Fox e mc donald resolução de exercícios, Exercícios de Engenharia Mecânica

Baixe Fox e mc donald resolução de exercícios e outras Exercícios em PDF para Engenharia Mecânica, somente na Docsity! j | | Prabiem “1 2 TA Biver! Common sutstantes | o 7ar Sand deling dus Totupaste | “sita Petregt | Jetto | ax | | me 0f trese Ssudastanees exhubir characrereshes ot o lts and fixids under Atterent conditions. plan and give examples. É & 288 GNEETE 3 SQUARE 286 SHEETS 3 SQUARE Ter, cuolx ane Jelto bthare as Solis ar mom temperature 0º betous Sesi ar ordidare pressures. 4! high presseres or over long persocs, ; tney extibit Pluta characteristies. A+ higher tempera dures, &é dé Apre lrguiefsy aro become viscors Fleids. i Mode hng clay and sita preta, show Pleid Lenovo” thea sheares Sloiwty. Flowever, Éhes fracicare under sexeldenta apples stress, which 15 acharacterisie of solids. aa PoInpaste behaves AS di So! then At rest 17 tne desde. Inheo the ese +ube «3 squeeged hard, tootn paste “Bowas * out the Spot, showing fura behávior. Shaviag cream bebaves smart. Sand act Solid Usher 1º repose (a sand pre). However, d+ Pleros * from a Gaout Dr down à Steep meldene. o Frotltem (2 va TA Civen: Tante to contain t0 kg DÊ Op at lema, 35%, Frad: Tent volume ara diameter nt Spherical. Solution: Asstume maeal gas benavior, Basie eguanons: p= pRT (= Subbia tu tina, tue obtam p= MET,so vz (p= absolute pressure) % From Table A.b, R= 259.8 Nunlkg Ke, so r y = UR = 089,25 LENAM (234EDK, mÊ * kg * Cx rob + ro/x10 JN W=92.0567 mm? Fr a sphere, = EmRS = frD3,5 4 L o-fe8]! fp sonsa et saum 0 «DU  Problem 1/5 | 14 TA Open-Ended Problem Statement: Consider the physics of “skipping” a stone across the water surface of a lake. Compare these mechanisms with a stone as it bounces after being thrown along a roadway. Discussion: Observation and experience suggest two behaviors when a stone is thrown along a water surface: (1) If the angle between the path of the stone and the water surface is steep the stone may penetrate the water surface. Some momentum pf the stone will be converted to momentum of the water in the resulting splash. After penetrating the water surface, the high drag" of the water will slow the stone quickly. Then, because the stone is heavier than water it will sink. (2) If'the angle between the path of the stone and the water surface is shallow the stone may not penetrate the water surface. The splash will be smaller than jf the stone penetrated the water surface. This will transfer less momentum to the water, causing less reduction in speed of the stone, The only drag force on the stone will bg from friction on the water surface. The drag will be momentary, causing the stone to lose oply a portion of its kinetic energy. Instead of sinking, the stone may skip off the surface and|become airborne again. When the stone is thrown with speed and angle just right, it may skip several times across the water surface. With each skip the stone loses some forward.speed. After several skips the stone loses enough forward speed to penetrate the surfacg and sink into the water. Observation suggests that the shape of the stone significantly affects skipping. Essentially spherical stones may be made to skip with considetable effort and skill from the thrower. Flatter, more disc-shaped stones are more likely to skip, prpvided they are thrown with the flat surface(s) essentially parallel to the water surface; spin may e used to stabilize the stone in flight. I By contrast, no stone can ever penetrate the pavembnt of a roadway. Each collision between stone and roadway will be inelastic; friction between theroad surface and stone will affect the motion of - the stone only slightly. Regardless of the initial Val between the path of the stone and the surface of the roadway, the stone may bounce several times, then finally it “will roll to a stop. I The shape of the stone is unlikely to affect trajectory of bouncing from a roadway significantly. 5 * Compared to the negligible aerodynamic drag in air. Problem 1.6 (A TRA Open-Ended Problem Statement: The barrel of a bicycle tire pump becomes quite warm during use. Explain the mechanisms responsible for the temperature increase. Discussion: Two phenomena are responsible for the temperature increase: (1) friction between the pump piston and barrel and (2) temperature rise of the air as it is compressed in the pump barrel. Friction between the pump piston and barrel converts mechanical energy (force on the piston moving through a distance) into thermal energy as a result of friction. Lubricating the piston helps to provide a good seal with the pump barrel and reduces friction (and therefore force) between the piston and barrel. Temperature of the trapped air rises as it is compressed. The compression is not adiabatic because it occurs during a finite time interval. Heat is transferred from the warm: compressed air in the pump barrel to the cooler surroundings. This raises the temperature of the barrel, making its outside surface warm (or even hot!) to the touch. Veg E ta | | Re ottvem NA | We A Nondord conditions — P= NA Say To sa ET , RE EU TU PO SE Ada MR 28 a dm da, Corse sponás Neo AA qa Tmáo Ac “X sacos A Sa CL Sade. 2 o SUA Me, sJolue . Gisen + Ea “gs * O. 384 A (a ca Sa l&D 8 esc vera Pesa SA son. a s& AM WºR A NSAV p= as E SAN Come & R= o .O Ns Now tg” R A “Ne TULE a Sena, * een REA a USÊS “0a SS 2 a = *ON B E na Ee = o=A Mg e tom — lv tos º Rã E (EA se =4, ucidi total, Nes o a aVh 2 - “es A (49 Les8N Ml ass + (oc À  | Froblem [10 Veg E Tal Crven: Pet food can H= loZf Immtzoto!) D= 73% 4 wmblotar) ma 397t1g (zo tot) Find: Magartude and estimated