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ENGG 349 (18)

ENGG349 Ch17 problems.pdf

12 Pages

Course Code
ENGG 349
Craig Johansen

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Problem 17.5 (4,t ,
'[lre unifbrm c-vlinder,,1" of tnass m and radius i', has an angular velocity ro, r,vhen
it is brought into contact ivitffi iclenticalflinder g whlch is at r€3t- 'l'he
coefTicient of kinetic tiiction at the contact point D is trto. Atier a period of
slipping, the cy'linders attain constant angular velocitiesTfEqual n"ragnitude ancl
opposite direction at the same time. Knowing that the trnal kinetic enersv glthe
system is one-half the initial kinetic energy of cylinder,4, derive expressions tbr
the ntrmber of'rel'olutions'executed by each cylinder before it attains a constant
angular veiocity. gosfdo"' t : aoa= ti,) -t0 % edr3.l {pS in fricrl,'on ,^rt4,n st'ot'?
2: jo^rt bt{""t-2 ott-r"1&4 n-.p-A l^'n -t \raipu'{iu
*^)= Oe)= to I
&T=? -o
11 fi,),r ,?du = ), Tu tDoL
ft, *rc.g, ,ltaa;,'-"
= La,!t I
no voclru b4-
b1 n3,N * Av
_ .:; ]-" --
I rn5 r\
'i &-^") ',
| ) ,:
t, r1il.r{
:.i\'r; i -i
,1; -,:- I
tr,. .{ t i
.J i
,Polo 9r'r-61 Lo:s I
fr --,t, tr
3- e d{ ' , i(+ }o i,op")
p{ , * nr"
uonJidr,r 4.aal*^du A "
* )Z$r = Ff r: z/.\r
(Urrr)e = - (ztr'a) oa : -4y"'3r oa
Problem 17.9 (8-th, or 17 11 US system !n gln)
The double pulley shown has aInass of 14 kg and a centroidal radju!_-glgltt4lien
of 51ry. Cylinder A and block B Ne attached to cords that are wrapped on the
pulleys as shor,vn. The coefficient of kinetic friction between block B and the
surfaceis0.25'[email protected]
lAK shorvn]?etermiie (a) the"velocity of cylinder I as it strikes the ground, (&) the
total distance that block r*)^a 7,
lill) lirtrt :rr:-:-
-.. ,, ,t*J l^:.}r;:{un+'*"i};:],,. o.t?nt\^/
, "',.,t,i--)j/"-u"""' *S4 tg-qsr" --+ g '# :3.crool S6"o'flrn = oislst)*
.r .,;'"' l,r?o116, o\ A : (rnoJ)Sn :(lt.r)tr.El)(oqo) : /ol.$JyO
' l,,J {rc't'"" oF B: F{:zAr.d; 0.2S p)Cq.x:it: d{.0?fsrJ
u l- trro'-k o-l f.ioho^ = -F{ss : -}&.oats (o'9q) -- -t{ '1rlU
56 i't' t'1rrr Tofd. wor[ - tol .SgG{ ^ ll.q,n = &l.cls {-
Kn+tic o45,y I T, = O
Tr = & N*vt.z + \1",t- *$mpvrl : .j (rr'3rr +thok" +rncre)dr V = td
rur.r-lA v+t*h'ou o-l -* O.(,.-f ta DL
twllcl c
(vtto +rz'r^'rtc+;")
F.ti.a Pb .l
L^ xe No"
C-rSioLrc, B:
w,.rr [r 1 {c,1.,re.l
6,)p t
urork d *tt {* A I
-l,lur^,.3r0a ,$Iaoql
R Msrn5 r
3r uto? , ,-
ta nr t ltT
