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Homework8-Spring-2011-Solns

Homework8-Spring-2011-Solns - ME104 Engineering Mechanics...

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Unformatted text preview: ME104: Engineering Mechanics II Spring Semester 2011 Solutions for Homework Set Number 8 Prepared by Oliver M. O’Reilly ([email protected]) 42-3“ 50 SHEETS EYE-EASE. - 5 SQUARES ’ - 0 42-382 100 SHEETS EVE-EASE. - 5 SQUARES '5' National Brand 42-359 zoo SHEETS EVE-EASE‘ . 5 saunas Problem (+23 1‘ Pg 9 Gum 8:122 ng achna on 855160: 5 pvla'do) l a L Oéumine. : g“ . g9 . Q1 . g7 int‘ficmg U .. m m EYI “"7“"? Soluhom ' Ex I: Pith orig'm So Hul- iml'idl3. m: 21% F = 60"J £8 = L 553 3 EV 13m 1" =. - LSmXEx R. = LSinK 5‘ and E -= 2 uml'ioma IFEY E "IE! N» E); —M.3§y ”"139 E 5: ms + me we 2m: mam”, FEW Wu EY + (M +~~)§y — 1mg 'E Home 9 _x = O 1mg._§y = F "Zma + N, +N1. Assume F {a Suyficiml-lj ,nge Hml- F 7 2""3: Hm N.+N1_ need k: be negokuc which fa mpessibk, Hume .Qés—Hfi- occurs, NHL 03 -.-. F ~2m3 = 15 _ 9-8! 2m = 5-19 Fri/std" £1!“ 35500 3| A ) + .3 | .3 M v lm < v 5 “' (21 + (”v‘mt9)§v)'3{t + (FE-‘1 ‘ El ‘21.)«yfi -'—' §-'(\_’q-_\!I\ + §L(\in—jL) + 'f FE‘I' YR Fg~,.ga + o - fiGFEqAG) Hue: E = T -‘ FEy.f‘n FEV 5| EL "EI -§1 (é €m‘ (Nl‘m|8)§‘/ @z‘m‘a)§ §| " §.'- we Mimgwcm in C'M'do (Nu‘m‘séfl. \1' + (NL- m‘5§)nl/z 50 SHEETS 22-142 100 SHEETS 22-144 200 SHEETS 22-141 mpm= —[ hub». Q-E l Givm: - §(l‘=1"’~) = 3"+§>t-r‘ Z-égy + 4-6 _E_1. Kamlsan (3017399 = 3-7 _E_x —- 2-7._E_y +l+ Jig: firming, Deb/mm. : “F“w. Sdut'o» 1-» 3 folk = (3(2-4) ‘ 942-7.), )1 -:—>§x + «Q, +352} “Ell“ -.-. _1_ ( (391+ («01+ Caryl" 0-7- : 2-95 Net-J5“. Problem Ll- ! N E (£er )5: vgx '“y b e ' . ' - b C 070 Ex mt ggg WM‘NC gu’ g‘ Ord g :33: Suki/TM . §§§ E =- XEX "' 51- =0 l’ = ”Ex ”g g. = 2-y- baneg. +bsm9_E, as y. =y+ bBSineEx‘rbGCaGg g: . . E )3 = s + bagels). + bSinS‘Ey A 3/.» =1: 4- bBCOGEY-rbeS‘uhBX E ~z( Rm 9' = m (V+bé$ln9)§k — mbéCoGEy 1 G1. = MCIY-béSine)§x + mbéCnBEy G : Q. +§x 9- QMVEXI 50 SHEETS 22-142 100 SHEETS 22 144 200 SHEETS 22-1 41 fits/m- = XE)! l“ -E :. b(GaS_§y - SURGE?!) + .ng L ~f :: b(‘%8§v -an8§x) + .Q_E_x 3‘ -y = bé (-ssnegy - caegx) +5254 guy, -.- be’(sme§y ~Gae§k)+.§.§x Wmmkmgthsugm l g: (mo+2m)v§x when v:>'<’on¢fl:=2mb6. C313 moi-2m Kiwi}. Entangbhs‘gsfim. l. "1- L l T '3 Qmovo + 7, m] y: y" ‘1' BM], \‘I‘, V1, 1— 'L \— *Qm.+m.,)( v+h) béGoa ‘i(rno+1m) GHQ? + mb‘é‘“ — 2m(v-r.é)bé&a8 N Assam ma Hence. G.§ X (b Cwsemd an”? “i wrote? we find +th— (YYIo+ 2WDV : YYIQVO \f = Mo \10 "To-rim NoxJ- “Div: ““65 awsuvdl'a.‘ ‘ o ‘L MeVo ' 1' . :1"!qu = T = m 1m (mum +52) 1‘ "138‘— - 2m(v+£)béqne 1. . ° 1 "L imovt -_- 7:; mfilm V;- + “mg V051! + m; m 'Q + "ma-é“ — 2m (V+-é)béC°73 where. g. = 2mbé Cme cu) Mu+1m Nu»: m a -o 70° 32 —o 0 (saw (an) and Em» (M) M = ""9591 Mo+m w (9 a i Mo b ma‘l'zm $11393. 