uneertarntes ot pet fovdl deosite, Souto: Densitg 48 p= mM = 280 = / Es 9” pela, Db) Frem uncerta inte analyses “ - 4 no 2, Da ? (G Sm tm)! + (7 up)" + (é a SE Um) Jº Evaluatag, mf mM f anta 24 Bm ss. = P am 7 py TOM À !5 tem a 0,252 % Dor DE um € Eri Colem ccpstpa É! e f 7 D3k P Tom jp = É LIA H ep Hen gm / f e = 1) 4 der. = =! ee e mpg” 6 F TD 15 Um = o = É 6, 980% Substrtutras = flo XocsoJta [Caxtrsn] e Ico a853) j + ue = 2 2.72 percent us = E TT, 03*mm 102 m$ -4 43 Vo & Dim E x 102 mm DIna8 tzyuxoTtm mm. 3a Ma 30 3 f=% dequio a * 555 = $80 bg lm Thus p= 930 + Ez kg /m3 (ro to 1) P 10 Problem tl Boo E Tl | Given: Standard American gotf bas: ms lbttoo! og (20 to 1) D= Lb$t6,01 1. Coto!) Find: (a) Desta and speerfee grau ty. (e) Estimate wuncertaintes 19 cateulates values, Soluwtron: Density es mass per tunit volume, SO = m 8 m p= Da = =b m do Emrr3 dr) + D$ , 0.453 Jeg 1n.8 - e, fbtoz;—— «DSG DO = HBgk 3 PT Seas los topisyêms” O 9 Jm and S6= 2 . H3odka LÊ (jB Pmo m3” Jo00 kg The uncertasnta 1m densitg 18 ques ey fe us =2[[2 32 “u/Dô Fr ? ls Em tem) “(e ES “p) m . SE” 2 = É=/ ; Um et BM = 0.617 percent D 9 2 3tb m Vos Cs. D/ St mi Ho k ma e o Pp 7 pf & m (32) =-ssup=t0598 percent Thus =: [Cum + (suo) + tflo.en)+[-s Cosa") “ E ' Up = É 1,89 percent (E zug eg los) Uog = Up = 1:89 percent (t 00214) Fenaltg, P= 30 + Z:%4 kg/m? (20 to 1) S6 = 113? gor (ro dba 1) ! | | [ Beam nar | Nes ERA Gisea, SYondorá VBekcás aee Gas ma 4341034 Ls No D= ANSA * O. Bem (es Vo 9 Fá s DenÃa asd Sqeef ve arossias, &y E XsnokÃe rca Xe rà ves am codes S es podede! Ed Veni ds esass SRA Snes SO 5 Ss <A . BW A CIT axe am GEN =w 32 3 - N a to . — = vko A Fo º casa a, * ASAS vê s Rae 3 end r valo Ra, « ss = do SG = Qae a * To Ne. sea sk oasS RS darei e sem a dq= Us 3 Se “ X 3 SN A - t Os Re gs Lo sos SB som ap Dat MN cafe Na 5, EE sas a uy= + = o não À Ê aus de NN de= + (uam * Caos = (oi Teste t Aç= tia A Cuega Lao Ve dg= vas (x set) Soros tina, p= io 5 ata talo? Go NR age Nidk E O ora (Go Ns Ss S& 12  Problten Lis | Rep E Ca] Solution: Laterat acceleratios 15 green by a = VIR. Given: Lateral aecelerados, a = 0.823 Z, mtastered om Z00—F chameter Skid pad. Path deviaton: t2A , | mta stertentar uncertanta Vehicle spted: LOS Mph Find: (a) Estimate unce rtaunty m lateral atce teraton, (bo) How could experimental procedure te improved? “4, From Appendix PF, Up = teu)? + (ua) | ” From the gue data, 4 Z ta vV=aR; V=lar =[0.822, 32.2 88. « 100 +] = 51.5 44 )s Then . h u,=t EV sós m Ss A, LO «+ O0ue - Br ssh mm Bhoo S and Up = h t+ AR <l u ns + ' + s Q N S Y " us *[(2 x 0019272 + (0.02003t] = 2 0.0347 É Ug = [347 perment Experimenta! procedure cota be improved by usa à larger Cirere, ASsumng the Absolute errors sm measurement ar constant. For D= 400 ft, R=200 tt t u v-/a? = |o0823, 32.244 1008] = TBA/s = 49.bmph se + uv =t 3.5 moh = + 2f GIL mph = 9.001 ; Ur 4 4 ua = +[(ex 00101) + (00003) =tp.Dzs Or + 23perent 15  Problem lt Neg Sd Given: Dimtnson! DF Soda Cas: “f D= bb mm H | H= HO mm —+ , ot Find: tuas urement preasios needed to atiow volume to be eSbinatkd witm an unerrtante DÊ LOS pereeat or kss. Solutron: Use the methods of Apperdix E: Computing equadons: = Tem 4 as e Bs ut ESET” Since yo TOM sen 2% + TD and PE = TDH 4 ed q oD 2 Let up=* de ana um = É =, Ludes PIÃO, -+[(-Sg me ex) a(o mpH 5º] “= al(E “+ 289] Lay - + q 2) tapa E 2) (5) >) Solvrag, , é uyt= (Ep + (silo +69) bx d,005 : 1 a Ê Ux = tus + (eu95] = 2(0.003:64) 2 (0.0078)3] = É 0.00444 v” If 6x represents hate tre least Count, A minimum reso litros of about 26x Yo32º mm 8 nteded. o = ato MT, = tô óx = “Ra + (9º wo = ; E z Et b.158 mm H [Cs =) Tre) << . 4 8%, p brsg ma 4 - Check: Um H To mm * É Jeuy x10 + 8 t/NSE mM (+ 4x 1978 4o D dé am tesixto SG  i ! i i i Edo: Preeisida db twohich D MUS! be measured d eStmase Problem 1.11 é Given: American golf ball; m =| b2t0.0/ 03; D = 168 40. density cofre tocertonta 0f 1 percent. toluton: ApPIy UnErtanty concepts Definihos: Density, P = = gy =E7R = zpÊ bg Compunoo equation: Up =S[UERE ux)+ =] From tne detinrhos, P = Mo. tbm el, D) TO DS Thus Mal d 2 = € am” vao E = 8,80 me Up = + um) +(3u5)] um - Um +9U4 L 72 So/viPg, Up = 24 [uu] Form ne data gen, up = to.nivo = 150/06 (+ pooh Lbz 03 4 up = glfo.or0) -(0.006 n*]º -L0.00262 0” & Dzbih Snee ga o ; then SD= LDup E É IL 16006 = É 6.004 IA. <— | The bai! diameter must bt measured to a precason of | 000844 10. (bot mm) or beer do estimate density mito ES perento À mem or Catiptr toutd be Usés, Seg E Cal po “ Problem 1.19 (cont'd.) 2/2 Uncertainty in volume of cylinder: ô= 0.002 in. 0.0508 mm Y= 1 mm D(mm) Limm) LVD(-) vo (%) ui (4%) uv Ch) 05 5.09 10.2 19.2 1.00 20.3 0.6 3.54 5.89 8.47 1.44 17.0 07 2.80 3.71 7.26 1.96 14,6 os 1.99 249 8.35 2.55 130 0.9 1.57 1.75 5.84 323 11.7 1,0 127 1.27 5.08 3.99 10.9 141 1.05 0.957 4.62 4.83 10.4 12 0.884 0.737 423 5.75 10.2 1.22 0.855 0.701 416 5.94 10.2 13 0.753 0.580 3.91 6.74 10.3 1.4 0.650 0.464 3.63 7.82 10.7 15 0.566 0.377 3.39 8.98 11.2 16 0.497 0.311 318 10.2 120 17 0.441 0.259 2.99 15 13.0 18 0.393 0.218 2.82 129 14.1 19 0.353" 0.186 2.867 144 154 20 0.318 0.159 2.54 180 16.7 24 0.289 0,137 242 17.6 18.2 22 0.263 0.120 231 19.3 19.9 23 0.241 0.105 2.21 211 216 24 0.221 0.092 212 230 234 2.5 0.204 0.081 203 249 253 Uncertainty vs. Diameter 25 ——— L(mm) s uD (%) É DI NO ds uL (%) s uv (%) És $ E z 10 E s s E > o 00 05 10 15 20 Cylinder Diameter, D (mm) e) Problem 1.20 | sata Given: Smal! partite accelerating from rest 9 à Fluid, Nes mwetght 18 W, resistirg Force FDkV, where Vs soccer, Fmd: Time regured do reach 95 percent of terminar speed, Ve - Solution: Consider the parriete to be à System. Apply Mecutons