engineering mechanics statics and dynamics by ferdinand singer solutions
TRANSCRIPT
')t I
Publi3wtOittbola.lt:'
REX Eook Stoirt6t Nic.d e.v.., Sr. Si.
Ll- tlo.. 7al{9n6. t41.49.20197t C,M, idroas^o.
Tat, Nor tat -a9-5€ . 7:rl -4t-57M..il., Phililpina '
'*pa;a:paat* na'i -
Jojo BiIrM forulc@4'l
nBsfs I4.t Bor As.i.ti's f'&d[sdig_ A56diai! 'f
pErpu- g..&*tr-".(Af8t.l1 Hg=ffiH.f dle ftntlPiD€3 (BDAPT thililPAsociatim eEPA)
PEPA! trtE atioo.l Bd& /t*i{i(G ltdb6tiF A5id;;e-P",ts.- A.."d"d- 6PPAI ao.i'ti' " sd'rhiii G* ntu.n-' osEAPt lrrdl'tr5'l hh|;tas
. " Arraieiim PA)
Prbr4d br n rE( Fi$ltqco4rryic 8+86 P ndt'tino St-s- u*i fildrt " e,,"- cl'.Tds'7r2.al4-7r2'ar4t;Pd no- ?u5+12
T L o b o o k s n t l t l € d L o a r n t n ! c u t d 6 I n E n s l n € 6 r l n rf : " o . l l : : " : : , r r r ! €o r s t 6 t r , / r ; v r . , e . r . i r r , - ' p " ,p " i i !o r p r o s o a t r n t l b 6 p r t n c l p l € , r t r d c o n c o D t s o rE t r l r n 6 € r r n g X € c b a n l c a l t r e v o r y b . ! l c a n d u y ; t o ! . t t cr p p r o s c n t o n e l p t b o i t u d s n t t u n d € . ! t a n d a n O r e " . "
; ; ; . , : l : j " : ; , i i ; l i ; ; , " , , , r , r d6v6 rop rhe r . o fdo ! r y
I t l l h t t r o p r e . € r t € d t o p t c t , r h e u 6 r , w t t t t r a v e rv o r y c o t r p r a n € r s r v a s t u d y o ( t h 6 a u n d r ! € n t a t p r l t r c l D l € ro t . E n s r n e 6 r t n s l i 6 c t a t r r c i , h t c h a r 6 t p p l t c r b r ; t o ; l d 6v a r r e ( y o r p r a c r t c r l s l t u a t t o n 3 t r o r u a l l y e n c o q n t o r e d b !t e € 6 I n r t r o l r d r ' t o d d y r c t t v t t l € 3 .
. E t l r a s t a o r t r r s s : e r t e d ! o l b a t e v 6 r y t h t r t l lD e p r e s e n t e d t n I v s r J p e r t e c r t y u n d e r s t o o d , b l a t n r: l : l r : " " c o n . r a € t e n a u r g e . T b l s , t l l e l t D t n a t € o r
r r t r r e u t e d t d d e n t ' s a t t l t u d e o r h . b l t o to e l o r t z r n A t t r € c o n c o p t r t t t o u ! u n d e r ! t r n d t n g .
T h e r o t b o r r s t s l r t o { c r n o , l e d 8 € l b 6 t r l n d e b t e d D 6 s st o . u t . n a e l S l o n g c o , J e t t r e y B o r t o n g a n , R o n . t d oC a t l r d l s , a n d n o r e o l d . t a n o t o r t b € t r " . l u . b l e
t n p r e p ! r l n a , n d i r t t l n A t b e o " n u s c r l p t .
iri
. ACIC{OVLEDGEMENT
ctqifu o: Ucrs e of lrirlioC}+l6rip: ncaiF4ao- Tnar6l('lb
'
Oroglir rt : G.,-iti.!oo- Trqr6loli'r&-4rx5-nu*,2r3?t'N
. vtt
I
l1
'; I a& lba.
coii;Aar tE aoobh' -+oo cr,a <o'
. - so42 lts.Ts'.-a@ €i" ad
- -257.12lb€
p,- 3@;65 --:1508L@,
Ps- :e@ 4^*":P-b-
,17".,s'eE l\Y cotrrr',",nts of cdt of ftE to(€sewvn in Figuee P-aot,congido. lho 7221b lood,r,= -nz (finr)
-j!@r+_tD6-
nb 4+€b bodl
Fg- +1t (*l'7dE) ltu ritorgld@' btoch ehown i Fig' P-M is ebj@d
lolrE loods P'1@br,tF-6@b- f t \D=Sh\Dc=6'L,resolro coolt lood inlo coopr;le ru'md \ lcgcnlirl
.conei&r lt,p i6oo lb lcod j
sinc--L aase-+h- +-'(16co)
' t26ob'
h- Ltl@o\ = S6olhc.,&- l6';6i
' toa-
2
co'isidc,r lhc 2e,b loddtP,= aoo co. e: f-Jg@Pg= 2@ s;n@' | l'73.2't lbs.
8
l t
i 'r"
- P979.!b ,
"t-- ?9,41 fr-lL_
fo,.:a oclioq ot the center of lhe 1ox!+ in rectongle' Re
mt thewe,lht of lhe mole.iol cll oway W on upwoFd lo'€e
ocl,hq ol ttp @i3n of the cfule Locole lhe posi|on ol the
resurtont of ihes two forces wilh 'qePeol fo fhe left edge
d = .:ryL - ?49 !1,
2+o) lhe shodcd oreo in tig p-z<o Tepre*nle a e|*I plola
of uniform ihichness A lole of + in diomele' hos bea coi
in the plole Locote lle cenlec oasFa"ifv of lhe Plole Hini:
The weiehl of ihe plole ic equtvotenl lo th€ we'ghl of lhe
origrnol plofe minue lhe weiehl oflhe moi€nol cut owog
Rep.eseni lhe orieinal weighi ol lhe plole bv o dowoword
t 2-n
n.et r -AA \ -Ar xzX'1.rc<1)-12,s7(q)
onounl k, posi{ion of lhelhe Fink true6 .sh@n h
R= zcb+ te+ a4o | 'aa +..n t zooaB-a39]! (d i@t€d dodn*o"d )
R'- 2.ht tsoo r aal |eoo r 2oo
L - ]4!@,,s,ta4 d@"-d,t )aMc - 14oo(5) = Toooi] lb-
Rdc - <uc , dc = Taco/.14ro - 3-o6!!.;st.+ or
i) ' 12196 tl. r)g|,t of A
za,) Find the lotue] of p c,)r @ thot lhs ftur fb.ces shoal]n.Fig. P-z+e pr-duce on upword resutionl of w tb oci;nqat + (1. frcm lhe En end of ihe bar
zMp= -f(3) + 2cnG) + i.he) - aoo(z)r= 2oo tb (do\9n*o.n)
.MF-.c 'o(1) - pG)-1oo(s)- 2@(2)p- aoo ib (upword)
; ' ' ' ,
( 1/.rz) - rb (/.d6 - @ (k) 6 - $r(k;k)
4=!94]4:9 ""'
2az) Ihe lhr]je-'lep Pullel shown i^ fkl P-2+7
to ihe s,ien couptes compuie lhe "ol'o of jhe
p)e. A)so delonire )he 6re rciing ot lhe
l 4
c- 3oR(4<b-1oo) flab - (412)R
R: l4 b dncoleA rcrlicattyLJp ol A B do*n oi B.
25o.) The conlileve. lruss shown i\Fig.P-2eo cor.ies ov€rlrbal lood of 24<)c)b. Ihe lrr.:s,s le s.pponied by beo-rings o) A \B which exenl lhe fbrces A-,Ah,\ Bh.Ihefou. forces shown con|lule lwo adple€ which musl hoveoppoeile momenl effecis lo pnevenl movemenl oflhe lruss.Delermlne lhe nlognllude of lhe supporling foecee.
rn o.der !o corelilule o couple
o &:ZtpLb epwod)2400(6) - bh(+)
Bh -Ah = 3600 tb
2.e1) A vertlbo) forcc. Pol A b onolhe. ve"ti&l FotB inFig.P-zst pr,e4"o" o reswitonl of loo lb down ol Db o6€Ba+occlocl.wi.ee aauple c of zo<j tb-n. Find ile magniluoe
\ aireolbn of lorc€€ P q F.
lvb'1ao(1) =-2oo ' PG)P= :o96(do*nwo 'd )
ZM^'-2oo -a.4 (+) -t G)t:29pb ( uPword)
+) . + 2. .T-ptJ )P- , " ro
i,I
i
l 6 tz
e) A tircc .rsLn corEisls of o cbckw€ aa?re ot-p]',:.o 4{o r! rcrc. aicled r4 lo the nghi lha,+ trE o.-dnof, r*,Y oEs ol Ot.xt- Recto<t lhc a."en eyslco ty cn3c"":bil srnqre fo.ce ! canp,te lhe nlercc"t€ oi ilslinc of clion wilh lhe x 3y o,e.-
B'-F, - 2ao @5'= 4ezlelb-(ro ho rirhl)
B"t 'Ft "'o 5 xt'--:-la- (uP*qd)
M - c - F , L ,L, - ao _ ?pllfr aane o
xrz6
it =-:!@'-+!l= t t1 ot ol1'<'
t s) ,Iri-F\-
p-6 o 6.tr6lcm a/f (d@ .E ]]vc(F loo aowcvorlicol
-frrceo ot-r@ b lhuugh ^ ptu6 o counld.ctocxw;canPv d qD b-f'
-tu?F,dfte lho sr9t6 ,bve lhol w.,ll rro..re .tr q'I@t€/l} effei
Aj:@.b downwad
a@(+) -eo - aqtt
r:2JL ridri oFo
o€ €r.own ; F4.I'-2ss-tn sl"ens,th of moloFtot6 il iR
t* ) RffiX fitob- 2€ if the s'/stedr reducco io o tarl_\,.€.d rEnzdlot foi> d 3@tb lh.oir+ pdnl A pt 6 o.*t<X*t* @)dc of ra tb' n
3-t-: sqqlb lo lhe |,aftMn = r4o
oy =eoo(4) -75o
_r: :99]E G,.,E'b bor,w o)
:d. I "*t oo'nF€cs,o., membef, oa-r|s on eooen h-E
l:y P = a@b_ eil-uolea z n_ fmm lho orie of lhe rEmbef,.
rned lho) ibe in)ennol sleeses ore delon.ined lrom lhe
equ;.alen} oriol lood \ auple inio wh;ch P moy be re.-
E tved. Dele.m;ne lhie equi"olenl oriol lood $ couple'
I wi)h lhe oadi|bn ofo poir oi oppositcoriol loode eoch equo) io zoolb )we ae\
F= 2oo lb ldowoword)c'2oo(z) - :@a]bjh cw
zso) A ve"licol shoft nB i6 sfl long h boited loo r;qid sup'
pori a) ils lowe. end A l i)s r.,,pper end 6.re ollached ol
rizonlo) bor Ec whrih is 2t1 long . Al ihe end of C ie oppl;
a farce P - 1@)b. Force P ie perpe|dioolor 1o lhe Plone con-
laining poinls A,B,%c Deleffi:ne )he iwisling etfecl at Pon
lhe €hofi .^8 \ lhe bend'hg erre6) ol porn) A.t f"lDO tD
- / l ' lw,st ,no efrecl - 1so(?)' ; / " B . n f t . b n
1". o"na'"q elocl - lso(s)h = 9oo f l ' l l r
E?) Reptaae )he syelem of lo,r-.s ocling on ihe r.o-e in rigP-2sr by o ros"rionl ,e o) n q, o coople oc);nq ho",%"lolly
R= -so tb (6) neons do*nwo'd)lMa =C
6oG) -r,ch) = r(2)f - fo tb ltu'u B \C oe shown
f li 't l
l
lii
:
l
2s Rcpbce |Ae egolcm of foroee st'4n in Fiq. p_2ss by onoqu;votenl forEe lh.oJqh OV, o coupte o;;"" jii#;,...':i',X"":;3'::"'e:::.:mi:::,,
zF, = |a1.a (rka') t 22+ (46) - t61 (r/JB)
fuaq4r!(lo lhe righl)try = ,+1.+(1k ) -22a(/8) - r61(./JE)€F-t = :3oo.s6 G, ^e"^e doanward )^ - ,/(10a.o0. + (-300 36r
: Pt4.Zg-b(dot!. )o lhe nlght)
0r. lad'zoo, f@,osgj|: !L99'
ol C =<Mo
3F = a6 1 (a/r3) 6) r 3o1 ( s/J:t) ( i r ft1 A(1/.rz)(2) - 141.4 (t/E)b) - 22a (2,/.rs)(1)- 22+ (t ':t")()
3F - 1AO,1
b) +p= 1taa1.lP: 2993 tb-
260.) The effecl ofo ce"loin non_concc,nreni fon:e egelemie aofined by )he fol)owrhg data : .x - +rJorr ,<y - _6otb,onazMo=360lbfi counla-o)ockwi6e. Dele.mine ihe potn) olw/clhe n€sul loni rh)€.eec)6 the yo, ;s .
. -T ' -
l ' , ix-ao zy =.F, Ly
l.r"* Lt - 360/90 ' af l belo|9 o
2or. ) ln o cenlo,n oon.<nocunecl lo f t .e b/ . te !n , t B fau^dl h o ) + x . . s o . b . ? y - , t e b , \ z M o = a a o b
f , I n o o o u n l e . c | o o t .y ,* T. : :
uere.h:nF the pornl o) *n(n )no ree. , lon l rnlor6ects the ) l o) , ; .
L, = +ao/46o:-:4 n;ght ol on,gin
lh.r'4h B eic.
l 8 t 9
l i '
252) Dc\ermine comPlele)'J lhe'|ing
on lhe s]eP PuIeY €hdwn
fis. P-263\ t}€
o' le
ih€ r€sullonl of l}e 6rce sy6lem show^ in
r 1 v inlercePts
R .' = Gs9.e2)2 | (-37s)'
e - Q5+.Ag h dorn lo riqhl
4t, - loti' 81s/oes,52 '44-
Rd- aMo " ztu(|es) - 12so(<,5)-2eo625)
!4:9::4:ojs'R poe€* ihrq,eh lhe
o7*i* - ."o .t"'. t z"teqe) - zz+(e/s)
:-ll9iq(]o the."iqhl), zta - lt co3s) | 2z+(t/r) - 361t4/r.)
res"llon) ol )h€ lorces oc-
in Fg. P-e62.
@ 1ft . z!,o cos.6 | 2so
-: q994zb(lo lhe 'iqhl)
4f:r '7@ strl3o' ' r25o
1,*!arq(- meons doMw
,:-t94! ruPwoftt)R- IEFV-IZFV
. - ft@-eEY t6rzrl''-l!.Ab GP io lhe 'iqhl )
Io"ev - zrt7ar, - ss allae.s-e. r -+an sa.61/149.9
2 M ; - :oa s ' n ' 12 J ' 2 2 " ( / n) e) 3" ' G/ ' r . ) ( t
- -L, r ,6 n 0 ( - neJ.s co"") -Cw/
- 1.67 f+ r )qh\ of O'Ly -- 1oo 6/1+9.9
- 0.67 ft below o
202 l
,6a.) Complele)y dclcrmine ]he resullonl wilh reepec) lo pi.Oof lhe ft.r,e syeiem slnm i^Fig. P- t:A.
,bl___L
zMo- 141.1 (1/.$- 2tto (9/'{-t.
zF,- +1a(t/.t4) t *to 'tnoo t za(?f,a)-2ao sinao - :89.79-Jp:
zFr - l.j.a (/rz) + 26o(9'b) t24o caced-.o.Jcos6a'--g:93_E
R " \EF7-+aF7-'@Ai6Y I Gsri.F
B_-:___sst9_A t!(up lo lhe .,qh) )
9, = | o n' 1 257. o3//+rs.1s
)(a)t eawc<iG) + ao eina(+) + ao( a)G) - lil9.19 rLtLcw
d' zMo/A - J!19!p- - 3.27ll.44.68 -
?e) Cod,pola lhc rcs"llonl of lhe llrcc ,;!e€ sh6en in Ftg p466. l-ocale t)6 inicrecolbn wtlh lha r ts y ores.
1F,. ao(%s) | 72.e48)+d(Eh3o) - A@r11 io lho .igh]
zrr - a@(..,L) - 722(t/,Et
9, . lon-' s1o.1/01o.11
9a:=A49'
:,:gOacnEdn6 do*nwdrd)R- GF? + zrr..
.,/c1_-+rgsloEY
E::4231_doq. 10 nsh+
lMo = 3@(1,1a)Q) - 3so("h)G) + 122(2/r,')(4 - 3oo sineo(3)=&: a4.91 j1:lb cw
Lx - 1121.97 - 4LD, righT o1 O
ty = 1121.q7 - 1,3en. obote Ouo.47
-
iliriiili
iilitrliil,i;Irii
iilliliri
!
i
z,;o) Delecmino ]he recu)lonl of lhe lhree 6rces oclinq on )he
dorn 6hown in F;a. P-za,rtr loo.le lls inlens@lrbn wllh llle
bioee Ab. Far s6>a desiqn, thie r erseolion should oc.our w/rh
lhe didd)e lhind oflle bds@. Ooes l) ?
<rr. rc,ooo - 60(b c'o€ to'. ago:.!a tb ( to the
. iqht)
Zfy- -24oOO -6o1co 5t.l3o
t 27)jA( neans do*n'*ord)
,,/66atf; CeTaad"g, - Ion'zrt/ara
- lp.,' 2n P/[email protected]+"* 2s,91'
Ztt;A = -uooa0t) + poaa(b)'bo.P( )= -228.cea fl lb (- meons ccw)
ZM6 = aFlrbxb - zzeao/2zoco =--€.t]tL(from the lcfl of E \
hence *ilhin lhe nri&le third of.lhe bose)
267) Ihe Ho*; .oof l..,ss sho./h in fig P-2o7 cotrie€ lhegiven loods. The wind )oo& o'e pgrpendiculor to ltte in-
clined m€mb€Fs. Delc"mine ilre mognil:de of lhe resu)-
toni, iie lnolinol.ion wllh ihe horrionlol, \ whar"e li inle-
R = 2?424.02 lb.( down lolri-qht)
zt"-zo<tot++u(1/r)' +oo9,32 lb
u 4s"--fi-f666- rca -<+d",!t)
I :--.9qf.93..b-(- mcons down-*o"d)
^[email protected]:o.)rR - 1A'278.17 lb rdodn )o lho
rrghr I
lb.z.ia)b.ldblb
l o l l o l l o l t o a
22 23
+, - lo 4 z?//zF - loa'| 1&7.oe/a@a,62-+, - 64,2'
zM^ - 4+so (1/F)G) | aeo (',/r)(1,o') | zooo (d + aao (d| 2ooo(2o) | looo(tso) - hoa87 72 O.:E
.t - 16008r. z2fooo7.oa - 1!|L dqhi of A
zoe.) The resullon) of four^ 6.ces, of whbh ihreo orc ahown.in FiT. P-26e, ie ai o oouple of <€o tb-ftl clockwi€e fh €er'6e.lf i*ah sqore ie rfl. onosdo, aets-mine lhe fb""lh fo.ce
Zr' - Rttr , 11o t tso e/s) - o
ff-:lqqlg Gmea"€ lo thc lcfl€F.t . RJ,
Fr -12or 1Eo(a/s-) - o
? 'rt : 29alb +o Ihe lefl
+ao - -MP + faG) + 120(4>\Ar.2oo ( l - lb (ccw)
. d = 2oo/2oo .{ obove O
26e.) Repeol Prob. 26e f lJ.€ r'gtf onl ic aeo tb di.calca d6lmto lhd ght o1 a .slope of € lo rz passing *hrough po;^l A. Al-.Eo d61eFftine the x \ y rlencopLs of tho m,bdrg 6r€e F.
4o(1%s) F | 11o i 1eo(3,,s){E_:j6qlb (1o lho n,'ghl)
Q1 ' ZYy
aeo -reo fr'F) . Fr -12o + rco (1/s)
=t=:=:P. Goq^wora)R - F
+2Fr2 - (60)2 + (-tso)2
i :_21-?.!?&(ddo ro nishr J
_-L
-ga - lE1zJr/.t, - tdr-l @l@' -+r::19-
ua'€Non{*'E't"l, n{'olu)t2) -11o(+) | rfuk) rtrt
l+:,fli:D- dti, = ao/po - Z4!L rtgt'l or oir - @A&o' z@LL eo"B o
zo) IfE ll.Ec tuEca 6l|'m i\ r's' p-27o o'v r€qt'cd ro
ote a lgia,lol .€artd't @ti.g lhrorgh poinf A' tf F =
sr6ID, &l€.niE lhc volucs of P ! r- ,tr. ' Applv UR-€'lt
1o dclc.fia R, lhcn ltn- €rac lo fi.d p. 1fi'ollt €:llF- [h-
-'&, (',/h) 6) Bt (./e') &)' 4 GlR.* +gg-6+ lb.fio llE .i,|l.l
lk ' {va+t-aG) - e*(.A-o)b) - z*,(r's)@
aea-.a (a) - -1 (?t-t,y.'').'6(t6)G)
|;9 th.q,9h p-,1 A. lf I i. Evkr to ba 3515, canFd. the
-xt(+)(a)+eat(16\4=e@)
8:,iqqJ rb (da6word)tth. -€llb
.:@.+e ti = r e/&>(.) - r (.ftY1)
L:-Ec'?,b'
P(.A.'tG)rGE5.ae)O/ra>G)-a'e.ai(h)G')'aoo.at(+)!-:!tgY
Chop lo r 3
Equilibrnrn of Fore Syeloms
l
*a) The cyhM€r C ;^ fiq P-3o2 weigh' looolb D'aw o fBD
of cyl,ido. c q of rod Ab.
( " i ' " F
3os) the uniform .od i^ Fi9.P-3d3 weglrc a?orb b hoe ilc
a6l6 of 9ro"',1/ ol O Dmw o FBD of lhe rod ' tlegleol the
thri:rnoes of lhe .od b o56u-e oll @^lool su'{^o€s to besfuoth
a+) Tne fiv-e che*n i^ f;9. p-3aa i6 surf,orled i^ Pivols 01
3p. Eooh membor wo,ghs €orb Per f l Drcw'o FBD ofac\ '
s<z) A tuotb lood is supponlod by o coble whlch rune o-
ver a pulley b G fo€le"ed lo lhe bor DE in Fig P-eos 0m*
o l6D of bons Ac \DE \ of iho purlev Assunc ol l hrn-
dp. t. r,F G-@lh g heol€o{ lfe ee'9hr of eo' h
26 27
!a) ol!& o FBD df pullq/€ Eq D 3 of lhe bor n D €h4n rnP-.oo. nseu-s otl hinges fo be sm@ih g n€loot th€ w6,9hl of
.<"-Kv".
eo€) Th€ cable q boom shdwn i^ Fig. p-tsos eupporl o tadof 6oolb. Deiern1'he lhe lcoslle Col.@ T ;n lhe cobte b, tocomprEssivc ,Ale C rn the boom.
r Mcthod i (using horizonlot \vc.ri@l^"".)
r@se ' - C .a6as t O
I6'n2o't Cst^aE' - 6ao @eb6l. cq r to2 t.alolo I i. tcms of T)1 6h 30' + (1 es.d/coeq.)(srn4s,) . soo
J,:!!!=?9:4c - 1BlE Go*tVe. e.
S:!4.%s rb.* Melhod-I(using tulotior oies)
- , ) , 2 " r r w - o . c s , n'.'.
- c _ e!1.aazllL
l@ -c
l
l
ztn.o: l - 6oo@6,6d r cc6,zs'. a coset + saz ea6(coeze')
-E34!4-]k'r Melhod tr (u6hg Forcz l"io"gle)
si^B- e 6o-
i. hold ogo:n€+ o sl]@lh in-
rod AE,n f''s. P-3oe. D et. Pqfl c.-*,J A cylindo" woighing aootb
M"thod r (u.i"9 t{\Y o'*)t8 of aanido. b
/-Krltdr
e- )d.\'1-ih.Ot Pc.6&'- llac.f
P - dc63r.'//@.t' @
Psins'r dsin!" * .oo @
[N...a€ (.'",{r/@.F + n.i"aa- ,+oo - l:3!aj6glL
P = n @*/@,e'
- 4e.6os(,o.a4/-. z.'P?194 lU
ll.4n6o' - .oo .t rs'
.Fn-o I P . .q @.6; + il co..o'
p -.roo 6 66' + 41g.6os @1 60'
MathoJ )[ (u5inq Fo.c€ r.io.gb)
;.;- :;.c_g-
B1o) ,oolb bar i6 hcld at r6i on o srpolh plo,g bt o forc,- p
irclincd ot on ongle e { thc pla.'c 06 shc'$/n in Fig. P 'eto. If
e - ?s' dcl . ltc volrc of P b lhe nomal p.s.6u€ ^t eqlcd bv
2a 29
FBD of +he blooK
Melhod r (u6ii9 Rololed
Method I (udrg ii\v orce)
' 300 - Nsin60'- Psin+s, o
P.DsL ' llao.6o'
P ' tl cbs6o/c.,.1s' @
,a'6) 3@ - nEi^6o.- H@Edho,n
11- 1@. 7 lbP" 212,1a2 lb
Method [ (us;"g Fo,.e1i.ongte>
sn.E .,flor q:d
<f t =or f i€ ink ' 'BoosrnTs.
d - +oj,ao1 tb<fh'o: P= ri co6,rE'- ioo @ 7s.
P= 4@,el (6k)- scb@1..
nl) If the vdlue of P i^ rb. p-e1o6dtvc il musl be i\.trhed w;lhthe 3oolb b6r in equilibrium.
i6 18o lb, d.r€rmhe iho ongtcthe. Gmooth plone to hojd
r.l6in9 sih€ l.wj q = L
P'r@!
!ir). Datcdinc the nogniludes o' P \ F he@ssar/ to k@P
lhe co@!ft.i For@ .r'Ia6 sh@n in Fb p 31? In equniL'rrum
3oo4^@'+ P6 4' ' 2@ st^lcb'
P- -1t3 245 to
F ' aa/2 a'E 6tS I Pcd z'; - 2@ @s 165'
7 '.uasao'- oa z* (cszo)- zo <'x'*'
F - tu,87 \b.
s1a) Fio 3€ rcpreechts tlc -^cu.Ent fo{Ee €v6lar e}i^g ato
j6i"t of o bridge trus€ Detcmine tho voluos of p k E fo m'n-
to;. e{ullib.lum of thc lorcee
u6ihe Rotoled Are Mettod
'@ 6ih16. + e 6i^i/5' = ao6.'nat { ?oo si^l
F - 412,439 tt)
P14@@"a{ - 2@@1E: t 3d?4 ; ; I Fa ' *
P - 1 @ ' 4 4 t b '
:*) the fwa 10l@6 shown i^ Ra P s ore i' equilib'ium Con-
p" le $e "ou€e of Pt- / -
zast '4t'r 3@ str@' '46 s'n E: t FGh&'
F - - i 4 6 3 3 l D
Z F h = o
P tad@*" | 2@@.60' - r@ra t3@@!d'
&b.lilulo lh€ volue ol f
P,@6sF'to@@e"t% = (aao') r roe:o'
P= -€3 ' 12€ l l ' '
30 3 l
!1..) Ihc aoolb fol% & r}h!1..J lhc aoolb fon@ q thc a@lb firrco sn6rn h Fig_ p_s15 otEfo b6 held in cquilibriun b^/ o lhird fo.€o f <ntinq ol on unkno-wn a.sr6e with lhe ho.izontol_ oeta"-ine thc votu€6 ofFqe
.oo6in!o. = Fsrn€- O
3e-a@@a.. I r.a;a_ @4b6l. O ro .4. @
\tn = aao coszo- +/+@6ta6d\ /. -a)
-@- 4ao c.E o' _ co6s _ cdl6lltoo 6'n !o'
-e.- - -76.93s. - 76.93s bet@ \_oai.
F = .roos'n3o _ aooEna.stn 26.t38
r . 20s.315 lb
v6) Dete.mlne the votqe6 €|1- fhe o.st€s o( \€. so fhotcca EhoM in Fs p.3tb w be n e4ott ibt tun
ihe tu*
2 Go)(14) co6e-
-o- - cos-' o,ezs- e ' 2 8 , 9 6 ' - 2 9 .
_29_ =_L
"n* =t"o ("nzg,)l/n
i r :I
ll, i
.
il
t l
l
./ :r7) Thc ayslcm { l^ndlc' cire dlt?a^ h Fb" P-trz e'FPg't
lhe indiootal $/€ighls' CtnPute tlE lavile fo'Eo i cdrc,,n'
ecn.n ' 'aoor ;canat 'B - 36+ .ao(stn&')
I . 914,162lb.
-s----9---2--
D' &7lb
A -- cc66 | 9..s15'- a<n(a"a1 t q+ra(a-1€)
A ' e16.11 lb-
Fototcd ,tses Malhod
ae) lhr€c barc, hi,yez ot A\D\ fdtu) ot p'C a' do$a
in Fls. p-318,6o a ur-linr ncoroni*r' Dolxtte ltrtd*
of P lhafwill Prevonl rDt'on'
s6,'= .d)an*'
i = 15t2rs b
tFh=o qb<t A
c- w.@+', A46o'
33
<F,. a
. P- 22z.or 6tnr . .
u6hg rotiz t.todgle
-g- 9, - _-LEt 60' .i.r.d .tn$'
v-d^;i- =
#i. -;1_
P = 223.07Gtor, )
P = zo4,7t9 tb
n I R)A stD,g . Boo
t7 - 8oo 4oo6t.e)'
11 . 463,6 = 4s4 tb .
-,1, --. "" toqcd [email protected] o 9tn6tt 6po.e. a.po6t,m lwa
?t,rd6€ eeh
^sasrtnq 4@tb q ;"",, ". ' i l ;r"; ;P ete , ayer frictto^b{s ou 6,s ta |\e;, qht+ ot ?ootD \[email protected]€re':n^: jhe oaebo\rhe nordot pro.€!,! N t4t. the o7tia.de.s \ the sm@ih raatuhtot ^urttu
ec.:t fhc FinR l.us6 €holn in Fig P'322 iE 9"@o ca
ler oi A t') o hmge aI B llg gNen loads ore nordol
i-'i""o ^"^o.' Detc'd,i'e trE paotronc at A \ B
plac<. )ho loodc b.}, fh€i' reculiont
to lhelkl: Ro-
.ona " eao(e'"eo']lat)R^.451A,Alb = a62olb,
Rsv r Ra = gooo sin6o'
P,a< - [email protected]' 161A.e
R e " ' 2 3 o 9 I l b
P-ah - 8@o ct'e'
6e'= Rev'rRen" - (E<n 4)' + (4aoo)2
Re -t(2aas.4)' I uaq'Ra- 461a.e lb 4 4620 lb
+o.O- - 2309,+
4000
e
R6 ",+6zotbs ot 3d" w; lh +he horizontol
l4 a5
32!r) TI€ l.iir66 e,v,'*n i^ Fb. p-32. icdt A b o .olfe. dl p. A lood oF 2@lbttE €oofione ol A b S.
cuplo.'ted q o hi.saic oppbia ol C. Dol.
zMA- oaoRb - 260 (@Eeo)(is) t aa(etnza\<a)
RE . 6s94,76_ 30_
Ra.2tgg.za b * zaoo n
R^\ = 2@ C46 so'&\h - l7Bz,O5 lb
R^v = Ra- 2oao stnaa.R^i - 1199.8s tb
R^"- R^h. + R^.2rs -,/ t11t4,os)x t (fq9,35)2
R^ = 2106 tb
l o n € - - P ^ w , 1 1 q 9 3 sHAn 11a2.bs
'6 . lorta {99,3s1132,Os
€- = z4,aol
R^ - 2106 tb down lo +te tefi al-6 " 84 ,7 '
:z+) A wherl of oin rodius co..'ec o lood of rc@ lb' os 6l'6i/'l
in Fiq.p-32+.(a) oele.mine the honizonlol fo.ce P opplied ol tl'c
cenler which rs neceieory ta slart lhe wheel ovc' +h€ 5-h
bbrK. nleo find the rcoclion ot llle bloch (b) if the fo.ce P
nlcy bo inclined al ony ongle *ith fhe hodzonlol, dolermine
the rnlninurn volud of p lo slod thc wheal over lhc block' I
o"qlii ihai P motr,es wrfh +he horizonlol ;\ lhe reoohbn ol
the blooK
.t e = o/41 - elo =ae
") p-- ,7
,439,Z r 4 d ' o
5P - 1o@(locos3atp ' 1732.651tb
?. Pd .rs3o. -_ i32,o51Ra = 2@Olb
P i6 min iduh i f i l wi l l be -L to Fa
hence,-q ' 60 '
10 pnin = \oao(1o.asso,)
P6\^ -- 866 tb
Ro cog3o' = Prnin cos6ops -lp^;n1nsaod/cas tt
- laeo Gosao'l/ cos to
36 37
tsl Dol.;rn;nc t'hc o,,ount q direct,bn of Jhe smolesl forteP ftqu.tn b E,o.i lhe wh6et ^ Fb. p-3es over brock. whol i€lhe reoclion al lhe bt@r : ,
casq, \y , cb.714 _ %ZMa. A
,aco(a) p.o) p/(o)'a "^t..,",.1.X"'l,r''riL1,l"26t ( t .ae) Pcos- h .6^ F6, " \ / t sq , ,a " ,u i t , . o . t ,q .
Pd{ (d6+) r p6hq(i.6e) . iTso(o6D P('6i"q) l 0,6+ jF a"q l 1.se p coe< + 1.se de 6,nq . o
#1"**" *" ." , "_, . , f , " ," , -* .d 'P * 19 6apa^q - r .eep@ \d 4 l a 4 @ 6 4 + i z q d r q .
Lag C@s- - a.a+p.,n-,
lI1 = fod< = l€1o,6+
o,64
< - 7 1 . 2 9 ' + 7 1 . 3 '
o
h(W .;1s.,1'
P stnso' - "o- 1.tn n, o" '
P = 1es4 h ot / .a"Rsthsd - z.co (€D1s.r1")
R- 641.6 lb ! 6+4 Ib
w',h
iIr ll r
l
l
i
j
ird) Thc c/l;ndcFs i^ Fq. P'326 hov(, the indicated weighl6
r., d;mendone. Ascuning sruolh conlocl surfoc€s ' delc^-
mine lhe rcoolione ol , E, c , \ D on lho cTlindors .