35500 ll 4’9on LUZ? I Wu, H Sm "‘3 a ”L thn’ teoaioszo)5c=o -7 ”I: . O Ex Dwm'm 9C, emK when 9”} ‘80 ~ SO‘UKOn [I 3 xEK =9 .YI 1' TEE)‘ >5, :- J", + L<Cea emx £7 '1' SinGmKEX) + CLE% 13 = fy 1- L. (Ca: me g, + smemKEx) + (:3 E? y“. ya = x. + Lém (—smem g, +cnemx§x) g = m‘!‘ + “‘LYL 1' "‘913 = (rm + mu» ma) SEEK + (mm-m3) LQMK (”Sinsmx E7 + CTJSMKEA) 1 T: l'IL-Ynl_y,\'.\../\ + l—LmLiL'SL'f {Mal/3.113 -mxB E7 firm; g, _ 52‘ _$3 23 :fi: T” 1-. "‘ng "r NEE?- ~mag§ y _ rm; E)! —@,_+ W13)8§y E3 5’ E = E -(m‘+ mz+ma)9 Ey = (Wu'rmL-r W239. 35500 ' Co nseN ens q) §.EK = ggx : fix =0 51ch Shirl =9 §,_E_x z (“.1'm1i'm3)5£ -' (mt-1‘ "1-3) Léme‘JJemK = thskaxk‘ h) ’f‘ = f. y‘ 1- 8.31. «- F3 1/3 = (u—-m‘2§v)-y. + Sz- (1!: mm + §a.(g,-y.) =0 bzcameL baa-:1: §_a..L_\_Iz—)_I. =0 been: _L_ -' W3EY'1’2 " M32EY'Y5 = ”fl “3 = mzegy-rz + Maggi-=1) Heme, E = T-I- U2 t'o Gavsakfd. so“). . smug)” 9M=o , i=0, em = 0" Hence. §.§_x =0 ) T=O and “a = (mL+m3)gL Sc; ch C. ,ch'v’hme udma W55 and. mcmmni'vbm Ginsu-045679 0*) o .—.- (rm-rmL-r m3) 5:: — (mm- "2371.. émx Q5 SMK 6‘99 (hart-magi. = {(m\+mn+rna)5c1' + '1‘. (m1.+ma)1}é:7.x + (ML‘me) Lé’mx iCmeK + (m~.+m3)3LCa99m NM; we. won? X. cad, é’mK Him-n Gang = l?0° 1 “Meg Sum (*1 dc. = m..+m9 L GmK m|+mL+m9 ad 5.55th in“ (M7 5-! in, (me) Simplifies manivdn b_ ZLMLA'MQXEL ': m\(ml +m3) LLéMK 2(m.+ m1, +ma) Shawna W“: Zml m‘zmazm 8‘.ch émK‘; 2, 178' ) i=V= ,JZZL 50 SHEETS 22-142 100 SHEETS 22-!44 200 SHEETS 22-141 cm; m.-.m;.-.m3=:2.Ka ‘- : 5°Omm P -.~ Ffix = ‘l6_§x (New) N! “W“: 8 5 whoa 6=é=o I 2‘ wk. 9:9:0 gun-Hon; IKCnemekcs; I? ‘-‘ x§x*8.§7, 1": = L’ +d§e) I £3 = 1' 3 X *’ dé(‘§r) at = g + dé(‘§r) — aé‘ge F§x ‘méfi 'mzaév “ne’er m: F:mg' E' Hndgs‘s “"7 “9"“ 8:0 mg = (T*(m.+m;+ma " Lb) To Mann: 5 m. 9:0 mm 5‘ = 5 EC = (-L'E)xth‘ ~ g 4- (“06°53er ‘3n30§9) -(m. + Inn-u- m3)3 §y - FEK + 7“”957 ’Snef") = "'9 .éLn-mxft £2! (‘1 = E + d(-C°S&gr -S"n3°go use: H: = dgo x m. (X -d:0gr) + d(-Cosaogr - Sinaogo)x m;(y-dé(GbJog ”mag,” 4.. d (agaogr _ Sin30§e)x ma ( y + dé (993039 - 5‘"3°§")) mag“! + m.d‘é§z + m‘d‘égt + m3dt駧 1- mad (-C-naogr-Smaogo)xg + mad (Cosf'mgc- -$in3°§9)x_\[ $3; = Q‘“ r2m156030)x >1 (as m.=m‘. = M9) 388 "' -u + nudgsxg 4- (m.+m..+ma)d9§a §§§ - fig}; = (m,+m1_ tma)d‘9§3 (m Swat): "1) a? , .. 5 5: = (mm-m. +m3)d1'8§a ”69 3 m; = {‘2 (lg-5) x f; = dgo x ('F_E_X+ Tgs - mu9§v) + dummy-mac?) x (- mag Ey) Q + a (+C»a°§r-Sma°§o)x (-rnasér) gag“ : ~6n6§e : —d( FWB - (”.35th 1- (m1+ma)asm305m8) E; §9¥§y = -Sin9§a " " F4959 Ea (a. Shae: 9‘, ma'sen J) fig...— m. + mums) d1 ...
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