Second lauro. Gasic equation: Ef = May Particle <p w Assumplas: 4) W (5 nek werght 2) Resisting force aets oppostte to V Form kv & Then = Wo - =emY «May 2a =W-kV Ema, =m “78 º dv j- & e” = gu DV) Separariag varabtes, ev = gde fe ty Integrating, Psting that velocity 15 ger mibaitys v Voe dv W E Vl = - Evo Elm Ev)]= Sgt - gt vv or — degt bot “by ve Wi ,-t8 mEv=e Wo = [4 e % | But VV as t-200,S0 WU = = | Therefore kgt Voe E We tg when É =598, then € W = 00 And car =3. Thus ke. + = 3w/gk 2! Redem NRA o sa ta o Gosem 1 Senso ande gsreeNer os Lee cad R a Sed E A vo NA, Tens A Ot Ca. o Co des A deco À e Trad Veares coque ad às ceods “5 ves ask É Sereno Quad Se SeNNsos: Coma: “das See qatde No er a. saSue, = 4, Sra Nes astomd Nous p= . . o ads Rosie Capelo " 2“ Dea Rsbes—> + Mentiras 8 Ne net AN “ NEN Resina Sor Bs sqesisÃoA da sã ES Ven, Les sa-ÊN = mass E Sta Sô FO Sa os 3 a VA Nessa sua G4= O end “A =To Rs VN 2 DN da” a Sears ssos valsas 3 3 o NS à NA 3 “es a Neg Es SA “Ss, A dessa > 355º a = aa. A Gs ONE er O AE -osss Cada ss - GS -AÇ Toas + tnocos)= E SS a los 4” = 2 8 Ss a Zz | Prodam 23 sata Gsen Verá Necsus A Canas = NEXO TA Woo fera E astow dé (N= De. Negheà quo cesstance . Craár Cake É (65 aqued . esa ts) esa , S artes UR: an cedensa squid | asd 43 sao sas a Laden eh ENT NX =utaÃão A Cossissasã) 4 Zeus a Á= -"a te Ato Fe TRA = na , and fç= 2tço- esula, TE-+& —+ NV Neo , ves =-"a 5 Nrdr = ada ,; O- 2 =-as Boo No Soa, E = não (So U=tiç= cena (on Cs uÃ= Teo Tosa À a= LS e S = Os - As cu: “Js e 8 Ven - E! . o z si sotado Soco aade AL “= [resta ANDA a Nela NR sh NV = nan “4 se Ta Oss Pas: Frow Eq.s Se = Seas = A AB O S=Es Va A v? 4 ? “ = 88 [Cesta ses aa gd Se PC E ASA (Eq ny and €,= SAY (eq st are qrescieá Nasa Eq. 4: Initial Speed vs. Max. Helght Eq. 5: Initial Angle vs. Max. Height = 8 a 80 E E q 8 £ $ 40 i “0 É a < 20 = 2 m s B E E E o so 0 5 10 15 20 25 30 º 5 10 15 20 25 30 Maximum Height, A (m) Maximum Height, A (m) 7 o | | | | Vedas, AZ | sata dO Gac Ma doser AA = gota Ghca Neca dosss. EN Coca so “y= Bo a ea, 46 Sperd Tiesd «3 Vesenhad Squad Nes da deem às Vedrcol LA anca No cas dA V=0.ask «SD daXicd dass To cen some squaA E Es AA: EN Squad De SOS, ond id SEMA EANNINS . Ey= da Comedor Ms Anser as à sue: so . a Rate q ves UE ad = wa, a - “ay N Sesi. “ENE conÁÃsSss V=o A Neo q8=o - . = QN as cpgosTe. No SN Ren TE “ay Yara ano SA TarençãoS squud a=o amd S=d Rec. = RW RAL E) sã Nç= VE «) e ae «ss . a. 4 Sj= | o via * oa Ne” tab = Sa.a ele Vw] às To cds. Loc s A dsoas A q toe crendo Os esqrestim cerca | and a, From Tg d q Ze A Sd As Sac VS o= nd or *— Sal a de Sugertiia dos Conhes arA Ne pokada - A és = e &s No Mnt “a, C A º = * - - 2 A Qs— OL = Ss er epi Es os ce PA -IS . EN Toc Aco asa, Ven o q: - Ly tota E. QuÃa-(oas) VÊ mSa s ” = GANA S Vaga e O For Cree Soh Us Red cus Tess once ZE “ae es JS cn tor PAES “ E as or açávia, ] sz “a tb I : [Rem Nota Cola) Nessa “a, + Voa Seen ap « s= Y + eras (sam m E E Nes mar Ce area au ssesà cas LAN Bases Sai E N VN Sweo | venda O gps squa. From a voe cos varie S= AS as EA Asi Ta N- e. Ta Seia é os expressos for de SAS voe usei 3 Es= mna- Sar =" 84 Segosesaãa, sos çNdes asmá sds SETE voe rose C SR = CEB 2 z ad sto ESA NAN E Na A Se asd Ae eta Ee RR RENAN ES da 4 GR e ES Da A ES Fem “as A oná 3 ore NASed. Nona Eq. 4: Speed Ratio vs. Distance Eg. 5: Speed Ratio vs. Time 10 10 3 «Ss 08 08 06 06 04 04 Speed Ratio, V/V. (-—) 02 02 00 Do 9 100 200 300 400 500 600 º 5 10 15 Distance, Y (m) Timo, t (s) t 20  Problem 1.22 [o AU | Gen: Unit conversians pad! Convert (0) 1 Pa to tbé br* (pressure (b) | gatioa to lrtees (vo treme) Co (Absinto tofos he? (uiscos tes) Solution: Use basic detiarheas (o PRB IN IM, Lt ulo0esa al À pg 107 JE ha me mu teaE S Zn = OD ligas = gal, t2/ 08 SD to00L « 379 gal 14.3 mã Te (> 4 Mestm' = [NS 4 ef ul 2048)tm* = 2.09x197* tofas mm datas NS Pr fp qm 320 ds (b) (c) a Froblem 1.28 Givea! Unet conversteas pad: Convert (a) | Nro? to def has be) lho to Men ls (es 4 Efe lb to nº Solution: Use taste debarhens as IM ef (a) mea a AS b hp = 55 bh bf, 0.20% s 2+ (cs 1 Blu + MEL Tem + | Blu 2330 Meo fa 2530 1.) tém kg 31 x (075)? BM E APIS 2 To AS ar be * 7% ER IbÊ Q3098 PO x th PIE Ibema | AS Coressure) Cpswrer) mlks (specifaé ererge) = GE IDT Jet (as Mu /a:E um Cb) s bm «em Jbf 0/9536 kg (2) a | Frobtemm 1,29 | NEVIS i Given: Densrtg of mercury 18 PP = lb.B Sig Its, Aceelerafion DÊ grau nte on mass 13 Gm = 547 fé fa Find: (a) Specrfie gravitay 0f mereursg. (6) Specific volume of mercurs, sn mB ug. €) Specrfé ceght on Farta. (4) Speeifee evaght on moon. Solution: ApPly detinitirns: FP = Egor lp, sã ele ro ( Ne tnGt the mass- based quantirtiés (56 and v) Are independent of Gravity. . 32 Thus SG = U3slug, fra ” prs " nagatag = Be 56 fre do so4e mB Slug tem “mB = , = 137x407“m “es Slug” Ars *2,2 bm OGSBL kg 137n40 ag v €—————+1— On Earth, e Y = 2 3sug ser te MS gua be /ty3 g E “as SET Slug fr Per der) On the moon, X= 23 SUS surfe Jefçã bt fer3 %, m Ars * SE Cao dp o et 4 */ , [ | Rede var | NIVA | Goes, Sears SL anão Vomiá on dsrentions sf Lora N NR, & Rome asd S Loro = Sasidedh = 24 usE Nes = Peca- quites = AS osà E tece = snáã do = ass Em 8) comserseos Lados No SI sas do cdros ás wnks sf noss a Refis supuns - Grom. 8 Tie cossesseos fados qse Noca Ne Peas Quirtes & N SA dá = “as à From Nekoss second laro E = a z . = (nd RN a oca Be vet sf vossas NR E E “Res - eras “Vo comseà mas do SE vago Pele. Cos eta 6 É Seegader Raro Neca od redides GIRA CÊ ge E “BSO ta mass (Nei ÃO) qo enoss (SE vnAS) SO às Vodca = Vsodcdloa 4 ZA VASO ÉS 2 SANA Ts * a N N Bicas po es = Recs oder + as —* O dote = sow TA Eeé Vedas vas SAO | Casaes Gen SL