FeQ of Enall c-/litdc.,
er l1b41ao' .R6a6ra@e d - P6
Ft . <o asto'
2e' P.r. stn.d
P |a- f @lir,q oldg lhe rj'ore eto*a h fig. P-327Delernhe lhe votue ol P \F
$(r) aAsti - 1so (6) t ae82)f - 390,15 lb
ts(P)snsz,+ - twg) -dha)p - - 1a7.6,4 tb (- @66 colnptce
10 Mrl
FcG ea'l- P@6t4 - t6.o
zso ra (aseai) - ( 1.'.6,)(@E6a.a) - a<to . o
38 39
tsro) Two wc;9hlle€6 bors p;nnod togelher os shown in Fig p-s2o supporl o lood of .sotb. Delermine fhe fircc p\F octiaqr.specl'rety olong bo€ AA i! AC thoi moi^to,ns equitibrrum
Io^ P' lL ) p.s6.a'
to.o< r j_ i o{i3s,66'
{{z- o(+)fco'o< t (r) fs'ns " ..Eo(s)
a F6o6 se.6dt 2 r(s,"!e.66F so(s)f - 6101 lb.
zPs.np a [email protected] - sso(Io\2P(ane6.a') | 2P(caE66.t1) - zsod
p= 901,39 tb 0c .t6)
E e.) Iwo c.tti^d.re n q, 6, wc&hjng lootb \ zootb ,€dpcclivcty,
7". ?'"-"r"d by o .igd r€d cu.vc, po.ollct {o fhc anoo.lh cr
lnd.icol 'urface Eho\'^ in f tb. P-a2e Dalcrm,hc lhc onato" o<\e thol danned the poirtr'on of equiljbn;m.
e.cd ' -< @
lodl.4s< - aoot@eloocoga . .oo @(eo-a)
rcoa-<-m(-so&,.".an^\loo .G4 - ,oo €nEo 6'rF(
l]!s-i t6< - rod26a@.
- ,o - 26'a3's,4.
&orb-l -a,ltu -opI .{€o(a) roo(+Xe) + R, (1o) - !0066) - o
. R1 I R, = 3oo r rood4) r .oo
RQ - s2o b'-
fnzn .e@ lo on inle4sil/ of 4oo lb pe. n
es) DelcFmlnc lhe reochbre R, \R, oT the be.n in ta P-#3
looded;th o concentmled lood ol rdoolb &) o lood .oeling
Pl= Feo lbs
fo. the tlem looded c 6hown h
t6R.' 16F.2 | 4F1 r1600(a)
r5R, =1600(16) + soo(a) + 1600(3)
R4 = 2loo lbs.
R 1 t R z ' 1 6 c , 0 + S O a t 1 6 a AR1 _ 19oo lt\s.
$Rr -Mo$+gQA.) + 60(6)(6)
R, - .9.ss lb6.
P4i Ra-12o I eo(4) | 1149)
r\trr -l<ooQ)Vr, {t*o("W\- ea
40 a
€s)-The .oof -1tu6s
n I b. p * ,s [email protected] b./ o mlk, ot 4 !,o ht gc al B Fnd the 6jues of lne rsc rrorrc
Rsh.o . . . Rp _ 9s i ,39 the.336) I}E cont,h'@ beom shdn h F,s.p-sec is burft hlo a rcrl
1 , , " ,n 'o . - lho l , l roale oeornet po,n l< A\L rh€ beoh i6 rz .
ons \ h€lgh6 jootbpeFfi n concnltuted tood 6 2@a tb j6 oDottetaI the tree c'4. Comp"l€ the n@chbn€ ol ,t kS.
. 3a R\ = !ioo(10) 1 600 (eo) + ea6s)R^ - 966 .67 tbs.
1M^"a3oRe,- e<,r(1e) | 6oo6a) + soo eo)
Rs" = 9f3.83 lbs.€Fh"o
zRa.e@o(1drtua(12)(6)
R6: re60a lbsP , ^ . R e - z @ a - r b G z )R^ " 1s@-zaza- 12ao
1dR^ -ad(14) , Faa(1) .o
€ o o r 1 9 a o = R ^ r F i e
1'l tP ** beo,n ,h F,o p.ra2 iq €upec.,e<) bv o roaL,,on
;l .:: : : -*.
,ot n whioh_ 6epo.ore€ ,hc upp6r k rowe-b€od6.D€r"- ih€ lhevarus of d; ; i ; ' *"
^**
R1 - 1760 lb
ss) Thc lwo 12f1 b@tns dl('r.n n fQ z-4o oi lhe Poge @ 6c
;; ;-J ho.' zo.lo / with r€ePeol ho ooch olhc' 9 tood'i
tiiJ ," " "^" posi:t;o,, t' CD so ihoi oll lhrcc reoclions
;';; ;;;; i."r *,'r "" q n' nen bo? Ilot tor qilt P
be from D? p.edb
F . 34O ' R1 'R, qRB
zF"- oRc -Ri rRs
Rc - 6ro lb
R6 (Y) =Pa(12)
Y = 320(12)
Y = 6 f t .
tM?.-oloPe - 16oo(t+) - 1o@(4)'o
R4 - 3a4o lb'
toF,l + 1600(4) - lo00(6) 'o
co.sn4ring th€ 'rPPc.. b€om '
PG) - tk 62)PO) ' 6.062)
ga r. " 6a.62)| . 6ao4a-)
960
x . g F l .
. . R r i L R 6 i e 6 f t o P o . l .
P , e a f l . l - r c - O
42 43
a/4 (D/4) ̂ yr(d/r) r p(o/4)'NDA -w{a = PV,
wA @-d) - pD/2
aa;a,w-3L
(o'd)
tto)Forlhe sy€,@ of pu e),e €rfrn h Fb.p-ero, delch.incthe ratio of w ta p to rcintaia cguilibiuh llcaleot orte fnb_I'oa L th€ weighl€ of the putlors
ta) rf_ aah purlg €br. in Ft. p-Bro wei9h6 36 rb \w .7zol4F,hd P lo ooinio.h lho cauilibriun.
r,1' 2s.2b p- e6 | 262)/e
i!1.--
s.r) Ihe *tr€el toods o^ o i@+ orc.gi'o h Fb P'ea oel5'--'*
"t ,Of.* " so thot lhe reaotio" of ll'e bao al A rs
lni@ oG gFAl ..e lhc Eootld ol E-
aa!)ihd we{ghf wof a l.o"eri"g a6ne \c 2oIo s dit'g o56to"^
'^ i,t ,- "nu lo p* *nt the @^e l (tn.lipPtnq 'o lhe r'gl'twh'
- l"*.ttp a @,r P af 2a t''ac'.o..@^td *'ts1 -S,: ::i ,.f
il;';:'il"r"";;" ,r'q *t*t the oo'e*rrr re#'n in e4uirr-
f*- ia^ *i* the @'imum taad P i' opPtied t" wfEn lhe loa
q = 2o +ons
U- 2Rs GPe'ltcA .aii+ion)
tsr.a= 6oaG) + 2aoGt+)
.5p.6 - eaor +eoo - @
RArRe ' 600 t 2oo
' v A - e @ . R 6 ' e @ A " @
b GbVa) " e.ot) + aaa
Limilinq Condtlio's,
\ thq P'o r P.2 'o
\ rh€n P'2o ) R1'o
ztAq-o (* ton P-a
4(x) = zrG)q' = r4oTon6 _-O
aMR,'o ($.6 P'2o)
q ( " s ) . z o ( . ) t e o ( r o ) -qi i\{sl = 22oTons - -el
- 6 f 1
4445
!€) boom AA i6 9uworled r;r o hortzontol posifirn h/ o h,.seA x*. o cable $h,ic\ tun6 fton C o@- o smo puite/ ol D os6hown in F,ir' p-ra€ codpuJe the leo6,bn I th the cdble 1^ iheho.tzonlol !^ve.irbot oomp@ehls of fhe r&otion ol n. n :lq l the. jEe o{ lhe put te/ o l D.
zal.) R'paat pftb ea6po6itb^ at whjoh il islood€ retuln verl,bol.
2oo(z) | rca(6) - r(s663a3')(+)
I = 279.s2 lb.s.
Ph = r.oe63-+a"- (r7e.ez) (.663.ai')
R i r l 6 i ^ € a , + t s ' - 2 a o t r c oP.! - 3oo - (21s 62)(6n6a4z)
Ba - bo,a6 Lb.
ir +be aabte putls {he boo,.1 AB in{o ot cl:ned ol 30' abde +he ho.,z6+at. rbe
6tne' - V4 lon€. - 6/4@ao"
4t .1,t{z).,tet | 1&(6)@ao'
Re+I6h--. = a@ r11x)
R! - 3ab- 216.. (etn6d)
Fa - 1 t2 .5o lbs -
B Eoohftorc etos ;^ f b P 4+s i6 tupPot'tcd h pr''ot6 oi A \
"*"* ".;ut " soi p'tfi d"p"le tho f@'r?io:T'--
n * t " ho.,zonlo! \vaticol oo"poale ol lhe
rrg) The teuse. shryn
&-o hinge ot A solve
Beo) ComFrle lhe lolol @tioas
O E
i^ f ig. Pia is oPPoriel on re e's ol A
fd. the conpo.'€n+6 ol the reoolrorLs
Rsh - z'to lbs'
21R^ | uo(15)'dL) r '+46(56)
q--!4 R^= 71o tDs'
24R6! - @(12) r uok) - 4b62)
ol AqB fo. lho fruso shom ih Frgu
/t /t-. / t / |
/ "l/ ,1,/1. ,,fr>E I
rU ln^ 12@tb
-- 194c
l!.'bl) = s&Q) t4l6) 1'8'h')
lit' ' 2455 67 lbs
nh . Eh =?+66.6? lbs.
&r -^ao+s@r@raoao
46 47
Rsh - soolb6.
R^= toag,7tr p@(eo) - se(^d- a@(ao)bs.
{fv .O
PlNrR^-6o0|12co+sooRa? = 12j4.2e tb6,
e.E - GAAiGTGAF - Pa4.?e trB.tang. ;p1i .ee/eoo . . e - 26.12 '
i. RA a12so.7s tb6 up to |he tefl ol 16.12.3Er) lha b.4m shom in. Fig!,re p-s6r i6 cuppo.te! by d hi.tg,e ot n\ a mlle on a 1la2 6lq,c ol B. De]'eaditn@ lhe resufont rechbne
ft(Ra'\ - a{t<12)
t6(FLw) ' +oo(i)
Br Rol.o \ Ptuporlion,Rsh - r R$- s,(1/.)
KB -Yflgo)' t (3oo)' - 335.+r lbs.
R^ ''Lrr..-ziG'jf - Bo ,, tb6
!6r) A pulley ,+ft. h dioreF. \ sdpp. "r'^g o t@d of ,@tb :e @n-led dr € on o honzonlol b6n Gtq p- e.2\ Thc bam ,6 guppor led b, o
I
. eoo- 2c6Ginao)
R6- loo lb5
Pc(s) = 1co(a)
zF! -a
R^v r Rc ' 1oo lb6
P^v - 1oo - .eo = 60 rb6.
5 f h - o : R ^ h ' T @ 6 & '
P*\ ' 4oo @6a'
' 113 eo tos
rOD of lhe beam,
e - 9 - e . 4 = 0 , 5 6 f l -
R^- @o)a t(18.2o)z ' 1ea27 tb6
lo"$ = soy'tz.to ' r'1o'' , k^= 1oo.21 lbs ot 16no'uPfolhe
ngnr .
sse) The forces octing o^o r-f1 ledshl ofo dom ore sf@n in
Flir' p 35j.The uptlo.d qrou^d |.@ction vo'es un;io'olY ftoh on
' '1i .n"ity ot p, b/n. at-A lap" lbA or B Delemrnt p'r p"\ol-
so +he ho,-,2r.'lol' re€ieldnoe to €lidrng'
R4,Bionce to 6lid,iT,
F - 1oo& - 6dx @e'
F= +eo3.ss lbs a 4600 ros-
R= 6a6tetA3a' | 24o..
R* -- 2to.n(1i r axbG)- rc.|:a (6 )
48 49
A-R/B(r6e,b)-#\tt #E 12 t&_
P,.R/B( '6e/d. tg l 11 s t (s€, l - . :aow.1 9 1
3E+J Cdnprtc the fotot reoonbns ol A\B on thein F(t . Prn5a.
tong- -iolo - 1/4 )e-- 2o,s6o
8oq6r r ac+oG1z6,66')(1o) t2oo(1o) . e2.a/c.Ee6.s6)(6b) |'eo(6o) | o.tu(ao)i bca(ro)
R6\ - 4622.+91b6,<Fh -o ; R^h = 2c'b t 2Z4a s.2866" r 3ooir€ rbc.1M6 -g
ao p,^a - e.,.'rAo) | rc6 (6a)t z@a(ao)+ 3a,t (b) | z2ao(@s 16.
lonq ' 33u-o9
| 224a{€,n "6,s6)(1a)
€F. +an_1 3976, 09!ca1. *)
.'. R^ = -+er7,e7 lbs up |o ihe ri9h1 ol q - j€,e6.
355) Dele.oine lhe.eocib^s al A\Son the niik +ru,ss 6h Fig. p rss Mehbers CD \ F6 arc re€peot&ety pe.pendic, _br lo n E \BE ot thet. midpohl€ .
iX!., ^ = poa(as\ l ao.x)(a 2e)+ +ao \et iQ^ - 536i 27 - 6360 lu€
t!)'r]" ' -""n., , ""*6ets) t <aoa(+t zs\ +oco @e6 56'(+1 26)
Rsv = 6131 67 ! 6130 lb€-
Rsh = .ooo s'n26 66" - R^€r^3o" .
- 4oooatn26 s6' - 5361 27 stnaa
Ran = a92.Og5 lI$
Ihe c,]ntilerer 1.u36 6ho'n in Fq p-a% ; suPPricd-bv o thn'.i
i; , .tt,r BC Determine the reoolim oi A h B
ton + - 13/ta t+'26t6'ac =sa ' ts/cosze Ee'
r ' lc- aa' $17 f)
Ao - 39p9;a: s,.ed
Ao -. BF '> 16 17/cd
Ao" BF = to,75 t ] .
-B^, - -!999-
Q^ - 2ooalbe lP
50
35t The unilonm rEd in F,!t. p-ae7 wc,bhs +2o rt \ bo6 ,lsof em"ib, ol d. Del+mine th. t.";-,;;;;ftX.:tione o'l lhe 6moolh_eurfooee ot A\8.
aM^-O
2I r 440(6) - a f i sh4o ' i 6 r t@€.b!l, stn lE - aosa6.
2T .r 2s2o - t6 tlstd.'.
T - ad@sa5. - 1260 ^. e r ish+s . - t?6o
-
s u b 6 l . d 1 z i a 1 ,
n@94s' - grlcD.+s' -e6a-7n.*16.! - 1260
, r -dcoe.E. @
fi - ?s4,sd tbs.
2R^ r aeo(a) - d 8ha.G) 1 n@*.f6)RA - 6dsn4s.- e+opa - s (2.+.soxsr"+s1 - alo - 2!}o tb6.
js in €quil;bf;um unden ihe @lton of Jhe fveFis. P ess. Detemine p, R \-r.
R(16)i r@se(s){ r6nef6) - 6co(4)
| 4ao(s)r6R 1 9T66e f 6ro@ _ Eooo @=Fw -o
o1! {l'""'u.4 e- 6 .a7 . R '6<b- t@6e @
$ (6c).- Ioase) ! elco.+t 6rs,no. €6@015 (6@_ roo6 36.s7') 1 €.r @sr'e)- + 6r€,n !6_s7- . 6o00
T- 12es.7.t tbs_
R ' 6oa- (128s,7) es #.s>'
R- +2e s7 lb6. (!p*a.!,)
P +1.,t1+ - 1@
o - <a- Gz*z)'a=s ez' -'P ' 37,.qz tr,s (ro rltc lefi )
# '#4'o o - ae.afrE
@.r$ols ' t=P^@4'Gz) A-:|, - "r"^1'*' -1 tuo llF = 1'e 2" tE
*",',^oii-*'i' ,'* as.-'who' .{o\re or 'r ocrirq or '( = 3fl
ftvja b tig NeeP lhc bo' horrbrtlot
& . , 1 4
- t c ' s ; 7 9 f i '
caad - f r t N-+.3e
- o o = + 2 4 - . ' r n l l '
I t a - 6 - 1 ' ? , = 4 ' 6 1 f l
1 6 61') = a@O a")
1 - 60'3 b€
52 53
?6t.> Referdrg Io tM 34 ,-'F f = ?dttb r( r - 3fi r .r6lffii.!€ tlpagle €- ol wh,ch the bo. *tll be ,rc|';€d l., the honzohtat
rl is in o poerlion oFegu;librium." (!4fr!e1sct, " t-*.ffif4d)
Us"9,+brlb,tu@tn," ,s, - n(l-,')
fo. &,!-o = lof.(6)Ga)
3- , 16@-. qR^.b Ro,-g-tzene = - lqd i'-"a,*e)
ft. 'he afd;"ales d pl-o
r 16@ = D (caee + 6ns-) -x
x =gGseCt_6'!9)I * fdn@
fo- a+ p^.
J = .tzGne+e.\e) -\-..3pr.3 = Pta at (cast st'e)
nl'a"*t-pL -'**1 - $q[ sa6€" - "(,..e, e r"o)l| l ' l . . a ' I L . l . t ^@ ]A{ e.t i - 6&e - 27.8e - a,(@.+',na)
1t l@ao 1r+on@
:: og+ - 6o(@cJ eno)1+ aon6o
3B@€+6rlon6o) = @ cGe | @ 6nea6€fal(r 1ro"@) -@-l - "td.6,.o
[=(r **an eo) - oo] = 6.6. (eo)
ldtot = A@26279-O- - 26.6aE'3A7'
-
ChoPlor +
'Anolysie ol S{ruct':rcs
54
'1{,a) Joiat b of lhe lruss sha-n in fis. P- ao2 ts euajecled to
gle of+ degrees wilh thi6 slnoghf line. ghow thal the lor@ in
Bc nrusl ba ze'.. Ae e.alne lhi€ r€sull 1 lh€n €how thol 1fie b.cqs ;^ mSdb€. cO'oE EF,FI,HI.,HKI,\JK t€ obo zelo
Ane. At o jo'nl €uqj6t€d to the @tion
of lh.e€ flembe.€ bul r€ d{ha lood,
il t-o of |he menbe.s o€ corl,'1@.'
the tc/ce i. the thin menber musl tJe
the 6rces ererl,ed br lhe lhrce membeoe n8.6c' \BD. M
AD\DD ore in lhe some elrcighl line'but Fc ls inclined dloho.-
ae) Delen;6e ,he fo.ces ir €ooh ba. of lh€ t.oss 6haah ;n Fg
P-e3 . llkl: Fri.sl daiemine which bqre cd.-/ @ load oihq
p.haiple ddeL'ped in Pnb to2.
c E - c F - o
P - cDdn@'+ aeet 6o'
6'i!€ r CD=OE
P - 2cD e t^e'
c o - o , 5 7 7 P = a E 1 C
CO - BD ! o,gj7 p
BF = BD@s6o'
bF - o.67aP coe 6o"
Br * o 617P (o.s)
BF-- O 2A9P - f
.aa+) Del€.dine #E lorc€€
6ho.t iA Fig. P-31
the membene of lhe rooF tnusE
atrEid6irg lhp rhole libur€,-tu =o I R^v + Ror' =libtfiosrnb'
R^v r RE^/ '160-. .O
FDs - 66.6|b.Brv @ Pr'A
4,.a--lF"'
tfa'O: gr,cinr.,', AB.i^N; '1oo +1e6&'
o.5go t o5y'O'1cDtsopo+ so ' ts(z) ' ta-@
<fh-a: Bo.tE,go'= /.ba6io't 1@ctag'
bD = ̂ 6 ric'l-*@
@ p t B .
.06) Th6 coniilove. l.uss in
lhe fucs in oooh tnemb€r '
R ^ v - o e A 6 - @
Ac' 0.A6 AB-@
F^v - o.e(.oo)= solb.
&- Ao ' oe65(AB)'o,E6cje) ' E6 6lbjr
@ d cAB) Id | /\b ' 4')
^ 6 . 1 @ b - b
,,. E,o- /.E+,loo,, 2ootb - c
. ,Ac - CO ! 46,5 lb, -T
8 C . 1 0 0 j b . , . - T
Ft4 P- 46 i6 hi.€€d ai D \e Find
@ P t ^
AS6neo' = 1dO : ^A'ao.'dtb' 1
<Fh-O I AC 'AEco6so'
t\c - [email protected]' /, .C '1- f t2 lb ' - c /
67
bp . 1.?,12 r
@ p l a zry -o 9c.t.6o' -pD 6.nao, . rooo r AB sn3o.o sBO r o.g66Bc r .rc,oo+ 2oao(o,r)
o.eaD I a.e6ac = 2ooo -. - a<Fh *o : 60 ccs3o'- Eccos5e. { AE @s !o "
0,466 ao- o.6ga + 2oaa (a,366) ___.@q , E l i m , n o l i d n r r \ t
+ r.a sso + o a66B. - 2@a) o,5(o,e66sO-o,eac - 179?) o_€66sa'2a9- o,6(2F@)
bc.966tb.- . c /
@ pLC
o.25 BO + d..+€3 gc - looa
CD6t.6v"- Pt,E|.60' I lococo- g6sfos66) +iooo
cocos6o'+ Ac+ scco.6D'- CF&- 2o2o(o,a) | 17t2+ 86{' (a9) = s1ru ib -. . _ C
^9ana6 - ftoo eo,5o.
Aa = 11321b - . , - ' t
Fg P-a<r, coip-le
l"e lL€ . 'L$7 {"
+oz) In lhe co^lileve. l.uss €ho{o irforoe in m€nber6 AB,BE, \ DE.
@ p l - A
@ P I B
u6,19 F.otdt,b^ of Ax,e,
i ee.rrsiro l- r
+ o,25Bo * d.rqi sc - ioo.
' o?s Ao - o..!e3-bQ E lgoo
i^ eoch nember of lhe wor.en trucs.osJ computc ihc fonce
6hdnn in Fil P-'o€
R* = ABs|n6o'
A6-A!9_
A3 ' asoT 62 < 4910 lrc
coneide.ing the wtd€ nborc:
= M E ' o
R^t(n\ - e@($) t L@l1a) |
R^e ' 4240 lb
ZfJ aot A1s;n6ci - aa@r
rc' -4s11stn6d -2OOa
srn5''
, , rc.2@tb- '- 'T
Agco6so' - Ac
tc- <qto Gosao)
/c ' 2459lb-- 'T
@
4h.o: BO. /\6coe6o' r bc.a66o'
ED - +e1o(o5) r 1600(45)
BD.3755lb- -C /
p i . clFe=O: w6n&'I caen6o' ' +OOO
\EDok @l r co&'06f)' aoe
co = eog94 + 4O2DIb' ''f,
ZFh-o:Bccoe6o'r /€ = oDao6@'ICE
2b.o(o5) r 2ass = 2o2oGs) | CE
c e ' 1 w a r 2 4 s 5 - 1 O 1 OC e ' L r + s l b ' - T
5859
ct = 300 lb-..c
DE6tr|@' , a1st @' r etd
DE- 2o2o(o.e66) t so@
DE- s+94.2 v s+€otb c
ai1.) DolermlrF thd ftrce in n:E]mberc ,,a, /c)BD,co, qcE of tk)econiilev€r lru€6 sho,n in. rQ.p-411.lf lhe loods were oppliedoickE in€l€od ofol E\D, €peoify whioh memb€i6 *ouldhove thoir internal fo.ct ahooged.
ton6-- 9-
@ pl . A,
@ p t B , ZF .O =Fh.O
r.f,l.Fa3,as'-1d) AC- Bcos
AB - 1eo,2g lb r'.c- lsotb
@ p I c
t*/* .
./\B@za.@' .eDa44.@)'
AA - ao - 1eo,29 tb -. :f
ta o -94?
PL- A: I oE'i..e4'
co- aso)b-.- ' l /
Ce - CA.:ocsol2 | /\(a- 2g)< 6s3:12 t 190
A, +De - io+t/6(12o\
... 2OJ = 12or e/s(12o)
2Da - 192
D v - 9 6 | b . = A v
lnta.tonsnq hinge k rclr6'
eppo.t *tll not chonqe ltE fo'ces
in cocl' ba. e,.oopt {ir Ac &' cP
a c " q , t e / , o ( ^ s )= 22a tb6.r'6td\)
co - B,o(s/e)= r2o b({..6€n)
&--
Ac .12s |b (lo^.d^)
66 - 156 16 (a"p.ccaoo)
0 1 D :€ to,.c.
* \ t- e6-
s--+Bo " i6o tb (cdnpc66'o^)
co = so(slo) -oh
b q t , O h ' 9 6 | b
.', Co '321b (la5o'r)
dt C: 2?r-O
AY TDA ' BCgC ' 192 tb0€'€ion)
@6l
aoe) oelcrmo€, lh€ for€e in m6nbat.5 AS,BD,9E,qDE of lhetbwe rof lruss ehown h Fb. p-4o9.
A" (ao) - @o(3o) - €oo(2o) - ..o(ro) = o
H"(1o) -,ro(€o)- ooo(ro) -6.()(4o) =o
Hv: 9r5o lb.
a.
sEsh6o ' -6oo(Eh60) .o
BE - 600 tb (@.nprsi6)
[email protected]. r@(@.6o) - atoo60- rsoo rb (cepr!<,ir,)
t'a) Oelermiie the liJr.e i. €och nerba. ol ih€ pro$ roof lruse ehoM
AS - +s@ lb ---C : FHAC:6H - 366tbr-T
o, E, 'Y /@ u5iae d* ^c,
,Y ' ze" .o &=1s&bc-F64/ l* a lhc at-,s,rct o,6
.aS-ED=DF - asoo tb-..-Cat c. f.d-
E w-.E_,q-_es_g .ti5
:. co= 463.3i rb-.-T " DG
Ac - 2/r-n q) t cEcF . :,64)0 - 7A (ztee.az)(F = EA . 2400 tb --- T
D E = O
aM{-o. ,6oo(ri}rad(€)t€oo(e) = AY(3")
Aa- adttb
'/,
l^w
&=4q-_Aq
a1t) comPuie lhe force in eoch rn€r'be' of lhe lru6€ 6hown in
f,A.p'+to t lhe loods o{ B\o a'e shlfled vecticallv do"
-o.a lo oaa io lhe loods dl d b E' wil\ lh€re ba on/ cho"gp
in the.€oohbne ? Whioh membsrE' if ohY' would underyp o
aho.gB In hte.nol, 6rce '
oonsid6.i.q lhe i?hols fi?u.e.
p,y rp'd - 4,o t2@r2@r eod
P^w i Rry ' 1600 lb -O
1MF.O
9^,Y (eo) "4oa(4o:) r 14("j,o\ t ^blao)
+ a@(?a) ' eealt)@b61. lhe 6l]3 of R^v in 1-
Rt! - 1@o - ego - 12a la
a b o = L A e ,
BO . 9e5Z' -4e2.5< 4 9 2 t b - r c
+eo++,/b = 4'.o te.
l-. {nGe') t k1e8, - a"a t ac
<r., .b Bc- 7o' o+ ='7@lb - - ' r
B^ , -A ,Bs , ^ a3 . @ptc . 5 C( , ' B- 9s3.er { 94elb- -C
<Fh-o tF! 'o l . *Ac - .^a @€6s 43' bc'Gco | 2oo
- se6 @66? .4 ' 7oo - \ c0 | 2oo - Ca' l feo ' /
/c - 44o be | ^At : ' tb - -1 ' ' - t l to)b - -c
<tn-a : /cr Gco ' t F
cE - 4ao+4G612o)' 114a:16 '! 1740 lb - -r
62 63
@ p l E , @ ?t. F,
Rw' YE cF
€hown in rig
DF - [email protected] 4 161o1b,..-athe force in eoch m€mb€. of lhe crsne
@ pl. A,
b ' - 02 |ca - ?occ@Bb. - 6. t e. - z.G>(s) c.E126.
b = l 3 . o a -tn | , 62 -@-os)'t s2,.G.oaXqc.FA
A" 22 ,Ep l
bD6D5o'- Bc6h.ir'
o,5 60 - o.s66Bc '-ta
tzo"o . o.eor(ff-e6) + o.sacBC = 6c0c '26 ! 6000 lb_ . .? ,c
,,,!a = 13O9A 61 - 131OO frr -. t7
1Fh.6
ACc@2aa9'- 6
,'\D- 1t1oo'(6e2.6q" - 12o23.4g tb
tB = 12cbo tb_-_c/
Bo'=*ad = rcsg2 rb ?,+ lA lAAtb- : . -C
@ P l
,^6 -eo@s& +Bcoa6o.12t)Ca - o.a66ao r a,aBc -a
aft) Ocfc.mine thc for€€ in mcmbcr AB'BD'& CD of lh€
lruss 6hown in Fig P_a14
K-,T
" ' T , ' l q 'u, sblb coo lt h
4Mq = o. A"(36) = !oo(27) t .ooQs) r @G)
\k A8= Goo
Ag. 948.99 lb --"C
Z F r ' oAC - ./& AB
AC= qJo tb - t r t
ol B, &taaon "
&$/a rst
r/tio Bo - y'F ^aB A - 6 3 2 . 4 6 l b - " c '
'/It Ae - l/.Fo Ao I eaPa - 4.o li) - _-T
;e -E-c.l"-
CD = 125 lh - - -C)
64
atA}..',@
+1s.) Solve lof th€ fo.cetrusb Ghown in F,i?. p-4rs
in menbe.€ Fri, DF. s, 06 ol the
Fr = 1274.19 a plo tb -. . - C
@ Pt. f, @ F,
/,tz FH - 16 | t/fi DFt/E h2io) - 16 r Xi baz)
F6- Eee. 4 6a'tb
co.r6,cren ng the whote,
Rav I Rhv E too 1n@ r ocroR^w*Rnv! l soo
tuNfr6) = aao(e) r 3606€) ,
R^v = 15Oo-9oO - 6o0 lb.
7.r, FH - 3//.tri6 DFor - A@]li)
(3' tzoF - 9+c.6 4 947 tb_.._c
@ pl. 6,
4/5D6+6t t ) -9c ,0
pa - 3ao (s)
D6 = 3.75 tb _. ,_r
ru) u6inq fho mctthod
be.6 BD,CD' \ c€ oi
ofGsctrbns, dele'oi'e lhe fo'ce In med-
the roof lru66 6hown in rl9 P-ar7'
con6deri.9 lhe Y'hole fiqur€
..28 F^w r FFw . 360 -O
F*(1D 'ao(s)
bo - eob2)
p o - $ a l o - - c
co - s/. Azo)C o ' 2 o o l V - - c
cE' 3zblb - -1
41s) rfE wofco lruss rood* -06:0::l i ::j-^:'":'iffi' a1|(d of oe"lios'. - -^,,^. ^r r- \ a I'nqe o1 A ar 1r'e n
- . . r - rh6 {^ .ce in lhe re -m^e w w\ ,5a t
ooosldding lhe {fEle fEu€'
1?n-o' p-6A ' 6aa ltj
4W-O
6@ Oo.l + 6@(0) i Paabo) 'aobOb)1
P.d (a)
Btu p^eG6) " ze6.)
6667
,l{s
or(2o) - R6v (2o)
DF - SoOJb - , - -C
cE("o) r jooo(to) r R6r (2o) " R6., (eo)
cE "4oieasfu):_ogacsl
c E - 1 0 0 t b - . - T
ap) u6e the rethod olseclionc to dele.mire the to.ces in nenb..ED,co, \cE of lhe wonEn True6.
9C-+47.21a++Al i 'o- - -C
cohcidenilg tfE wiEl€ figurc ,
RvF ("o) - rooo(1o) I sooo(F) r
b.b(.)
3o(s.66) =ooo(.)+ also (ta)
BD - 32E.o/e.66
B D . 3 7 s 2 . e 1 b - . . - C
cE - 231so/e.66
c E - 2 7 4 2 . e t b , . _ I
ri .,"-'ro =.".? | \ e- a.66 n.
l / a \ "
RvE as) - co(1o) - soooco) + 4o00(6)cD- 412s9,4a
c D - 2 1 2 s t b - . . - I
- cD(e.6a) + 31s. .s (e.e<) . z.<,o(.)co = I sooo _ (:zsoo., r+)
CO- 2O2O.A lb .2o2a lb ---'f
aad Od6r'ino lhe focce in ltt6 ndnb"rc Df'06' \Eo of
tb$,e lrure €lto'"n n fiS' P'+b-'
aM.'O|.r'.o\=a@6'2)Df = 40cD|b' '-c
2r ! -o i @ot t / to6- A@
rJ6-76.Db"c
1fh.o'. DF r./to6 -e6
tu+ 1/'4s@)'Eo
E6'a<t@tt"--r
R^Y +Rry r 2a@t14oo
n^v l Rov - 3600 .-O
P^. (16 - 216G) + 12@62)
i ^ r , c ( i ' v -9O'2@=1e 'b '
BE _p@lb.
-w= 24<Xtlb -
.aa) ro- rhe rroe siEm :'q i-rfl'ilff,'fiff t*",b,/ llt€ msltEd oej.ints \ ltF/' €t'€cr rhe r
Li^.. n-t ' 6 opdl. 'e meltod oc se''l;orF' fir't obbin {h6
\oloe of EE bt iftP€cr|oo ^,.. cotr6t,-,i,q the whol6 f.gpc,
aa{a(rd/+
P;o' (126)
68 00
:ir_o**r15B]o.,,[email protected],F- fr,6 | *rten)-.,t'Idil
BF - 2@tb -- . -c
r,|.lrEd of g.olbo , @ 3/sBD-BE t 60- *a6ao)ao= 4@tb.
Pd. EF - 1]E l0+ 21@11,6O
EF = a'g(,db) r 2& | 1zd): 2@
* - q+16,fE-12@'1
gF r 45OO lb -. .- c
{.6) In lhe hiL t.rr.e ct'o.d nr Fir. p-a€B, lho Gb momb€r€I't tF o|c F.perdirlor lo ttla irlctirFj r|lsb€.s al lhej. midp<r^!c.l,rco thc drelhod of, €ellon€ lo dst6.ainc th6 fo.€o in rcmbecDr,DE. lr C€.
, R -
-- '5-
4F;v *a" - lrara+4.r1 -gB.