N t15+ Bx
dooy tuo
,,^.lOi^ t'
Cb/t o1L;'arltr
* iNrg*?..
*C5} *l^'\" ?Btn/
R ,/n e^t
r) i^6 , Fl
(Urre)p =
r : Ar o"1r
(zue) 0s
- k i,vr(u. ryt t". *h c1l;"-tt*-
t = * 2F 't lo.o'
.^ArA &1vzrw:;t d{,
ust .t4"e. stot..n"
flo VO d ,' aJJ cr4^.h.Lo[ 6<..t
c.ottsia(,rr e1 t$t^. I ,1
i oU-Jr<,rrr^;r,. 0i -a 0g
br* =c Nol
*-, )
B f Ur+r, =Y
U1r; : 4o.[t .I
Ss -- 1o'lr7
Tt.t-L ot = S9/ +Sg
: 2.3Crvt
(*l ))"
t" ts'
(u,r.,.\s =G)p
,utt *1.6o = +hrr.r')r"ro'
0g= +-"t ct*,.l) z
/t, ut 2
?r.inafl, "{ "oo'k q e'N-'t1"
/, + Utaa = Ta-
&4.0(S = o.er,, dt
aJ ) tl. ?Boq
Va :g.fls- C(r.Tao<) = a'qSnls l,
Sg u,*r. Vge o , ar"O-
na9s 4 rs o, rl o{ S.1rfic,a
T3 , *3 ooz r 5*uvr,
oo: t[,]30+ -{+.o a.
1i ' * f rt.{tro' los)z a 6't[o'ts )2] ( rr'?a:11 2
= 4o.t.rotr
) t-?r = -&? 'OlaS ' Ss'
-fric,Fn'* fuik"p.u 3,4
92jfi )/.vt r/)
3 r (.tsoz _ i6r{)
tbAY % -/
,,ttsr3r0o Ci" 5or..--*"1i"^)
Problem 17.38 (Ott ,gotv l$
'['lre ends of a 9-lb rod ,18 are constrained to rno/re along slots cut in a verlical
. t l.
plate as shown.
plate as shown.-A-spring of constant k : 3 lbiin.' is attached to encl I in such a
rvav that its-t6ilion is zero r.vhen g -:-lLJ If'the rnrl iq re'lr.qqerl fl.rm r.,cr r'h--
7sl'tr I t
Tr :o
M =o
Vrr, {-:rr-,t- orl
le @^ 7{+y.f, Tz +V, T2 :-Vz
+W'(r: .-- 4 roe f l-6piso) -i r, (
a- alel6*.on--l E*? €9Pn1'oilt
e : .[ - Lt,rsgo -Vt .AKn" - Wah skt-t"^)
,.h. * Itin3, .iipr*r5o)" - N cl;^.yf;)
. )tJ' Ct- ^*) - {rt '' L
Cons*ra;uCl ,
"-r*Ji"^ r- lG=G t'o = $ tu:
d,r^k oo lV*
n =*rrl,2
'*(*.c,,,f* r i(b^a.-)*-
= L^9^a'
Y r.(7o), +fw) r [email protected]
:o +jCsoo)1o."ra)2
Problem 17.15 (8tn,
A !g slender rod rotates in a vertical plane about a pivot at B. A spring of
constant k: 300 N/m and of unstleched length 120 mm is attached to the rod as
shown. Knowing that in tt . ffiffiGhownlhe rod has an angular velocity of 4
radls clockwise, determine the angular velocity of the rod @r it has rotated
throtrgh {a)90", (r) i80 ". s4ru-+ r&o I d.{t r*f on.g .syiy =-eD -r.,a
]e z$r^P.z
, [crYootz = o' tttoGtY b'b''n'L
cdo"twrn f+r'f :&n), 'ffiatt =
C,s , l.olt *d {5, )VB 'W O , *, )'t'o
: V' zas 4l/" I
141',f o. ?G2+ 0 lsl' - o la. = o.?}vh
: 2' gq S
0 1r,ls
r ;3 il6{} rnrn
=ro13s{ i I
i.r I
). I
' { rn LVo),? *$ no,,
'ib)(o '{)' + t&\G.*,uroXr)'

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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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