anão Taxá en gas dimensions of Lea e Nota and Nena SRA es desta = tocado VEN SE 6 | ER SAM = A : UR É A ENS = “9 “e Fred) conserta o ta SE us de as neo a e psd, ade E anão (O ceNdisci Iagas ST ora) Nº Bda sf moss Sais Se comaer sen Cadiers ose vraselnad = a itasaisoM « SAS, « NE camada do vmazad & Seas, NeE Lx V Nsmemass = Ceraron » SA cida = wa o à God = 8 Sad « On “e ESA Gamito us 22 To Loshoa Secos to a = OáS IN às USB Isost dosmensens af E RS Ba Te À ONA nosso ase Garendosu dimensions . as e Sea ds To Bs t=T From tias second Vas Tema = “a so w =” Ea , a . = = NT Na > cod Be ani feras 1 = IN (Lana s 3 To cossesl enoss und Xe SE e = asedi Aromeran EVA WIN Loo & x Ra Cadu “ioasdeid Temeras Qu vê > « TS W = OAOS ta 3t  | Proa 4.3 | ATA Crises, Comgia, comer tochas as a mass ST ras Ra, unem CNed Co8S, Ted”, «oo NheiaNt of ússias a Vo esses NA CA ao sachasme ams RÉ Toa <u SEADE Coe Ra E= wma si = tão indo hs = Wind = sa Ade “ao Nas Seg nana See Ne ssdiare 1S quase = ae nd - io s R& R& From Tonho NAS p= tas Ava Lã? A Ve AS E Code SaalMs & s x Sus Rea o a e vas duo nek vão - edad 37 TAS Neg Snes esmçã 5 ca sf ENA o soda, Sa, e tas = sa aà NNdz | A | | VeNdem 2d ERECARA Gin: Sedociy Geda , T=atitay Casbe Na) Vão Eqpedixem toa Se Las dAreorhnes , and A Ce presa one direasmunes Lor LZO and se Sototios : Ne Nope A Ve DAracelives m Me *e-q Name o ao da AM V n Ss q Fo Na est -tsu3 , Bem um or sr = - Sa, - Nena BLv.ta Sm “o cal To shoe Be AL Tesenliol ea putos (êa (E Ss , Sapos che sas velahes ond Sucpa 47056 4 Ang = -D Ay + cond act Qn a = AnWã ata ese condats And Nem est a& A Ê -& a or Nena “= E) “ou CAN Sida, Se condeno a ond do arm Cred. E . selocê & ERA y qa spa AS Gere, Jolaes Vá es resmas asse otiamned 'ea, ass Ro le condad of tiearatron -. . “Severo ed e ae Nem avo = 4 ando Re Degomines ase ANA “a Ne eo NO == s o as É as ã a Fa cre ae fo abs onã t=0 fer ad 4. A jts Re ese en = S 5 Re esputa em of a age Ba . Cosses se Seus la AMCeresk sodoes fc Co “o | Vedder 2a | azoto Gases: Elas OS aner O - «Sqónteé. a e Sa Lda Nec ais oa LS Ted am a: anal ros Lor a Gas Sreases.. NA a Va E cnsrbeas vs Va Ca apa dra q Asdar se Ssesal qo ka SS eo Tae DNA testa The Nope € Pe Arenaimes NN Se tea ane. & ae a, da ot FATO a Nes Sa - ENS q Nes = OK and sm Nesse, MAL Tl BA dA a Ta = & Do da . ara 5 o . VAN cas Na os cd 4 e ENE = cena = ta c Nina com aa Sie do Nos are que -€ Cor amet Ve AM = o VMA A Breasses “A Nur & AM are Soliaas o cesdiast SS ES ASOA Toe Se Asqoeg ca Be gos (SS Be cana BE COS arena? e na For c=o , as o dA and tro Sor sd A. Ne. NES = che e Corea A = cast oa , Me Gas Ão Qe Coser as Lee = E “o Ve. ão ASaa a tl Rede 2S | 222 Ya Gases Fios Sick . “qa (GR Aa DA —. adere = 46 Gel. o aê % Ev, coarbarlas en. Met: a fers Areganlimes seduda Oo a RA qosses | Rrcrg o qo ED Ras | Soc. Snes A ARS anã = Ás do Pe same a da Nos . à s Sicepanhmes ase qosada ko QB sda so Deca s TN - 3 RS RES É Aa Ha Nine da e SA S AR q =º E Seacia, dnad De LENA er (ua “a = (ua Sar cen tara Recuad tas O (as (Cat = = 2d = (e 2 4 tendoÃL = do - SD uea coma = ão | 1 Be-o36, ] Cato do C=4a c=2do C=tu do C=aA C= do | | | | | | | | a l tz | Problem 2.8 | ara ta) tvs, mato Gun: Steady, ;ncompressible flows im Ay plane vorte V AY = V= t+ 2 É when = Emtls and coordinvses arm mn meters. Find: (a) Eguanoa fr Stresmmbine farough (ug) = (1,8). Cb) Time required for à fieis partie to men Prom x:lmtdbx: Sm. . sy > Soludsa: Tre velociry reta 1 Veuttvf do ur É = 07 Co mpttin. adons: =! = mputing equadons E) nn ta ST E Substrhatidg, dz = az - Z So E = y Integrar “grana, lux = bug + E «ly rtwe or qy=ey Pr por (Xg)=(h3), O =5 -Í Thus x -5 18 equateos (a) Por a partict, up = SE = 2 om xdx = Ad . 24 Integradng, f xdx = xt a So t= tão 2 += LAB meo (tm, É lts ; co» m [A as | Redes Va | are t! Cossess + Saci CAS A - SAL vas s WSvere ese N Fa . Find E Srs Ss sd sm so de ses orá. ay De Vos asur “a prior A ç= Ce = des Sam pane = qc E SN Poeira A tem Compare psNeline vos Ssessrce Sender Some vet Sewlaem So 8 God veda 1 Ve Ye Sa Lo a N= SA U as vo os essa “o o = OM NR ANS & da, Cs Ve qR O er E = ad sã (E =Çast RS er CE e CR da a E soa VA e Lua “id “LX egrara Egs. 4 oras we SK ass ESTA o as A ane, : + As os as e e oná dee ass de as AA + Aa ce o A e ORA =ce . g, a às To Has Ve epa & Go pelve vs Amd À Cory Ve Porosvels ae tape. R N A = cel o MNT = A A da 2 = A oe Às “e = ar Cree E apatia, eAgrestismo So que SR a SE AA dO o CM T=dn o Ca SD e do Ce (AO ê Mt t-o tm N=C nas val. Crea ass Bem Ne qe & Ve paid 1& A = 2. RESNS (Ny Be Aressine à Be Au None Vos à da. 4= Ta Ras da a e a zo Ra cos ta Reage do PANPEN ta 2 Ana - E cs Saà Ane . | o SS e Shaus e. =c NOS Noca Qu ! neo ces este (OD o Pes Lito | Problem 2uo | arete | Gren: Velocity Bela, V =-Axi+bg?, where azb= 25) and Fne coordinates am measeres 10 nters. Find: (a) Fara mttr re equa dons dr parhele Mmoten. & Parnine equador fr particte at (ug) = (2,1) at t=0. (0) Compare wu elrea tre Trroagn same porn. Solution! Velocity fieis is VEL +VA O Urcax = by Computing equanors: Up =, = dt é das = dk 'strearmtine UM up = SE «ax do Hb = - ad and tw = at Thus x= we - Za Vo de -=+by So dE = pbde and bus +tt Mus y=met = met Parametrie tos : at g Sotumg fr CE e “%” = So Xy* A for particle at (X,%) = (2,1) Xy = Emyilm = tm? Path tas Cb) Pe Stremmtina 1s dy «E « &y .44 —-E dx 2 ax ax x Separating vanrabies and sntegradang, Jg + Sd =0 0 buy tlng *CCatol or ug = Fer pone Cy) = (2,1) the Stredimbne 5 6x mama Zmt xy = 2m Stramine (0) Note! AS expected, patinhas and <treamtne corneide for | | this steads flow, | “m | Reddem TAS | art fes ResACEED WeaiTE 4858 OO RECOLED WAITE pa ato" Greer: Ledoiisa Sida We pa (MAD cul | Raros, B= Cel Ss S coordmplxs wncasared ms wekgcs . Vi: Re gofico Re quaiide RA posses Reougin Se ge NS E Vara Neo + Na SS Cos OR Re Sremahimes Po e ey e a es Nronaço Cia Ne post & Me mãasks Teo, Soh io: . de For o pastiide (um ES omná nr= tala as x ds BA LAO = de (de = ( so (ss RAL , 4 + te e AÊ An Des sttasat = arabe a de sçePS ES) : a = Cu = Sal aa , (cas a “. as ap . s . Ne qe eso ta qNRies “ea, esa, Los Svcnise hos Ne Rec oshine ds Sena A (od aysem KN fem da, Ned . res da Es E a O UC 4 B+ Coe da 4 = Chtslne e Ads cg MD Seo nune, Broa pos GAS ques Css. ss OR sotoá is via for WB, anã E DAS o = mt tro , Aa 3 5.0 aos . ceara: red da Streamiines: t=0s Pathine Tets AEW *= às, <= 30 vm 7 n o 20 1.0 00 so  Seis ey: | Recedesm Cada, | rreda Casas + Seossa, Si Lda Ni= GA ANN + EEN “Vesa arte =, - p= os (ANE COTiaNoNes GSE ANCasaTEd «sá ds | Na: Pe GAR Ca à este org Este NY e 8 WE Veda REM : 2E NS Compara SAR JEANS SESA Mesa a8, Sasme pork dA tos, and às. = For a spas teve , = dela end = du fax Nem Us ca (DS e É E & = (aca ta É o GRASS and A Ares ãçãs e A=te ri 1 = exe da , (eat = Ce asd ar “e E Nie come te ssa sas Ras ron bos e a N AS ve Se A censo + ÀS Cousnd (a S. gs Cam 3 AX = “ Sem a cd MMA Cd SH O qa GO á a A de - o q CAM LS a E Ana sâne, s CAD = tensao MR Goat a. ON ques CA. Ben Ss ss Aisha, Coe OU 6,4 od € um Kas . | +e als «285 Sah | Wui=o ( 4= Ato, de Ne “9 fareamines: 1=05 t=1s EE te, d=w 40 30 y tm) 20 1.0 00 E)  Gasem: doi Bwis | | Veces TAS À penta ba Dedo asE essas. VS des RIA Ve Eae: ( deco Ro ass otite sa se TESE e. Ae ER ERAS qavt ( As ud Ye END ash e Arterdor qoind Seu ve DOR ço Senso: Cor a gosiide us aro ord = “a E qe ado lg (e õe | Aos dn Ãç= LA anã pa A er E 28 ta a, “se sa Ago (alpes ã euçãs sa ae e Se Se Ne eng doa Sases. a E cs diodos Va Necarhuve vã Send (a RS Es dali E q Sem da = So ana Be Rea aehise Pena aa E Ao . Ts d+ ANA Sa (é AS q + or a der SAE = o Ee EN (Ato ond se ua EMT le Wux=A = Nas tn ha Xar toa veces / ! = ars Ata 10 Streamiines: t=1s / -Pathline | t=2s y tm 52  | [ Veces EA La | A e, se Es Bão esta XIS | =. 2 SÃO EM pets CAN ouned Voa sms çõe EO om Ve Sair vos po (ao A tras | 50 Streamlines: t=0s | | “0 | 30 > 39 10 00. e a 2 4 6 8 10 | x(m) ; | | | | & | | Rede EM | tt TA gogans E Ê | de A Gresess Neceias, Ca Ne GA DT + esa . Vere. arCeis, | = OF, ond coscdsneies gre veogaredi w enesass | Ma: Be Acensire Ra qustes Reu Be qui Cao gi asa Ma leo GERE sue Na Compete 8 Pa drecanhiras ASSes. Proud Re Sosve pod A NES Naná US Sedutor, ; tre chne Às as connedis qosdes as passed Pesada po ea A costas turmas Teo vt, ond 55. For o qostade | as dela ans = Salar * à; Cas e ae ate E ara SÁ é - (ecciiar “= o = Me A Bos a&a E - aus Blu A AAA E (q A= A so da e a x Vo . - A = CA = as Va ES ão etasd Ss | Sad RA das Lor ade, As, Ud Lo vees | As ARS a AD , us ES 8 (a Ná NA Re decoder Var ea Na, Ss stora mscluro Coe om Re vera BETtas os Srs Vando. Rea Mre coke ds Cound (Ca E Le das + Ras e 3 - CA day (O d+ Cesbar GALNÇES ora 3 LE ns 0, A “o a É s ES T ans ds o Sr ar Ao Solana Suas Cor As e . ads e 5 Vo “Ar + h BA ue vs NEM . ="5 , = 3 Eb RR , tro 2 oe As 4 à Ave!  DIMNOS E But CTONQNODE Sepr DVNOS S ali ENOADÕI OO, Gees SANDOS 5 dera alas DOR Ger dons é Soa siena dd NOS S Bau SISAMSDOS RLL e a N ol o —| u o LA - £ E 2 le É 91 Is é o “4 o , E - z x ta nd « of 4) li . E Po lã [ed ê o — a o o e o o 2 Ss 2 2 2.8 tu) A | ao faro aece peso rena o a < “A E A E - ê . o o 4 E 2 4 * 3 a e “ E E 4 É e 70 o bd “ o (u) 4 aesross 2em axu ate Bee / a £ ae f | Problem 2.21 RPA A em, Crer: Velocity Bed 19 xy plane;V-ab rbxs, where a=2ms and bz ls! Find; (a) Eguahon fr sirearmine tnrough Guy) = (2,5). (b) At t=Z2S, coordinates vt particie (0,4) at E=0. CO At erZs esordinates o! partie (L Gas)ar t= ts, (d) tormpare potniwe, Sirarmine;streaklpe. Solutroa: For a stramtne de dy tu vw Fr V=alrbxs U=a andv=bx, so d dy pm Oo Ex | dx =X dx z dtg Indtegratina x* a 4 = b 2 Tr gute or daqui te Evaluahas c at buyl=(25), c=y -Ex* Em Ebro Cm) dm Stream ae Hurongh (x) “(é ge Em u E E To beak. parties, cerne parametrse equahens =“ <p dx =adt, aod x-% = até-to) “p dE , vp = Sb «by, dy = bxdt =blxotr at —ato) y-y = butt) + Eleito) iate (t-so) for tre partick at (Yom) = (OW) at t=0, Z=0 taé mat t72s, x= Mis «Ym ga qr E & at tris, gem +gx mB gy=Bm (be) 7) <— [Problem 2,21 Conta.) | A re parte at Guy) -(,mic)at t=)s, X=mWralt-to) = Itadt-) So at t=35, x = + lmss = Em = + bxlt-to) + Et) catoler ts) = astra (MelécD + fu tm(po,)- 2, Is (t-1) So at t=Bs, gz pa tl += = ot (cs Au these pomis lt on tre Same Sirecm ae, às etwn delotu: C) (Stores) /0 [ 9 T 67 (14,3) s E 9 L Siam ne Ylm) LH Ss II 4% Re : st (0,448) Z IH 1. õ 1 ! | t ! D / Z 3 % 5 Xe) For tnis sjeadey flaco, Sireamines, patnhoes, ar Strmakhoes tornerde, as expected, bz  HEM SIOSHEEIS FILEF, 6 SOUARE 8 sá os teem, Guefhoo , arg its de As . , 6 Seta Secad gos GS spa So» = a (A CAN apra ES o ares CD trend] too q A = te 4 SA-a Ez uz USAM Streamiines: t=0s t=1s vim) » Streakline x(m) bes | Problem 22% | ve netah given: Vebcite fetd Veaytt bes where aals torta Streambines at t=0, 8525 and u = =ay cal mst] so da acao luhere, Mofo AME coord mades of partie te at ty g=2m+gniSm «MÍst s00m » 3-9 L=Im+ Ex 2m(2-0)5, Lulu 5, (time +09) 46) = 2ms Lx VE Etsy (23%) s> «3.22Mm GS Shows on Ine néx page. The stregminde 13 fauad (at gra €) Lar Lx Substatuhog U=0y and > &t Z Fim tro, EC sat lo m)=(h2), the Co 4 Ei, gt= Entes; AF Cho Go) Ch 2) then Ce t=2,y*= Sé = bt, so dy =btde and gym Eur (At t=35, particle tnar passed (ht) at t=25 (O Plot patnime and sireakline frough (2); compare Solution: Path ie And strakine are based 01 parametriê