F ^ y - F 6 v ; 4 x!9 ^e/2l o _ : - i -
..:E--i-6 try.f -r4'5'
EG.E )n(a.6) + t('e.s) - Fe! 6e,.)!F -S.e|!9 ryse4 Fip. _.._ c
&f-o|. +lbllE | + - ,|FDFt a t1DE= arxJ iE - . - -T
connot determine the tb'-
lA Fio P-4?5 Then use
force- i" Uo"s fH 6ri,\EK
* r''\'tn Fig.3
en3o'--PE
DE = lo '
p^,Ua) t NQ, 3-2o\ - Fn($) + 1.t(@)t 'zb('br''
! ' oo(4o-1 ' )
r i = 1 1 o 4 l b - - c
-4".^'"^'44 ; , ; . ' , "*(1.\ ' i aeo4 " ' 6H( ̂E')
*Vi aA ' .eO' ' ) \zqt 'z1s)
r 2@G"
6t1 ' c .19 6. zs2arb - ' - f
70
zilr -aR^v (,) - EK(rz3a) | roo(ao) ) .e(eo -LB) r 26('o'1s) t @(a.-2..6)
ER - .9A,94 ? 699ltt - .-r
{rl) Dol€dinc +h. ft.ce in the lne4b4s Dr, D6, q E6 fd' }hc tb'r€'
rF/ -o, con6id6 rhe *fde fiaurs,
Rr = R^v = 1Cr5 K
PN tu>ao(@)' e(d+ rfglA
+ 4-e+ DF(L')DF -161.67 +162 ktqs - -c
2sfuoF - E6 r 26/(t6e D6
6=.fu(6.)-ryt;@nE6 - 1io.7 7! 1t' Rrpc-.-T
R^\ - 30+60+ .&+ Dr t lkfu D6D6- ia/Ilo, -4=o_ 3t6.+o6')J
6- 3a.61 =sa.., r:7s '*.. -r
<€a.) u6e lhe 'nelhod of s€oiioE lo edpu+e lh€ lor€e id
AB,AD,BC,\bo of lhe lnuss .shown in Fig. P-+32.
6 pn6ta ol .s'- 2<).
lr- \ .
FxG4'zao&i | .d16)
Ag ! 5909.31 i 59lo lb' -c
<Ms.o ;R^v(e) r ?g ^o(c) ! 'tlb AD6€)
D - 3 0 @ l b _ - T
€a) co.npdte fts fo'c6'
lr{.c €hown th.. FriJ' P-a!''
4@r e6ao' W r\sBD- lck @4-41@J
EO r5oo1-Or' + 5OOO rb- -T
<Ftt-Oec - +/@ ^b + 1/s 60
w'tr@s1o)t +h(@)
!E'6a.Dtb -- 'c
AB,^c,or, \oE of ihe 6'i6sa-e
< t - Oe.x <@) '12'(.) 1ia(a) r 14O')t t2(to)
I e(1o)
R^v - lox
/t l"' 6,/"1.^? ^1)
/1'/ r '^--6-
<. / l -{ / r
"!
l*"
- .,*o' zw'o
p.',!(2o)t .,b ^8(i6 = gk|e ^sQ6)e=,L lsor,ot
[e(o)_D6d].
AB . 7o.7s = 7o.e klpe i.,_ c
€ M E . O
R1v66I- a,1; ^cdelta = 6/+ Go) C - 46-02 -i€ xip6 ....-T
eG.,). vQo) | tc(o)r tk oF (22 - 2a)
r y@ DF (a)
Df - e3s - 42.s k?e-..-C
a2r) Usa 'lho melhod of ecclions lo compulc lhe forEe in lhc
mcmbers DF,EF,\EO of lho conlilever lruss desc'rbed 'n
Prob.+11 q Fi9.P-/r11 on Poge 92
oe. ao/3
^-;t
a22) fe. Ia ihe desor,bodpute tha fo.c-€ in me.nbe.s
rMe " o (Rd6olving OF ol D)
3/rE Dr (ao/3) - rco(ao) r 2&(^o)
OF 'a6o.56 lb - ' - |
.MA'o (Resolv inq EF al E)
L ff Go) - zoo ,Jo) | 2.to(2o\ft
EF = 335.44 Ib - -1
Eo (2a) - @t(ao) r qno(qo) + ca(rc)
E6 = 450 lb _"- C
BD, CO, E(cE bYpage a2, t\ com-
Fv(so) - 4oo(ro) r ?ro(ro) r soo(!o)
7eoe4.) = z@(r,) i eoo(2a) + a/.rs bo (ao)BD- 491,93 tb --_c
ZMF -o (p-@t \^S CO dIC)2aa(ad r eoo(2a) - 1 G coho)
co - rn1a.a3 tb ,-_c42.) Use the helhc, of seclion. to detcnmtne lhe force ootingin members 0F. EF.8(E€ of the Howe irues dcgoribed in Fis.P-aas a^ page 91.
rS
cEQo). 72b<a.'tF".@rb cE = 1440 lb _,-.t
:Mc-o (Rc&l"t"d Bo ol F)
A\ (i4) - a@(4) \ xro(b) r <a1o)de = gso lf'
rME .o (R€sotvins oF o+ H)l"(ra) = .oa(1o) + aF (en3d)(,o)
DF = 1€oo tb - -c
ZMH.o (cccotv inq FF a l E)a$(1o) ' EF 6'.b' (2o)
F F - r o o l b - . , c
'ne merLcd or sec ' idq Hi l I . lo oppr , thc _el rod
i" (,o) . Eo (io 1o"3o)
E6 - 16+s.4s tb --*T
.+2+) For.thc l.ves she^ i^ FiT.p-a2a, dd{erm,ne thc fo.€e
?i-ry ]Y fllt :f io,nt E ihen check rhls rc€u[ u€;ne
br, hsp€l,on.
tMo:oAt (16') - 1MG.) r ,ae(91
Aw ' zaOO lb *'
&-a leAaAE ' 25oo rb -'-c
AC,cF =tg.o tD-"-T
21.o(d | 1t@Gr). +/s sF (16)g F " 2 @ b - - - c
76
F6 - 2.24 N
.rt Ocf,a.dnc lhc fdcc in trr.c BO,C,. \DF of lh6 nocottelrui6 €ho'6 f FtO. P- 4z
c"b.)| r.ID(6) " @(2a)t fe(ta')cw r t6oo tb.
tW. o : 2 :4.(.a') = -.(a^ *fi.Xt)- ,(5'n?,.!"Xro) i oF(6n ,..B'XEo) +z(@ e. 6, ) (b). e (@ 2E5't) (....J
DF - 2.s Kip. -..-c
r/& oE ,t 1@ - &et @oE - 512.45 tb -"-T
ot Jornl D,
Zli6 -o (?.ov6g co ol9)1/ft DE 60) = 3/b ez)(co)
co = s@tb-''- T
A,(zo) - 4@s 26.r,.110, zo) + (E ̂ %,sf)(z)(er1o) + ot (1s)
6I - o_,rse Kip3 _.._r<M^ " ot Fo Oo) - 2 (as 26.sa) (.to I 20)
+(z)(d 2GE7'.)(6no)
4k co . r/tasD | y'{ooEBO= [email protected]!5 tb-..-T
,r2G) Uc6 lhc 'Ethod of ccctiorls *o aotrsrmirs +he force ir.r 'nen _b.,rc Dr, F6, 8\61.ofthe lr;ongulor flowe lrves stbw. ;. p;r.*+re llinl Fircl oobraine b/ inep.,ct,on lhc forcce in ihc robl'Emb€.4 of the .'ight €iCe of lhe irucs .
b], ;nsp@lion *cb tcnbert Jh, r, |lt,\Ho corics no lood
+ - lo^', rh - 26sa'€vLFo, AaC6o) .2c,o62..6r.(t ') + a
(@4 26 s 7) (4) - 2 (6n 2o.stX'\ - z (o)(si,n26.e7.) + Ay i 2.+6 Kipg
2 l G = o ,s/@ or@4) - 2$'@r) \ ,.bGo) r
a@Q.')oF -- 1256 4 lb - .-T
lefl of B-E
at^t. 'o.5/R rr!o)=1e(4o) r 14o60) \,!t(@) +
4+c1=4<r:,<2o)&@(1t)r'.(t(.6o) tte(go)
A I = ' t 1 6 6 . 6 7 l b - - c F H = 1 5 6 4 6 1 l b " - T
zF,.ot 6\ | 5/.l6iFr = /giFtf \ =2aa.27tb-- -C
rcfl of c-c .zrt^. a : 60 Fa = .k]x(6o) + a.a(ao) r 2.t <2r)
f6 =.733-33 lb -"-T
aeo) The lod& cn ihe Po.he. 1'u66 et)o{n in Fig p-a3o o'€' in
^t". O"" ^t *"r" "r-lb' Delermir€ lhc lorces in menbe's Bo'
z?! -o
Av rJv ' 3o(7) Bul Av'Jv
<Mollhe inlc6el ion of Bo \cE 'o
z?ft;-'s+ or(16a) r :o(rss) = rlo(roc)'
BE = 63- gg siPs _ -T
@ft of b-b:M ol lhe Inlerteolion of ooqce'o
l.usc shc^tn i^ a9'P-429 dclern\^c
0F, FH, Ft,6r, g\ ro.
rco(a) \ $a oE , 30 ($5) =1oe8p)
oe - rc'873 x.tq. - -CCE- 97 .22Ki?6- - -1
1@ (ba) ' 30125)+ s/EA bvr.z )
BD. ,143-41 &tp.- -C
78 79
e+o) For tho lrono loadad o€ shofn in fg.p-44o, &lor -
mirE lh6 lbrizonlal \ vorjiool compcnonts of tf,ro pi" pros-. 61,.D ol B. Spoc;fy di'Eotion"s (vp o" aou,t; l6fl or right)of
tho lorso os il oot6 upon member co
ar@\ - 24(e,) + ab(6)
EV. 590 tt)
:Mr .o
N (.r) - 36G\ - 21bQ)
Av = 360 lb
:Mo-O,a(a\- aso(a)
gn(a) 'B00(6)
8n - t€o rb
bJ - esatb (dorn)
( lcn)
+<t Tho strucfuro sho,q{ho hori&ntol e^ vc.tiool
8r-2.gO-39O-a
is hin96d ot A &,c. Fiddof lho hinqo lbiE€ ol B-
8..)
y''rr"z,-zf
8Br = 1oo(e) + ioo(6)
BH . 125 tt)
<Fx-o j BH.AH - j75 ibZFl-Ot At - 166-|,46 =a
Av - 2OO tb
C d = B ! = 1 7 5 l b
aPA-o. e,D(3/s)- AA-oeo 4'4)AA
Zt ^=oi lzo(4\ " Er(4) . o
EA ' 12O lb
aVr.g.1 l4 t - At-o
E$ 'Aq " 12olb
oi i6olatirg bor A_6
zMa-O I A!(O)'120(4) = o
Av -- 60 lD.
Co.'cira^i.g tho wtPlo Gono i
zF\Fot Av +e! -12O 'O
E ' t2b ' to
E! = 6a lb
BO= 2oo )h -- 'C
8&\-a '. oo(4| rc'(a) -bD(4/5)(8)=o
EC- lCOtb *--T
aaa) Thc f.omc etown in Fig P- +aa is suPpo'lcd b/ohin-
god oI A A' o rollor ol E Compu{o +he horiz'nfol \vo'rF
,1r .o*pr*"t. of lhe h'r4o 6.ccs ol Bg'c os.ihev ocl
bor 6D
i{^za j 42c(1\) - Er <ro) -o
Ev' 26'r tV
z f ! - o : E r - A J ' 2 4 O ' o
Av - -24O1EY
At = 24 tb
2ao(e) - a, G) - o
O' = 360 lb
xo9\- s!(6)'o
Bv = i 20 rtr { upwo.d - /
*p.ol" u". rc]
,p."."-P. ry'
808l
bor CE
cv + EY -Dv -O
Cr - 36a - 264
& = 96 tb {d@n@d *i1h rospedl to^ r 1
:[1o=o:cf(5)rc,€) r , tz) -o "- '
Cr. 2.4(2)- @>
cd-40ro t I 'N1 i ;pk r ro Ac J
zN,,\ -o I Bc(4) i cv(s) - cH(b), B"(z) - oBA = aoAo) +a2o(2) - (e6)(s\
BH = 4€ rb to tho righl
aa5.) Thc frElne shown ln F9.p-+as iE .eupportcd byo hin-96d oi E k, o rollor ot O. Computo iho f'orizonlot \vcrti-ool componenis of .ll-D hinge focce ol C os il ocis upon BD.
o'@\ = 240(3>
Or = 90 lb
E"G) - 24o(e)
Ev - 19O lb16olo1ing bor DA
=M^-og! C6J - 240(4)
& - 160 lb
zMe"o(6)}.v- 24o(2)
A Y - € O l b
CA(3).7oG)t@<r)CH- 2SO lb.
+a6) n +hr€c -hingcd oroh i6 coflPoscd ol {*o {'uscs
h,nocd looelhor ol D in Fig C-+a Co^pwio lhc comPoncnts
pt tio .co"llo. ol A \ thon find tho fo'coe oolins in bo's
/lB\|Ac. Hinl: Frrsl r'6olole oocb ltu€6 o6 o frcc boaT
N G.) - .6dct - 6aoQD) 'o
A! ' 42o to
A"Go)'3@bd + A,A(3a) ' o
Ai(t) - a@(@) - +2o(4o)
AA - -32o tA
;. AA = 32o 10 Iha .lgl\l
, /c_- _ 24a t r j . 24o tb - . ._1
a+7) Two frusgos orc jo,ned os sho*n in Fig P-+a7 to {brm
o +h'!o hlrgcd or€h Campulg the horrzontol kvo'ljoolco'D-
po-onts of lhe hjngo {b.oo ol B tN. }ho.' delarmino lho }/p'
e, mognlludo af forca n bors BO e'BE
z(.'o G,.o.b) + 24o (zc) r AA Oa) - A" (4o)' o
Av(a) -AH = #ao -@
l6.loting lofl lrusc
loro . zFf=orc ) a2D /\,8.\n 36 s7. -o-;.7i
,LB- lao\o c/'\' \
zF"-o: B2o- Ac - Ae @s 36,6i- =o, 76- 326 _ 7a6, (cos za,az.)
gr
".,1 -'
a2 83
AaOo) - Aa(b) - 24o(1o).o
/ * - A A . 1 2 o * @
6q. @ &- @,A" G) - AH : rfi<)
-laLal-:4eLtsA_ - 132a
Aw - .katb
. t \ A - P , w - 1 2 0
= 4a -124
/Ad - 32o ltr
An - 32o tozF" -o
Av -B!-24o-o
&r. 44o- 24o
B a = B . a + E H 2. (m)z + (e2o)2
b - 372,+ lb
a<€) A booh (ar|ig +ta loods shoM n rig p-+aa i€7*,W* { lh.@ ..sma.ts t{ i€ suppo.icd rt br vee _1tc.ct t:c,aLto s \ jo-oa 6, b.o f;cl,o^tace nrngc€ Octcrmirte iho votucg of lhc rDoc+ion6.
@
.n *,e at!2@tb
c. cf r-'lo I ot-- -t) ---1lG f lR+
wl = 100(6)
RaG) -.6c8 (z)
R 4 = 3 a 1 t b = C v
RzOa) = 2o.0a) i 2e&(7) 3ca@)R. - 2120 lt)
R3Gd - 2s.n3> + 3&(14) -4ra(4)R e = l l e o t b .
.s9.) Tho bridgo sho'{n
€oolion6, coch *oighir€
6, hingod ic o unifo'm
@ nanb.r co
i
i^ Fb P'aag
A, B, E, .',\ F.
ocnslsts of lv'o o'd
oonlor ofgrovilY ot
wo;gbihg 12o tone Ctn'
o" (@) - 12o(:,c') | 6oG4)
Dv = 1OO tong
C,Go) ' tzo( tdtaa(eo)C a = A o l o 6
E"(@)-Qtbbo)r(a( lo)e\ = 26A *o^a
zlr\E - o
F" (@) - zaoQ.) ' lctt(2.' )
N Go) - 2ca(2o) - so(2a)Av = ae tong
zvl^. ae.Go) - 2cp6o) t s>(1o)
w = 212 lons
45o) A billboord 8C woighing {ooo lb is subjccicd tc o
wind o.cseuro ol 3oo lb por {l os shown rn Fig P_aso Nca-
locilno lho wdrqhls of lho supporiinq hcmbors' doiormrno
16 66-penonts of ihe hingo fo'cos ot A E( F'
wnd PrcEGu'E = 3oo lbl{+
. 3oo lb/${ x lO }i- 3OOO lo
84 85
"oaa(e) rooa(6) | FN 6).r, g2)
Fv (s) - F{ = g2so --O
tc@(s)- rcca (6)+ AtN(4)= A" (12)
N(3)- AN - 22so -@
CB(1o) . eooo (s)
ca -1s@lb.
Z l ' ' - O : 3 . x A - C a - B A - OgH = looo-1silo = lsoo lb.
:ME.o: O,.r (i,) = Fe C4)F{ - D{ . {sootb
zF =a: e4 -Bao-19ca.o
Ec = i@O lb-F; -O: Fr.t r 3oOO - AH -o
AA = asaatb
@ 1 ,Fr i3) = e2so + 15ca
Fv ' 32SQ 1t)
@ 2 .A!(3)- 22sA + 49cn
Ar = 22sotb.
s@ lb
EaQL)-sko)-2ao6o)E! = 2sq tb
/v62)'2440) - e@G)
A Y F 5 o l D
@ .nombor ' t.rht=o
DH C4) - 24(o)
DH = 4€O tD
zrio=ocica) = 2ao?)
CA '24o)b
E a ' 2 1 A - O
E' l , .21ob
tc'c ll*cn
{ot-Ho
o"G)=e<dtdL)t.p,,A2)Dv = g1O rD_
:F ;O: Dll cBH:a6O lb
EFr'o
8 a ' A '
Cr '56010.
6! - so+ 610 - ry
Bf = 9o tb.
86 87
Choplor 5
Fr icl ion
,05)A btock waiehine w ,o " ,"11^if,";"jjll""l",
3il1l,#;ir'1?:;"d"i''lioill r ie (o) gr.ore't h o n e : ( b ) c q " o ' l o e . I c ) l c € E l h o n e
) ', l i i , i ' l . aiter lhon e- ih€ bloch wirl not siide down
i,i.,""j li *i,, reloin ils poeil'bn be'ou6e ihe f'rci'onol
?,n,'; r ;ff ,:\' ilJl"Jl'*, I T'li"S jit. i:1"
* #.2: :-i,:;^, :: ;::;i,z il :. T;:il#;Tf i,"'il ;;? ,.4'"""o '" 'o""u mation la mpc^d 'f aP"
*lr l,#,i.]:*':t g'*i'tl': lji3'#;::L:1 5
t p t t r y t a \ ) 4 w ' 1 w i l t € l r l l b a i n o _
iir fi.'iq n",i" the r'aro^ot, ta'c'l:ll^:'",11;i:
fii l"[,:,"';tl:: ? iii :.: j';* T ;:iJ i"x',;-" "
io etort the molioAP = <n!2 .,
P = ftatb
P - - + o o l b
P: 239'2 E
#*E-#P^:- - l10 1 lb
8889
5a7) Ihe eoo)b block gflown in Figore is in contocl wilh oab' inor:ne.I\e aeffticient ol f.;cl;on is o,za C4^p"1. 11,.valuo of the tuAz.ntat fi.d-.e P ncccseonl io o) j""l s{o"{
thc bloak up tha inc|ie (u)j"gl prcvcnt molion down thcinojine. (o) Il P-aoc lb, whol ie ihe o-ounl \ dr-ecl'bn ofthc J-.,ct;o^ fb.ce ?
> P - COOIbF.n ;nseq' 6n6o's6'
- ' l*\ P - o.,c.br)t___:g,a
q l ' a 2 s . . s - f t a 4 -'
11 .- N p . 5oottrA\.V r T\ b
4K","- * { -"-^J-"il,i"'r',J41\!\ t!
. t w ^ Pc . ) ^ *e,+at4{P 2+:o :4oa(Los15') t f Isao\ l@sao'\ 'o
'&^" r ' 70 lt tb
5@.) Ihe 2oolb blook shown 'ta fiq. P-soo hoe imponding
rrction up tho plone cnoced bA tte tarizonlal far:e, o{ltD-b.Pel. lhe o:nffloienl of slalio lriolian beiwcch lheconlac4 €u.foce6 -
zfu =o:N= aao (stnno) | zoo(ar.aoN '37J .21 l b .
<Fa =o: r - $o(cos.n) - zoa(snaa)F . 246 .+1 lb.
l L - F A = 2 4 6 a 1 - a 6 6' ' , t J t 2 i5Oe,) fl,e bloak, 6hown in nA. P-@s are cnnacnled bg fldibinetlendl'to cord6 possihg ovor fi1bt'bnla6s putless. Al Al]rr-cnefftoienl ot frrclton ore f. - a,oo \ fk- a,2o whils ol Blhos orc f . -arc\ fk 'o.@. Canwte +ho nog.; tudout d;rcc -
i,bn of tho friallon lorca oali"g oi each btoo"..oro) Whot weighl W G ne,coe9arlJ lo 610.l tha .essJcm ofhbakc ahow^ i^ fig, P-o1a novirg lo ihe F;ghl 7 lhe cocf-
I
el ..og. r FBOor $oaf, Al
frbr'cnf of fiichon ie o lo, \ lhebo fnrolionlese
pullege are, oesumen lo
M^-L^', i*\" *''21'*'
*rl-o n^ - u*,-" ,..n',1 1 ^ . 2 4 o \ b .
ldc
-tx-
'F l 'o
'tt - 204.6+ lb.
'' r^ ' f. N^ " (o 2X rao)F^- 4b lb
{f-o : nr- 2oo(cos6it,t16. 12O tb
. F. ' f , t lB ' (o. \(11o)
Fs - a6 lb.
6 6 . 1 ^6mArd =,nrf
l ^ ' 6o tb
=fg -O: ll. ' JoO co6 ro'
HB' O'1,6.+Jb
FBD of BlooN b:
o5Y"fFD of ElazY,C I
II,
l * l--T--
k-@1)lra4t60rt@
v: ry.!:-l!:
80 9l
!nr) trnd the leosl rolueot P rc.quir?A io cousc lhe sgs_lcfl of blooks 6how in Fig. P-sr1 to horo impendirg rraiionlo the lofl . flv <noffiopnl of fnr'clion \e o.z unao- ea>hblooh .
fbo of block^ , A . o . 2 . . e . t . a 1 '
F (n o l " 9
W{Fs.o: li:roo- Psrrq T = 1oo
r {Fx'oi Trf-Pco6a -O slnrl,rf sin7r,69'62", r(..z)(w ps:,r"\) _p6q "o !!Z99l!_12J.O2 - A2Pstn\ - P(aE <-o
K".zs'a"r+cos"<) - pt e2Ib.- p= 12z.iz-s!L. P(o.acee.s6.<) "o ais, ,- , , -r"' - o . 2 a N q - a h e . o p - 1 2 4 . 0 l o .
o.2 E \trnq - iorqcoso<
, :f! 5L
arz.) A hoingcncous blook of wejghl w resi upon lhc in-- .w , . v r i r vg r , r tY rEDr uPn r l ) c I n -or'ne l9tlown in Fig.P-.et2. If tho aeffioicnl of lriclion ico3o, delerrm o lhc aletel h.,iah+ A ^l *,hi-r ^ c.- !'gleic€l haight h- ol whioh o for€o pporollel fo tha incline "at "pl;.a 60 {hol fhc bl6'ck wirls_tu6 uP tho ;odt;d w/o;t lpp;,4 ove.
<r j -o tn<Fr.or P. F+ Wdo&,r7.
p . (d4 (wcos!#r) +w (enaa,er)
{M^'oP(ti = w.-€ 16.01'(t) +we'^ e6/(.)
oofnalh) . ,.\f 1.6y(h - l_
Fr,Dol ElooKJ :
E6) h fig P-512, lhe honagenoous blook we;gh6 'too lb \ I
cne,fftoteni of fn'alrb^ ie a 44 f n'sitr ' dcleti'na lhe
focoe P ta,q"ce nol@n to rmPe"d
\ rP\l, <F!'D: d'soa cosrb/' = 24o tt '
!=1e!:s1+) Ihe rco tb c.Jlinder.shown in F's P 51a i6 hcld ot rcsl
or the .to' 'noline bg o weighf p 6uq6de<t ftEn a 'tt'd
wrcWcd otaund lho alide. i f s fi PPi n9 i-Pends , deJe'rnr -
na P\ the aoffiaienl al fe'cl(:n1F^'o: Hc'oe e'c' ' f c:oa oo''t+co€6o' - ttta.s*'
,/t- --@999- "o6773
< M . " oq ( 1 ) - F ( l )p = t t l = F
ZF!- t t : t16hta I F6nb' -P '1oo
N(stn6a'I o sln.tBd o..113)=1oo
i ' 1@Z w\r ' 173'22 tb
r = @ +)(24o) - s61b
zvA -o : sP = w 6h e6 s7(4) t \\@€36 a|'(a
sP . Pao)bn36.ef O +.,'za b1'O))
sP ' laaob
P -l,l = (o.s11i07a '22) = loo tb
woig'r€ 12olb' blad< B weighs 2<{jlb's15.) BlocK A ir\ Fig.P-s1s
\tho cord ic po.ollel lo ihe ino|i e lf lhe coeffcic''l
of fri"tion lor oll eorfooee in co-tooi ie o'25, dcleirlne-
+he dVle 6 of the rnol,ne ai whroh molion ol' F rinpende
12A . R,1;^r.*'
-"'^(a,'4>
R1 - 123 7 sin (4o - e)p1 - t u,1 (sin ga'cose- - cossa'€n e-)
Fl - 123.4 coso-
92 93
fBA o f b , €rx-O I w6rns. &sra1..ar | 8.6n1+.o+.aoo6,ns .(Rj '8.) 6rnl+.o?.. ( \+R4) . 8e1.+.ha A
<F3'o I Ra a<E fi-o+ - R1.pq daf - Wco6e(qL-B') c8la.oa - 2ooco6e
R4-fu ' ao6,2 c<E+ @1'@1: Re - o2+.4sne- -R1 >
a24,16too - R1 -R1 - 2.b6,2(jo64az4,+€ioe--2R1 - ao6.2 c.€d
: tut nj. 1N;7 case - 8a4,+ 6;ne-- 2(1zazot e) - zo6,2c<Ee624 4 €ine- +s3 6 @4e
lon e -ElEsr zo. ez's'6.) Reran;.s to prf.b. sts, il fha coc"tirirbnt of f.;ot,or'rs
o,at V, o- =ro' what farca P apptiad lo B aoling dowrt\ panolrai Io lhe rotine wi,l e{orl rnofion i whol ic thaleneion ti the, ct t dfiaor,ed la A?
Rl , '12ost16 6h6sa+.
fu - 121 ,1e tb
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R . ' 3 2 3 1 1 l b .1F\-a, P. B2s;nao.a6 t fu 6tn aae6 -
P - 1 2 6 . 6 t b .s1s ) JF lt1 Psto, l4o bjoo\s ore .b^^ei@ bs a sot.:dslNI oi#oc.]ed to eoch bto.t, w,ln lrrcl;onte€s pjo6.,[t lt- aeffrc enr of t^,cr,b. u@e. eo.h oto..< i-L.zo\ € we6hs 2rotb\ Fhd ihe min weight d A +o preverrfIrotiort .
lL.A26 :.O - la,O+'
FBO at b: t -a. t- . o- 16,7'
of friot;c,^ ut\aer A to p'ucni rnolion-
w - . e t ' 4 2 e - 1 1 3 '
.ln4.r'
C. 2J7. S+ lb
H -4Ct t Cen.o' <t"-o : r-c@624'
n- aoo | (2s7.s+) s;nzo' F -Ui1%
r l r r / -E "206a6- -o . ie /I r e 1 o o 7
szr) r" fis e-s,o \f J.a 1 urde. both bloois \^ wo6he aoob.rhd he. nor' *eishf of F thdl cnn te 6lo.leA oP lhoirottie b9 appl)nq Io A a e's6l wo.c r'cnzoalol tcr<:z P
y'.!-.o.a z4-o : tl - +o3 I c6in3o'zJr-O: ,Ko. Ca€e6' I F
c . 2 7 0sn$,95' s.z+-o+'
c - 201,9 lb -
\/r' a aOlA
w^ . s98.3 l r t
stc -caeao't @,2o)(+,xt+ cs'"zo')
r b - . ( 1 o j 6 ) - C - 3 7 4 o z t b .
wa . or+.a"(. 'o*", i)
wa = 263,7 tb
g4 95
f i . 1 1 2 , i t b .tF,.o: p_F + c .a6so" "
Vtt te+,e)(o, ca)P"@z)(712.a) r zs1.2sp- +a -7 tb
l.*.) | t":- ot 4oo tb 's ";ffi rhe purb,j shown in
,!: . ' : ' t l" ,pi, '? ie p-etenlea F.on @tdt.:rs o,j ota:: P.opdEn
.:" ly .-d cf the brotf- re,e.. rf ,he @elo|ocr ,on, . r r ihe bdl ,e 6u- foe is a.eo,del the,a lweofp
. ft_ r//rL= zog,iMa-o i . r caob '
P(4b) - h&\- F (B) - fioa(.to) - 2oo (a)pGi) = t+too _ p_ zcoto.
:,-) A
:"o",;-: t", .o-m r.,,re a bu.h:^g 2,:^. ton2.,q ,, t ippez:)
, e ^ t t . . a , t @ . o r 6 h & - . n F : g u - w . t h ea.e 1 ot t .ato.^ ba lhe tu6i9V lh. .ad E o. iq CD^p.te
:: :, o:r^ A oi *y' {.,eh, ^ @^ be pto.@ ta ptll"a\l
6|pPn9 cb'v. thc rcd ,)er,ar 1r F derqnl
A f r - o ) N 1 ' N z
n',t 1-o,zN=o,/tt.
w-- Fl t F.- o.2\ (a)W= O,4 l
2M^'Ow(L-1) t r,@) - tib)- o.al$Fl t o.2(z)M- 2Y - oo ,4L -oA roA-2 -a
L - - L
L - e i n
szs.) A uotlorn lodde. 16ft lotq V, weigaioq wlb i6 Ploc€dV one ed on fhe grcund \ the otne" hond ogo,hst o ve.-
trcol woll Thc orgte f footbn ol otl cnoloal s"nfoces is20'. fthd lho mrnimum volue of lhe onglee ol wk lhe 1oC.
O g.r i l rb
"lr=4,t**t".,'S\ to td tvnro' I
@ (!,d__h(1-a)(!-L6tne)" - to. n'(a-L@ea)
Ia^id r - Letno "lon2o', + ton2o't @a"r,(to to't lo^,a) "1."{; L@se + Lst^e
a. Ion zA-L<bEetLetaeIon1a" I Ion 2a'
O<M6.ow(x -5 .e€ - )_o
27on 20' L@6o I zLqtne - L6.t( r o n 7 a ' t t o h 2 a ' )
lLst e'L6the(ran ld t ron2o -
-srr9 = 2,39i2
+-:Po:Ton2r'!od<e1L6,ns
lon 'L.o.r+
t L6nt+2
9697
\?a-1 A . toda6
eo I j torc +. ,gne ebi . , ,
j ,6 ,q at grc, t . t !l ' 8D . f r tn
l fF rDro- f^e bdda . . p .o.4J oga.re. a "er t i
Y^*:' f,-yt,ir mo,e€ on ..st. or L. y,1 trJs,o,.a. u.*
^ o t6) tb n a1 .,.mb b-fd_e lE Io l s tpp.oq lhe ar 'e , G , .^- - , - "
; ,? " " l l " : , . ' . : : " " ' ' ' : " : " - f t ' o - d , o , . Lon
@ { . d i 1 b * u . I o . 7 s " x
, ,"-,"trl.)*; aJ ,,^, . -r, :, A \ Z [ ^ " ' " v " ? . o ^ ' ( ^ . . o )
, i \ " lz
Tanzs'\ '1t.tz . -Ion1r, r tolon.re( to 'z ' ' ' 1o" to ' ' , ' ,o
.ng-ec.€ad).$a(x-s) x -sf t .
160x - e40 + ^ _ 5.2s 11.52r) A. hon"gncaaG celincrer rfj. in d''*'a ,, n i,.q "" i;; ,";,"_ o";i::'";J.^l"lf*! .!',.?e-
or f' n'oi G w" to. on co. t..t I eb,,o.ps cad.lpllo t6" noq^l )de ol the cowp,e ratdq rctolrs """.k-;";;.""
' e1u'red Io sio'l the citi'
wqr'3@lb ot cg:Jilibnun <r:.o: d, o6is.. D, @67s,
4! l \" ' . \ l
, - n7 .r , 'co376"l r \R\" qr J.ffir:= Jl___,., t1,"i'c^s::".
4,t\>r4;rr I\n l*,1 <rs.ot 1116t.76.|tj.6t t6.. rao
tl,q_e t/k,@,..\ s,",.. - 3,\,{ M a ' B r I - ,
rt, r.^*.+ -,,J t""rc.) . ",,oo ",r. (1c) r r, t.s) n1 = 2os,7e bB . l2o,a)(1,s) t (eof t ) (1.s) . . . n . , tz6stb
_ 0 : : f U 6 A n . E , a t . . . t , . p h .= (to'6)(%s76) = r"tis.Gt,ts)
- n '77,41b. f?= zo,s tb.sr ' . ) l -s1tuo 9t"
r - "o ' - dFl -_d,n- lhe m,n,mud hc,r rzcnlo I
:,x^:-T:::?, ronee.liolrs ro tha jefl .i rh" t";;il;;,cuti^der ;c^*z ;-,;"""; ,:-.,:71'
or tha rop of rhocounte.ciockwise- ' the calind- ro+oli.
tl
Mm
ili
Ptrd' r;fttd. F,{}FI
P(r€l = ,o 6(1{} r z6(t€I
N r "ooe.o'O " o'gaa
p{tr) = w6)pU t o t6b) - 12o (6. 6)
P = 1o..o2tb - 9j.!9 tb
J- la.r€'7 (t-o\'-'^.d(^4) q'Ion6c7 U-o)- r6ad ('.lo)
i",s\ ' -Idn,f.a t ton.(it, lo^bs'7 = -1a6L')1i1ctan1d
r. (tonzo' tlo"rc|) - ,Dtaooo' r (ro" oe-rton +o)- to lan ro'' l = 2 ,81
< M . - o , p ( 2 , 6 1 - ! ) - o
3 . 2 + - 1 o r x ' o 2 4 1 4 ' O
|= 0-76 tL 83418-"tl ,;6.- pr""K of wctsht W \ totol Ldngih zL i€
ploc.d 06 !;ra'a ia fig P szt wilh ll ends ia oonlacl w/
ii;"a'i,a do."a .Ttu orgto of f",cl'bn \c ts'. Oe|ctsioe
98 99
otrJle q al whi.h
"(^ffi#:31*r.*.)."t 2Xor1a,@6o. - ekt^<+ l o ^ q . 1 , 4 6 + 1 ^ d .
g" - r rb ( s -g ) , - - { : - z ; ) o n _ r " . o .U- Ionrs'7 !rzL.ti< - -I@6a'(x-2Lbs") :
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X' 2Lc41fo^6o-- 2L.;n4fo^1 . . t lan6o.
