +£4- -+0 Valu e, we gig; notl'fcc +L~+ “4 {Br/rte: {:5 u ”73 “Jew Bah“ on bail. Side: GOA“ o n H4. (7 afield S o {'qu 57w {5 we. Aka bCCawe 02 Sjmm+rj, ‘Hérc )5 m r712. Liz-U FHA/3 z] 31 Hence We] = - [33‘ zlzo)[(n+ozzx) - 043121232 Lxclz ZL z. Lxe9§[(ZZ_Z°Z) (\ +0120 —- °< Zg‘fzz" Z :lch 2:. 3 z 1: Z 22 Z“ —_ Lx/Doj [('+°<ZR)(—z—-~ 2/) ‘32" (4 _ “7)12L HOVI'y PC anal Eff) H4 ref} 0‘2 'H-( G'CanJ'IW i; ‘H—e 5M4 a; Eefcvc. ...
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