eguations tor a partie, Thus ve So É ud, al yot +8(E- o), 4X =X tOmltoto)+ E, alho For (23, ty 20, and (Xosfo) =(,2) Thus at tr2s, y=& j b=08 mó ts Find: (a)Att-2s, particle nar passes (ni)ax €70< -to) = + to =p (85 At t=25,(x,b) = “Sm For(b), &, = 2 5,00d (hoy) = O, Thus ALto3S, he particie tá ax 607, 3.00) m At t=38, to=ts &) Farto, tre sirathoe me be plottes at any é by vagas ts * > dk = AM des or yt= Rbt, + 2. zbf bé As Thus c=U = *o byte; at Cut) =(h 2), cz 2 ty t=35,€=1 ] Ce 9) - (ays83.25) x(3) = ime quim tona, dao ((2lur, trça-=))s?a 3.59 mm (e) LC Probtem 214 Contras | ed UV = % tt» ae” . Recall! V=ayt + bt? ,whee a Isib=as IS os Go) * (1, 2) mn. ess, Part (a); Pathisme of particle located * ia Pt met athiine Plot A€ (eo, ) Qt s*0s: “8 Ez t 69] tes]xm|y tm 4 [ol 0[1.00 a , e ê e D: ú 0 E 0 2 4 6 8 10 é x(m) . E « , ; ) 8 : Part(b)! Pathine of particle located Pathine Plot i at (votar t=?S! 8 E > sOp top em) 4 es 2 2] 1.00]: 2.00 a y 2 2 4, 7.67] 5.00 em . o x tm) ate, Part(c): Srreamtines through pot (rag) At t=0,2,and IS: Tre 00 1) 2] 3 8 ts) Streamline Plot c=| 40| 30) 20) 10 6 to ()jx tmb y Cm) | y tm y temo y tm) E 3s O] 1 2.00] 2.00] 2.00] 2.00 > 4 o” 2/ 200) 224| 245) 2.65 E O| 3/ 2.00] 2.45] 2.83] 3.16 a o[| 4] 200] 265 3.16] 361 2 T tos 0" 5/ 2.00] 2.83] 3.46] 4.00 o| 6] 2.00] 3.00] 3.74] 4.36 º o) 7) 200] 3.16] 4.00] 4.69 o. "emo s 1 of 8[ 200] 3.32) 4.24) 5.00 : 0| 9; 200 3.46] 4.47] 5.20 0] 10[ 200] 3.61] 459] 5.57 Shreakiine at t=33 of sc me em particdes that passed thru Streakiine Plot pont txo,go): “8 E Pos) topm[y(m 7a FRA [ of 3) 9.25] 4.25] 1º 3] 667 4.00 2 ao 2[* 3[ 3.58| 3.28! o 3] 3, 1.00] 2.00 e a = o 2 4 6 8 1 x(m €7 | Vedder LIM | 2a Gisen : Flo cl qudes ese Sáiscas gas, quiias as Shown. q Seleção * NR + he O So, a am Una = Oro ls Estas Findo Sens Acaso om e qe (indicate Atredio ) 4 MAS Pe Nom A sivaas Syrass across RIR VAR Jose equidios Ler E Ee Afeto = . RETO do Vivas [EN 24 tone à, BA agree que | qu + Tso Tau (eu 3)- » E) % Few Tolehe Mt, for cut ses, pa ismasE meslati Rus tm He = MENS Ms ,otom A wa Ss Ses tm Lam -2ma nt Ne spças qiiie so unas susto . Suco Tuto | Re dress Aress om Re “pas qe IR aà ms Re qias + Avreson. Re dear Aress sosves Nesta vo sA 4 <= po -- É Str 4 Be ticos res sm Ve tos Loss q js st Ac Qua tienes mom < Co quilo, merlaro ve NO Vivdicoked sm Re A Sb e Jo Problem 2.18 REA TAS Solution: Apoly defindhois of Necstançan flued, shear stress. Given: laminar tio betrseen porattel plates. idos td tu cpf 4 Umax 1=€ p) A VYT7er T=15€, umax = 005 m/s, h= mm, water Find: Faree on A=03m? setor of fever plate, . Vs .E dia Sasc equadoss: T=7, Tl dy Asscemphons: (1) Mecotonão Praid . é From tune gen profile, U e umas[|-(E] »S0 & = Umas C2 XE) At lowver surface, dy = —hfe = — Fumar S hE To liocser) Mm =u - Limas (ht | - re Sema Tux >0 and surface 45 postos, so PD rega. Ea max A h Faltas From Appendix A, Table AB) pad x E Nisim at 18º€, 59 —3 F=talyxiO NS posm Bm 1, 1068 com me 4 S mm mo P=00!81M (to rights) - q! Problem 2.29 Lo RA TA ad Open-Ended Problem Statement: Explain how an ice skate interacts with the ice surface. What mechanism acts to reduce sliding friction between skate and ice? Discussion: The normal freezing and melting temperature of ice is 0ºC (32ºF) at atmospheric pressure. The melting temperature of ice decreases as pressure is increased. Therefore ice can be caused to melt at a temperature below the normal melting temperature when the ice is subjected to increased pressure. A skater is supported by relatively narrow blades with a short contact against the ice. The blade of a'typical skate is less than 3 mm wide. The length of blade-in contact with the ice may be just ten or so millimeters. With a 3 mm by 10 mm contact patch, a'75 kg skater is supported by a pressure between skate blade and ice on the order of tens of megaPascals (hundreds of atmospheres). Such a pressure is enough to cause ice to melt rapidly. When pressure is applied to the ice surface by the skater, a thin surface layer of ice melts to become liquid water and the skate glides on this thin liquid film. Viscous friction is quite small, so the effective friction coefficient is much smaller than for sliding friction. The magnitude of the viscous drag force acting on each skate blade depends on the speed of the skater, the area of contact, and the thickness of the water layer on top of the ice. The phenomenon of static friction giving way to viscous friction is similar to the hydroplaning of a pneumatic tire caused by a layer of water on the road surface. 9 RPecihem 2.3 CA val Gosen! Fodk of vota vos té ; “Om. an each <a, $ porá ap a None imdined A AS No Re Horas ones o (Na of smE sentia or. Se aged Tal Be thoM do condád AS Gio os Me GA LAMA dinero 44 O.9014 R Seat qrefide vs Lie ts Minos Force Tecqured. Se Ae. Fa Gunca Bye the ds encima À cordas selori ES, Sem SEaxd Considar Me Lotes o Me áreas é dio qnd lost Ra Loee Vota danço of Ne od. E mt £ RN ns Sw LF =o Vier , Ef. nsszo Nos Be Lidia Lorca R Seda Gere t= pe “a Fa sewsl ESP ( Nuseas seo prelio <= K 3 Nasa as Setas pLa ana Sus a . E= pane me =- Bm st SAB ro . “ . Free Fa “2, Neçendra a, Los SME Nei oi QrosF (38), pa=3105 as slot E = RS A Sp «2 + = anus Ne zona bis Mm sm UT ÃO A rosa has e Ne s Secos Zi A) E= 3u.5 NX 75 Rede 2as | TMA RAN Grao: E 3a ste tuga ia do Vo te BA o eetA duo sê Mica 4, É] 4 Asmie ms Re mastova La y E CN RO, 66 Soon + , E c-ciorim. ts asa izodôn E — Cadortenrdo: = on dalÃos. «esa Ce Sp Tecla toe as Nes Ss ? Nose, ohevoothe Cora e *apo + E=1s WE. Funã : Moss alovadde Aape speed. Seven: TELE MaL Seca 4 = Xot (Men ZE, = and drisva, Cerca o Daloncad doq o o Ee va feudo