@2) In Fig.P-!€2 j lwo btock4 eaah wobhing t.b tb oe ca .,ae-td fuo ,itfo.r.n ho/'zoofat Loe whrch wdghs lcotb.If lhean_
€htrng
gto of f.ioltb^ ie E u.dd coch btook, nid p di'l>+ea rs.olto lhc as' i.ottio thct w)| ooueo impendlnq tution lolto |.ll.
O iEdoti^g tho ba.
-s<;._9_
c:n. tao6;n*'t rocqn+' zn.o, r" +a-;zs< - )o-o-*+s. pn. 2e2,8+ tb. (o26s)(.rr.ei t o - p
p:Zq€Arii,l
,,y'a., bo. .^8, wa:tsh:,as a;b 1i€ ro6tq..a be .1
l r lc r ' rn l fs6 p:n- lo o a loc, *e,gr , ,aq zoot t as 6ha*^ h lhe,/a-t @ wat , I . a.26a Fhte u oet t1e atocr . r.a.?o Dete.-
n;no tho fo...o p necica b s,rc{ nlolb,1 +a tho r;ghl.
e.1{ . . / ' .o .26a
l l.r__J1
t " -r-l!_f,__ i
ZFg'at 11 - 2oo I Ar
d. jo1.6 tb
. ' .F!"o : Ar - +2+ tra - so| 6 h
W E D 6 E S, 1 . a
53s ) A *.dge t€ bger'r ta .Pt t tog. rt e ) Iho angte ol fria-
lion br}t'ean lhc \ldgL\lhdlaq,dd lla nor ' ongl'< ollho
, a F ' - o 2 R q . | 6 1 t t ) ' P' - 'ra1-P'**' 'i'"'*P]"eaP - ,Rtd.|ttu"4&) ! (@Y.Y+).al! a
1M^'oa24 (b@'6) r r. ra+E'dB a"s-L'a
tt.\@.+s' | (o.t6t)tt6\.b4t6'-d'\s'na6 -o
f tg.q = O,s1gf lo
N a - 2 8 9 4 l b
Brt Aa ' 116 " 26e'4
Fa /^t15 ' (o %6)(2Bs'4)
' . O : P = A A I F
P- 2a64 | bz)(1o1.6)
cos Y.&EQ 'st^P st'"{'
cas.t/2 - et.dst "t/2 coeq
Ia ' / - &1"1/ '
s.6) h fiqur-, delonninc lhe nrnimum wa'ghl of 9loch B lhol
$tt t heep t l ol 1. ,61 o forco F 510116 gloohA uP lho ) 'c l ino
eurfaco ol F lltc weighl al A te loalb \ lhc ongld of fttc-
lion lbr oll surfoces in oonlooJ is tsFBo ofn iF '
LJ--l ,*F{'l$t L?
I
100 l 0 l
ah'O I Rrcosas ' - F, co67s '
0n.a2) cc &' = R. - 3e,6 a tb
\ ts . B, s ,nrs &s,n4s 'ws . (as6 4)6 n zs - (F1.r4)€jn4r'\ttb - 213.2 tb
$,.) ln riqlro ,dcle"nine the votue of p Jusi .s,fficienl ro€ilorl the 1o'wedge u.de. lne 4oo-lb btoch. Ihe ongte offr'otio^ ;s 20' fat otl aanlo;ct sufiac?,a
r*s
- 81 .". !19.4b,
s38) ln
'-f={--
!::!rJ!=Frg.sst. aelo"mino the yotue ol p oct;ng b te tetlrc4u;.ed to pult Iha \eadgo oul fmn urae. tE 4<>o tb
--EL- ' 3L
_L' -P91:L - p - zoej Ib.
$s.) lf the wedse de€aribcd in llusteofton hod o wdghiof +tttb,whot votua ol p wautd b. re+ui.ed (a) I;stort lhe we/tgo uncle- ihc bjock,\(b) la pu lhe\|edge au1 f.r,m ctn<icr tho d)o*.
*"':+n" " #/I vtnr. $a L./1' i--)<--- l V o, - +aa
nW' -;"1or -;*'
dngiE of fnbnb^ ' 19
A*P - +16.7 tb
tr\- a : ?n si..' tW @ts' - o
R, - :&_e:::
R1 '641.1t0.
ar/1y
6't A. R, . 2aa ..ao l;/ a'4 6€
V R t " t " z t v
aFa.a ! zPn 'sn ' ' 'P
P. ..(n e)6,^3o'
3,:::3 e
htcrc*< |\erc ;a.eaecd lo ts@tb ?
!fr,.'p-
<Fg.o , F . @6' I R46D,€ ' ' +oo
a,ryc - 8rslrl/.. r') -w
Rr (ce" 'cnc' io"rc) - +oo
& (o e7a) '+ao
R l ' 4 1 1 . 1 l D .
s+o) ,4s 6hown in Fig p-'io,l-o btoars warllri€ z@tb\Esl-
i9 cr. a ton:anlol qfoae oft lo bo P!€tve orrjl b4 a tc'
w.age' lhe ongk' ot l"ial'b" ic 1s' fo' dll ,@ioot cuFloco6
wroi nr"o ol p ic rwqoirea td €to.f mov€hal o{- thc blo'k6?
t1o* woqld thie ohswr be cr'd€cd il ihe wor'ght ol oe ol fho
to2 103
-&- -_:99-
wb Re- 1og.g1lb1Fa-o
= ql 's ' 2 t .2
P^ - ft,t Ib
P - Oos,b1)c.e't lE.4.nip. - 91,Etb
dron in rhurc P-eat . fhe @"4a of lni4rbn lor o svrtocosn ca,lool ie P'.
fOD of b <t ' -o:B ' . ,1 ; -W5 16' . @
s+i Detornirc tho forco p rcquircd lo €'to.t thc, wcagd
&. A.coslo' -s.rb
afr.ot R..os ' -R.6nni , eooo
(-€inrs. /
R" (costs' .<i €) - sn.-t is' - R. s.|.d. tu )RzGoss'<al€- stnrc') . zoe I soo @! E'
R. (.3.a+d) * !666
R. . 7 l ts .4 lb ._ L - 1 1 , 5 s . 1 1 p - g 1 a . + l b
s..) whol lorco p nuel be rypiea to thc wcages snomrigt o P- s+2 to 6lel ttE,n utu a- +t1o t',och ? lho ot.Eltcf.,,itoi for olt @^l<yl €;tf.,.rE ie tO'.
P - ed ,q
_f_ '_le.u-tb
sa3\ To adju6l tha wtbol podlion of o posllbn ot o c'rlvn^€upportilg a 2boa lb laad . lwo s' *adgc6 oro u6cd os ef'ownh figuro p-gaa . Octo.mine thc n)rco p ncc66cory lo clortthc wadqos if llE anglr, of fiichbn oi ol! surfoaee is 2a'.Ncale. l lhe (r ,ol@ ot lhc FolJc.s
fBD ol B i, ..N
s+.) In itlue. P,oal@+e o1t sa.fbces i^ @ Iac+ dolarnae tho mo,imum wclgcd.g lc . \ lnor w i l l g rve lhe ^edqe o ne .^ant .a l od"an lo7e,
R - 23aS.4lb
__ L.__8_
P: !9PLLL
$+ lf tha atgto of fniJto^ G b' ol illre-
t< tL6) .a . \ ) - 1a&. n1 .a '
€ rb l t l l l eP, ' - - P - qa+,sen@'T ;;G;;'4
: . e , 6 " , < p , . 6 s l h o " l h - w c r q s l w o r I n c t l o - | . - .
-l taaa_ - f_1t ::) paas rPo rq ) 6nO, - ) € "1& r< )
(s1ntu';.- -@1;6'"^) hab " baa(6'n .''44 - @s'o.6'n<)
I
l'l*
r04 105
G':,o'* '" - -. . '"*\(et ,r'@s1 a,ee-e.q)
, 1 + st tu'@-@b'6'aq -6'n2o'@6q j
(sDo.-G-&J o4" . (*-"., *" *) ", "_6 ,n< _ Grn2o ' -€ ra2o ' - o+66r
Io^4 = a .446a
c< - 2s"gS!^RE THRE-^OEO 56]'EW
sas) A s;Bte lhrcodcd jootca@q hoc o piloh oF o,s t^
\ a meon rcdius ar 1.a,5 n. Iho creft oiaj of elaj( trtctbrof 0.1s,\of Alhetic f.iot,o^ ol o.1o (a) Deternine tE torczP opp)teA ol Ihe cra ol a Ie.6 zfl. to^g which witl €+o.tI'rling o *ebht of zbns (b) whot wtue or p wt| yc-p tE
jaak tu* |o.hids ?(a) y'." t."o --p.z (b) r^-o.to ta^ 4 . o.to
4 + - - e - 1 a t e : * ) 6 - b t f
o ' Io'r' 6;'@' P '{l t"^ (P ' e)
f t "a .1e P' 0"4)(,, ') u" (.,t t ".2)
f - a f t - t o^ f . oaaf ' " ' t t '
l ' a s "P"+ :Lro . (o te )n' Ge@hn\ b" (.ata.*')
j ' sj +JbE6a5.) tho d,Aonao bot||$ oalo61 lh.cdds o^ o ,.iple_lhrcoac4 oou"** ie 2/.3 in Tte, h€o^ Mdius i" zin, ltecoemotcr,l ar ff,ot,oa o.ro wtot toad con be roised b9eae.lirg a nonvl ol zaoo tb - ft ?pi lo6. 2/ . ;^ (6,^@ i l j6 lnp l . ihedcd f r " l i ipr9 r ic_p+.h b. . P i lc \ = 2;^
,,6- l" 10^ 6. ?;Gi . o lee
lr - g,a3'z F r l f l - a 6 6 i t l
' 2 1 4 .
r-wr 10^(4le) * 2oootb-tt - w(o.ft67 rt) ton (srf ie.ot2ooo tb - Fl . w (o.o1E6e6u ^)
Pilor. . o.zEi^ (;, @ d1lbto nEadd
@tliPrS bs 2)
lo^e "-19j14: - o.os314( ' .s ' l r )
I - r,t. ta^ (0 ra)- 14U rgF\jf^) ro^l b.sz'
T " 1 0 2 , 3 l b - f i
€ ' lanr (o ossr) ' o oez'
, " . a - ' )
srn) A 6i^gt? ltuc-ded 6gua@ s.Ef t'x. zvzflraae / i'+'-lt-.odI atanolc,- is a,6;^ \ tte ootElda d'2rt* ie ein . Thecdff'ot^l { f"iol,i'n
',c o.ra. Detcmi^e tho rp:r6l r*,<:zset'-
rg io €to.t lill;ng o \"t-li.ral otl'al lod ol <o,o<n lb. wralrnor"eol ie rrrcasory lo elorl. toa;ng lt- tood ? .
P - L - - L P - ' D o - t - ' ' 9 a " 2 , 6 i ^tPr 3'si^
'/1a+ -ne .gL '
1 .- . , n;nE - ^ . i ^ " < e | 2 1 6 + )
lane " o.x€t f 'o.u
e - ' 4 ' 6 ' l o n y ' o 1 'r E - w . r n ( d ' e ) I - " " '
. <oan n ( + *!) l "" (s.z't z.; )Is = 6e1.82-b:fL,T@o ' w. lan (C *e)-
- 4<,@(1i 'f,E) nq/".ti-z.e')
sso ,/\ repo tuttg I v+ turc orcu.d o 6rolio^o.j ho^rn-loi dF.h i6 ue.a to s"rlt-l o t<rarg wcAhl. lf lhc coe(ooc''t of f",alro^ ic o.+. whol sagl.l a.^ bo @p+r+n bgc,cofi^g a 60 -tb (bt@ al tv oll* o^d of ll\c .+.?
B€LT FRIATIOII
t(Xi ru
vb o"s;.:r c t"a ic G6o ' e4 - .'eo'
:-.;tu - 1, . 2 ut . 1"o;"-,{*"k)t" f, - 'o 1"' 1+> - 11s7 tbbll l.w ... ri "-j1eLb.
36t ) n ropc "."tppd twiac o.ouit a po€i {ill 6uoDonl aw;'?hl af aooo tb wh€.\ o tz.c€, o/-,so tb ;6 s*led ol ,hc o_!h.. o d. tulu:f,;e tte aetr,otc l cf ftroljon.
t.rorb ongE of co^l&) : /2o.
r ) , "+-J t -L^€?. t ( , * . , t r " )\_-4
laat,tb L^ so - | (lr.s)
I ' Jt-!! '=> Ylo e'st 2 . . 7
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Ln -\-- tp
P L": ,4a - ! t4e'_. tnL. t+,ot -a.t oaa
.11,6t | 1yk = e31j' + 6z7.f ia6d = _?:EJe!r--.
g^a.) A loftlue of zao b,fl oci6 o^ lhc btukcdtuh €hcM rn riP-s53. Jf lh? brcN. bond h in c.nta.i *ilh lhe b_Ed.._lhrcvg^ 2sc' \ ihe coemc,al of lnctron ,s oeo Detah.,nelrE hfta P ol tho e.d or the bmN€ tcv-.
f1 - -14')L@'\ tu)L
JL. e.,az . . r , ,
( r - r 2 l ( r a r - f R ) . 2 + o t b f l
T r . . L . q , 6 o t b
f t (o tcoo) . aa - r t ,4ee.2ab
T r3|a
l
il
plre ^- c*) . r, l?,:^ '+)p(1 .333f l ) . +qa.a3 (o . l / ,61)
P ' 6 1 7 t bss+) Jn F,a p -sE+ , lE acetficjtql of fnot;^ G o,2o b.-+qae^rdp? b tho fh€d drum I bo&<-n oll ed.tooea i^ conlool. oa.lc^.m'ne the minihuh t€,ghl w fo pl€lal da,v^ptdne rcirin of the
-J,- o. .(r4u*) - t ,at' '
f t ' 1 A 7 I z
d1 'wo636 ,57 '
<r\ 'o: Iz - tu " w€i^36..) '12 - (a,.) (q @ 36,6, - w a^a6.?1'
12 - o 16 \ t l
4F3-a | \2 - 1o3o.@e6,6J . t i1T'
rl2 ' sod I rir.€rx=o 1 I r r F l i f " ' Pao 6 i^ r6ar '
\ | 1t:ti t1t t1- - 6aa
H..Boot t1\ ; = 3oO1.+ 2W I ot6vl t a, | 6w' 4oo - 1 6?t
v , t . z 9 2 . q Ls's.) J^ F,s. sss , o fler'ibB bctf .un6 fdm A d€^ rhe 6pe^dpurlca E q booK o@ P ta o 2&-h wc,€}'t $o avff|o;6t of$tolrcd )e ,ti bciweo lho bslf \ the @apound pu$% p rhdT onoxrhurn weight w lho/ oo be eopr.fted
vaal mlolingtho putle4 P or etipping lhe belt on to p"|eg h.
!z= ut-"'"11-"t 'n,'."i12
but I ' .V21" I1 - 1.6+e (Y'/z)
108 109
Z M p ' o(9T, r rz(z) @n" Pttt --
5 f 2 , - 2 1 3 - 3 1 1 ' o
,s ( ! / , t 2 (a a41)w a(2 . ro ) -o
6 e 1 t w - 6 &, w = 7 0 4 7 \ b
l
l
C h o p l c r 6
Syelome in Spoco
r l 0 l l l
€o2l Dclcminc thc mogniludo of lhc rtsrltonl, ilc point;ng, qils dir€clion c.sincs lbr ltro following.sFtdn of n6n -ooplono..
cdcu.rcnl forros. 3oo lb ( e, -a, 6 ) ; {o lb (-?. +,-6) i @ tb(-a,5-3t,
FORCE (D)
4
logcl Di6to@(o) le o!r"yrr!'
-a1.4-_4!--3a o
lta/r.rI - ?n/3 ... A. - 1ls.?4 lb.3.4/7.e1- Al4 .'- A' - -1:.2.55 tb.zao/ral - d6 .' . /e. 24.17 b.
-L" -L- gL-,L- lAA6.71
:. Br' .-119 a2 ; pr' 236.46 i Bz- -29A-06
_L"_q"_Q--L-_@z D ,'a7
.'-C\. .-r1a-1s i Cr=r41-l.. iCz- -Aa.s7 .., porhl,iq [email protected],<r - 115.24 -118-23-113.15 - -117.1+ tb. { uprio.d to the left.1t - - 1S3.CS | 234.49 | 141,41 - 226, 2+lb22' 2.a.+2 - 29e.o6 - A+.e7 - - 152.46 lb,€o1) Dolc.minc tho mognitude oflh€ rcultdn{, its pointrng , ondib dieclioq cosines lo. lhe folto*ing s)€tem of m.-c.pto.|or,conorrenl forcos, roo rb(z.3,a) ; B.btb(-3,-a,s) ; 2/btb(a-o_a).
Fd.ca2
-e!=cL"SL - 2e-z +
: .Ct 'a ;C. /=OiCz - 2OO
C.t6e' -a/R - I1zMea.oo" 0,34-9
aGo, - 226'.24//46.00
CGet - $2.a6/2s6.
to gpl lo) uso ot - x'ir't t2
_aL=^L-,aL- lqz 5,345
,'. Ar - 37.1+ : At - s5.7 i Az. 1a.2gs,,/r " Br /-/ . Bzh = 366/z.0-7
: . 6 r - ' 127 , 29O I 81 - - 169-E a Bz ' 212. i6
= ( sojso)' 1 (-11a,a2)z t (aj6.aa)z. R - so7,7 tb. pa;hl;S f..*ord \doMabsoa - zt//F\ = gaiEg/s1z7 - afiBcosor - tr//a - 114.o7/sa7,7 - o.z2sIi)6aa - az/e - +aaA+/s.rJ - o.s3e
<' - 3r.14 -127 2ge 1 0 - -9a 1E6lb
4/ - -111.02 tt1
1t - 7+ zB, 212 46 | ztA ' zre6 44lb.
s" = e/)' t(.r)" r(+,)'
Cosez . +a9.9/s24,se . a,gaA
6('J Dolcrdino th.o mognitude of the r.osultont, its point,nq, \itc d,-.r-o" cosines lor the fo ow,ilq sy61eh .f ,,-,,""pt-"",concurrcrl lorces. 2oo tb ( 4, s, i) ; 4oo tb (- 6, a A F.r. tb ( a,- 2,
- 9
roge+ D vee I D2. a2rr ' ,zeL-AL"!:L..<@^ r z 7 0 z l
,'. A" . 113,15 t Ar - ,t.+i,44 i pn - -s4,el
-L= !:-, -EL - -@z o,17
,'. Br = - 27s.46 ; B) - 152.4 a Bz - - 22P'05
L- -q-SL- pqz s,ag
." ca = 222.63 t Cf - -111 .32 t Cz " - 166.A52t - 113.15 - 2t3.66 | 222,63 . 62.12 tb.2l . 141.1++ 1A2.+1-111,A2 - 21r,..6 tb1z - 'a+.e1 - 229,65 - 166.sO = -17s,a b.R" - 4""+zf2r <2. = (62.12>" r (212.s6) . t ( -a,7s.q)"
R - g2r,5.B tb.Cas+, - 6212/s29,s3 - a,118case.r - 212,s6/s2e.s3 _ a.+a2
.'. poinl,n9 bockwo.ds, \ lpwards 1o ihe
t12 t l 3
6at ) ftr@ oonc"@ai k€aE p, e, \ F ho€ o Esu[,onl of j tb.dirc-lcd fotuord \ up to.ighl ol e, =oo',O,= 56',3", - 1r5". p.-q@lc zo lb \po6s< through fhe ongin \ {he poi . f (?,1,a) .Tho\olue cf Q is otso uo,b \ il FDsse€ th.oueh ihe p6i^l G,2,2).Ddiomlne lhe nog.itude of lhc lhi.d force F \ the ongtes;lnoke-s wi{h the reference oxes.
3
whee p 'e lb . , -4 . =60 ' , 6 | - a ) ' : ez . .s .
. . qr ' 16.23 iQ/ .6. rs , qz -e.7+ - co€122Aa/$-6s1t - Fseax . s(cos6o) = 2.s -6" = 46.2'<y - easo, . skoseo') " z.s rj, - @s', e.a6/23.6azz = Rcose, - !" (@sa6') = 3.sa el - 7s 6"
!!--L'lt-= 3!z 4,5e
: . px=8. r3 . p f - + ,37 i9z -11 , raq-4L.-44'_?e
F, . 2,s - +,37 - 6.19
\ - -a .36 tb
F r . 2 , 5 - 1 6 , 2 3 - A , 7 3F\ . -22 ,46 tb .
Fz - a .6+ ,9 , r+ 1z+a
Fz ' 23 .G7 lb .
' (' 12 4)' | ( 6 26)' tC n 6',)
'+e=cos '23 .67 /33 .66
.'. po'nl'ng bockwa.ds, \ do*nerd
60,.) A font ol (n tb i6 di@1ed f.om A rowdrd a in the cubc6h@n in Fiq p-.p7 Deleffiie the rcrcnl of the fole abo,+ cochof lhe aoord'no+e o.ds
t!-' !r-" !L' ig'Y
: . F | - 62 .5 tb i Fy '4 4 \b i Fz '626 tb
1t , . Fr (1-) - Fz (4), , - aa ,eG) - 62 .sG)
tu r = -62 ,4 tb - f l . a \z . - rz (a )
.t$ - F. (a) ' 62,t(a)Zr,4r - 2so tO.ft.
-- -62.s(1)
eooh of tho coa.driold o)las.
6c.0) A foftp ol 2@lb. 16 dirccled f.pm E toword C h the cubc
sho{n in Fig.p-5o7. Doterminc ihe rnomenl of ll",c force obout
t -L"EL- @-
rMr - F!O) - 1,+8.6 lb-fl.
= - L8,6<4)
l l h - - 3 9 4 . 1 l D - n .auz.-tu(r)rr 'G')
- 7-+,3 (i) | n1,4(4)4M.- s1o.S lh-{ \ .
ri - {1 i tb.:, Fz - 140.F tb.cos) A for@ of:"oio ieai.ectea Fb- B loenc D in ihe cubo6hown in FIi]. P-6o7. Dele.r,he tfte Frornenl of thc J?rrre oboutdrLh ol the a..di^olc o'es.
-E-'LL'-L=4
.'. F, -o lrt- rgol6 lFe-2ao16.
tMr- 244 tb- ll
- -z.to(+)
atAr - -9@ tb- l I .zMr- tu (4)
- r€o(a)4M2 - 72O b- fl-
r l4 l l 6
6td A fot@ { a@lb i. di.ecl€d frDm C tor.arA E in lhe Eubsctn i" in r,6. r-aro Dclc.'r'i€ the hamen{ of }he forE€ oboutcoch o[ ]he coordino]c ores.
d - a.e fl-
+-++-*:. Fr. 1@31b. i fr. z26,sb i f.- 1fE.a tb.
611) A h@ P,dircakn ftr6 F ta*otn607 , cov.es o momenl My - i6oo lb-ft.obout lhc x hz orc€.
iMx .F (a ) -F i ( . )
. . . 5 ( 4 ) - 1 6 ? 9 ( 4 )
.M'- 6s2.Altj-fl.
tMt-F,<+)rFz@)- $3.a(1) t163.i(2)
1Mf , 979.0 tb-ll.{Mz . -r,(a)-Fy(r)
.-t63a(4)-3 .5(e)<lY1: r - l:06.2 tb-ft.
I in lhe cube sho^n in Fig.p-D e l c m ; . e P q r l s m o o e n l
-!L - !L.- tq3 2 !r9.5d - E,36s f'1.
P / ' g @ t b= -aoo(a)r Foo{.)
M) - -.{ro rb-{l.
: .4=6aotb. ipr"4aotb.4M*--P'a.)+ryQ)
4tiz - -Prc+) .PL- !- .., P-1o17 tb.. -Soo (+)
Mz. -32oo lb- f i .61.) A fot c p is d;ructed f.om o poinl n (a,1ia.) io€.d o poin{ S(-3,a,-r). lf il ccuses a rlomen{ Mz - 1coo tb-ft, Determine themonl of P obool the tt &,y oxes.
d . 0.11 fl.- L a Z - ! L - l Lq,1
... p, - 7p/s,n j Pl . 3p/s.11 i pz = sp//eArztA,-p"(\)+WG)
teoo ' 7/sr\(p, + '&)pA,rP . 9'll lb.
Miliiilldfi{
II
pt - 7elb i ry - aootb t p2- s@tozM,- -PzG) P' (1)
= -g.tO) ' 7..)(1)
r1't - '17oo tb'(l
zttf - PaG),p,(1)- s@(4- 7.b(+)
}'4/ - -8oo lb-{I.
6i+) Ths sheoFleg derrich shoxn in Fig p-61a suppods o \ic.ticallood of zooolb. opelied olA. Poin{e B,c,\Doc in lhesa'ne nori-r.ntol plone li A,0,\ D orc in lhe )(Y plone. Delermine {hein cdch menbe. of lhe dcrick.
Go,,ro) da '(o-o)" ' (5o)'* (o c'5)Y
d^b - lS.7oo fl .
drc" . @' o\" r ks- o)' r (o' o)'
d^c '20616l l .di - Eto- <-zal' *s-o)'.
aw..r- o: '!r$(1a)- ot en) - aa/, = laoo )b
. L. !L' !!-"!ra
Dr . 2cballl ; D.-o
lsololing Top view-
c/ 't @(.t/$
e " 9 L ' L ' 9 2 .
AC.1 !?4 ,s tb
Ba - l2t'ooAo)Y$
-&"
l l 6 tt7
b6.€ Ab, Ac,q Ao whose tower ends o.€ in the some ho.ir6._tol plone. horiz.tr,tot fo.@ of 1@ lb oclinq pono et id lhc xoxi6 i6 opplied ol A. Delcmine the forc6 in eoch nedbc.
d; 'Gr)'.(6af ,@o).
a-1r:of +<crf r (o-<-::)'
a;/.3-oy..(o-f 4e"ol.* , oN. s .a67'
lcolole Right Sidc vi€w,
65) Thc frona$orh shown in Fl9.p-61e con€ists of thr€€
;
.r{oa. r. o : B/G) -1db(5), o
as-, !L. _4_
-1@(D, rcf(3) ,o @(z) -o,(oJ -o
cr .62Slb. Df-a lEtb.e- - AL -6IL - __9u_
Ac.76s.olb. Ao - s22.91tb.
AE.lll€ tb. i gry.5ootb.
616) Refer.ing lo Fig.p'61s. r-Jpta.n hly- looo tb jarca ta v€i,li-col down*ord locd ol ea@tb. Defemine +he lorce n eoch.tE1i1*r rnda. {bis rc/isod lood,ng.
d^a.,@Gioi4o4Y
d& -r'G;F ,G;f t Ga\61ArY
da " e36r ll.
lsolot6 F.onl Vicw,
leololo Righl Sid€ vi&,
-4C-" ,9'-
AB- 1r1O lb-."c612) The poinle B,C,ir,,D of lhe oonliteven frolnsv?orx shown inFig. P-617 ore olloohed lo o v6.tical wolt The aoolb toad id F|orollel io the z oxi6r\ lhe r2oorb tood € veriicor. Compute lfe lorce
qk) - 2a.oe) 'a
- 4 L , _ 9 L
lelole Ftunl view,
'-t\
-lL- -jL. _4aaq
AO = 2382 tt) - -I
(2a&-tuaoxs) -c,G) .a
AC- 53A.3
DrG) - (2ab1o.,aY.3> . o
A O - D .
A O " s 2 2 , 9 l b
d4 "446.)2 | (b o). t(4:a +)t2 - 101t
o^. .,t(1o or | <a-o)? + (+-o)2 - b.n.a^o . , t (1ea)1 t (6 o )z +@-ot .1 t 6 '
1 W - a
to.o (4) - Lo(.o) - c, (a) . a
--lr-- . sao
.d* ot/.6) - M(4) - +o.(1o\ ' o
_6q -,qeq
Ag; 1615,5 rb - ._ c
l . l8 I t 9
610)'the un6./nmel.icol contilcwe. fftrrewo.h sho.q in Fig.p-610.suppork d we ical lo(t of 17@tb ol A. pdnl€ C rt- 0 oE in lhebodo .dlicol plone whil6 g i6 3 fl. in lron{ of thi6 ptoi€.fi€ nnce in eoch @mb€..
a^s .t@-ifi6:F-,|77litr' . 6.vt!.d^c - l6al;Gzf-aB-Or - 12'
Isololo F.ont Vie*,
d^o. "/(s'a)' I (+<)' ' (o' e))' ' e,16r'
c,C1o) oeG)-@(a).o
1,@(e) -B\(O -e/6) "o
s | (1o) t 6/@). 12..b - " -A
i 6 . g , - b r . g tAre 5
;. bf ' 6/68t - 5,b.,lo I
e,(d) | 6 /sB,G).13(a
b t ' Q a , t b , ' . B r . 1 2 . a l b
. . . nB "r7s5 tb, . -C \
A C - 1 2 6 0 h - - f
fteG) - 34d(.) - 0, (1o) "o
s.16s -
T
A O ' 1 9 a , 3 t b - - 1
aB) €de P"d. ate tl lhe 11.,tb load i. Fig 61A oak hodzon.oulwo.d froi n ,n ihe drrealicn lrom E leoid A.
Ftun Piot.'F.619d,^a - a.i|s l+., d& = 12 {1.
d^o - qf ts f i
,l;,; t:rz
lsololc Frb.'l Viow, leolate Top view,
9' 6.,) | B"t@')'Iloo?) - o
I ' G o ) + R r G ) ' 6 w - - A/ \ B . A r - 8 . . S i
f f i E s . +
,'. sr = 6/59r - s,B.t&1ou + G/e g'G) - 6@
13,6 8, a6g@
g-5@tb. iq-@tb: - o.(1d) -a/i e s.G) +1@@) ' o/\e- 8-/r,3 tb---I i B, -aaolb. U(to) " -5.,/c)14o(3) | E@
O" r21otb
.D= gL :. AO -,1,{€6.+\,.4166 0
aro) Thc fmnc*#tr sho{n in Fis.p-62o suPpo.'ie o €.li@l
l.Dd of 2ooo lb. Pdnls &c,\0 oe in thc sdE ho.;zonlol plcneDelcrmine lhe fo.€a in ea6h nEmbec.
d;- .((-t-1))'t!o4)" r <o4)'d.,b - ao.7zotfl.
- (o-o)'+(io-o)' + (o-(+))'
d^c . loiro3 fl.
q - b t b .- _ L
6
AC - 120lb -- - c
o -.co),g,,6;r &(r) -.,o{n)=,
a,46)- t6{E\ r.@(t) - 3e
i....'a)d,'' - (6a-o\2 +ka-o\' t (o-(sr'
d^o. r+, i+ f t .
r20 t2l
zrA.ro. -o,(te,) + Rf l4).-o
W - 6.6./aot - -@
zMa- o, 2o@(1) - CrG\ -D' 6za) - oat(4) |q02.41. ac<t> - -@.
lsolole Riqht gidovic*,
,.. AA , _95O.r13 ., Ac - W.2S t _Lp_- _jEL1o &fio1 10 lara ^o
AA -ros5,3lb- -o I [email protected] i Ao-6.1c'6lb-C
62t) n ve.licol boa p = @tb oppl'pd lo th€ lripod showi in
fiq-Q-621 @u6f,s a codlp.esgrle lorcc o[ 2i5 lb in leg AB \ ocornpree.i'/e fofte ol 2@ lb le4 l\C . Deleernine lhe force h leg AD\ lhe ooordiiales ro \eo of ils l6de. cnd D.
d,6 = ]|e,OO6'd^L - 6ofr (o--eiGi.F
l$s =o, Df(') - Cf (1) . O
Dr ' +/3 cr - -@ .vb.. +o@in @,
cr<+)t 4. c./ (12.c6) 'oc.o
Ct O+.Pe\ ' adaCr = 56.-2l'1b
in@, o' = ,15 G6..25) - 1$ k)|'rO, q"8,G6hGE) = 9eo.7,t4 tb.
q(rd'qG) -oro . [email protected](6U/4tb
lsolole Righl side v,ew,
' M c . O o-0r(6-2.) , @oG) -W41) -o'aoo (6'zo') | as@ - 21e6.6 - o
- 2100 + 4co7o . _2001 .4
Za . 0 ,997 '
-PL " -01-10 o.t.t,
o ' 'b$bes ' Iy 'oDz' 3s,s6 tb
trO = '(aOf , qa' ttzs.6e.fAO - 432.7 lb - .-C
- & - . L ' @
; 8 t ' 1 9 e , a t t b_9-_q-29L
:. C-/ " 2oo1 lb
ot | \999. .O44-*U-O
4'+ooto
Io _. t '
t c - c , - 2 a 3 _ C "1+t+2 B 1.n2 6 '
Cr = t6o,a lb. ,lCz ' 12o 1 lb.
622.) ln Fig.p.621t tl P'12corb. \ the coordinotee cf Oarc \o-e'!.,zo-2fl, compule +he lorc€ in erch leg of lhe l.ipod
d*- 6-)\ (*'d7 t7oZqYdM - 12,$6l l
d^c = "(o-o)' r (1o-o)'+ (6-o)'
d^a = 1+:1+2 fr-d,a = t6'14)Y t1aifa eeY
d^D = i1.3s6 fl
-i-
t22 t23
lsololo Fronl View,
q Ls) . c/(., - 12(,@t . og/ ' 6<bo -.'(t ) --@
lltlo - O IC, G) | 12@(2) - ot Ao, . o
S./66)-qG) - 2.e - -e)
subs. @ ro @.
Q@'q(a) -Cr(a) - 2a<t-C/(e) - - 96@
q _ 32otb.: 8/. 6@ - (32o)(B) . 36s tb.
