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ENGG349 Ch16 problems.pdf

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ENGG 349
Craig Johansen

16.4. ptane fi/totion / Rigid Body (Handout) .,/ . planmotior rigicl. determinedoY-li bodYisc ."urtuntu;;J,3 J#,:;iill[".f"",,T,, ZF., =nD, ZF_, =,ro,. l,rt, = 7o 'ct'A.lemberprinn-r^'@ ***{x*##ry.*:,r' ii . Ceneralmotiono and a bodv: rransration "riir"iit:ffi'flt **ff,;**;ffi"3s.-+;6,$[i ,,,\_f T5o,,,,-J* ;: ilflT-, r---*\- l* da . o * Klh€fia+ca ^ 4, .. (r'u)=o {4 } vw|-|''.'na o1 ''Bc/7Sg t a! = BeiSj,f* tr,,rr.ltat =(a-o)^= ."ff 3?w1,ra*ior,: on -r --7t dr'rrrr,,,|'#m, =Tffic,. lcy it zM,, =[ot =o r)a"'.'ErT Of ^lqs.qq N ,?:,1"€ry)'m F).{.** rr"o< , 11?.qlN , uY +01 -^1 -lmq" sin(zo uY @'?s) -o.3a*r3 t 0 Bl t.ts-ltu =-fh ec,sinoo ro_r*5 J = f ----- IzFy (zF])rffi.** = t31+'?--3 = -n Aa Cinoo .- lq3.qq T\ 1a3'aaru ' '1, -s if ro PoD q. 2Fr --hdr 2F1 . hdy loe-t&[email protected]^'1\'a- DZS\6= lcc( r G vnr^rt * Mv< +rca --ofinrzt .("v,-,+ fBD": O {"r* wukd ov bodl - ^Wird &"g *t *ypo.+-! _wC,.r6ht.\ O wt*. rnd C"*tt" Xc'( Problem 16.52 (8th, r\drum of 200-mm radiusiattachedtoa diskofradius ,: I50rnrn.lhe disk and drum havea combined mass of5 kg and acombined radiusofgyrationof I20 rnm and areuspended bytrvocords. Knowing that ,: J5N and I,: 25 N, determineheaccelerationsfpoint,land B onthe cords. rn /n+u-0 = .Sq Q to'ts'n raai"t'{ 1Y,ro{"^ K--o't}'n (f fg = o.Jy', =,rit") r T1 ss,U Aa,AA=? Tp !9N = (atn, Problem 16.106 A half cylinder of mass m and radius r is released from rest in the position shown. Knowing that the cylinder rolls without slipping, determine its initial angular acceleration. (Given mass centre G, and OG 4r I3n ) - rlN*GG349 Final2008) Page of l2 StudenlD: Question 3: A drum with radiusX't'he iqattached toa disk with 0.30 m radius. diskand drum have a comblrfi.-d-ilaEtsf0 kg anclcombined radius F of gyrationof 0.20m. A cord iswrapped on the tlfii6-ashown and pulled with ahorizontal force P ofmagnitude 50 N. a. Find the angular acceleratiof thedisk, ifit b. Findthe accelerationofthe mass center G,if the frictiocoefficientsare# , =0,08, ancl,ur = 0.07. :1 Qo c(3" w f" = e"Co{} -o B ,2 [n.= 2 Cwc\c(rb: .9oCo..ts) = I6d4 h%(.) :Icd ! rn(ra)r- Qo=(d --0.9d't &bco'e)2a = o,eCros) C &.GS r*( (r- = I*o =2 Cpao).*' . SCo.f s)+ FlCos) lc,d C = P{ =l'tasor rt-[urr'+rl-"? {.{ru,trrtUtt-/ sU&t^\*^ * " tsn.,+ioJ.LS=ls#€.1o.,'c,Qg: ,UrtN. o.o,(zc)Ca.r1) = iS.+ > l.qa3,d,.02\i{os(icci,V ,Ukil ro.o+ 1ZdCqt\) otGcrnztse = Qa i",tff;'"* Cafltwrr^stahq: X .9\ kAcrst.-r*cr)-ro\ ro(tr/ssIar2- 4o u(*-.(d.f /Akt/ Xa*sr-t? Ft = + €D-Fi >Yma a =1.fl93[e,u,rh5 t0.st o,Tg rw-rv"'.tt14u+''''e b"t" x+L ,V* "bcu no rlai't"c"i''"^ lnhrr.Js'*'-$ Te tTfe ^1n43: wa3 Co = A'Pt"ls= t = [email protected]),t = 9t.o?sN O Y- For WA' '.b n'#!+o*i"rp-o J :t.?g3qP @ '3 -Tr=enrP " orF ' F=ae-B tb Lr,.gs tAJfrt,n/g:Glb t4a,"O'"tf Cu.+-4 *B) iltz{+tb 46 =O.\g C"u/sr,.r{a*) f= lirt = ,\,J A: -t-1- te =i*., =* q)" ;0.o)?Gostu-ttsl ( r+tu C#r) _}a7id)a fr>o.tdNr !7.\Lc +) _.. 2Mc = !.cd* : a Ca =21.+ss *a6" E 3 f+ tu^W(+'rtr") = O.o))0oScX* [email protected] 2 q"tb F- = N2 +)>tAa =}cAe -fr)(u'u) = o-orle'ofS + db:rE'?P^at*S ru)(+ac >l} rneg'{t3 ,J '*t, 5 ho = 6Y3 d 'gc oA/s'E !-"; Pin/ ? d roaationAx *4f ]'-';: rv$$taw rtuc,eisk ltlc Aa= O '?t^X'\\ 6" ;aL oJ-r*/st'a"! EihcLdt lO ta+ O'wd\ A*= O'tJr'n'l ---.------..-.- . ('tco't'): fl+ ' * L' ttr b'l.)'= f, *) ztte=en^^)-l! : 6 .tP * 0.ta{er$ = ]a.1 +I,.^ + o.lA1TlryOt -J ? = ilaolNJ )zFx =Pqf4\ '. AY o'Mlvan , -ce.taN 2 Gq-D H/+- r{ Czry)+{{ : Al - nro3-llhep3 -?= wvpai znu, = t?t.qQN t Ay
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