Cora e EN NPR q K foca A haras Poe Or op sur apa, 4 Pesa GAS Ave T om postuse susfaco meo Deatide À Tão do Vet = da = +. est Da N Or Moto asfalto Sep dg pasa” DE Qui se L en negeinie Surfoee mea Ec oÃs to RE enero ZEco = EV ds Eç eta were T=p ma Es Et a ala (ral c= PER TR = 2pER Solana, fer * v > . &. A a Res (A Ca “= Ce = 15 %K+ o. ne "oa * sons WE SE “O apa . “a & NS N= 343 “ a To  I Rea Ra BD DD Grace à Vos É eras A dNdas om PR coa a Nei Ca SL SA of EE | nus Acme ds. Coros SIE Oil film | tviscosity, 1) ; SC Tio ta RA, AX tive T=o, TNASE vm AS celeese d Ceesen ca. mas Fusár md Expressos, for “3a ais gre oe od tas O CONS A a RS) Viene cha “ares US anda a Boi, sq. as o DA seas A mel (O Exqresatem for Visa qua N= SC 4 NS A. Ny Se RSS a In » da 0 a 4 Ee 3 E E Emas , . : Rose capela + Cuz pa Sa, EE=ma TR i Wesusgisons O Neon Na BoA =) Assvegs eso a, qretde NR Sa CAs. “a, Fr k Vea da Roca cplino pitas ÃO Cor Ve Node, E= EE = A se SS O Tor Be Lola, emass 2a = ma - Fe = . s de & Sta Ag= EN , Vier asa N Ra Bom E So vo 4S as oo, ES as DO RATE A E MA go 15 E deb; ar Rs = Gra) ED Pes. | arde sorvetes asd ks cd Sa te ÇaeS SEDA DR into ES, fe “Ne todae voe ta EMDDA A (an PS 4 à dedo = “as - E Sama Sor 4, * a - ABL . Ser q Wan (UI — o a : q an Pa a sos Mece otas esgonetnsdu No Naa Pa 9 | Vedder LI | mma RA Coen: ve , donder à, to de .— ars at secdos > à te — — q LS Barao: PR “AD n. mota poa e PL Ver rad pow As Re epa Wimsesm tose and die NE nus Ema A speed, Ee Sonhe- Fwd: Fosco ceqpired No qui Ve voe Selo ZE =mas Sysce À e = cesso , ApQNea: Lora end Voe esta Ne tona frios fora v Fe das Fo E <A ubhese Te p &e and ns <a Tssusmma a Niveos sichocs So clodaes vs ser mish Via Sa, SN er) “Pos o Asa Ve Shoe Ao os Qoshase f eusfors sá o s reapinee 4 Bsedaas = Fe = Entas EN te Ps je E= “Oca an « 2X, SOm 4 O Bens Oem DA mr «Aa, RAS: 165 un E ce E Om Arm vescan ha = tora Po Vrehem “BE | UMA Rei d Guaen Concanhire senvindar instalar | RENS m. d=o cera alem, | | “Xones Vindas solcias SL 25o cen q | | | i Es Gap LNea. o cosas 64 dA ar. — | Verne Norge SEM pired fo rotode Ne | wner eindar CD Ne ceara Nora cad Tabanea Nye ceseara Serge & Me Eras Sá Ve Seos Lora 4 ae AS TA abere = URI Fec o Hessniar fina Ts + Sa Fer sema E Cear qrefdoy A = x + USere N= Nomgg nos. sstocdas of waner espdas = Rus caça — tus LeRd = 2x Rua 4 & ond Ye Nocque T = pra 2x nê ud a N Fon Fa fes cndos Sh À ade (32), pe Io no mM stvd Soda, nomenind ssoves . <. a TJ. 2x nE vs = 24x dioso de, prosas! “e = eb «BY S Ro res dona .&. a a R<rod ma q tes bas R$ To s3 4-6 — g $1 Veotham 2.3% | vma Cê MN Gien:, Comerc cmfndas Srsesdies & ETSD Tras eptndas cas A úseweo ren, N Cund Voce, ef Najia chessonçe a Seslios Re “enpoted ergue mad bloco Re candura Norge SL Re eos Cora |. Ra Swen | AOC, INE tSOmm Nora > “Tm O. im Ne Seas Corce ae da Esta Ber Weix An Fer o Nesdoni Roud Cm ja É N Suvia Be sda, rede & astumeá da tr licor 4 e» a Rus, abrace A as Re Nongeia socios, Ra vrer condes Ne Rio N Re W Estas nã acto = Expe tem = asp ess aná Ve Tosca pa Ta RF = SEP eta Sohanra, fer + pe pe Ná . oe tm om, Lido amo (A es Ria 2 (AS at O roses É Ema v o, * tes «es 4 Seso) em Re coã. ma E Gorvas! muslor Pz [ Veda 2a | tema Ta) | Gram: Tem oder cdndar Cmoss t, and todios VI EL a comcarkse Eilendas is tader 15 Árigem . Va Cody OSS EDTVR Ta Ns ara Solienesa mmer cicinias do 6. LESTE aus CEO NEED & «est Na paid é Be Sie cssetioas “oa Na redpe Sed Tião. qo adere A é, Se STE oe ad às Vejo des CERTAS A s o ES “E Std €N expressem Ley ya Sã NS, . . San Vas en polises + fz p» Sá, EV=sra EN TTA Wesuame, (9 NasKoraas, Guia en Neseoe motoca, qref de + P TR Pe U e ENO am pago Ro E é Te tuto P(A m To UBV o : ao Pusóa, asealesol tom, ta Re Tens vs Pe cora de Fe Vos So caldas sas ER Tete ad e «MN ns c For Re enoat TR a E qa SE ne IR E= Pap WA dee fre EA A “Se o 48 às | 14 WaR E eo ss = (a E “a Mto OS ='s pistas e Ca NNE = =€ Ea 5 'acio =f te = (E a fem . Thesgiiha , dt-= Ele = às NE = Ml Ga = ES, = o GS) 5 ae Bda Susana fes B < a RAN o “tg e SR AD vas ps de G- Seia Be - aii sDosarivsa às cuuss À LS Droit ER ia e | Problem 2.43 | aaa TO Solutioa: Appiy summatos of torgues and Nestor! sond late. Crea! Cireulor altumintm shatt 19 journal. Symmetrie elearaner gap filled With SME Ioo-30 ar 30%. Sheatt tumed by mass qnd Cord. Find: (a) Deve lop and solve a drtfererhas equa fios for angular speed as a funetron of time. bo) Calcelate maximum angular speed, (6) Estrias fame needes da reach 95 percent of maximum Speed, Basie equations ET =I ça ZF = m V= Rus “ . am = Por the mass é Z6, emg-t em = mk da O + gv ma For the shafr: ET > ER Ncous = (e 9 to Tuiscous = TRA = my RarRL eme we + A a Assume: (NNewtonian gu te, (U) Smat gap, (5) Linear propfe Then EG. 2 becomes tR - UAM = Teto Time ds Must iplenia Ext bg R and dombindg turfa 69.3 grves mg R - meto - Er aaEt 1 = da or mar Ita ty «(Tema do Th mas be curte A-Bi co where AzmaR, Ro = Itm Separahas variables dm = E ds [mu t Invegradng $ o - “Blula-eu] =-Shult 88) -/ dt . “ a . ! Simplfgrg = Se -€ de or uu = gli-e-*%] 6s> = 8) we) Me maximum angular sos (t nO) “w- AB. , Niogã 8 A = mgR = ODio kg, 9.81 4 x 0.025 ia = 2.45 210 É Nim zum REL 09S 3 O sê “P unants B= Ze = EU DOS de, aos Ja 1050 m O esasn Bd "UBE Mi pr | Problem 1.43 (cont'd.) | t) Evaldo fog, Comas 8 2.82X%0 Yume Thus Umas * “estad , re bos 25.1 rpm =A «Zumo Lo 242 radis. ET limrod ma Mimas From E4.8, w= 0.98 WUmox eshen 6 PL = po,” Flo 2 S;t m Se C=Ttmbta imetemee =limeme Ma WR(LSL ALI CSTRÊL SS for M = USTdb sm, dose muco ka D.b4B 9 3 C (ix D.LYE kg , Doro kg lb .ors mt , 09x 107? kg um* Thus -y 45% ts 3w L.oPxp 0 Dt = 075 tas The terminal speed conta awe bile