6dro:cr6'\o)-qG)- 24@
- -?L
Cr+o,ta./-12@-o32O+ W r&9-12AC,-O '
-4L= _lqc-p.ea6 p
A - 471.31b C /'C- +sz.E tb-C-/ \D = 512\.aso 40
0 = s81.5 tb -C
68.) 9elcr'l'ine the nroxrmum sofe verlicol lood w fhot can besuppo.t€d by the t.!'pod 6ha'n h fiq.p-G23 Arlhoul ett:e*d _lng o cdmp.essive l6rJ 6 2arblb in dny member.
w
) d."..[:7'TG;F,G_gdo^ - 1.aw'
qu.6,n7 doe' 6i'tf ,G-o\\ PIi|'Cj06 .6 ,C62
dva-"6-o."tcarc(+AoJ o.o= 7211
ll
rI
1
* i f . M" 24eb.,2 @ . - L = A L - 1 q,.103 2 G
., A, - 6445lb i At- 19,:+,* tO i AE.12s2.C1lb.Isolole R,ahl S,ae vi*, leolc,te
tif DE '2.@ | ,
#'+'T-+
(srt N\z -G/G).oq - 2(t 4.p}t 4)-
q . 1.731,e2+ tb.dt ct. jf rc >24.r.tb
*pL - 1731.921tb :. qa = 241.4a trra'211 5 "/ildoetu)c&
n(4'at(A=",& -(1i21.s246) - srds.etb
t t l D C ' 2 e t21Oo - Ct -C i ^C2
A'(1) -B/( '>-o
192+..6G) - BaG)bf - 1539 '@
dEcrK \l Dbr24@hDB = 153q.46o
Ee. 6-
.'.DB- 468.561b ../ tl dclol crd
B'. Ees.a tb i gt.11gc.16|At. $q...tb.o+ the nbhl 6h6 vi*,zw-o, Ay(1) - s, &) -o
Ar ) t/a (17a6.rc). 2232 -1 tbdv:k 'f M> 24oa
_w. -22122
DA - 27s+.s tb oo totl .x4t tti6\atle bd@E il er@&s za<Dtb
ct ' 1q6,9 \b.C . ' O
t24 125
EQutuERtuM roR ofl.coilcu^RrNT Sp cE toRcEs62c) the Flole 4arn in fb.p'626 aoti$ o load c,f loootb aoptieioJ E L) 16 supporleo i^ o ha.tz.nta. po6'r;on b/ th.c. *l,".ic"bl".ofloct€d dr A.B \C. Gopule lhe tef,,e,on:^ o..h a.]bte
D.\ ' 2 167.25 tb.
.. thiE @nndl be o@pl be@|s tl witl eo6edlbc I'mll vhich i. z{.ab.
,. sae dar. vot.e of w i. .sigg.S lb
t*a,r(s)-r ' - (o).oAa" 229,61 tb.
ahec'. \f g > za4otboA - 73s.61
-6G)r 1.,60{6) - B(s) = o
6l-r.L-! _-.]
W.-4,4. ,0o(+)rc io) .oC' 4oo tbT
AtAIC -1atA "A
A - 1<><b - 4oo 4oo
y1()4@ t - 't G)a6)(61 ,/s6) + ,/l@(d?/e.6)
t = 5 n .
s'-3p@\i@@
627.) 6olee prob.6 if,t^ add,l,on 1o ihe loootb,the plo{e w€,bhsj
'U@\@t " Ue)qt)(e,/.\ + 'fG)e^1qe)g r ' b A . h )
j " nb l l .
c. g@lb, - f g- g.o tb .T
ztr.a --A+ 12@r 10.o'g&'a@ 'o
A' 600 lb"l
62c., Refe. lo unsynrnetrrcol conlileve. Go'r€wo'h dosc'ib€d
in pnb.61g on poqp €6 q rep€oled heneosFl9.p_62c.lf lhew:
ibal\lood of 17oolb i6 shrfle, b ool o1 lhe midpo"l ofmem-
ber A9, oomptrl" the componen{s of lhe ceoclion ot I E lhe lb*
oes in lhe bors tC \ nD.
nn6 g,otal , .m 6) - c6o) . o ebG)1.&o G) - @ta) - aLs) -o
dn -.[.e-af ,O+ef '6aY ' s,7" Xa"c- .@$i6 -ofi@-of ' tzfia^p - t6of 'Gaf ,GEiff - sftaq.
^ c - c _ . . c r . e r
A c''cr/2 | C, "Ca
A D . O ' - - 9 t ' 0 2e,.6s g
Q c, = ot lz 1 az 'D. /+
sub. @q@ lo @(o,h 'Gh) j ' ( .^*o ' ) la +a2so
6 , 5 0 , + g s c ^ ' + 2 e OD " r c ' . e d o - . - @
9,6d+6/( ' )-ne(6-2 ' ) . as,(a) l qb) '$3o--@
@t , ct)e)- @, to,)(.b) | noo(z9) . o(0, . c') (i) - (., I o,)Go) { a26o - o - -19
I
a./'
t26 r27
Top viow, LVz'o O
o, ts 02(.) .0,(6) - Q(a) | G (+). o;i:::=-" ut: O! o'/+ t,cr-G,i . ' " / (D' / , ' )Gt - o ' l .o) c,G)tc.<i 'o.V" c ' " s .2so , -@
""{2. qbs.@ b@,x r s 2e D' 'eoo
0' . So lb F.N@ | Ct . t.Lt<eo> . 12o tb,to.fu(c.rcsl/a Ac.kao0z):L/1
lc - 126blb.Relcning lo FrD.t view,
zMo"o 0 "b G) | s.e) - e(.o) . oax(6) | az G). +r.. - -@
zMc" a 9BxG) -62(3) - D,G6), o
9*(4) -bz9) - 600 - -@
^oD (, L@
i n o ,.eoQ)-Be(z)"sat
ii O,s@(.o) | 6, (!) - e3so
br = lasa tb.
ar k) - b{e) - @ae, tn) ,2.6 ' +aoo
b, Go) . soaaB* - 5.b lb.
6ao,) Ihe b.f,,n BE of ltle sf,fl". l% de;|cl(. €hawn i^ Fig p,6sok tuloj€d bNo.d jr' meogurcd in o honzaolot ptone lhe nraslnb i. vc.llcrl ( ls s"pporled ino g>or3.t aI A The poinfs A,C, \ 0 orc in lhc sorle ho.iz..,lot plone. oelemine lire li.cesin the lEc Ec \BD t\ lhe. conponenls of the beoring reootion c*
dao 'dsc . t r2 tg
l
j
riIl:
I
N@)- '[email protected])"o
zw-o oq(6)twG) - s.,Oaa) - o
A(s) rt G) ' 4aaa bq , v / ' a e - - @
." E: - 99L
R,!lh{ Side Vi.*,
aio'a, Cr<i) - ]6at!/l) -o
c, ' 6a3lb
n e4.4. q 1o1 's66
oy = t63 [)
- . - A o . \ 9 1 4 ' ' 2 d 9 t bi a --A,(.t r (c'* o'X.t r soo(s6 6)<1tt X')'o
^" 6r , (G r D")Gs) - o - @
A,tst = (,r,7 i t1)t14A" = 2ag7 tb
oz . 6114/s_- 61 tt)
Cz . 227a(s)/i= 22a2 tb.
Or - 193
<j: 6-PL
Refc..inq to llbhl .q& V'bw,zMb:o: ^z1't(hiaj)(s) + cr G) o/5)'saaG) "o
Az = - <2271 t61)(1st633 (s) r la3ci) | 2w
Az - 166.7 ll).
63r) The boom Bc ofthe ctiff'lea de'rich 6hown n rOP6?1
i6 conto,ned in the XY ptono The mo€l AB ls "e'rtiaol \ rg.s-ls in
o soohel ot A Poinfs A\D ore in the same horiuonlol plore '
Points DkE ore in lhe.eome v€rlicol Plono Detormine the
foroeE in 1r'o 1o9s BE ?^ BD \.!4ryw"""ts ol Ihe bea-
r ing reoclion oi n.
t28 t29
a". ' u[-a",c-Y ,<ao-y aif - p;?ago " ,6<',o)t'Go or i6Zo-' ' lalsolale F.rni Vrew, lGolole Rqhl 6,da Vid,
<M' -o; {oo(ro) - Ay(o)- Er (s) -o Zt'/^ -o .Ay(2)r E" . , tooo - . -@ D'Oa) 'E G):Ey6o)-o
A A E . O o / ( L ) ' E z ' E ( . ) . a - @
D(E)ro6a(?o) ̂ ytu)-A,(!)-o e4o '4hs ,,, Et . to/tsE/ '"6'"
t\r@)t A\<s) - 9,<5) - 2ao@ Dr(t- 1d$E, Er(z) =o
A , ( 4 ) i A , - O ' - . t o d - - @ q ( r ) - a o A , E / ' o
ZM^-o. D, - 4o/3oE/ sub.. to @ro@(io) - E7(ro)-0r($)-Er(s) .o C) 2E, tDr-1do
BUI: E4. " E,lo :- 4- 1.5Er 2E | 4b/3oEr .looo
i@<2) - ( \5E/) (2) -o ' ( . ) 'E -o B!+ '4. t .bE)
aEa t2a, .e.ao - -@ 2*r a,bo(1bE) - a@o
. ' . E,=( .Eo-o;) /z @&.raA +8, ?1o.o . . .E, ,2sob.ar/'a -O,ha .'. Or " o//z -.Dbs.1@ Be/@s. r5/1o .'. BE-58.4tb.
AtG) | A"@'r, 'e<'otb -@ *!'rg Et "tse, . a,s12ta1
Ar (.)t A\ -Df/2 . 4.)&th
^t (.) ! (@;!L) - aaa!)
N | + ) t 1 @ . w . B a a ota)Ar or ' Totb --@
-A'(Q.A,(" ) - -B^= 6doo
-{&.a t€a j_3g)
El ' 375 lb
usn]g q . 4944 - ao/eo Gas)Dr ' soo lb
bo//@ ' @/aa . , BD . 612..+ lu .uahs@ NU)-Df "7eo
Ar &) ' 7c!:4 + s.22Ar . 7@r/4 :. A-/ = t61s tb
U6ins Ez ' 1./16Er .4y'6(379) . 2so1b .
oa'l6e(ot/za ' zso tb.rcGming 1o tujlhlside Vew I tF: =o-
A z ' E - D z ' 2 . 2 5 a = O
. ' . A z ' o
632,) Thc boor of ihe &rich 6bo* h 7lgp-632- k rolol€d bock
30'f.6n lhe fi rlone. Dek iniie lho {iroce in gc kBD }, {he
1 . 1 0 . 6 , . 0 ' . a . @ t l .
rolt.6' - b/^:6 :, ft -.o$-
.\n6o' - 6 /.o .'. 6 . ir.32 n.
1ar,@. . 1r.r/6^ .-. A . ro fl .( G e ' - $ / A , . ' . & . 2 0 l t .
de -,GoAfi a.A:ofi6'i-Lry ".a 2t{l L, - 10 t a 5' - 'e '6 rt -
ae.6il6;f'('+. $r.2e.2. $ @'aoton@" 11''att'
L' "2"'" "' 9c'816 3lo
l n E 4 Oq I Dt'1132
. q .fi32'3173nA '15444lb
8o - 11e4.6a+ -'.go ' \63tr lb' n A T
- Ai Ga),2db60.6c) L o
zM^'a OC',o)@- rlro(s..6) ' o
Al +O, - i7z2 - -O
loble Right gddview,
c,'-trzfi@24
ce .199.96 tb
Dz = g9.ec lb.P.l. lo Qbhl Etdevie : .F-'o
O . - A , - C z - O
Az - 939,96 -199.96
A z ' s a o t t )
ot'!91e.L9,
02 - 1t9a 6a+G1.32)
<Mo-o: -382 <1rt2) | c' (21.6+) |[email protected])-o
Cr (.1.a4) - pegg.z4l&
r30 l 3 l
l
of Groviiy
C h o p l o r
Coniroide \ Contors
ihe ccn{fti, of lhe shod€d oreo shown'|6 barrdcd by lbe l( d'.i€, the line x ' a q
k- e% - b1a
a'.- bay'a - u- blr&
n-f, aa, -fi ary*a^
i" rg.th" pd'
G,b)
7 = 3o/s4 t - l l e ' 9 ' = b / 8
+7o6) Detffiir€ lh6 (btroil of the quo.+e,' oircle €ho,n in Fs.
P-7o6 whd6e nddius is n.
A- fed' -("$.+ U''N'r" e J;"+ .,,:;,". ...6,^< _,/.
. 1 . N p , . l $ q d . ^ 4 ^
l.; f,\ t.t!'-*?.-""e-t *":e"l " ^ ('" f -1-a-^':ld^.('(adl -(fl4,-"""1a, r"*=G-F
{'*'"'.,".. -+t-''al: -+l'^'"d " #1) - h . % G ' - ' " ) - L ^ . \ 1
-' l t '{i,v";l Ai' l,"a 'hJ'!ad'
' r, (: (" ") d' - t'l'"' 41:l t t - n. ' ^ i _; i , " ^Zl - " .2
t32 133
7o7.) Oelehine the6hown in f1:9 P-?o7
cantroid ol lhe qu6d6nt of lh€ ellipseThe eauolion of the eriipse *
* !fu-,
c 7 b " ' 1 - \ 7 o '' d -
,t = b/a q;n-;t)
^r =f iG;,) "f,,(u.e:r)a^t.f a' = f w.F:ta, .8"1-,^.wd"-:,l{iLeJ r=o6,a .. slnq='/d - Va[ h@+y,o.]
dr = ocdsqdq yl- Ai - !d = eEI iJ7.V
ac!s-..Fi:F 7 - &/'\-
^. rt*")("-"-" ) A,a 'chgud,) - hr e! d,-u"l!!;.a.,,^a^
_ -f h,ll(*4) a^
. o b L h L 1 1 @ a t d 4 _ o , 1 . . 1 a . , _ t % ] :- 4 f " r € r 3 : l "
- ib lrh tt 'PL ' o-'E J 14,tq"4 - s_uZ,A - obi/
7oa) Cfivlle th6 o.eo of lhe spondrel in Fr'g. P-7os bounded bylhe x o,i6, tho tinex .b,q the cuNc g=x,n wheG n Zo.wlEt ;elocolion of lls c€hl.oic fr€m lhe line r -u ? prepo.€ tfe lobke oto.eoc \ lo@tion of cenl.oid f6'- 6iues of n.o,1,2,ta\e.
'%.f,1.Ji "%"i++-"-l
^- -f,,(dr.f,.(#)d"' h4^f! t" a,-hA^t#7:, hr." T-hil: - o'1
-!\r = rt"
r = !Gd ut l'i" r i"nr' -tf.*a r.(oo)
a'h\Yb^
edx . t'4+ai
--L lu--'r1
A - br%r
b - !ltl]) - b(nrr) - b(nr1)
; . t l n ' { C c ' d l - u z -- - e -
7oe.) Deledine the s coorditule of lhe spondEl deso'ibed il
Problem 7oe
^e ' [: '/, eQd") - af' e" a'
" . - - t . " " , ' 1 b' Y,l: h'i/b- d, ' h:i4l' L+"'-k- t/-*^ l.tl" - of ratu:<'':s)
) 2 ( t n t ' )
: !qa - :b[ . t = h(a ' l )
7,o) L.@fe lhe cstroid of lhe o.eo bounded bg the t ot'6 lt)
the sine cu.ve A= ognayL fiEm '=o to x:L
9'an^u uf = a's,n n,/L
: ^6-!: ' /"eed' - ' /" f" u'a"
shown in F1b. p-7+.How lor 'E
tha o@^troid of the or€o obow {hebo6l
L(€) r 1(6t E = [1(6)(atl, ] [1(6Xo sI
1+a - 4:
t - 3.o7 i^
t34r36
@rdinolcs oF t|€ c&t#d of fhe d€owith nespec+ to fhe eiven o)(ec.
I xt x"t , y,r r't] s -Lt^Gxqora:' , [hn.,]-l# , e ]41j44 - 30723
q - ".+r i^al:'+t - l/r(.\(e)(k.6)f tlkr6'O1
4-11i ' 96.41
, = 2,31 in-
n6) A slendor homogeneous wire of unib6 cross sct;on ie be4finlo ihe 6rope shown i^ Fig.p 115 0et. lhc @rdinoie6 oF ils @n-
[6, rrd r €l t . 6(rr s(4'nr) r r(*{:d)
5 ' 2.+a ;n26.@t = -6(+) 1 e a4@s 3o'r 4 )
t --rq!: - 3:r-eg: , ae65 ; .< zo,,/tu
" ,"u '- B/e". ; - t . 1.4ts, n.
l, (, E^ (:4'^ 'l&.)) + 2f s -[z(axzr(zo''4o)'t(.plJA2Az! '8996
.g- =1.o36in i i -ottE oenlrc;d of lhe shoded ol@ slEwn in d9. p-rle.
[Gt@\(t)t v.(6Y.<\t v'GYq1t .f h6*4@n .6)']
25 st - 3s.1ee
i ' 1 3 t h
,17') L@Ie ll}f @n+K;d of lhc b€.+ *i€ €tan in Fig. p- ti7. Thc w;.c'F
hon|oq3h€ous q of unifo.n orc.c 6etion .
n5) Dele.fiioe the
st'ovn in Fig. P_715
| | h @G)CA.<)'] +
t'/, G\kr(%'c)1i 26 - $2
4 ' u , " .a2 7 " l,h 6.2) ('/' 4 Dl I l,/. Grd ch - d1 \ f r{.)@ @'. 6 !.11
t = 5 i n .
t , :
,o) Dele.nr'n€d lhe ce^lrcid oF ,h€ l;es thot lom the boundo-
rij of fhe €foded ored i^ Fia.P-a1e
ltz,7-eo r s t.F4 + -.tr-!,-l ^ = 1r@ | I6(8Eb/4\(,/r) | W(r,/")('/E+ {nX h"z)('/tr) | 6)l
ao-aeii = 251.322
vdlu€ 6hould the 6ir. width of ihc flonge be cl..onged so lho+ lhe
cenfroid of lhc orgo i6 z,s in. obove the bo6e 7
I1(e) l b(1Yr.r) = 1(s)(ar,) | b(rxo.6)
l[|1a
F ' 5 2 6 t n
.4e.eiq'1eG),6(.>+@f g\&A,4rr.,(9)Vd,.f r,(WW.n)4A,3e7 t - 261,65e
t -s.4 i^of the slEd€d or€o i4 FIq p-72o ie ncquired to
Oelermine lh€ dictonce b lhot will fullflll ihis
t'a GYstlty'. s7 -[h tbY6rlr3 d€s.33 i in ' = 2 inb '?
bt = 42.666s n2
,21) Befe. ro the I_ 6€otion of prcb. ?t+ shown io Fiq. P-7r4. To
? o r a . i b - 4 + o . 6 b' 2b -20
I b _ 1 0 n .
722.>t@le lE @a+rcid of |he ehoded oreo i^ Fiq. P-122
by cuiting o €@icicle of didmeie. r frod o quonler c,rcle of
f+ +il' =e?X!.,r,(IlL. X-ei:).r".; -,2 #7,"ll; = rl --i -gL = 0.6.7 .
12r
s' ( /,Y,'th' (- "16)(/,)o"Zj -.% - \.7ts - 16t:: str'
r,%_s - 6 5#:'
E'-e!]g-r- o 3aer
r36 t37
,!) Locolc tho cenlroid of lh€ shoded o.co
[h(.d(G\ , +b@ .'Jdt . tl'. r,ttt (,..tt..'). (1.d' (.t (,. 4) - 1' w (4+)
| 24.4a112 . 4..sX - t .o+;^ .
2 +. 1a 1 12 E - 1.*> 6) | ('h) (t. r) @ (% n) - +2-* G - g)
24.4a1+2 I = 63.5ee
5 ' 2 6 e ; nthe coordino}ee of the oonlrcid of ihe shod€t o.€o
/9. P-7.a.?\- k@O-%6r&) -!ktJ' - r(eb)-ge)Q/,Gr t',) - !!{ G\ -.!F @ - 49)
t4,rs3t - hra.'s1t . z.ra in.
'41 eaa1 , '2^.t(.)- /e(d(dr"rt tp'6a - {t)'!#("-#)1++s93 E . Ea,a6e
J ' 5 o € i n .
z26) tr:.afe lhe @l.o:td of the .sho&/ dr€o eotc\se! b9 +he cutueU..o' \ lhe 6frc;9hf l,ie shos in Fi9.p-1t5. HinI : ob€€Ne ]ha{lhe tuNe q2. oa retot've to the y 0,,6 € of 'he @me tbFm 06 9 "^xz wilh .esp@l to lhe I a'i6.
, l:!t@ - n ctuelr = ly@k)(E',\ [kbtu"X% aq12, - s7.6
t - +.€f l .n i .[.h & doe/a..\ - lh a>o) & -d
,t2q - 3€9 - 3 f t .
zr) Locoll3 lhe lglrc;d of the cutvenl st$*^ i^Fig.p jz1 tlnl. lntog.a{,bn ie onneceosd.g tf lho o.€,a i6 €ubdiv;dei into the elomentb be fdrnd in foble vr-1
, -'+ [r(kJkx')t 1.o-rs(+Ydt,fa&)1.\')(./') r /.it't')7/A_t - e/!)(4)(1.)(ye.,\
I 4 - i ,6 f t .
rrd wifitul usitg ;ntogef;n- c!.nPulc i foi lfE 6so b.u'dod b/
fhe )( o'i€,ltp li,.e 1-t2 ,i.ltg o.,rl€ g'a\ t t/s-a/ao '
A . (qd: At .€Ad'
^ " i i 1 .^r , ' /6 . t / f la)a, , " ' r - l : (a f , '7e- ^ ' /e \d,+ - . ,A . Iz" + \i6+ rlr'1. _H,r | ,.h, r7...1"
A- 292 ttil.252' = 1q1s z
I ' 760 @'ts '
,.e) A rcclor5j:B ;. divided iato two Porle b' il'c cuAr'e g-^r"
oe ehorn h Fb.,P-22e.u€trq #E knd$n bcoiion of t's conl'olt
of lhs lo{€,^ poei A oc aivon in loble vn-l' 6t'ow ltlot ttE cen-
hoij of lha uppec po"i B i. t(rolea WtB-/,iA\Eg"24^..6't o rhot c^ erAhbl^
-b- *n
. b(.rz)-b
r ^ . 6 4 4
/r&'\16rit/FD-*lr"=br' \-E{,1
bhn i, -)L-EL
= b."!nti;?b'h.
S r-a - b\,&'-r-o
16 _ lod2(e2)
#Bt'=bh("'4)-(*)D#}l'F-5"- b##r-*ilE".W
5. , h(nrwri .. l. .2rA7,o) A b@n hae lh6 oro€c eotion shos ,ir F9. P-%o,Cc'nFrle
fia moft€nl of o'€ of ihe sked Po.tion abo,t tha ho"iantol
an+rodor o'i. xo of lte *lire €e,lion. (flole , tt ic e-t'o.. i' 6llq-
€ht df -ol;ole llot th c E€.lte t. laa i^ cr'P'li'q J e n@-
x,itum cheonrg sr"esj.
138 r38
fiO r'(t), la)Ol g . 1i,|,tr...) |t(1\1)!j,(1\(o,).o, - i11
. g -o;7 in .
zW - 1(.)(7,e\ , (t\ @)O.cs)!.t/*.. 72,+ \nl
E.) Two 10 in.- 15.? ti chonnolc orc werded ioge{hdn os €h@n h
fu. P-7:1 . F;d lhe momeni of a"ea of the upre. dhonnel oboulthe ho.;o"lo j @^|rc;uJal oie rro of ihe o{rro ceul,o.
o@ ol roi^- E,e lb - a,ar i^'
2(aaa) 6 - a.+a(e+ rrc) ' +.+r G)e.9t5.67seG1
g- ,.86 i^
f F{s. p-72r. Rela lo Toble vl-z 0. +t? FoPe.+ies of the o.9t6sq b.-te,.!"e cntrcid ot t€ bu,n-up cal,;n
[e(i)r r(E) t 6,8 i.ft] 5 . €^n@!.') r (i4)t.)..,s(.-otu) r s,sGrs)
xa5 " ale.ra1s
t- & 'sa '^ '
enlrcid of lhe buill -up solion €,i,bn €hadn ;rto lobb vn-? ftn lhe popo',tic* of ltc ebrcnls.
tF ' 'E { 4 (o . ' ) , (+ ) j t . B ( . n . . - , . . , ) t . . , , (a* , . ^
| 6.Yo'Y6.r.) i/6dYo.')
27.7.s 5 = 462.4d
J - e,+e in
l:
ll
ri
7e6.) A riqhi t.io.gle of sldes b\h t6 rololed oboui ondxte
coinoid'ng wiih €i& h lo gerP.ola o righl cl'culo' c'r€ '
IA v ' ? r t . t na -Ar .kb- |Abr l
.,"1'\ 't = '/'rb'h
-,1ij""1*-*" -r-*ion6 l; the 6v.fo<,eio@ E vorume eene€iod b/ rololing o semic,rcle ol.odius . dboul ilq d;m'ie'
, kho u-or'4.^@of horr o,rcreuW _{.{ , r .+
..L v '+/er"'
r"l \ A=2t i L6alh of ("-e- lV - 2 t .2 / k . ' t .
I A - +r.'73e) .sfbw thdl the volure of o Porcboroid i€ eq@l 10 o€-hdll
{ha oiccumecn,brg oyllnden ,1-^., i A.J- l4 ' r \d, A; ' [ " r i ' . 1)a'
+r'.^,' .ft' ?):. ..J.:.th-"%id-/;-L'o. *"i:: #r: #'ft1i"o'.n,.{+" iq +. j,,j""tt_ " - '{;t
. _ ,., _.i- - i . A , 2^bh + ; .+_+
rPi --!PVfFbbdldd = dr ' i A t - *b
= Y r . l i . 4 b h{ 2 3
' t h b Q . h
7e.) Delamlncd {he vdluBe of the cllipsoid of ^€"dluiion qcro€-
l6d q rolotihq oo ellip6e obout o) .,te
mia'a'ic (c"olote ottrpaid)
I b) ik olnon oxis (oblaie etlipsoid . Toke the lo.e{ s@;o'h o. d
\ thu smoll+ semi-or-'s oe b.,7b" ' ' 'Z'
f .q" .G ' ' , )r > . " ' E
140t4l
At=C sba,)- f e"d,'f- okG'-t)"- ut.l", i'"1\
Yepune - st 4-A- "*.:+.+v =;fr"u.
- b/""|d - "% , ""
A4 .bTl l 4421"/f,
n . a b"r
to . '47b . '1 x?o. - 1 - t%". t ' ' o"/6" ( t" -5")
Ai - t"r,'a./ vdqre' l',"/v'(t'':')av_ "t/b,lbr. /%l:,. o ' /b ' [bt-b%$'-b%]
- " * 'F 'Pv - +ro,b
at . a74[+a)1]rcht "
+o'hi - 9
7ro) ,A oille of -a;,3t" t;'" 'r lhe xy prone witb rtc oaltr oio d,6+dn€ o obovc the x-o:is. Royolviig il oboul ih€ xoxiswill gene.ole o doughnul-shope ri.q aoiea a torus, poraeao '. 96al* thon.. Coopule th€ €urlo.e a,b q votume of
,a1) A 6a' ptpe eibow ho6 on inlenot diome+.f, oa 4 in. lAe .odof cu.votu€ of ihe pipei oontrt,re ie ain. F,nd +he inlqnot wl.
v.Atuo x hrrcid rd6io"* +"..*ed . t(4)4 - 6 _ (er' "r/.d;)V = 7€.e6 ih :
7ar.) n;d lha yol!rc of thc Ephedc,l wedqe fo.ned ,y.rlolidl
lhrough oh ongle of .6' o cemici.ole of rodid r dboul ilc bos€
\/ -"rh, y?r -rv -_rc-
A -ah . ay i . f t aA -
't.,/ '
Iotot Lufh6 ^eo . \:
, 1,,
A'i +r."@.lo.e ole 5 volude 96€^cled br rclot;ngFg. p-7€ th.ough one bolulid. oba/l l6cx.ot;
4 a t s ' n
. v . 2 r . 6 t e . 2 ( 2 1 . s 6 . )'
v . 1 6 6 7 i . t
th\+ ,t a.[f lF t 'rC)(#L,4' ,@ t 2({r;t o"cs..+)
|'fltf, *l t . " t +tt4?, 4, ̂ l+.11,q l21.E6.9 - t32 132
,t-
az. t \ - 1sd e6
! - e't'" -
?i+) The rim of o pulle/ hos lho cros6 s@lion shdh h Fiq. p-74-l
,f. tP.T i:
6odo ar st@t wc;\ehiry aeotb p.. - fi. i**f--t"e }h.{.ishi df the Flm ,
14,n, (., ;1)7 4, a(a\(.L), (!+2\(+- /a)11.e 1 . 18.5
! . 1 . 6 1 i ^ -V . 2 T . ( 1 t r c ) . 1 1 . .
V. o,aess l l 'W . o.ages <asa)W = ztB lb.
t42 143
z,+!) Tl€ oreo con.loined tEiween h^jo ocicenldc €€oioil.cte6of roal l t .s; t t q. ;n. iG .ofor€d obout clr lo: ,s +rn.owou,i \porallel- lo lhe boee diooele.s oF tte eemio,ote*. Co."putJlhe surlooe orco 1,) vot vhe geoeroled bg o complole re,olu-l@n
, l thk' '+)f q ' u,!)t l(Q1 r/-/ taYfa^.d1
16-6oa t ' 1A - a.25to,6oig - 1s.75
. t - 1 a s s ; n .V - 2I . (1.+se 14). 1o,6e.z
246) Dolerdn€ lhc €u"lo@ olg B votume qe@Folcd by o cofrptresul,bn oboul lhe r ori€ ot the €hode, oreo of ptub7is.
t ' o ,n t = ! i n
A - 2r. s.a1. (1, * | F;A , ,V;e)
z+) 6-p"le lh. €u.jo@ o.e \,.i"ffi ge@rcte<) b/ o @mplete@olullon ob,rl tha x or,c of lhe 6hoded ow of prco. ttt
3 -5 .oe , i .
\t .2r. E.os l+.s(dt t/z(c)h.d v@4/+l
v - 779.e2 ;n?
A= 2' g. tangth ol c;N,rtvibina ArcaA- 2v.3.erf a( 'N t e r. ' 6., "; lA = as2.sz i.:
r fo" t6elh
J' , . , rp. , . r" , , - : l t " 6.- , . . - t " . " , , , 5; ; , ( t+\ l yr, . )+ t t )4(6 : t : )a )
19,Be7 E - 7e,,2s
.5 =3'e+ ia.
7si.) gctenmine tho crntnoid of o hemisplrerc of mdrus n' tc-
hing lhe otis of egmmetng os lhe z oxr€'
$' '"1*f1 ' r
zar) A u.ifo"o wirc is bal in'lo lha shope €ho{n in F€ p-76?
The cleoishl s"4@ols lio in |ho x-z Plo(6' \ thc. e.in l4elh
rnar.a o" o"qtce of 30' wilh the r orjs. The .enic'"culo' s"g-
menls is in thc x-Y Pldne Locdte tho oool€' of sE;'lv af lhe w''c
(e *rrdre)r = r(+)(+)r s(er+@'o)2..s4t = t4r'elo
i -c .5+ in .
;r65€ag " r G\(+)' e6,s6c g =32
g' 1 20+ in '
26,s662' . ( ! ) + e(aetn3a' )
! 26,66.2 - 3+
z - r 2 a h .
7e+) tocote the ce.i- ol g6wiis of o st€ol .ivet hovinq o cg-
I'hd.icol bodg I in in d;onclo. b 2 in long wilh o hcnispr'e"riol
hcod of 1 in ,bdiue. Uso lhe.6ur l o f Prob 7s1
ae) A bodg codsi6+s of o nqht ci.oulo. aonc whoe ba6o i612 h.
\ who€e ollitudo i6 16 in A hole s in. in d,bncle/- h a ;n. de.p
ocq a"iled fiom {ho bose lho o.is of lLe lbl" co'rcidog -/ thc
o.i6 of lhe aoe. Locnle +he (gfroid of lho el volume. Uee lhe
tusuli of P.ob. ,{€.
. " . ^ r . ?t l r ' : - r l - I - - - l
144t45
F/" @.(n)-t (.ft4-17 - \/{.ftdlu*r.o1-[<*t Gy-",1.'2-127 - ++4..2c
i. -11 it. frcm opa
7!6) Dol..ninc tlE hciqht i of lhc cgtindc. mountcd on lheh€mi6ph6.icol bo€e s*'6^n in hb.P-7s6.Eo lhol the conDasileDodg w;lf be h sloblc equilihium on ils bose. flinl: y',e tongos lhe ccnlor of groJlg doos nol lio obovc the I-x plonolh6r€' will ori€f o rcslonhg couptd whon th6 dq ;6 l;ppcd .
r("/h(h/) -\trGfW4a)h' - 2b't
h = r.4l+ fl.
?s,.) Fcpaol Ptub- 7s6 if lho cyl;d"bol porlion of tho bodqin l lq.p-t !6 G raptocad W o r,qhl . t \ t :cot po. l ,o. * i lh o2 ft rodiuG bose q oll'tude h.
A ,\+/
7se) sleel ball ;6 dountod o" l,,p ol o Lrnbor c,rtincre. osshovh in rig. p-zso Sleot woighs +eo b po.or n q timtc. *o,qh,
h " A = +
h - 3 + 6 4 f ! .
1oo lb po. c, ft. D6le..mino lho pos,lion of 'ho ocnlo. ol qovi
lk efh(v) - 4//0f(//@)
w,ra a"rr fv: r (+r", dLJf Gx "yrr"1
wti"bd" - [r (sr^, lyp^)'(ra^" *\(60 tbhf)
Wr = tog.o9 hi
(rc.o2 +te.oa)g = rc.oz(zet /1e) t ta.6s(p x /z)1a5.1 g = 2a6.$
3 = r.es fi frum boso
Choptor a
Momon{s of lnoilio
t46 r47
So4) D€le.mir€ lh3 rnorEnl of irE.lio of o tdlo.Bte of bose b\ olhiude h wilh rospcd bon o.i. ihrough the oper porollelto the bose . Uce the lrsneG. lcrmulo \ th€, rBarll€ of ilto€ .P(& soz.
l"- bh'/$t = 7r ' Ad' ' bh/r6 | bh/, (zbh)a
' bv?/& t 2brP/s1 - br?/4
60!) Def6.d,he the norcol of inerlio of lhe guoder onljtein FIg. P.8d9 r,lh r€.p€., to th€ g,sn orc6.
tt J- lp.d^
DY*']P1 r- f,-r(4/.dil/r \, . L+/'4p. r. +/.)" +".
j ' i ' r i , ' r '76 ' 1, +1,r, . t .V61r - n../.a
8od Dete.n;B lhe dorenl of in€rtio of the €ed€Fcte,h Fig p-ooq with rB6pc.l io thd q;6n ot€c.
