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ENGG349 Ch17 problems.pdf

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ENGG 349
Craig Johansen

Problem 17.5 (4,t, '[lrunifbrm c-vlinder,,of tnassm and radius ihas an angular velocity r,vhen g ro, 'l'he itis brought into contact ivitffi iclenticalflinder whlch is atr€3t- coefTicientof kinetictiictionat the contact point D istrto.Atier a period of slipping,thecy'linders attain constant angulvelocitiesTfEqual n"ragnitudeancl oppositedirection atthesame time. Knowing that the trnkinetic enersv glthe system is one-half thinitial kinetienergy of cylinder,4,deriveexpressions tbr the ntrmberof'rel'olutions'executedby each cylinder beforeitattains a constant t: ,^rt4,n'ot'? angularveiocity. gosfdo"' aoa= ti,) -t0 % edr3.l{pS in fricrl,'on _ .:; -- 2: jo^rt bt{""t-2ott-r"1&4 n-.p-l^'n-t\raipu'{iu :l]-" *^)= Oe)= to '! I voclru &T=? -o nb1 n3,N b4*Av I rn5 r\ 11 fi,),r ,?du =), Tu tDoL ,Polo 9r'r-61o:sI 'i &-^") ', fr --,t, | ',',t ft, *rc.g, ,ltaa;,'-" t, r1il.r{ = La,!t I 3- e d{ ' , i(+ }o i,op") :.i\1..,. p{ , ,1;'r;-t:- uonJidr,r 4.aal*^du * nr" tr,.J i * r: " i )Z$r = Ff z/.\r (Urrr)e (ztr'a)oa : -4y"'3r oa = - gln) Problem 17.9 (8-th,or 17 11 US system !n The double pulleyshown has aInass of 14 kg and a centroidalradju!_-glgltt4lien of 51ry. CylinderA and blockB Ne attached to cords thaare wrapped on the pulleys as shor,vn. The coefficientof kinetic frictionbetween block B and the surfaceis0.25'[email protected] lAK shorvn]?etermiie (a) the"velocityof cylinderI as itstrikes theground, (&)the total distancthatblock r*)^a 7, :rr:-:- lill)trt -.. ,, ,t*J l^:.}r;:{un+'*"i};:],,. o.t?nt\^/ "_{_,,., , *S4 tg-qsr" --+ g '# :3.crool S6"o'flrn = oislst)* .r "',.,.,;'"'j/"-u"""' I l,r?o1o\,A : (rnoJ)Sn :(lt.r)tr.El)(oqo) : /ol.$JyO l,,J {rc't'""F B: 0.2S p)Cq.x:it: d{.0?fsrJ ' u F{:zAr.d; l- trro'-k-l f.ioho^ = -F{ss : -}&.oats (o'9q) ---t{ '1rlU 56 t'1rrr Tofd. wor[ - tol.SgG{ {- i't' ^ ll.q,n= &l.cls Kn+tic o45,y I T, O = Tr = N*vt.z + *$mpvrl : .j (rr'3rr+thok" +rncre)dr V= td r___-J \1",t- rur.r-lA v+t*h'ouo-l -*O.(,.ta DL (vttorz'r^'rtc+;") F.ti.Pb .l urork d *tt {* A I L^xe No" -l,lur^,.3r0a ,$Iaoql 0e= 3 r(.ts_z R tbAY i6r{-/ Msrn5 r TiE?nf % uto? 3r , ,- 3tt)o\ r/) ta nr t ltT 92jfi/.vt C-rSioLrc, B: ILJ& ,/n e^t q)@6 R (*l N t15+ Bx r) i^6 , Fl r : Ar o"1r \_/ ))" do,,^.lOi^ q Cb/t (Urre)p (zue) 0s ,,ttsr3r0o Ci"5or..--*"1i"^) o1L;'arltr = * iNrg*?.. t *C5} *l^'\?Btn/ VO d ,aJJ cr4^.h.Lo[ w,.r[r {c,1.,re.lts' floo{G^di,r 6$ T T1*'tfr ='tr+Vz a3"lfi-flo.ola= o'l'1c"2-t't+ ?'t1 (D Fd(s I -G'ot71 a* Lgo : (p52O *b A Prorrk{n l+-sq tI ;-io-')-rs1,=rt4-arl-cer.A --raA-:*S!q -.-*4-*:-?:20--.i .'i'' -U-:-e-E&- d -:-' --* - -!-i.?*-iLreegrsasisge$.- -*cf;-C"aill*: -evusu+)-- 2zAW:-t *t-u- V=(Az- i: Etll_J:hq rbL- -*-tnsroqffitEr-e - jlY ' 3 i-ryjzt\fl-hz-?- j--U:fa - *- ik*, -_t,:.:::E.--,l-:l::]:-:::::.-_-:[email protected]:n,fE-__1bL-_-L 2llun -b:-:-9$ Princi fl. "{ t/o.k { Fh€/5Y t -' $rnVcz + * Ioutz t.-*-i-,"-t L '"{-as(."tta,. l'b|'q.Hr, .^/p.r:35 6.t!7rr4y\a Cj,.{^.Gj"^- Cr^+,c 6 3I *l{ Yoi, r0orr\ ui\? &* *.,r.rsa^.i". 4+< ,.a B kan^,} -r.,r., U t -ll L.h1 .ft,-er .'w ;;\. .!:.h,.
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