Computes from Ep. bg setting deo [dt DD, initnoud Lo lug Ft drferenha! eguateon. f9 | Recdemn Cho VA Cai Graam: Cone asd qioie stands Bios . Ber SL cone juá Noucdhes Re quite SE cera nto e no po Cica. as Persas on expression Cor Ve Snes ERA po case do Re Irapaado Adi Che Re age E E, & Emalu die Se Ea on Re árden de ae Ts Sample? — cone a Teses sf Segs dress aná agonia + Ve sudo SAS Rey Seca Ne enoie 8“ Sera swod, Ve Ones age See casta, a dão sera Emo. “Eis Cebsonaide Ko sósume o Auseas evoca qefde across Ce GER anã No efe VA eMRÃo Ne Seas (doeeeisa) ride ds Fr qse da dao ER E. 1 = cho NR “o Wu Sana, vadias (S > Se aveia, AS = us Gead Ne SER va W= vÃsns . Us 2 TO AS *= Trans É Ian Sce Ds ses Senolh AonB= O and : “a = o de: Ne dneos colo às esdagandosl & u a Ns Sasçõe 15 supresa, to Ve some Sens CO Ne Nerape a Pe Arusem cone a EV = (rar Bee SF a Ta 88 Sea 4 é a condos (Ls a aysen “5 Ver Tons cerdas ONA R, = ( TSE = (eta = EA < Cervo à o — .< q? T= ã W Ta TY Go | Problem 2H | MARS Gen: VistoUs Chetch made from pair of closely spaces dusts. Input Speed, toy c N butput speed, tas . SS - ES — Vistous Dil 1A gap, pt bi 4 Do Find algebras expressos in derons vE Ms, RA ti, And Loo e (a) Torque transmita; T (8 Pover transmitida tes Ship raio, a = Blur, in decems of T (a) Eftierênco, 7) 19 terms FA, Wk, dna T Solution: Aprlg Nevstons lar of viscose Bosiceguanoas: =ude dpetdAa dr =rdF q T 4 la F Asstumphons: (1) Newotonian gua RA () Marcou sap so velocity profile 16 lençar donsider o segment of plates! fo sz pa arte “a Eça o du su DU CO) E ” == Tt Am dg e dy = E) def Plyo de . da = rdrdo End Vitus Boto View de «da = MODO args fab pa dedo ; dr Are o fabio dns & E : a Tt, = E ad Ceower transmettes) à = At) ( tar dk TUR bo Pocuer out Tido op, But Ub-ty “AM, So Power in Teuy ty , td Aty = LOC.i- SD =tImw 9 7 ri Ertiuênca 15 7) = Os [Peres vas I 2a TE) a Cosas Comcadime, ca estelar Ses ti LSrem neves Nam das e NA a SL e dos E 9) SNS umas See 1 Ata Gras GSGUÁ CSS Rae Sl Fer Colsnãos esa chdas TS. «em esspressasm Ses EE Nara pre doa 25 [ So o end o f às cagfed em fer rsss do err so Vosiam, de À e > ese of 's to (A Tre AA Soo Re oq SG AVONL - SE a R seio SEES é ON S4 1% th RO Tor q = tem vo Ma = e. aos =D “a OS Te o ques ddr of ela, Ve assess *b Cass e ÇÃO E oesnieá Volootra os Bu per A ds Door Ny O da tunes am (For Saio, tos A “Bio cas grondsi Ia de 6 G) tp Er. Aos? en ASR COSAGAS COM o ce cerrenã? Sds. Rose dai Rua PM Wasudmçiions «S Neas ae do Nes Somar Ng pu (8 a andor as & 2 RE S ss Longe Sepp Be pao E qu E RE ETA = RuE E test do agua | a A a too Ep Le DE e. a Date da o s Ps. o “o 5 5 re ads SRA Nem” Car = Ss E = (Las = a ç Eme dr “T+ = TEM 3 e o) Ve a Tora = pio (O ta o ESSAS = RR by A For TRestom [Tarado É vos , Sem ns “Te E pad a Mono Rea, END FA ú ao SA TO *SO a Problem 2.51 am ATSA Crer: Sphericas Incust bearing showa: h cu Do Find: Obtam and plot ar algebrare a yo expression tre the torque 09 fhe i Em Sphericas mem ber,as à funchimo E» of &. o Oil film (viscosity, a) Lo dolution: ApPly defrartoss = Computing equatrens: Copa T=hrtda Assumptions: E) Mecotpniaa Elec, (0) Marnw GP; (8) Lacuna” flow From the figure, = Rans wet =nkS108 - - [E 8 7 pndie = p(ÇO) qro cpa tas JA zimrêdao = UTRE sinta do Thus e T =P Rsins( es Ss) py pt smo do = trtctof Jsunsado o õ 8 T = cuca ft osip css)” = mesto R[auia su +53] ô . 3 .z + ” =| Costa E E D plot, nwmatize to T/2 to e + os a. tosa E Plo trsng! 48 ' , f Ê 0. T j T Norma tiged 2.4 Torque, T/ 2a RV pa h (--—) ; to So So 0 40 Spherical Member Angle,& (eg) T 1 check ctimensans: | parto R$] a ELLA A = FL vo h Za t t as | Problem 2,52 MA Ta séc, Gen: Rotating bearms shown: Narro gap filed wrth Vistous 8 Dil, pues (250 cp. . . é = 60rpm [|| RS 7Smm Find: (8) Algebraie expressos for Sheor o=0.5mm dl Stress 009 Sphertas mentes, 1 qe Eds Olin gap bb) Find maximamn Shea” Sress. ! [ (e) Algeterese expressa fr videos . Fo= 20mm ee on spherreal mese. (dy Eva luate Jorque, Solution: Apply definrtmoas Comp vting equa Boss: € = pu rh rTdA Assumpteas: (1) Newtençãs fluid, (1) Marrocos sap 65) Liam nar mohon From the figure, P= RnB, Us ur a tuR Sind, die - 40 de h=a+R(i-cose) dA = emrdr = 27Ran8R cosas) Thus € = MR SAD AFRCI- case) Fm the table below, Tmax = 67.9 Nim* ar & = los” (not at 8) Tmax , Bmax es Torque 18 Taj Pashnd SB COB ta o A FREI-Coss) This must be evaluated numercaty 00 graphicaltgi From Appedis 6, 1 Poise = 0.1 kglmis. Thus ja = Es KGlmis = LIS NS] am» T = SNIS, Em tOS, DOIS, Sin b.SR / Mm s 2.0005 + bd ti-cosb Sn Tatulating resutis of smitar coletados gues! = 47.9 Mfon* . , 2 a Here "turcos" is S0Êtosa memenaa cnoncnos com ArRLI- Cosa) 0.s 10.2 11 1.5 29.3 3.858-05 3.968-05 Ap = | deg 20,0075 Pad 2.5 45.6 SLO7E-05 1.308-04 anel = !etg vo au SMEOA 5.178.04 ua . . +. 29E- «17E- a 5.5 66.6 2.95E-04 B.12E-04 for the numeral integration. 65 67.9 3.538-04 1.178-03 5 li aa LER ko . . «ASE- «OLE- =t -, 9.5 63.6 4:798-04 2.498-03 Lomax" sn É =sm 428) = 48.59 10:5 611 5.07B-D4 3.008-03 . R as 1.5 58.5 5.298-04 3.538-03 12.5 56.0 S.ATE-04 4.098-03 13.5 53.5 5.61E-O4 4.64E-03 14.5 51.0 S-728-04 5.218-03 5.018-04 5.798-03 Integrated torque = 5.508-03 N-m Probjem 2,52 | EINE ren: Smau gas tublboles form ,a toda tule opened; D=0.! mm. End: Esfimade pressure difference fr saside to outside Such & bubble. Solutroa: Consider à free- body dagram of half a bubble: Tivo frias act: f Pressure: p= Mhrg D —> Surface tensor: ge STD 2 + Surmming farees far equterimm > -E = 4p 2 ZA Fo -& = 4rEE-swD =0 so 4p D — =0 om At = dá 7 o 2-5 Assuming Soda-gas nberdacê IS Sicnrtar do tuater ar; tes = 78 mim, and Ap = texto 2 t = "2014103 A 2 2,4) PA m Sp x = ro ox t0"2m 23