1. -- ! red{.gfy '^"vyaoay
= f, l' /o2 ̂ "+ae=
[ P/* k-,ed.)];1" ./a C a.'ede
. r./a C y. r.coe,6)do , t%re - s^,e/a:. r'/. f(l-o) - k'"ry - qho],7
I' " ar/6I ' ' I " a a
ry.J;l:p'.nbldeal .f t: p'dp.e\-de . ( *+(cs.+aelJi. li ,./, (^,.*ae) - fl+ !: h,e.d de- "/o lc _ aAe]l. e 1e frt-ot - (qstr - ao\1
I/ . trTo
I
€o7) Sho"v the momenl of ine'tia ofo s€nicircb of rodi'Js r
rr 'IJ
is orira with respecl to o ceo{roidol o)'i6 pomllel lo the dbd'etgn
r-. i , rAd? - rc' . I ' + nr'- /rr-\ '--z --u-'\3{ '
o.921ra ' ir I o 26Lg4(+
i, ' o.\og76ra * ot1ra
€oa) Detcdnir€ tho momenl of rnerl'b fo" lhe qr'roclercircle
sho{n in Fb p-8os wilh respecl to o cenlrorldal X-oxts
#= t " * ( * f01 3t-7r + 0.11147 r1
It = oo549r+ = oo55 14
s€e) Dele.-irE tfc mo6€nl of iner{ro with 'especl
foc lhe o,.e.a e.eb.€d b,/ the s{iPse *hoee e4"olioi " 4 , + , ,,l,lec deler-i"e the@iis ca gyrclio"
4 . * ' ' - " ' - l ' " & 7 d, , - "toV1;
, ' i ,-Jy,d^ =J./.ardyi,. +f,f (otow ) at
Y _bene b= b6'r'e
. dY'b.ae€de e 'e4 - a- '7 /2
\-+f b".ie @/b) (b'- b'"."4) a b co'€- dd
= +fh o'o " a"+<'x"ede- is (' 'r"a ,*n)ca\(, , cx*"")l ae. ab. l / ( t , ex.,e)da
ob, l"' (t - lr(-. ' .66,t de ob" Le ek - 4^'a/s1:
- "6ii-p - ""*761!" = ob'5B./+ o)-6n'?!-5nolol
?,.p- =Y1t14"aiy.r atf "
t , , ' (bZ) ' - b /L
148 149
sla) D6{em,ne the morunt ol ine.lio \ the redius ofg7.otioa,Vrespe.ct to he Y ore, of the oneo cL,l f"om lhe first q"oaront b'{he curue y . +-r! where i \ y ore in in.h6
r - / "Cfd^ t d . rd ,. . t , . t*rd, - f t ' "X"*) a"
rf6r"-,.4)d"
\'La'(A- f/A:+(4t'\e-of - (,-o)'/4
t - 32/s - t2/ /e - 16o- = S*- '+^'frd, .tr'(..")diA 4+t - t'h l-^ -iy<*a :t -ttl
' 8 's / - - - 2+ '6 ' LAinr
t = -(oa) . a >
\ - ("/^)'h
o11.) Dele.mine
:.,t.1W4,V6.h) =f,6ihe mmenl of nealo w/ r€sp€ol lo the x ax,sPoroLlrlo q8o shadn in Fi9.P'€11.
I , -{ faa d^- (a-t \ar ; t -x1" *=x1r"' t / 'G-"/sr ' )d ' t -o/b'r ' .a/b'
. ('6v'- &'(t') ) ati,'[;;1 - "/t('%t .[2,<"-r" [+utfiuoll
. 1r. oF/" - ob% - "b%"(s-e) . 2ob/ase.2) De+smt^e the I/ O. the €hadeJ pa@Wrttc otta of fig.p-o11.
rf ' l , .dA
L l - \ t ' b l 4 o d t
'f, ott cu o,.fo/.a rt,y'n!- (26\o/1") (o_ o),h. z/, (b/.td)G,e)
'r./ - (E.Ydb) - 2osbl
8'lo) A rEologle 'e 3in. h5in. Do€nnina *tr poLcn rtrnanl
of irF,r.tio \ firc mdiue of gTroiion *,lh r*gccl lo o poldr Q(i'
throvgh ona dner
l- r,=!, rAdr-f/,///) t. - Iv+Ad''V,/)
,|'*l +.('xe)t ' ar6 n1P 1 2
I/ - qFf + 6(!)( 5F ' sa inl
- 216+9+ -270in1
^ . F 6 . - , @ f f i - 3 . 6 a i nsrz) Deteffine +hc .romcnl of ins"l,;, \ rod,us of g/rat'bn wrth
reepeci too poloc ceolrodol oxrs of lhe o.gss eclion ofo l'rol_
lo, lubs who€d ou{sde dio.nols i6 6 in q ln.ide diomele' it'+1
@;f. ,.,,::;f"it*A'v+Q.'-df)
.t/+(eo-+;) i - t/zGa'-t)
A.]E,r1\n J - r/2(ta-aa) - 1o2i 'n.a
* ' 6 - - @Fn
=zss ' ^ '
8rs) A hollo{ squorE o.l,€6 6a.}'on cdltsist6 oF oo 8in squarc
fro.n rhich i5 Eubt.oct€a o con -nl-1.c,J,lll PlcrB cqlat'e 4inbf'+'r'
F;^d llp @. na.neal of inerf ;o ,\ the @a" rodius of grrclion
*ilh reEpeol lo o z oi,6 Po*iig lhrpugh one of lho q4e'ile oomers
1" = i r,^d'
Ii, -gg!* 6(o)(+t = r?65 rthlr, - iZq)". e(exat= rsee 33 in:l
I .Ix. llr, = 13es.a3
I.^. 4G)' + 4(i?rjF 272.33i^+
r; - .-a-f * +G)u+")' = 27733 n', . 7
r\34s,93. 2730.66 ir.1
^'w-' Jvn
K : 6,73 in .
Jz " 7rttlv. = at,g +zttA "ss+,ee'n1
h 'J.-Jz - 2730,6c-5!ta,6c '21'6n1
150 l6 l
6i9) DaLrrnine the monE 'l of ir€plio cf lhe T- 6eolion shdMi^ Fb.p'8@ d/ (f,,rc'i +o 'lc cenlddol oxi.
s7 . L(6X2r1) t .<o)<i)
i' - 4Ol | ,(6X..'r'4&f ,z<ox..!).
1, - 2so,6, in!
82o) Oelcmine the rrc nenl 6,f irrorlio of thc oreo etrorn in
nI I
rr ---f
li.r@Ya).3an'.
Ar = 6( l ) r {2(r ) t€(r ) = !o in?
et - 4z(i.)(o,e) + 12(1)(1) | 66Jh3.r)
i, = a{;)' * r2G)t'.z)a + ilgt + i6)(1.o'),
+ jgf I c61.s),
t,, _ ess.e inj\ '!4t t !9t + kE - rca in!
12 12 l2
e21.) F;M |te dD.nenl af, irerlio oboui lh€ irdica+ed x oricfon the shoaed orEo sho{n in Fig.p-62r. \
I i . i x r ^ d ?
r" '+9". 06oX5)" ' 2er,6 67 i'!
_, I'" . o,l (+la r n1+f(o' 1g))2 . oao.sz nl
- - - f -
e24 F,nd |he <lJnlra,dols'ha*n ;. Fig.P'922.
2666,az - trco.6a . 90c11 in1morcnls c,f ine.lia of lhe lrapczzid
^t .tut6)(6/z) - 72 na
i' -lgf , 'rzcaxoxo.Sz + eg3+ 6&)(a,s)'
t " = 19g ; . '
lil$i.iiHfii
iliiiII
i
8zd An aquiloh'ol t iongle hos ile bqso b ho''tonlol- srx
thai ltp centcot&l rornenl cf ire"lir x'lh 'espocl tot'o'i-
h.JE-(&Y - ds6hi,. b(ae6bf - ru+.lo-'ba
,'449', " ryrtwf = +eo+''rieb+
oea) C.actprtr- lt'e n'a'srl of rls-lb *ilh reepcci roan ox;e
pascir€ fh'ough i*o opPo€ilc o?crcs cf o .q'W tetqrl
6 s;de o.o-- aao/6 - G.,. e.o- b/o
tq?o -@cVt b-,y'2<a)
Y.E :6hvhui\y!x\11!\irz h - a L / 2
t - of* (ott/z)7z +
7b. ,z.sG)t r n-t(.)(a)2 , s@i^'
l'.- 12sG)a I y. (i2"61(6t(vt.6f - 22!. i,f.
,4p;sqon,tfJ+42
r- dr ' th t oa!a/* -sj 'o+
ezd Caipule lhe morrp-nl of ire.t;a of lhcroh.b,.l;n ruo-
torqb €t'osr n FiT.P-Bzs oboul the x a''.- lo whrbh rl is
;nctird d 61 @sb-o . sn41/s- Hinl: R66o[,e the ffgur€hlo porl6 A,B. lq C.
\-; ' f tu\$r1=ph"'-v" ":."';,1,,-^'\/smi.fi' = 12.5 h.
cos 25.e7' . h,/A
h=c. .36-sr(1J ' t=61n.
t52 163
ib- 12.5GP I h(i2,5J&)(6 t 1b.6)2 - 2a7s in!
i1 - L^r i ," .7 'c - 2ar6 +22s+ g& - 3coo ir i :
er25.) lt|c cross seclon strown h. Fig.P-o26 i6 thoi ofo 6ttuEf maobcr Nr'"wn os a z Eeclior,. Dctermine the yaluas
L - e(i. 'aa') i- a/+G.f ,l:..o/af F 'G,/+\(a..8)'I2_T- -"1-
7, = z(1' + ̂ d')- lerfut t t*,!Pt + a/ae.s)(1't$ '72
ir ' rs-+r in_aA'+5(vd+f35(a4)'12 " 8.62s \n?
o2z) Thc bull up selion ct|or,/n v\ Fig. P-s27 is conwsd ol
fio Ar6ri in- dgle€ .i',elod lo o l2)r1in. web pldle. DeLmifttthe rnarEni of inc.lid vrith rospc.l to ihc cenlroidol X orie.
Ar-f.(r)is(rt2+r2(.r) " 3s in:
a$1 - i2ttk) rle6r0t.e) t s(1)(s,5il2| = I .s f n .
f$ax.szl'Jz ,l.r?' | 1GJ@'a1)'-l2
b. a1€;'c+n.1
U.ins Tobla vllFz Propc.ti6. of St.rralral Seoli.ie
o ' r . " r ' : i , - r 6 . a h a ' i - i . 6 E ' n . i A . r 3 ' n :
i, = l39E I r.<i)Qc,)'z ,lt6.o + 11h3e)if 2&
1' . :z.6.s, mla29.) l*o Qnt. ra7 tb ch.I1(fili arc lallic.-d logdhc. lo forrnllE 6cclt:cr €hom i^ F;q.p-s2a. Del"-r,^ir.€ how for oporl lhcchonrefs shajd & plc,<pd a oe to more L eguol tolv fo"thc eccfri:n. (liosl6t lhc lollicc bo.s which ore rirdicalcd b/lhe doeh€d linee .)
I ! .=( t +Ad' )= 1G2\t rr2(1YLsll I-T
o f L \ I r .
irir!
i
Flld Tobla vrrl_z
Prqc. of slrucluEl A.olys;s
GEher S,ze Areo i, L t te'2on 6ot 12s13,9o:r o
I x ' f i A d '
L -(12a.tr2
1, "fes t aa@/a + ot)'f zi " = i ,€a.rfal -\.[s.s +sos (d/z . o.r)'f
d? 1 ,co tn
a2s.) Del..r.'it-F- fhe dslonce d ol whrch the two s in. tsin. r€c-tongr4 shown n t iqP-s2s should be spaced sol |E/, i , -T,.
I , , -t ' .Ad. r [39! , '<a>@)12 . i ,
L-Lt^d. l f63t! aG)@/211,s)' f z - i ,
i, . i, ; [:-<er'' oj ', -[QG)" + s^@h t t|)'f\
t2o = 1B | 2a<d/2 t1,r),
d '1.29 i '
83o.) TIE aho.l tege of fou" 6 b./ 1br./2 i^. ongles orc <.nnecledlo o *b plole P h io by sl6n. to fo.rn thc plole 8t ongle si.doFEha6 ,n Fig P-e3o Chpdtc rho o,ue of i,.
i'12'..
i" ' 5/'6.k3 sf .l s15., e<."t<,t,sfl+ ,To.5(!.e)! r 0.6(r.5)cc.Ef la
1'-tur*;TU6hq Toble vnl-Z p'ope.iie9 of clruclutul soct'bn€6 t4/ t/. i A@ _ 4rE inl
i , . o . a ' n ' t n i r 1 z + ' a + : t . d e e ' \ t " 1 . e e i ri, ' [e,: t+,rs(r.oo'.J+ !{'/1GGzs)')/12i, ' zaa.as tn?
€€r,) A plale x\ odgle coluhn \c conpoed ofou.ebr46/l in-on9le6 w,lh lhe sho.l l€gs connccled lo o web plof€ 1a in by 1:.plu6 two flongs plo{es coch {g;n W 2r.;n.E 6lb*^ in Fia.p,gsi.
154
Dclo.minc lho voluog of
i, - 19?a +lel;49-" ' | $A.zs\(e.tsl'f z '
- leii;I. 6Gtd,.*ry ,FS8, .(,)(. E)l a
t, . t$tt1, tz,z-g4atlz +ILQ]E + rax+.rl+t l<P+ B(rX,)._l,r
17 - *te.ee th-tU6ihg Tobb v r-. P.opc.ia. of sh,,ctu.ol s&tion€
s;{'i" : A'€o . fi ,i1 ii, = 11:6 F tlr. 6s.6 ina j r. 3,aE i. \i.. i.os i.t"'fit*llJla tla1.6 | nG.2)Ia +k6?.25)z)lz | .ts(2.26)(s."1e)e72
i, - 7661,ag-n!i, - f*G>iJy'z t fcec t tG'r"'l+ ,E z.reOB)aU| @)
1t ' 3oz1.1in!a3?.) D€lc.miie thc cdnt.oidol homenls of iicFtio of lfre bJrll *
up colurnn seclion sho{n in Fig p-6a2.Il ii cd p$d of {wo ro',r'ptotc5 nvcled lo f,o 121^ 2o;1tb clbn]dla.
F.Drn Tobte vttF? Prcpcrltc. dsi.!,cluml eation6
12'-47tb ! ANo - c.o3tr'. )1,.r2s1,1 r " 3 e i n J ' t . o q t . o T l n
-* 7' -Q.1(2) tW+ $d(6.s)'.f 2'!:'""o 1^ . $1o.s ,n
t, {.e,".ozO,fJz ,l<{l z11 ' 9s5's7 in:
siri) Fou.Z be.. eoch hovi.q ihe 6i2c \ p.opc.{i€s dclcmined lnprrb.026, o.€ nivot.d bo t2by 1in. plole to Ontr the scolionshown in FrS. p -433. Oeiemine th€ c€nlroidol mornenls of rnertio_
t, " (#P,ta?EE' uaG.'r(1.2g)271 '
l2E{?t!X | 4.4/d(s.625)'1" ,1_#d ,3/+(..syn)zl+
L . 12sr.3E i^l
\ = .24)x tr3.slt:/a.t3 | 3..(s/iG.61')zf +t ls#EJJ, !/. (* i) (+,)'1., | *ga,'
l
l
I
1
l
I z /1(e.sJ(612d' l+ - i r - ss1.6 in:
ar4.) n rcin.larlb chonncl is Yicldcd 1o lhe loP of o 14wF 34
beam oc sharzi rn Fis.p-$+.T!c *ide flohqe beom fros on a'cr-
ofl hcigh'l of r+i.. onofto ol nqt in?. \1, of 339'2 ini Conpule
7 q the nodrenl of rirertio obo.,l lfr ccnlrpidal x oxrs '
Fi@ Ioble vDr-a pEpe.hee ol s1.lEluml &cli
ro'-re,!lb l,r wF
Arco.4.4zt^L h- 14rn-
1,=6c,6n1U-l./'a.1inl ArEo'loino
i
Ar '1or41t - 1147ir '
Far, ' 1o(1) + a +7(13 6)
t ' g o + i ^1, - z.a + +.+z(+ ce)t t ae2 t 1o(2a4)2
ar = a6.dt ;na
s35) T*o {oin re.3lb chonsls o.€ @lded iogelt€r oe 6hoxn in FB.
P-€3s. Cornpute tlle olucs of l' 6. o.ranqen'en+s6) \(b) Eoch
ctrnnel wcb ia.6za in. lhichF.or. Toblc Vlll-2 ro'_'i5,3lt)
Afto ' a a' ' .2 )1r ' 2.na t^J, = 66.9i .at - o.6a;^. \7 " o
N7 -zAr - 14r(2)7 - aa7(e)r a a'(e 6)
7 ' 7 3 \ ^1r = 66.s + 44] A.3) ' +23|aa7(2.1)2
7r ' 116'4 ia
2(44a)7 = 4.4"(s) | 4.+1(a.6a)
t - 7.82 \^
i, - ea.e + +.+z(z aaz t 23 1 a +1(2 e2)2
I" = ro9 in1
o6],) gl u6ths lhe +onefer ardulo q the .cEult ol prcb. sqde-
tcrrnine the morcnl ol inc"iio ofo homoqencous .ighl circu -
lclr c-/liadcr obcut on o'i6 lhroosh on elemeni on ifs e,Jrf;ce.'lhe
cyl,nder hoc o.noss M \ o rod'ue r
r
t57
I = ./z Mr.
&5) By leinq fhe lmnsfitr lormulo g. ihs ree,rll of prob 862'
dcld.minc the momenl ofincrtio ofo homogeneare spherc of
mos€ M \ rodius . $lh rcspeo+ lo o lo'rgeoll . f i r a t t t ' d a
7 ' 7/e rkL
e66.) W 'JEinl tlie l.onsfc. forflulo \ the resull ol Prcb s63. de-te.diie the rnomenl ofinerlio ofo rod wllh r€specl loonoli€through lhe cenler of goviiy peependiculor 1o the .od
F--- I = , h M L 2
t - i ! t4d2
hML' . - - i 4 r ,4 (L t . )z
i-r]!t
ase) By usinq the tronslb. lormulo h ihe resuli oa prob s6l'dc-
ierhine ihe monenl of inerfio of {fe rectongulor ponallelepiped
stlown in Fiq. a-2e wiih @cpccl lo o aedion lme oflhe z face-lo.c l\c d€d'oa li.c poro.bl lo the ,i orig
.' _ Mb, I cz)(r12) +M1chf= 1/12 VG' I c.) r 1/a vc.
I = Uz t^(b. r 4c'z)
s6e) Dcle;ine {he md"Enl of 'her'iio of the |^%tohgulor po.ellel-
eop€d chodr in Fi9.P_€6s o. F,9 s_29 w]{h lesp€cl to o^ or,e [email protected]
6e slP r.rolbl lo lhe Yorisr " M6, 1 Mdz = r1, M(o.i.,) t M<o/2), | (c/r),
. u, M(o,+c"\ + Mlr@. I c/.f:]'- U, M(o"&') | M(o7a + cYa)
r - % M(o'&'1)
gr2) DclcFmina lh6 rno.r'cnl ol inortio o{'o holbw 6t.ol cyliwith rcEpert b ils georneiric orie. Tho 6yl'hde. i6 r{1 long q hoc
on wlddo dioaelcr of sfl q on in6ide diomeler ol2fl. 9lcclv/ebh6 ato lb p€r fli
v.r(i.!'-i')(r) - 3.e2t ll!w -.9orblfl. (v)
-qob4 Gs27 X,
M " I Vv,'rRrh - mi -brR'h
Vr -lfrrh - ftr = lrr'h
w - 1924.23 lb
r. /z M (R' rrr) . tu\*e)ltt sf ' <,11
' I - g z n l l t b - s c c '
s7r) By ugrng +hc melhod d,icuc.cd in pr€b. sTor delc.hii€ lhenloli€nt of ir€rlia, with r€spsct lo lhe qeordc|c oxie , olo c./li/]-d6. of mdia. R liom lhich is d.ille, o conoenl.ic hole ol ra-diuc r. Oer.ole lhe n a6s of the rca,l+i.g hollo./ cyliaCc. by M '\ +he r''as€ porunil volqme by Y.
t,r \q mi for th, cvl'ndar(. \ .n ',.' -, ro. n r'4"\'P-" r"'a "o'
M-dv -e'
t - Yrlm, f -mcr']
M-Erh(R'-.i) : r', fErR'h(C) -Irr"h ('.'!. ,t b,rh I Ra _r.]
, = Y2 Erh <R'-r'\(?'+r')' ' \/ |M(e'+r',
elO A 6b.dcr rcd 6{1 long n lolcs about on o>,rg perpendictoil ot o@rnt z ft . lrwn one end . 'Ihe rod y.€i9h6 !alb. C.oinpul€thc mor.'€.{ of rne,.tio obou{ lfrc orie of rololion.
F.+'+-! --,1F d-Ktb. i . y ' r , MLt
uz(%ez z)(e') +(ao/zz z\(1llJ " +.97 ft -lb-s..'
€7s.) For o houo* cost-iron sfifi. ol 2p in oulsdc dio.ncle"\16 in inside diornete.. 6smpule fhc morr,enl of incdio q lherodiu€ ol g./.otrbn w,lh rl:6pocl lo o drbrnct€l.. Co€l tronv.ebh6 .€o lb per cu.{l.
6iven: tr6.2O'.'. R=1oin. w - aso b/llap; .16". . . y, . g in
158 159
u'%F:9I * .l.,a" n.,.N . 4e tb/frd (tra1 ,O = rrr2,as tb
f - Ma"=va@zgs)l@fiX
a2.2 | t42) J
I . 6.2 f1-lb-s6c.
K- wfr- 162 (111)(22,2 )
' R ? Z t s i n .
e7s) O€lc.m;ne lhc rronEnl ol inc.lto of lhc coct -iro.r fty*frect5t!6^n in Frir. P-o7s wilh rqepocl lo thc oxie of mlolion. Thehoe sir elliptr'oal spokc6, 3ra il |n crosg gection .,vhich mo7 be on-Erd6.ed os €l€Fdo. nodr. O6l iron v..rghe .tso tb pcrcu.fl.
w.-Er(R!-r .)L j r imwh =Er(R.-r ' ) ! r hubWs . drobL ; ftf, on€ epotesxf Qgla(v.-ze.) tz = tlss.ge tb.
r'tb .8gE(s2 -2a) I . .'\-aatb.
.
ij
ilII
I
w3 . G94f.(r.5X2)(23) = 56..4e lb.1725
L = y2 rn(t . tra)- * (aaze,hz. z)[*' + z d)l*)
1. = 2a6.9 l1-v>-sa.2Ih -12 M(e.|r . )
- Y2(32 ah2.z)l(s\ 2'Y 1allh = a+29e fl-lb-seca
I s - n ( l r M d ' )"^(! / , .Mr ' + Md.\" e lt^ z(sc,. +s7t z. z)(ttTrrf + @ a.+y32.zl @,e1Q' f
I5 = €,n fl-lb-eeci
' 2O6.e + o+29e1 a3,11.I * 230.3+ fl,lb _5€c2
Cl' 'opIar 10
Rcc{ilincor Tron€lolion
160 l6 t
roor) O'j a ccntoin slrctch of .trsch, tr.ihs cun oi oomoh. HorfoF boch 01- o €toppcd l.on shoutd o qo.ninq taryado ba r,tog,Jlo cignol on on coming t.oin ? Assurno thot lho brakes o.o oD-pliod ol once \ Etord thc lroih ot tho unilbrm rola ol'efl poreool
\I' W " 2ae , to - @}EBg- eslvsc.
-Ee'. -2(2)s
s = 1936 fl o. 0.367 mi .lhrewn vorlicoll/ upwo.d q rctums to oo.lh ilils niiiol vobolly q how high dij it qo?
\o. -e.a1(10) - ee,1 n/s
-vo - -32.174(1o) = 321.14 f1/ss-r rgIa = hb.s1\Qo) ' - 4o6.sm. ts - '/e gI' " h G2!7a)(1a)2 - $oe:t fl .
rcoa.) A boll i€ d.oppcd lrorn tho top ofo lowor soft high otsomo ihsionl ihot o socond boll i€ lhmwn upwo.d i..om +ho qr€wilh on inilbl voloolty of .ao fl/scc. whon \ Whor€ cb {hcy poss,g- with whol .6lolivo v6loo+y ?
!. vo.t , Jrqf - aI-h(rz.a)t ' . - . . -O
h - 6o-t6rt . - -@
8o - Jb'r{ = aoI - y2 ba,2r{"
h= €0-{€.1(2)4 . 15 '6 f rcn lho bodoms'= 60-15.6 - 6aa fls ihe top
vh = ao - 32-. (2) = - z+.< f\/"oovf1 - 3a.2Q) - c+.+ (t/.e,
Y " d4.4 - 24.+ - 1o fl/soc.
rIrl
rG) A dds ; l'.r,rp6d do'i| o riol \ 5d: loio' |lb 6oud
of $E splocf ; L.rd |f $r olottfr d soro ''G
r@ eI wt'6..' '
*|ul j. lho d@lh d lta"/G[ ?
ti = fi.c trtrbdorl3 bdlfPod
t^-t _ ud G. i{'odtd lobo hcotdiE Gdtd d =!st-
Crn.=r-- a=fg6 a=:F,,o(s-h)-@d'h(!,''dh'
dr(s ta) : rGr t t
@-flrolr'rjuiErSd-L E+ rd' d \- as66&
d= i6r({ €er5)'- as.3l ll.
i.d ffrT@l g.&- |6 if ftlosd'rd of, |lb +b6h ''€
lE'd dfid'
6- rro(+-r.) ---@
a&4trtdt r lor:
l@(+-ln-, - r64t '
,rrao - tnzol. _ re-r lt'
E' q.E*44i6 trq \= -b 1lF ..e r@ qDl \ -47 € / ' '
' , a
d= r."tb$a)2 = 23r-6. [1-
16r) A slFn o'uppoa Gbn o ood;io bo$dr at on oredftdr of
,* il L* ."*"r' !.r'Xd ofaltla'€16€ ic F'dl66tad 'dl;@[Y uP
rod 6@ 116 $o nd *-$i Jc&rdi'IY of 24€ ft Pr e' lf g-k ez
fl F €'" -fcn" \".se"6 *i$ ilio6la@6s F* "-*' dto'
\b . = zaa|@n-l"er.fi
" rd6-h = Jt (")t'
g-zen^!-.' h- $'a-raL' -'"-@
i- *' n-**t'L. h- 8 st|'X- v'(a47(r 42
i-z't ;rc h. w au"lvp h= 24'6t 4t* -1&r'r6F;t- '+- '-@
tw *{= z+at aa. $ta raL ca
€6o, = sr21*.'5s6- ;h=rd6o t6(5)a = @ ll.
d'12 dt i ' Y,(6L2)\ '
l6s 163
ioo€) A stono is lh.orn vorlicolly upwo.d flh iho qmund wilho voloc'l) of +s r fl par soc. Ono eo<.nd totd. oortor stmo ielhro{a v6rt,@lly Dpdond wilh o v6tocit/ of e6.6 fl ponso". Howfo. obovo fr6m lho grcund will €tooo bo of thosono l6vot 2
L. tioo f6. tho ict€tooo ae.3t-pi/. 12}.dl,!6.da ' n21t r - !,8 fb. tL 2".t etdt 112.7 = 6.'' L
tA. lho 1.1 sl@o L - ra soa.
h = +€.i (1,+) - j 6.1 (1 .a) ?
h = i6 -o6a f l
h- a.3t - 12G2.2)r,h ' 1 s . B t - { 6 . r t z , - @
h' s6,411) - rc,.1(t 1)'h ' 96.6t -96.6 -16.1t . t 32.21-16.1
h ' M 6 . a L - M n L a , n 2 . 7 - . . - @
iooe.) A bon i< shol vcriicolty rnlo tho oir oI o lataoi+y ol 1s3,2ft wr 6@ Aflor +3cc, orciho. botl i6 6hdl yo.t,oolt/ tdto tho d1.Whol lnilrol yoloo,ty mlet |ho 2nd bdi havo ia ordo. to nool lhofirEt boll i66.+ ft tlon tho grcund i
3e6.4. \a (s}s+,4) , 16 1 ( e.4r4-4)2'Ja . $e . 6e fl /eac
too. Y,6a,e) Ot.na - L')"2<n. 1.1\(n.f tb)z z(zf tat) - t , " l
87 qlodbf;c L. 1?.$e 6a. 212.. +7s6.1e s* asr, a %j I, 2
9 ' . D : 4 s 5 6 " s a s s s 4 s t , 1 1 6 1 t i "
t ' 1 4 + 6 d d s / q u o d m l i a r N g a \ , 1 , 8 , e 6 6 . . .
t - Limo li)r fhc rsl boilt-a = l,mo Ln tho 2.d bolJ
3*.+. 153,2 t 16,1L2
Ey luodtutic Et t = sa6+ b..l - 2,sj6 s.a
p1a) A sto.a ]E thrr*n vr.licolly up f.!n +ho gtu"nd wrlh ovolo_o;,ly ol ta>'|/ea tlow tonq musl 6o *dtt boFo.c drcps^q o sncslono [@ ]ho lap .f o 6cr, ld*e. ,f ]ho rwo sro^oc orc ro possooch olhor 2oo tl fmm tho top of tho io*cr :
.o11) /, Ehip boj^g louirhcd €lido€ down tho wo96 wtlh o con€ianloccolorclion .51rc lakos e €oo lo clido jho i"sl fooi. How long wisho tok! to €lido down tho v.o'le rl th;. longth i6 62E fl.,
roir.) An ollomob'l sto.t,;g f"om .6i spa.ns up to aoll pcrwnh o conslont o.a.la@lta^ al atl pa. s&,, tuns al ihis €pcod
c. I f l whon t . e 6- .s - '/e gL< - 12 ot2t . r z a G ) 2
.t o- o.o.12s fl/sq:
Foqtl , rcr. €p6d in hfh
\ distaooe tm€t o.tlhi6 lop apaad
ta- i . i
Gr-| - '/a (oa\%)(r2)
I - 2aasac n 3hi^ ,2aeaa.
n-u/'. o1, - v1 - etr
-v{ = -6t,
s'=vlta- 12 @r,.Sr .S . r9e - o , 5 h i i e
26tu - ry', vfL. +,tt\ - t4
o t;mo, L finol/ cdno. ld rc.si w'ith o docclorotion of sl\ por a:1E tho latot d;sloocE {raolcd i6 looo ft, fhd }hc lolol tima rcqU.oivon: vo =o soth:
d-.1V.2 \-en/e o' Bnl''::;"';:. ffi*ffiG+
o-.sft/sa vf-v, - ati40 -4 \ - t 4 - 1Ds@
ro4) A t.oin trovot. botwooh lwo €tot,b€ th nite od.r+ i^omlhihum iimo ofa6cc lf the trcin oc,elo^oloe !.t do&toE+o6ora fl pa. 6@" , slo.l froi rc61 oi ihc rai olalion ,\ ooming to o siopd It 2d elol;oq,wta, ;6 its morihum cpoed ;n mph / How ldngdoo6 ri iroyol o1 ihi6 fop 6pc€d ?6iven: d- ,/z h le a"ofl/.' sathl
tt - al eoc
Rrrid: tolot I;nc q- Y, 6)dq.- 26(r... ,t - s./ra _ s. . .aot,
v f _ v 6 ' _ o t 5- - { 0 - - 5 t e * + e - 6 e e
s!= a.l!,- v,6(6y = $oft .
i 9 + S 4 i S : * 1 e b
2tb I s. t 16o - ter * s2. e44 €+cao.4o t ,z -+ ,2=16e@.
T i - i j + t " + t r - 1 t t , 1 6 t 6 = 3 + s e .
164 166
4646 = rl (41-!L)
q, quodm{ic fomulo you eo{ vf - ,ao H/.b,, el - 66 4/s
rea ar go+ sa l1/186 fl/,$ " ElgsC " -4j19. ' eo -ph
2cao = avt vt'a
10rc) nb ou.iotubile mo.ng di o coneionf vclooily of +s fl ponccc po6€as o go6olrn€ .6lotion .
'lwo ea<.ds tqra, ohotho. oulo_
r l,i{e leavc€ }ho gosoli"" slotrbn ( occolomros ot thc congldnlnaio of eft ponsocz. tlow eoon w l iho c.cond ouror,obitc do._
6i$n I y1. +6f i /s €oth: \1=d/ t - 4st=d *aa ' 6 f t / s ' d - t / z o ( r 2 ) , * @
R.4A: tina atL - ,/a (G)(n ,+rr+)
ts t - ta _A ta19t . +,2 +,+
L4 1si t+ -o s / {uoarc} , ;t - r0,7e socI, " Biq _z = 16,1s 6ao .
1o!e) lhe not ion o{ o po, { ,o te ,c g ivon b/ tnc cquol ;o^ s.2t+_1'r 2l' wncr s € r. foci L t [email protected] (,onsaa iha "or,ee of v \Go
C ) r 6 t s - 2 t a - L % t 2 1 2 s . f t 1 ] d L " v = B t r - + r a tl 'ze"o oL
Roqa: vx\o \ t" 0/ ,6- eg: + +e) =zon/e
aL= o - , + t -+ ,4
a 'a+G)" - zJp-++ - ser+7"oto2o.)- A po.}]eb m6/c6 in o 6troigh+ hno ocoording to ihc tow6= t" - 1oi wham .thc€ ic i. f1 &-t in 6cconae.(o)Whon t-seocs,oomputc tho volocily.(b) fdrd rhc ovo. vctoot|/ du.ing +ho athso@ads. (c) wrE , rf,c po.i;ole ogain .._os to .e6t, wh;t is
-,te
6 ' v o n : . g - t 3 - . t o t R . q a : o ) v o l . b ) o v o v o t . , (c) oocorcrctio^
s o l h : ! 9 - v - 3 t ' - a odt = ts(5) ,_ao-e5t i
b )
c ) v = 3 t ' z - , + o 4 ! = o ' 6 t
- - 6 G 6 5 ' ) ' 2 1 s | f l / s c ' c 2
o = slz - 40 ot
| = 3 6 s 1 s d )
$22) Chc.A tho ore{oFG to lll!6 Prob io18 b/ the followrng nrc
thod r r ' ; , le on c lprccs ion rc lo l ;nq ' b- 'J '$ bv ouccoesi 'c
aifforcntiotion "n". ,n"v '1u' x|tfiFiV v- oa -ao^/Jfle +
h.'t^7,!1,57r3 conpu+e vB e- oa frth rhoso r€lohonc
lon Fr- - -'t6/./^ .ginc. vs ts doMwondVs = -v^{on+
xo+ho= zo ; | = { 'z; f + h_Y @
. = v " ( " a + h " \ r " 1 z , 4 t \ - 4 tdI , .tl
d:,=v^ -dr = vB$ =v" ip1e.- o"
whd'o s G in Fot *.v in foct P."f l por *r Flnd lho s-t ,v-t , 9\ o-t
t = o ; s ' o ; v ' 3FEgrd I s-t , v-[ ,qo-t
s==lo.s - *e:s,!eaE - z6,oo'e de
- y<\./;6. +r,a B6r)
* ##"& ri$ .iffi '/{(Hh{rt-q 6 = x d ^ t h " V a , ?
'.F1iz .{G1na"'/e -ts 6dYf4*e" = 6t1/.o" = le (iyJ-+,a' ,[ o" (o'\ ' /( ' tT,,x)" = 6c7 tt/s2
'd? iJ l l lo rcc l l l lnoo- , ' t : t 'o" o l o pai t 'c 'o F at 'aqb/ - ' ' te-e
€c.rhd. V\4pn t ro, seo\v'3
s r 9 - v - + ! ' = . l s r e _n9
166167
Aa -socad6- + 1'c -t 'r fe**r-ol
c" =&'-g)"
t v & = d e -.te -aE
- I ' | lE ,+ i l = t " c
t = t . ! {4t9 }qui _ ' = - 3 l t
r=€"+c"=l@-r"
e l l a = t * a - k
s , = z l 3 + _ L + 3 s = a t r z + r= 3
us = c(r9(tf +'t.s= r( .v)3 1r
x{-3 5 $ ! L + t
}rf(ts-r).{r = v{
rota Th6 .,olocilt ofo pd*kJa $odg olo'rq lt|o t 0'66 is do-
fii*d i"r=tt-+'2+6x $*Eo v'16 r f@l p6.6€6dtd \t( -13;
fcol- Cs'p,Xo li|o vd,6 of lho ooc'lcralm4 $tEd x:zfl'
d.a'. f-r"-4'+6r s.ilir: ,t=ei'-44ff + 6(.)r=a ,t= +Ftlw
Fsid: o vdv = adr
o =ydt/at
d Y d r - 3 " - a r + 6d{y'at __ zo = +<z) = a ftfe.
$-ti) Th6.4[ln of o Fr{rclo-re .!cfr6d hv l+6 '!nati.t! o-4t.
*}{,.a o is h fI ptq>a h t h 6.cor*- nl G Frse l*8t s-rll
\ v= z'pd"..c *ho t - t €6t' D6lctrlr|o +/r'D tulolirs*s bofrrc..r
{ \ i "s\ t ,Yr-6
.9 - | V- ' t - t
RoqA : Y-i, 6 i, v-<
s)tk: 6{/4L - 4' , t =4 : , c ' ' L2 ta
c=oril tL'1
' !=21- ' -L-{ i }G
- s = 2 f + c
1=z! ) :+c
6 i " o n - o ' - e 7 s "
L ! 1 . C . 4 , v - 4
Rcid : ! r, s-1,,Y-.,!,olh,, ods =,tdv
\dv - - s/sz ds'r4l - ::As\ +c
y . - 1 5 s - . + c1 l s - . + k v . 2 . : c = o
s _ ta/].
1026)-lha holio. of q po"licle'r. g6vax'ad t't tho oquotic., o'-s+'{hcro o i6in f@l Ftsa>" ksiEinfcot.Yv}ant=rsco,s-af l t \t=a11 pa'acc. Dolodnino lho rclol ;on botwc€n v\t ,G\t ,v\s.
\- 4/- - nt-
+t - 29Y rc+ = "'/' (*)'/" 'c
at = 2h s 'e t(-1h)1 2 t - 2 c ! 4 - +
Qt' = 2 (t%)e/'1 -a
P T = Q A - +
1o27.) Iho ̂ al ;o^ ofo porl tolo 'E l j taa bya=avvz,*no<coieinl lpor ecc" k v ic h ft po.6oc Whcn t j6 za.o, €=6 (y -o. F,hd lh€rololioo! batwcon v kt, s&, t, v\s-
R q A . I I , s - L r - s , f c ' 6 r < t - - o . ' . c . 6s o t n t d % L = 6 ' t ' / " 5 = + | : + a = : t 3 r e
du/clv - dtair,y,. " aat n -. '(rl ')" , ea ' , t v z - 6 t t o ' s = { y a " c
i f t . o \ v - o - ' . c . o E @
z v r t - a l g s = v e a + s +
t, . '1!/a
1o2b) tha rnaliatl al o porlplo i6 qoranad b7 lho "clolia", a.+1".
whor \o a r ,€ in f l /e , i ( t ' 16 in 6€0. Whon I \ . zc ro , \ "211. /s ! ^s=afcc f .
ftho lhc "ot"cc of v q\q whon I ?ecc
dtia . eL2-e - 9 l ' + c
2 - 4 8 : & - a - e : . v = t \ l t 23
v= ah(e)1'2 = p.zt fL/sR e q i r : v k s w h o n t . ? d s h L = + t Z + 2 . ' . s = 4 t + Z e t z t 1 4S o t a I d u / d L . + t 2 s - + r h z + 2 I t c e - a e ) % e r e e ) + +
\ / = + t 7 . r c i f L . o \ E . 4 ; c = 4
168 169
lo93) rron +hc v't cu.v6 in f ig- p-1.E3. dctarninc lhe d\€lotyol.olalad in a 6ock, olso la66cc. Aleo skolch ihe o-l &, 6-icurvo6 opproximolely lo .scalo.
Vr ' _14+ 60S,- ,et72 | at &,s . - & . 4 a t , . +40=-5G)' t6o(+)+c2
cr - -12O
s. . -5Lz ,6o1,-1?b
c . ' - e\4. -tlbl2 | 2ot - 6a
s.hG)(.o),4ol l
v.5tg . s t% t c t
q 'sL'/t
p3a,) Tho nolion of o po.liato elortine fron rr^sl ic Aovornodbf lha o-L cu.1o ehown in Ftb.p-1.Ba. 5r{o16h lho v-t. &, s+c1.t vcd. Dalc,nni^o lhc dEploccmonl 6l L.g6cc.
tl t..O t\l.o ,.. Ct -ta
Y 1 ' L ' = 6 2 ' 3 6 f l / s
Y . ' + / 6 t ' r a o L r c .
B6 - -+/. (.)'r ea(6 t c49. b./3 tq; \ | s1.o t \ 1.o.. . a.os1 - L'A =@f/s - 72 fl .
s. Y' <.)(.o) . ,a{1.
\h - 2/314 | 2oL- 60
s.= -z/st + 242i. ,@a t C.gr-q- 72 r t , l=6
72 = - ./s (.)' | 10 <6)' - 60(6> t c2
eL "-t/oL, | 1oL'- col | 12o
e.= - t /s(qt ' | 1oA) '1-@(e) t r2o
9' 22o nluo) An obja:l ofloins o valocit of r6fl Ft's<t W llr.lixtin d stroighl lne y{ilh oh oc.€L,rolion wrrich varice unifrrty
{roa zoa b a ll pae ea' ia e+c. Ctt .q'ta fle irnlial wlocity {l\o danqa in dieptacz: inonl durinq ]tu a a tulanol A*c6 uaioq n{tlon cuNcc \ .}Eok br (tlcr}\E.
AE = Y(L i,) + Ln@" \ -T"= -6 (c-o) +fJ,.,)/'7('a-.)
C = - 6
\ o . - sn lE\bn. fhc oar. 6 od otjlaol d&.6!as ettoraV fro.a €R gz. scc'lo a.o i^ 6 e,c al !/o lift, n yotc.tf k lall Fsa:. Yrd lll' in-itiol volacrly tq t|lo chonga in dl.plo..nanl d,'!ioq lte 6 @,inloryol. gcl"o b"1 "s'rrq moliotr cuR€s \.,lla6k bt alc^Aws
Y--. /2t ' to l-11i f v-v. \ ! -o
v. " -ftFIs
As = v{r.-[t * i'Eo z-{ . r.- i&-o) | oh GJ (4' . 6)
L. = 12t1.i f Y - @ \ 1 . 6
lhorcfar€ -c- -ra
st&
l?o t7l
ro.a) nn oblolo. woighinq s22o lb 6ia-ls G6m.?sl \ ocouirDson Lrpword \cloc,t of 6oofl por min in o d,slonco of zon. if thoocccloroiron i€ oonslonl.Whoi i. lho lonsron in tho ololofc. aoble ?
s .2o ( l
l r Eolh:
f\, (,n/6o), = poAo)
| , l l r a ' 2 . . f i / e '| | l l r uv -w7e(o)
1 ' i+1o h@4€.) n mon waithing 161 lb is in on otdolo. moving upword V6r occolorolion of 8ft pcr d.'. (o) Whol prossum doos ro oxcrion ll., floo. of lho olovoloc ?(b) Wul wilt lho prc.ecuro bo 'rl' lhoolovoto. i6 dc,scondinq with {ho cono o.<bla.oIic ?
a. qfl/e'a) Tr w - V/9 (d)
1ot) Thoblock in Flg pr1oa3 rooohoe o vooolv of go fl po- eca in€o{1, slor'ling l?om rtsl. Conp,,lo l1-o oofitijoni ol Kholio f^io{onbotweon lh6 blooK h lhe ground.
Roqii : o) prcE€uro ho 6rcFib) p.oesulE iF cldd.lc.
is d'x@'Jing V lhe Gomo
Boq'd ' cocfl,dBnt of hie1,;fr,;1,;n
I - 161 = 1a/s.4 (B)T = 4 0 1 h .
b ) | - * - - Y q @ )
I -161= - (1 ' /a2. i ) (4)
1 = 121 lb
' ' t2 -Los -aa ' . - 2o&,a)
o- 6 t l /e 'P-r =no * 60 - 164 (lL) .1.14e " 6)
y'L = 0124221o47) Dolomirno tho forco p thal will g;vo tho bc,Jt io Fig_ p,.to+t onoc.olctul,br of 6fi porecc. Ihc oolloionl of h,nol,'o l-.icllrl ,so?6i!a^ | o=Gfr/sz l i . -de @)h, r-(222-P./)a,2
= (322 - 3/!p) czp/ 4/sp -(ve 1kp)o.L -re4y'e22 (6'
r - - - - 2" 4/sP -G4.4+o4/eP -hot ' * ! r . "=" : " " . . ̂.2>v,,7|'7+2-
rc.r€) A tugnolio Po.liclc vdqhinq 3'G gmm€ i€ p'rllod lhough a
ooloroid wilh on occolom{ron ol o nrolo.e Pon sco' Compu'lo lho 6rco
in pdlrdc dolinq on tho porliclo llo{e: l b '4s496m6 \1h '2'atcii
6io^ l\l- 3'6g - 7s2s3rtri3lbd- 6 nlsa - 236.22in/s2 - 19,c9flk'
- 7.*z95r1o'' 6s.flt)--Ezn -
Fea: Fd<F F ' o'o0443 tb
*i,) f* lbaLt A t-B anr r€looe€d Fo' rosl o" o 30'holino
llD, o'r,'ofl oporl. Iho cooffioic.' t ot f"iclbn undor lhd wPor blocL^
i6 o,2 \ lini undor tha laio. blook B i6 a+ Compulo lho olopecd
timc unlil lho block louoh. ,
A^'a z t\ fz'a7R.qZ : I'lho lo clapcod unlil
*'o bLrks talch golulion I B6ine' - o,+8ut4' - e22.4 atqB - a.% f)/s'
A6i.e' a,2 A ctbts - if..2 <t^a^ , @,n fr/ee
. 3- ' /aaat2' ,Y2(1 ss)I"'
5 o r 9 - ' / e a ^ L " ' k ( I o $ t a )sa! 217512 -5.2asL2
1 4 23 s'''
@e2.) Doio.mlno ltho occobroibn of lho bodic.e in rig.P1os2 il
tho fi'xcd dtum is grnoolh \ n is hoovior thon F'su64. 2 to1
w^-r =w^(o/e) --A^ w^-r't6 -vae/d '\'/^(qs)1-\\b -N6(4/s\ -<) awA-w6)q - o
T.w€ tws(4/9) \ t^rw6
ro.e) Rofiedng lo Fig P- 1oea, ossu'nc A woighs aoo rb d B woighs1oo lb pol. lho oo.rlomiion of lho bodics rf lho @fnbio"+ of tu.otic
fnotion ie o,to bol. th,c oablo s- tha niod drumW ^ - 4 o o l b J . o 1 0
r^Aa " "fr .,(.r)rt/ta . e1 t . 1 , a 1 1 g - O
2oo - f^ - 2.144.. (o) - OIs - 1oo - tooAa,2G) - @
t72 t73
zAO- 1 .371Q - 2dy32.2 O ' 1
lrcd 2 tA . rco I pa1e2 a
@b6|tulo. 2 tD,i
n o t , u ( r c a r s t t o \ - o t t o
2AO - 117 - 4,261a - C.21A
O' 6 .4 , 11 /6 . . '
|a5+) lwo bod'es $-B in f6. P ros4 o,o ecpoelod b./o (;pri.g.'Ihoi..olion down tholnolino iE ros'6lod b"/ a lorca P = "a)lb lf'a
@om;,cnt of Kjnolic f.rollon is o30 undo. A !.. o,1o undo. 8. Do -
lcmlno thc lorco in tho firng.
J^'o,so5a'o"to
o+ A. -,@ | "A@o) - a/.6.n)(o a) ts ='i.%2.eo-s6rs.^242a -"4
018, 3/E(6dr) s - +/s @).Xoi) - aehc,2 azte -s - B.ezq -- .9
f r c t r , 1 . € 1 2 + 2 o 1 4 6
sub6Liulo 16 2, 312- 12,42o -86 =1s,63.a
296 - i l O9A
a. e.e4l7/s.s - 1e"42(6,24) |g = 1se.4 tb.
&8.) lta cAofli.ianl of Fnolb f.iolion Dfttar bto.k^ in Fig. P-tosti6 o,3o l\ undor blo'k I ie o,2a. Ftad lho ocolorolion oftha eyslon
al ct at, -12 = at/82e ot --O
^l O, 1^-11-2e 6tn3o'- 2e @6@" (o.2)' a'gtze a
c 1n-tn - ta1.c+- c,zto -- @at A. 1 i - 14 c'.e' 1e.zt4. (oe). pfu e a
_t l _7s 90 = 3 ,110 - -o- \ 1 . /s .gA+3,11a
sltgl. h lb@ ,14 -\ E 9e+ 6 ,11d) - 14,.+ - c,21 A
1 2 - 2 1 a , 6 , 2 . 9 . 8 2 6 - - . . Q
t( {lr lonsron n c<[i ctard,.
l
i1
Il
le- 2tdc2 l9,a2agubet,luio lo 1
z& - 410,621 I,aza = 3oa/4ie a
99.39 " 146+aa. +,e tt/sa :
11 . 1s.sb r 3'11 (1'c) - 9o.s1 lb
12 - 210.62 I 9,t2 (4'b) ' zas 3c b.
174 ,75
I, ]
il1lIilIillliljuiliiiiiiiil
ii{iti
Choplc'^ 11
Crrwilinoor Trd'glolbn
d {o2.) slono is thrown froa o hill ol on onglc of 60 to tho
horjzonlol wilh on inihol vclocil/ of'po{1 por sco Aflor hi}ting
lcycl around ot tho boso of lho hill lhc slono hos oovorod a
to'i.onlol ai"to"o" of uoo fl. Ho* hiqh ie +ho hilli
r = v6 c.eet
n@.) sholl tcafts o 6a.lar */ a nruzzlc vctoo'lv ol sooll/x':
dirEotcd upwo.d dl 6o'wilh lho ho.izo4tol Dotornih6 tho Pos;ltonof lf|] sholl \ it€ r€sulloftl volocily 2o€oc oflo. fi.ing How high
t - sa ,xa'G")
.t =\a6tral \h91'z
| =s'ast u; &o) -Y, Gr'L)(,a)z
. | _ 422o,2st1.v-vo -9f * vr -soocasrn" =o -v" zsol|/.
' 1 / - sds t e ' = - 3 . . ( . a )
9 " 21o,es fi/sv =J*';f -
[;qQo.rr. - 3,.1e i/s.
--98 ".-I- ,' . ' l' I
i l y -,!o 6,^et - y2gl2- "@ s'"6c;60) - Y262 2)(1o)?
/ - za3,s7 f7 - o. 2a3,97 {1.
4- I
rj
noa.) n pajoctilo i6 f i"od with o" iniljol \otocilf d 1w'2l1/s6o'uP{oid ol od onqlc ofro' to }hc haizoniol G€m o po;r} 257-6 flabovo o tovcl ploio Whol honzonlol di6lonco will 1l coron boforo
soo'sda6o' - 2911,5 ll
R-ffie(^F,t""e)
Io .P-s1, co6(=t / (
R =.lE-;t-
b - v,is,"ls -29
it cl.ltos Jho lo\&l ploia ?
176 177
= 2 (1sa .2 ) ' ?c6623a '
1 = n a 3 . 9 A t a 4 7 9 1 a . s h 2\- - 100a.9x - 447914,<a -A
x -1338.s3 t t .
/.f "t - rsa.c - 1s3.2 sm3dI - lz G2.2\ L2
- 2s7,c - 9c.61- 16,1Ie - t . = Ssoc
X =vo coset . 1932 coeso'(B) = j338.s3 fl11tx) Ror:pl pob.1104 if iho pmjocl,lc ts I,'rod downwo,n ot&"to tho hor.i.ontol
so\t\: '/ = ro6iet I '/29+.
2sa6 - 16r.2 eB.j t I tk (az.z) t2xst , l - 96,cL r 1a,1 lz
srluodmlio Fo"murd
x = !. c(lseL = O3,2 (.620. (z)
x = 33+ 63 t}.1106:) A p.oictclilo is fircd wjth on lnit;ot volo6i{y ol\o ftpo.e66 up{o.d ai an onglc ol a' w,th tho horizontol Find }hohonzonlol dislonoo corcrtd bafdt lhe projcclilo rotr:rrr tolis origlnol lovol. n lso doio.minc lho lr|]^rmurm hoighl o oit)-@ b/ lf'o prejociilo
&s,d)
J o-voEt^et y2gIt' to6t 4 = hgt * \ . 2,to 6ihe
I| =Yo(ce(.'tostne\ = Yoa str'zool ( ' /e ,h) ; t ' t , /2
' s ' - -T
rr = v"."e fav"ere _,hr(ya;41
h -vozs,nzg _ vo,s,n16' - T - - {
h = -voi-erq:qta
*.(&*.".)
.roz) Tho oo. shorn ln f!g.p-11o1 is lrrl to cloon tho wqtoi-
fillod gop. Find tho lok6 -o{T volocitv v"
h=Vo€'not - l/.91r
at 2 -',to st^tdt ' Y.(tt'2)It ' O
&za =vo.t"to'l -. -@
I - za/to
subcl;lulo ctol.-zz.a - $snto (n7g - 16.1(4ok)e
, t 'a\ot '6440
o,* \o " 11,14ll/66
11oO) bon i6 hro.,r' Eo lhat il iusi olcor6 o aoll fat$a 6oft
o*o". tf il toft tho hond .tfl aboio tho grourd u-ot o a'gla of
oo' io tho horizonlol, whol wos lho iniliot vclocrrtv ollho bo f
h - vo ,tn€l - t/2 9I'\o-e - uo Lt^a(l,aho) - 16.1(trg/,r.)'
go,g Y.t . zat1Etloyo - a0,+ ll /sac.
rlos) oolc.mino lho drsto.co s o{ v.hioh o boll lh'own (o\6loalfy Yo oC rco f l p6.6a6 ola onqlo A-ton-r3la wil lsl . ikc
ailont uo .16flls-e . la^'' 5/1
n ' 3A,A1'
RtqA; distonoo s
lho hclino .ehown h F&Z.P'11@.
r?8 t7s
€blht -f .\to etno-l -t/.g|.
h -r/a3 / - r - . .O
,( = Vo cAg Ct-f - 1@ !,intc,b7 I - 1a,1 f_ 7 = 6 1 , z c L - r c t l e _
@^ = 1@ @6tO,O7 I
2\'1, - a6,gsX . 6 ?-14 l - r6i (
tr = s'el 6<,0t - 726. (s ,4) = 449. l l .'/ . 48,s6(8,61) - i4.,sz 1.
t = t z 6 c t - . @ s = { @ t @ z a 6 f' t l \ t , el - 77,66t ) ' l -2s,991^.@ s, +st.z f l .
11io) In Fig- p-t1og, o ball thnxrn down lho holino etnk6; .il ald di€.la^@ s- 2s+.5 {l- If +ho bolt ni€ca lo o .no)(imum hdrghlh-o+afl. obovc lhc pci'ol of rolcaso, oqnp,rtc ils i.iliot voloctlyYd \ anolination +.6rvcn r h-6+.{fl. ta: sin p -A/s
6 . a e i . s f l . ' / n . r l / q s + , s - { - A o . . e f l .R4d 1 vd t\l @l = x/o
3A:a - x/ag,s - \-241,1.+f7._so,s = yosno[ _ /zgLa _. _O
t41 11 ' \o (rcE61 - -@
64,4 " f6:-g!1&- tvoitae -61.4 @5{]b6l i lu lo €di , L9
-8o,9 = 64,4t - 16,11.t _ s6cc
2n41 - ,to cb6e (s)Yo @6e - 4a ,469
v9€ma . Ton€r . e4,+/+B,t,A -o--satzz,yo.,xe
\o stnsa,137 = 64,+ * u. - O6,s f.l/sfltlJ Rofor lo Fig P ilfr r+. find "( lo ..,-ea lho W.jc<'tio lopolnl 8 ih oretty a soc. \'vtrot is.|ho dielodco ̂ ?
n -u- at - la'q1= -ro -e66hq((4) -x,1 G) {
IstA4 - 0,404167
4 : 24.a.x.voco6qt . casaa,z. (a)
6 x - 3sot7 fl.
I
r:29!!!g
t - ,
Ho.s irgn inolincd ol32'
x= v; co3s,t = a.1 . s66cose(6)€ - ' 3 3 - 0 8 '
flf.) Ji iE desi€d i6 piioh o golf boll odrDss a 1mp lo o grocn
rcofl owoy. Whoi is t;o besl olLrb to uso il lha iniliol volocrty
of lho U"U i" 6ofi p€rsca: nss'rmc thol lho bollsloPs dcod of-
1,o. st.;hinq iho groon, which ison tho€omo lobcl os tho point
Iiorn whioh tho boll i6 si.uck nssumo lhc clurJs hovo sroPos
qroduoloo ol rntccolq ot 6 'so thol o no 1 rron hoe o locc In-
cltnci ol f{s' io thc grouno ihc tio 2 iron 01 "4-' cl' davn loo
h.Vo.snet - '/z (s2'2) t '
h " 96 ,6 6 ' iea s6 ' (5 ) - 16 1(5)2
h - -133.25 F l .
X - vo'srnzdI
E22(@\ e'cast^24
F - 31,72' rl.€c llo.9 rrrr\
111a) n €iono hos on iniliol vclocrty of 1oo fl Poreoo uP io thc
riqhl ai so'wllh lho horizo"tol Tho compononls al oc'a)c-.u+'a
o.i cc",stont aI a^- +f1rrr scoa a\og= -2a tlPo's'<: (jon'
pufo tho hodaonlol disionco covcn'cd unlil tho €iono rEoohos
o poinl 6, f] balow ilc oflginol olovoiron
6i!c^ | va - (n lt /€+-3a' , ox. -af i /s ' .
a t = - z o t \ / s " , y - a o l lRoqil r ho.izd.lol d€ton cgth: y = Vostne'l - '/2 Al'-Eo . rco cF za | - t/a (2o) L2
6/ Quo.ltu1i. )o" gcl tfrY o t u c o f t . 6 € c c .
r , -roco.eI I Y2al 'x. @ocasaa(6) I VzCa)G\2
t = +47.62 fr
180
r8l
1r1s) n portlclo ho6 suoh o cu.v;linco. molLbn ihot' ils x cco. _dino+c is dofinod b/ x =st3 iost whcrc x G in inch€E s\ t in,eccoid6- whon | = zeac, Ihc ioloJ occolcl.dirb. ie zs n pcr Eccllf thc y conponenl ofaccole.ofibn is conslonl t\ lhc po.+i
€to.ls f.oo rcsl 01 ihc o.igin \^?hon t.o, dclc.m,nc ihc lolol\clod+f |\han | "a6d..
6ivcn I x..str-ro5tI - 2saa. a '?s ink:
a - JnT iaV ' 7s ' = 60 ' i a rzar - 4s ia/s,y,.
'tt -- 1s(+)2 - ios - 13s in/6Vf - arl - 45(4. fto in/e
, , / r2 rYf2
,i r.,-.16;
n18-) _Tho no.rul occaloftI;a^ af o rr,.ticto on tho rim ofo puttcy
@fl in diomcta. ic con6tont ot soco fl pc.€co2. 0oio.minc thc€_tE d af lhc pullcy in rpm.6tven I d=1o{t
o^ - a'.rt n/€2Rcoil spccd ;n .pm
o" = -vl - eooo =rd
,t -2@ fI /sv - nori2oo =l Go)n
tt = 6,+ rps (60) - 3e2 .pmnig,) nl lhr boflomThi€ cou<os o mrrmlrcdius of tho loop.
a n - s q / E e
ofo loop lhc spcod of e,d'rpnna is ao.tnpho€,al.rcIio(, ol sgfipa.€,C. Dc{crmrho thc
t6 a. = v ' / .s b2. e)r- Fa x szso t 1 /s661'
r - f la l .64l l .
1120) A rxrrlala mo\ra 6' o ai.s)tor poth of Zo fi mdiu€ co tha{
its orc diclo.co fiorn o fi;od Poi'nt on tho Polh ic aivcn t'l '6-
.+tt - rct whora s ir in lho fool r. I in €c€ond€. Otnpulo tfr' tolal
occolcrolion ol lho and of 2s@
6i"a" . r. zofl sotht !E. 1zt' - 10 "t
s-4t.-1ol at ',t = pG)' - 10 - Ba {1/M,
Acjd I o
o7 . ,tofl/s"
slopo - o,?5o- - lon'' o. rs . sl ez '
RoqA : or qq.
4= 241 -ot01 or= 2+G).a,f i /e
O^ . 10 @sta,67' - 6 stn ac,ez"
6" _ a.+ $/caq =G;167 ' .[d'-1F = ar..2o. - Qta t Qaa
(11,.o2)' . aLa | (+.+)' .
a, -va/r - @a)'/eoo^ - 72'2 Il/sa
aa.6t1. toh' - (46)' i O..2)4o - a6.7 fl /6ca'
1l?1.) A porliolo i€ trro"/inq olong a cur"Ed polh nl o c6'iotn
in6ton+ whan tho .6lopo of ihc polh is o.75, ov = a fl pot a'. t'o1- 10 ll par se,' . Cohpulo lhc !0l!106 of ob \ on ol lhls rnslonl K€Ko1oh how +ho polh curt69.6t:f!^: O,-6t1/6' solir I o. =otcdea - o'6'no
I qt = 1o'8 fl/s2lze) A stono'ie lhruwr wilh on lnilial volodly ofloofl po^6c.
up{o.d dl @' lo lho horiro"lol. Compulo thd todius of currl]lu.€of il€ poth ot lhc p.int who.clt is sofl hori?ontolly frorn $e iniliol po-
si l ion.A i \ e . . l o = 1 e ' f 1 1 . Y 9 - 1 o o 6 n 5 o ' - 3 2 2 < 1 )
P.60' . 4 'saf l \ r = s+.a f l /sRc<i4 r.d"& of v..l-so-:;46;T " B as fl/sOi.\l?furv lone '\'//\/* = qA/so ' 1 <9e
E'olh: o, .g"e2,2f l /6 ' -o ' .+2,4"t '
a - \o.ospt On .Orcos€ -et s i .b.so; rooco660'[ a. . 32,2o)s+7.4",' .21i9 fr /e1
I - i 6 c < O r " v ' / .\\ -tr,.as6d - o t '8t.gq)74ts
v! '5o fl/E a - 2so,64 n.
taz l89
{.r) n slono lrcs on rniliot velocily of 4@llp(,. {i,r'. Lplo.lho right ol o slopo of ,i lo3. Tho conponont€ of occclomlionaa. cor,slo l al o'' -r2 flpor€c6'\ 09. -zofl po.soc1 Com-pulo tho
Porn
ftdiB of cltnolu.i ot lho stort ta ol thc top of lho
6t:vct1t Vo. aeft/sd, - -lefys" , o, - -.o fils'
R.qA. rodtu. of auNllv.esoli:
tt -vo's'"'/ - k1r\'(a/d' - 6aon.---ed;- 4(-f
11 "to€,'^lI - ya,atl' -6a..b(./s)t- hQo)t'a4o. taoL-1olz -, $t. _ 16otr ! 640 . o
t ' - lcL I 64 - o - ( t -6Xt-6)-o
"' t "a4<!.t,- r.@(./s) - -12(.) on ' oy co6t-, o, ch+Y\ 'z4f l / . - aO.FO -146tdo
vt = q@(4/E) - .b(e) a. - aoft/s',tr.o , !-zlfl/s o" :v/" -r = z+/26
. - zO,6 I lli?s) po.ticlc novds on o cir€lo in occordonco with tho oql.ro-tion s " t.-ab who.o s i€ fh6 di€ptoaamanl in loot mccslr.bdolong lh6 oiroulo. polh B, t i€ in ooconds. Two eocords of-lor Elonling froin rdel lho lolot ocaatarclion ol lho ponliob ie48trT ll por *" Compulo tho mdiue ol lho oirolo .6Ncnt s- I+- Bt , L.aet.
v t . .+ f l ) ' - s ' t l o ) ' e - 2 .+ f1 /e
40. = (21)-
r - 1 2 1 1 .
o '46.1v l+k2Rqa | rcd;ue of lha
OiElo6 t i r s . t + - 8 t
OL= 1e(4) '= 46lys.o . - A L . r O n a( roJ?) ' -&O' ia ' "
ot ' 46l l /e '
'trzz.\ Sot"a lllus Prcb 1146 usrirq lho ff : dolo: W-loolb j V 'r':aB
L = t s i n .u ' v c n L l e i n " . l l
w = loolb r v=8.b3f] /s
solhtone =vu/a. " -r:9- - u/qY"'"6'
st 29- - va.ite+/gL
t aca+ voasa . o3 L
cozoo , t "aee - t -og L
@4?e r 8 o3act69 -1 =a + B/q{,od.olic co6F, = as348at.2L1.5) ,e, -, s-1,67'
*.Icb6e - rco - Ta.cs1 61'
I '187l t )
f - tst.]e = rs(st sz61) - r261sll
t ' zt ['79t""e = etf.t-fi" 1".s,.< r ' o q43 6ac
tw) A tud qtl. bnq rololos in o ho.izontol ptoho obo'rl o vort'@
ari€ lhrough ils c€.'ion. Al ooah da of lta rv3 is fcsloncd o€ord 3ft. long. Eoclr cord suppoele o woighl w. Ccinpulo lho 6-
lbod of roiotio.r n,ii rP'n lo rnol;ne €ooh cond ol 3o' w'lh lhe
x = i , 5 { 1 .
f . t . 5 r 2 - 3 . 5 1 1 .
Io^e = lYgr'tonzo' ' ,ra/3zzG s)
| - 8.a7 n/5
V - z l r n - 2 7 k , 5 ) n - g 0 1 k o )
n = 22 rPm .
t84 r85
,2s) A waighl ca.@^ltrtlad at lltnrbol Fondulum O. wh1ch tho po.iodvoloo-,ly Y of tho wcght if lhc oordtho \€rlicol
Ai ra . l -1sc! :
S o l h :
t -n/1sacj 912f i lszRcdC I lcn6ion \ FotucL-sPocd who. Fs-O
= .t Einso'- 2t1n - rtcyrl4 - 4h rps! =2afn = 2\(2)(4h)
v - 16ll/6
Tcae3o'-n6inro'-w = o*@
E2- o,sr +o.s.€t i - ao66Y3e@)
fion1, 1 -(zat o.sr,)/o,B6c
o,b(2oro,6n) , do66 11 - AO
t l ,ss + O,2g9l1r Ote66r1 - ga
fEi^so rn<.6{'- w"7qr .o -@ ,t -6,o7s lI /s\ .1* o GI -o,st |=2o \ l -4\an
t = 2r lr/d-1a.d1 - 2 t
lhc forvo o.r lho 6boll bc.od,o :orv?
r =o.an fl1€o) ln FiS.p-nso, thc 2o-tb bal is fd.evJ lo rcIole oround ihe€.n oth i^ei& su.foco of o conin I sholl oj tho "olc ofono rcvolu-l;o^ int/1Ee. Assunl;d9 ld g= 22 fl/6@a, frird thc tonsion in ltxood q lho fo.co on fhc conicol 6h6ll. Al whal epa€d in no'n will
a,\d ol o cotd fo..n o.oi6 1 6c€ tolo.ri,nc ihorolotcs rncl,nod ol 3d'V
Ione ' \2/6r+onad ' 'r/32,2(o)+11)
\2 - 8 js621
\ = 2.q6 rvs . o,so1 d/s
n - sa,2albr -39t!]99!d - s7B tb.
2.far n.0 , da6cl -9.54 - 20
I - A3 '1tb.a.sl i qt&n - 2ov',/2G2)
c,6(,31) = o.avsYz
o.ofi "le\ k) n7f on ' 2 9 r ' p m -
2/zz.z Ioazo'
l
lil
l
,11.) n body of tciqhl w r'6616 o.1 lho smoolh Inclinod sur-'fJ ';-il
f--o 's|'"*,'
io I is p- 1'a1 A ws o\l&heA ta ^
iil-t--" f"'.-" tho bodv fo rofolc V.il oboul lho \c'tic'r o-
.il i.f."-t." lho spccd in rpm ol whrch lho lcnsion i'' tho
ard \e qual to lhc worlhl of lho bcd)
r -<a#o'G) <Fv -o; ls i . t , i t r ls in6o'=w
l=w ara'o laa&!; -t1<.'6o' 'W! O
wsinio'r n3in60' ' w
ll - w- o,5W - 0,9774 Wo.ga6
subel ulo to t
/@sa.; -o 511arf ./Js6o' = v{r732'G)6e,1 - 8.stz ft/s
\=ztfti - 0,912 ' zr Pca'ao)n/con - 19.19 Om a 20 ryd
fi32) Tho hamricr 6f on rrnpool ldsling moohlno w^orqhs 6a'aD
;-;; ; i;;;-;i'o"t i, ot*roa io rho ond of o I'i?hl rod
+n L9 ',v'i"l' le p''aoa bo horizonfol o'ie ot A (al whol is lhc-
il*.'-".';o. c', lho pi'ol on,^stonl aflor boinq nolcoecd ttrn
il l j-
[u.o"', ot *hol rE lhe b€cnrnq roocl;on l'd boJo'6 i'n-
p*t 'rf
" if f r,. veboilt of lhc to.nrncr iq thcn e 9 fl Io'6ccr
' r . 4 f l .solir: a) Tc6ea -w
\ 6eto ' 44"+
T - 7 + , 3 6 l l ' * R
i ot'o "t(b) bl T- w twv'Zr' c+ + tlc++(s o)"J,/szz(t)
T = 8 1 ' 8 l b = R '
rc5).To aha€k ihc mdius of o 'oilroad. "Fvo' lha a$cA 4a2o
lb wo,bhr is obcarycd laLJn 2a7 6n o sp'iag qt'la susts)dd .frclfl'
tro Jf of o. e/pcnocnlol @' 'ou'di^g the curyc al aodph
Whol is tho rod,irc of +hc cuwc 7
Aie.'. v . a. ./lpt, '€,8 6 n/s @s6'' 2o/ao1
I . zo,7 tb ',\N .2alb a" - 14 9+a'
RaaA: rcd; is t?r=oi16;^6=*n'7sr '2a:7sn1+'sta'
son ' zr1"o lut<o' w,teo)1/az'zr ' 2o'7 s'o t4'Q13'
Tcoso -w r - +a,s fl.
186187
t*g) Whol colrnlorwoighl wwiu moinloin tho Corlicsgo,cli'o. in lho posilior' .show ;i f'b. P- tt:.5 ol q mfiorrolspaodn-rzo rpm. fr'ch plyboll woighs 16.1lb. NcAlcol '|howoight altho olhor I'hks.6i€n: Sol,n: str''D'- d/10 - d=s"
n,wrp^ k ( . Et t ,- G' -."o,e'
v-orn.zr(o,r$N
Y"jIl.'/lD\'' #-*ffi l'c'.an/sncqd:wlzn.lhs\\. " .;;;il '
(6)ABgh76' - 3€,.r66'n6o'(ro) - r6,r
AB - 45.1 lb.
Aa@s+i IAE@.. . j -w
+s.rco€'as ' (c) 'ww - 63,-rg1 lo.
rcd -Tho
sico .od ol tha onqirc i^ fis p-11"6 i6 en lonq \$/oighs{olb. Ihc omnKs AD\Bc aro of longh'l ..rsin. \ rolalo ol3oorprh. Ddo.m'hc iho rio,imum bonding momcnl M in lhc rod if M. wys,whc.o \( i€ tho +otol dieln bulod lood\L ic lho lonqhl ollho rvd.
6ivco:w'r .?lb colh:(,"fi--1.71 "',*.o^ tl.v!-Fa@)'l/o
. - - j . , r s i r \ L - s l lRcqa, M M. roo tb-l{.
rc7) Thc€camonl of rood possrhg o"on thc cr6sl of ohill ;c dofii
oivcti: f +fi. ; v-3olve
Rcqa: prtcauro R
\ 6pcod {hon Food
e"t '", + - g-r1
i =# -# - +7ro -ztza/noo
Yp ' 2/too - / 'sotl .3+ ,a"7s( =w
a - zzzo -fazu bo\a)/ez.z (so)
b/ tLE poEbolic o'r"c y ' 11, # A .o. ntsh;Fg 32e tb l..olds o-loiq tho n od ol o con€lonl 6p-d of 3(> fl po" ecc Whol ic iho Frc-€suro on lho *hccle of tho cor whc, il i6 o1 tho crasl oflho hill wh-c.o y "afl ? ,t thc whot 6pood will lhoMd proseuro bc zao.2
fiht: tho .od luE ot cuFro l".o br yp "Gt/d"Yh (d//di'l*
t' - +o, t +oo - o .'. (x- zo)(,- za) . o
lIilI.'
iliIlI
i f R . o
tri ur"'4 - &9.
- 32,2(sa) -$16
v - aa,12 rl/srar.) A loy running d fool mco rounds o fiol cu'w ofsdft r€d
if ho runs ol tf'o roio of rs mpn, ol whol onqlo './ lhc wniicol wll
ho inoliho his body 3
eiNcn i n-sofl tu^e -\/s. "[a tszaoftfi'/zz z ("o)
v-rsmph +a.e - 0'3@6
Rcaar €- -e =$73'
1142\ A dorcdaril drkes o lnolQrorclo on ond o orrculo.Vo'lr_
col worl l@ fl in diamaloe Iho f uol liroe \wall ls 060 whol i€-
lho mlnimum spccd {}nt will proYoni hl6 elidioo davn +ho woll ?
Al whol ooglo wlll lho nrolor oyclc bo inohirod lo lho ho';zonlol
whot ls tho ;lfool of 1ro'cli"q al o groola'epcnd?
6;@-,. . d-@ofl . solh j
f - 0.6 €* - lon 1o,o * ts1'
n . i a l v . i " t + t o ^ d ' q t h z ' z z z G a ) ' o e v z
,t,s.b tvs " s1.bf3cao/5zoo-l 'ss.a -p6
r1a3.) Tho gupc{.clovolian fogiltea lrock is thc numbcr ct
inotlo( lhot iho J6rdo roil 16 rorlg€d lo p'evcnl sldo ihrust on il
whcol {longcc ofcors roundinq lho o,.!c oI (ic sPaad- Oalonn,no
lho eupor otvolrtn o ftrolrqok boeng o qouqa of afl8'/2in ol
a@o (1. r',dittsv"o rolo.spcod of 60 mPh. Whol ie tho flongc proe-
srr6 p on lhc ,l{h€ol6 of o too,ooo lb co. +hol rounds lho cu.vc
tane =f/qr 'feo '::q'"^:32 e ( 4oc4)
ol u nph?6iecn: r=1ottuft
+fl 8.5 in - 56,9 n lo-|e = o 1202
Rst6: lho eofr.rdqol'on -o- " 6,86e for o ltwcK '
lane = a/t
o,1zoz - e/sa.a
e 6 t q i n
t+t) An a,'plono malo o l"m in o honzontol plono wilhoul
su.o doaE ho o'6d a)r, hie '@l 7
188189
V' 40O dPh
6ivon: Wp - 1so rb Solh:
32,2 Cs280)lohe '2.g2 3f = z,qz('r.o) - +3oA.
t . = 71.o l ,n = ftso';4t\- = 46a.gi tb
!aE) A ca. ratOhing 3220 lb rliv.de o aud6 ct 2oo ft rodios b,nt€d ol on ongla af eo'. Fhd ltD ftt:clioa farcc aaltag on lha |i.o6whcn lho co. ie lmvolling ol 60 mph. lho cooffioionl ol f.;o|irlbolwcco tho tr-roe \ lhc raad i6 o.so.6lvan. W'32eo tb .golh rf -"oofl;+.30' x!1-j3.1gof39]%;t - 3872 tb!"6onph / ,-o,go
3' a2.2 (2oo)
RcqlJ i fnirfion Fdrco lo"f -o,9
l - < z 'R -/6dddfi6ei4. - scss.so tb .
sinE = f/k +s6a2' = f/sors.ssF - 336a,s7 tb.
ra6) Ftid lha onqlo of bonkng fcr o highwoy cur.vc ol eamdius 66siqn64 lo a.x:a,iodola cors lmvoling ol roo mptr, il ihoooffibr's'+ of liolion bclwcan lho tircs q t. @oa i6 0,6o.Whol 16 +l-c mtod epccd of ll,o cu,,a?ONc^ |f = 9 @ f I . A . a , 6 o
solh IIonP - 0.6
q . e.sc"Rqa robd .wd ton (.E I e) - uU
lo (ao.ec +o) .Lto"!239,_"d_32,2 Goo)
3.,96 | e - 65-82.
+ ' e 4 6 6 "16,6 o = u.%.
h^s+,u' - 'r.7ea.2 (3@)'tr4 " s2,t (r@)+o^ 3+.A6'\t - 82,02+11/6\f " 82,024\ @/96 = s€nph.
,l
'1112) Iha rclca spocd of o hiqhwaY curyo of 2en rcdiag tsiomph. lf lhc coofliciont o[ fric{ion bolwoon tho lirDs \ tho
f tod ' ,6 a.6o. * to l ie lho dor imum Epocd a l whrch o concon
comd lho oonvo wilhout eK'bding ?
6Na^: 6ol i1 lt , 2 @ f l a - o . 6 r o a 1 - Y T q r,t.- eanpr' tone -lso t saw,/aecQ/zz,z (zoal
Rcqii: moximum spcod lono ' o'3o1'O ' 16 73'
t o a ! ' o e
Q' "a 'se 'loa(Qte) 'uYgc
ia" (.o oa'l rc,,e) ' v/ea z (coo)y . e+11 l1/3't - 04i1 (6o/06) = ,ez3s ftph .
1144) lha ./,affbianl of firolia b€l tho rood \ lho lircs of lhc
co. €hown in Fig P-1111i. [email protected] cd. woi*'s 32?olb ll G '?,J-
rdidg lho ardo of .5q $ rodi,rs ol irurihum srcod Whot is lho
votuc of lho fnct,Jr"i fo.co ooling undcn coch whcol i how high
otrluo lta rood m,,'sl tho conlon of 4-ovily bc fo limil {hie no-
i';um .epe€d t'/ t|,A +.,.ncncr to o,onlu.n,'
' , +6749,44 an 3d(2 411) r i1sg,ab
fow high at tho ouioF *itc€lc
SolA : AAa - o/ 11.(+.643) - 322) oxa?atl
+on l - 0.6 | s1sg.16 6n34 (2'a1) + sezo sta ao'G)
$. ao.oe' - E7sg,+6 cogeo'(3)
hn(l |o\- ' t 'b l le '726.46 tb
toa (ao,os'+ zo') 'vlez.e (soo) f. "/afi"' ae (126 a4 -a's.satb
'r-ito,2g fl/6 | lhc dirlo. '!hool6nr' . 322a (io 2sY . stgq. +8 tb la eo96' 241.667/h4- -idz7i{
h.<.ozr6 silJAa.o
dlQ,6333) - Bazo cosad@,+t1)
ctae(3) - r2ao €t s2'(3)
11, - 4963.|bn . /^r l - 0,6(4963) = 2S7z8lb
190 t9r
fl.rs.) Ropoql W.i1tu'[ lho nrod ie bonliod af06 eho{n n Fr'g- P-lr4r.
r =.9ooflw - 3220
RcqA : Ff".6i \hb l h l
l1n 3a,e6 - 2,a11h
h '4 0218 { l '
b ^ q ' 0 ' 6O- 3o,a6 .
lon ($to) " 't"/gr
lol (3o,e6 | ), v/aoz(ao)\ta - 19a$,ae fl7c,
w'7gr - zzu (teass.+q)3e'2 (66a )
- tsgfo.1 tb1M^-o, 111(+.N$) =S2aacaceo(z,qt) t esto.t snza (z,at)
t aato,z cnszo(a) -azzo cnza(e)fl1- 3824,611b
Ft 'O,a(3sz4,et) . 2294.b tb d l o iar fhcals<trla - Oi. (a, ttsa) ' 32eo.zba (e,q1) | 3a7o,7 sto 20 (z,4iz) t zz zo e,a zo (s)
'39m7 @< 2o' (3)ll4 - 559,81 lb
F4' 6.sg,O7(a6) ' s36.92 tb tmc^ whacls
6va^: d.61.1..1- 4 .p^/scc.
o - , r"/rid*,, 2rr"9Pl
<. o,+Z md,/s(f,< - or/raaz(1o\. ur
= t(+ z)2 - 62,e2 glrtat "F< = E(aaz)
Or = 1.26 fl/s2
6 = 6 @ f l .
Chop lo i rz
Rotolion
tn
solh:c. 26/12
s - f 9
yn =rtrJ , ,"u1a2.2a)' . .z a (zto)
4- -3jo md/saca
600 - (2,aa3) eO - 26b.ode. zOAtEd | 1rcy'anindO. +5.aa ray.
(qo\ha/6a).2.a6bv:
{ - 4e.2+tod/s
193
ra6.) Whon l-lc o.}Llo^ dac"tl ofo rfi o'omolo' pullu r src'd/s
lha lalol Br-Dptoltan .Jt a po'l on rle .im is 3o 0 Pc' 'a'' Dcla^mF
no lho onryla. ac'ela.<^Itb^ oflhc pulley ol lhi6 inelont:
6i'Ent d-.+t1. Rcqa ' <
a.30f1/s2
a ^ - r 6 " - 2 G faa.18f1/sz
at = 24 fI /62Ol - r"(2 a ' z < * q = 1 2 f t , a / € z
c<- 12 rd)/€,. - 3 f l
P.,tA' nofiao+ol Yvo.t'ita I c@pdionld of
1206) Oolorff'ic tho honbnlal ! r'c'"fioal oompoic'rls of Ile oq'-
loroiion of poinl 8 on tho rim oflho flYwhool shr"Nr ln Fb ela'6
At tho qworL posrlion, ur'+ 'ud Por€€o \o(=rz 'aC pr ecc'' bolh
( "4,\:r'
aL-r,^ - 3 (12)' 3,s F! /s2an. ",r.a - 3(a)a . ab l\/a.a
o =..Fl"'o"" - ya, 'a"
12a,) A pulloy hds a cdnsla"l onqular ooa\oral*z' ol a'ad par*:'
\vh€n thoonqulo. rol.'i)j ts 2rod ?1r"x>' +hal lolal oatda'd'an
ofo point o. lhe rrir of tho Pullov i' ro{ por ea>' c;onPla lho
dtonat.' al tr pull.,s.olh a. ' rda - r(a) ' . =ar
6Na^: .<= i toc,/c" Ot ' r"("r(3) =3r
af -erca/s ol - af ! aaz
a- 1afr/c' rc" 'ed' \ 6a"Roqd, dtonale,. too - gt2 t w"
"o- "r7,. - zl ld - 1 l I
194 195
I " t8o I].?cq'at L^- ?S.'? whon s^..a. fl .
6<^.2(2) .+tud/s ' o" /2.< lz + pa = y! (a) t
9^ ' rO^ + ibb - 20^
1j^ = qoftd
so " /z (t)t^.
t "r)-Orr* 'Proa vas,1 r . , rco; ol pJ|. t B ( ,d: (rr ,ngcd ta3.n.\ 19 in.
S^=18oflta \so whon &-zro' e^" ' /2"<^1.
a) u-,a" - 2<..
<^. 2.67 Ma/sas^ - | s^ "t 1oO = zylrt^
g ^ " ' / z < L :
L' 7.76 €d..-eo - tzx"r" - /z () (zzs),
- & o ' @ M d
G=nOD - .3 ( .o ) - 16o f i .
b) +)^" s^/. - ,L/Gah.)
si = t /2(2,6alz
tla - Yr"\ctz ' 12 k)k.4e),
so = r€osD. 3 (71 ,91)
' : : , . ) :M
ra la: . a t a auic , . . dct ,n"6 6, ,L , .a , an s.z t , .
, : t o 4 t a f o , m c . , . u r . o n . o a , r . s j t n , e a L o . d e G n p - l c
l : : , . fu-" : a ' qr 'o ' / 'o , l s orct - to- occc e"o l o, or ,he .ng
t :* , "
p@a onqu,o- ,c to<t , t ,4 , . . f 7o) . t . anouta, 616,4.o_, .on
b) +^- z-f,.1zoMa
sotht de/dL' ur' sLa'6aI
[_ be)a-6oLa) =2i2t d/s
, ) d / d L ' a ' 2 a t " ' 6 0a<- 2a(a)2 -60 = 321tod/s
121a.) Tho reloiron ofo flYwhocl ts gota'ncn 6/ tho cquol;on ur-
" . , f , " "h rod 'onE pc 'gocond \ I le 'n ccconds e ' ?od wk
, i ' r * . * "*o lhe voluca o[€ co. o l I 'e '1qon{ wh'n t 3€c(
6r\€nur =.+Jl
Rc4a 1 €\c{
€blh I rr.4Jt td e / d ' l r ' 4 { ,
de ' 4L ' t ' d l
o ' 4 Lahe/r) lc
i f t 'u rod Dhc. t ' l€co'2 . a G \ ' . ( 2 l e ) i c
c = - 0 6 4 7e . a h ! * - 0 6 6 7 = 8 / a @ ) ' ' - o u t
e " F . 2 r c d
^'rt/)dl - 4 -'/: ?),: t'
,' ' n. nr"t'' ' '< - 1,1s47 rca/ea
rzt) A body alqilos o.cad'og lo lho nolouan o( - 2t ' whc{'€ c(
; ; ;# por sc.ond \ i l" i'" 6oc.Mc d = + ;d po' scc \
a 'ts ztttu *ha. l6 2c.o ADputo lhovoluss of ur \O ot iht ins
oni ohon t -26od'
6kcn. o. '2t Solh I o( '?t
RcqA : u/( Fdtn/dr - n' 2t
t r t . a L " k r cil lr - +,od/s 'than
+ = ( o z t co - +
u : , I ' t 1 ' f l ' 2 8 c . .
ur ' 2 t 1+ - arod/6at
d a / d t - D r . l " t 4
+ : I 1 h + a t t c
t l t . a 9 < t = a . . o = a
I - L3/e t 4L \f Jt " 2eca
g - r'/z ++(a)
196 t97
e16.) )elcrnino tho number of.ovotuirb,6 th.oagh qca put-loy will rolalo licrn rcsl if i1s ongDta. ad:.cltaralton ie incnaeodunilormly fam zcft lo 1e nd por scc'du" n .q a.s€c \ lhcn uni6r-mly decftosed lo + rod pt ea! during lhc rtrl :s Eec
r t.* swc ' !.!' 6/"
-,r,-= '.,r\^' tz ' als l. 1 "a. ot ' 3!'
3 4 , t . - A r 1 ^ e o . - t , crq- 0I +6s ^ C
< ' : 9 ! 1 6 ! r l q ' 0 \ t ' o c ' d
Ll " [a I oa-6e/ .1! -e/Bf - a&.33t lc"5 , " ; f e j - e4 \ r . 4
i f r do \ t ' o . ' c ' o [email protected]@. e fu6 ) ' , * . ' t l o t +cut; ' 3/4t- c:6o'++z
M= le9b 4-sht ft,.e/6 rz e/.a13 -16,33t | 6a.4<e" 5 e / 3 t - \ l a l " t c & = : \ t - l
11,.t[j t\1"4 O,.6ek(7),-Blb(1f a9sG) t 6a4n3l?t . eeTs t+t - e1c 4+1' &. - 146.a2 rctd
c" -a5,33 -O.144,a2.tdr: lL - 23,2 r i r _tli ' 6Bht - ek( - $,33 zf rdd\
1217) Ihc ongulor accalo@Iion of a flywheEl dec.coses uni-&rmly fi.om 8 roa pcrsc.2 in 6 sac al y/hich limc ils anguto. vale.ily ib a2 tud Fs sc:. Coopvle lhc ntliat oroogulor ,lelo.ily
\lhc numbo. of rEyoiuiions modo duflrig the 6scc in{ee"ot.Gtopc .
E+--1
) t r -cc r r or ' ! \ r 'o e 'o3 dt/dt , 6aht, a/61, 4s.33
de/& - 6t -1'z/2 +12A . 4 ' - t " / e + e L t c
i f o = o 1 , \ t . o . ' . c " oo . 7 i l . 6
4 - +(e')- 161"/e +pQ\& ' 1 9 4 r c d+.1bot )4i - za,6s (.v.
dtf/dl - a-If - b L - L " h r c
f-aa t a.6a2 - B(d- 67a ra
c ' 1 2tt .ot i t .ot t - 6I - l ' / , r 12
Chop lo r {4
Worh \ Enorgy
198 199
lb= ze/+
a.o6,) Whol for€o p witl qivo tho.yslch ol bodics s,hoqn ;nfiap_A6 o .alo.i+f of 30 fl Wr lcc allor n|oti^q zo ft lron rcsl ?
a " .o'/2(a.) = 22,6 (1/s'
27, , 1, - rp6 goa) -[a(az.zl/ez,zp,3e9,ea - so(o,2) . so(rz.s)
P - 4.'4,2o tb
i
IrlIir
il
,a- 6s,o6 r [email protected]&'(ae) r aoosiag-[uo Qz,afl/alz
It- t99,2+ lb-t<t) Fhd ll€ wbd'|.1 of Lod/ A in Fqp-rot oflar'i hos nolcdto0 fiom esl isunE lt putbrt tobo {,crghllcsc &\ fr;ct,a,tc€c.
^ t r tl'@ \- a'3aar/az.z
A +-:ry+3'o^ - It
I r / I to. ,24^ Ii N-1,\ *r;= o
-l!t29t m-1, {?n/3e,4h.)
It - 20b - 6,21 06'14.
zd -6,.1(2a^)
l.- t@ -1L4zO^ - .-@
, (td - 12.42 a\\). e@ t sae a^
a@- 24.940,\ - 3e + g,32 o^[email protected], f t5a^
O^ - 2.a3 fl/c?
v|'$!ae)@\v^. 7,cs fl/s
sr,1
\ r F
laoa) Th.ouqh whal dislanco wlll bod/ A in Fril P- 1ao0 ma/o in
chonqing iis "doailv f"on a ll pa" ee la 1a-ll wt'e''
411 = 1 . ' c +4 ,66A^ - -@
2(2oO - 6.210^) .31. | 4 66 O^
4oo - 12 t+2o^ .3oot4 ,cGA^
1 6 0 ' 1 7 , O O A ^
o ^ ; s a 6 f l / s "v|" -u^i - zas^t22 6 ' ' 2(5 as)s^
s^ - 9.8 [1
.L S le@lI J - - ,
J l@ zn -t, -(a/to zt o^\ - 2oo'6.21a^ - -@
P^''11' a^'zae
v 21\-1,
4 l1e b_aaa.&%,.,)o6| @ h - . L n r a l ' a 6 .
k- 3oar e,32(o^/t)
' | \ 22 L - 3 d 4 , 1 2 . + 2 O ^ - ' : +
z(2o+'b 6+a^) . ea4 t 1..42 oA
S"< 4aa 3a2aa' 3'|'1 112 +2 o^
.)Q(.scd) 'o4 +s.i cirr6dlr i) o^. zosfr/<
T. 32n(o,L) - 24o -6oo/1..2)a^ Y^2 - 2ac
11'a4 rr,+2o^ - .-o ' !^ . [rdalfr4).,X 06 ?o.
^ y^, zooll /s
\1 T, '?r. - -@
-rI4%i."at*)
,&&'4' t"a-no(p,) v=Pa/et a\aa
1 a ' | d a - 9 e 2 a e
200 201
fo.) ln whoi dl;loocc will bloak A,of Fiqp-nas dtoi^ a eelo-irty of tz (l par ee, elonlinq frDm 16€17
l l \4
\ { . . 2 I . . e 4 r f , 4 4 a ^ - O\)a{'
)S'i'c'-l 4 \3
vsa.,t h 2(2oa fl ao,)' re t,? a2a\\ - s2o(6,2) + 2ao <[email protected])a^ - 4co,37,20a^ . Bo.4 ! 12,42 e^
It ' zo4 r v.az o^ - 'O b4 - 4a.7.7^,. + o. ' 2a^ a^. z.oo {t /< '{-Qq l,.zr, - -6 tl . ro,,
',iAfru
24o 1oo(o ') 12 'Ma.j Xla\ttE(td) L- 24 - I,a2Aa
+(tPt,/ f4.2.4 - oB2 (rd\)
fa.20+-rc,a41^ -.-<q1411.)
0ot.foca
bat ^ slol6 tm,n rc€l ;n lhc pasi l rbn shon in fb p rar l''ts "atoo'|t offar il hoe ̂ awa $fl oto q i.c {n.r,o.,6aa un
p " . 2 ( ^ a a ) € ^
S^ = 3a,a1{1.
Subslilule Y6 lo \tlaoa - 3,11(0) ' | 4 ,66y^a
Y^ '17 .. FI/s2".!E*{ . n'4. pia" - 6'
2.az/at . 2^dr /dt
p:N - 10/4g (y',\/"2)2aa G/, - a) = zoo/61.a vs' ! atb/.4,4u^z
14@ . s,r1\/8. + 4.6V^, - . . O1t12,) Fi :nd lh. \c lo. t t r of boar AinFiq.p,1a1of1e. l l hrs|rolad, 6lartirs i.am .asl ot tho gNon ryvitior,, lor gltdong lholnollonlos€ su.la.c 6hrwn
v^ - 16,66 ll/€
+cat t*o "t;a"*', cc,^"d'li V"Vt'+' 'isid link 1ofl ldng ' nalc- i^
lho fn.l;oalo66 quidcs sna,m In tiqP 143 Daicrntnc ltr- \ctel
i ; , i ;";" . ' in 'r p 'r '"" lrdm 'c€l whcn r'c' lrcorrt bcro{A
Ascoflo W^-We = 10, lb qwc ''eo lb
Rw - z*/ag ('t'-\"') "2d(0-10) = td/6++v; | 1'o/c+aY^
6' 'tuv40)' - -@
frcn'l, l,+@ ' 3.1.1'1.' | 4'66v^'
6ab.$lvla 2lo1' "rroo " 2.11(6v"/rc)- t 4,eevt
4,ro| - o,tA'la'
14la) Ropcal Pr,b i1E
f ' . 1b ' - b ' ' f . 6 f1
z/dt/dL t 2ldr /dL 'o
/ ' 8 t l2rd/y'dt | 2f drhro
6v6 " - av^
u^, ,1ev./e)., _0
RN - 2tt/t4 (!'-,k')'' ta (.ct .i) r soe\ ' @lac + t,' ',44tv| 'sn/"aavj
@o -- \..GU^' I l,SavAz 1oJ7CVt'
sao. l,rEV^4, 4 e1ve2 ' -@
s@ " 1, 66 (36'.^/61) + 2 33'/ e'
Y l ' .125 f l /e .
whon r '6f lv""(oYate) ' - -U
*N - z\!/2g Q" 'a.)
w)t3a-4 r 60@) = 1d/c41 \^' r@16+a\{'W,
s@ = t.ssv, ' t t .ss re': g!::A
202203
b& - 1,5c ' \ t^ t 1 t ,33Vs2 , -@
suh6lllla 1 lo I,
b() . t ee Gave"/ r . ) | , .3 . , ra.',t6 " 1g,ea l|/q
fir,/.) A soiq, | ;s a aPad] lrcna poei''on )uet atn"a, brl nd @r-ching, a 6pinq. thow tl.a hnrrmum dcbrnoltbn p.odrrood will bcf*rco lhat rf fho samo worght iE g@iualtr lowd4u/n,ll'. cpnry,
' /e kt, ., 9.
ak,.Ava4/0,6""6 - 26"
waighiflg 46,6 tb is dto$d lron o hcighi of afl.whosc modulus is loo lb po. in Whot volecilywilloi tho instcnl lho spnnq ie dolormd + in.?
50th iT=-
_-H_*(wb)-lz*t! " wv'/zq
96,6 (a I a/12) - t/2 (.rttz)(+/z)n - so.a/6a,+f! - 1s.32 {1/s.
i41g) A 6e tb dcak stidca daffi an incl;na having o stopc of z'!arIi<:al lo4 hartzonlal. 11 sloris lrom.csl \ ofra. noi.q af@I,ElrikoE o spri.g whoso modutuE ie ioo tb po-fl tt lhe aalficinloi i.rnelic iricl on i6 o,lD, ltnd tho morimum \ctaalf of tha btocK.
[w?/s) w(4/sYa.r))kl I -'/zxs' =wvfq6cb?t6)P/s - vs@,iil - iu)/1E "(at/64.1v.
26a6 | tus6 -soog - g,z2v"
tho blook hovo6lvaa:W - 9 6 , 6 l bh - ,+f l .
^. 1& lbln
t _g'6" + inPoAA !'btoc;ly
6i"cn:
d . 4 f lRcaA'
i
diffcrEnl;ofo voloc,ly wrlh rcstr..l b 5,% a - @ s ' s ' u k t d
6 - z.e+fl (6 aat. vatoaily)6@(4 r 2,64) l./s - 1/s@41- 5o(2.a)' " sa2'r'
y . tr"2a fl/e .
4n) thrcugh lnd dillon:, 'l'u61 l a .'a lb block of P'ob la1e
slido frDm;t boforE loochinq thc sfnnq if ils'laloailf ic bM
ol lho inrlont lha spnnq tc dat nn d 3fl f As.umc lhc gprinq cons-
lon! i. ahongaa tu s blh
Y.10l l /66 . 3 l l
K' aatb/in
?Jrra - "-t ux, "l @,') -po a "t o1f / z'lea*dl,/s+,+
d - 6.67 {1.
w1) A waigl\l of w lb \6 se€pondct f.cd o vc.licol cPihs (Ftq P-
z1l *ho!r'. n.i,ulus i6 K lb pd. fl. Ihe *oiqhl ia pvtlod doa s fl.
S utt\6' = rayrq
F . " S "\ 's J r'0fu
r22) Iha rtqid ho.i:o.l;l sha.o tn ftA P1422 i€ suPTrlc4 \ 2
€prings. A 3oo lb wciqhl i6 lha plocod uPn lte bor ai a. A uddan
btc,. priaots tho woighl la{o.d A wilh on inif;al wlooilt of 6ll/c'
vvhol i . r le /c loc t / *hcl r l .coaha< A? t tagtcLt {r ,c l ,o" \ ] t*c -
fnom ile cquil;bcru4 posil,bn \ thon rcl.a.ad. OclamJr.(, il7 lato-
city whcn il |"d1urd6 lo tho oquilibn,um position .
sht of lho bor3oo r rca G)0,) - so(1,)6
6 - o.5ft{sn/6+,40; -6'\ + 1q1,r)(a.f ' ub/rlz)Co s)"
\t2 - 4.161 l1 /s
204 206
t2r) Nagl.El friclion of lrrc ao-tb collo. ogainsl ii€ yorticotqutdo\ cohputo lho volo'lly ol thc ,:o|o. oft., I t6l. fottcn z fl , sl;d .ing frum rc.ei n tha posilion chown in Ft p-1a23. Jhc unsl^:lched
h2a.) P.pcal
Rc,2d : uat.rjV
PcqA: s e\l
lcng1h af lhc ep",nq ic :f1.| .
Fi? 'a.2aell6 . - 4 , 2 4 3 - 3 - 1 , 2 4 2 1 7 .aG') r t/, G,12) (1,2at)z -(aa/6aAJy2
\/ - 16,26s fl/sr "G r ; t . " r i .62- s-e - 2f i .
ao(a) - lz(sx2)(r), .(ao/6iA\(v: -16,.6s,)u2" - 332.21 f l7s,v ' . 1 b . 2 i l l / e .
p'?b. fz3 if thc unslrrl c*n long|l. of lbd sprtnq is 2fi.
L. Fl* = a.2+3 f!.6.- a.A3 -2 - 2,2a8l l_
a@) +,/, (s,.2)(2.2a3)' = ("4/at.4) yoY - 2o,88s fl/s
6' -s-2 - 3l l .aot+\ . ,/, (s^12)(z)2 -(co/e+.+)(v,^ - zo.ses")
Yt2 . 299,1\z = 16,1 fi/s
l
'423) lll, .or in FtA. P (2e i€ noetne lokord lho bunpor spring\ hos o klncli: oncrgy of 1@,ot in.tb Tho rrr'n bmpcr.Ehicld(9o) 1s .rnncclcd lo lho flbin sp.,ns, whrzh tr/€ a noa)tus oflooolbpor in. lho.lyio oq'riia./ bohpen 6hrold6 (b) o ra 12 n. *Aina aat^ca.
?,fio.h? 9 a.<xrndaa/ spi\ngi, @ch ol whbh tr.s o nadutue oi
5oo ll po. in. wlai lle otr ie broughl io no€l, whol will hovo bcclllla gralael n6tomcnl oo ? 't1:rnr ic.co^tooc ol thc eeaw hasoD.orlw W thc .tvt^ 6pnnq '
y2 (ooo) (er6)2 r'/.(2)(@) 6' = 1@'o@s@ 64' | 246 r b2') r sd)6" ' ta,ao
1@06" I a2o&6 -26cxa.o
6 ' t 1 2 6 - 2 8 ' o6 ' -:ztJ€dliEzet- - zin'
. S L 3 1 1 ? - 2 t 1 2 = 1 4 n .
K E s ' Y 4 k ( 1 2 r E ) "KEs 'h1o@\(tz1z) ' " sEot)o
/" . KA^E . s^a1o/ooooa 'ss'/
t+2s.) A l,oin watghing 1@ lans 1. baing WtEn up lo 21, gndo ha
lnoin €.sielonco \c cona+onl aI lolbp$ +ao. 1la sx.d of the lmink tra,.aeca tran afr per 6cc toaflparecc in oaistoncaof tcnafl.fina lho mo,'mum lo.sc .o|\cr ddclopaJ
9olh:
7- lolb/+ooes- 4bof1.
Kcqo fr {ch In nP.
2 .s - w/ra &'-ua"j
lr -lr,bo>- rco(iuol1o,46afl -.ao -We
, , " F - 9 , 7 2 6 . 7 1 | b' Hp. 7v -le,zze,r Gafl/sso
fr) walc. n""" ln ,n^'l *!ii"nt". aab.a* u'ndcn o hoodofa@fl 1o dd'a a l"$:1ne. Thc iurbine is @1, offdeal v.,k co""al.d la a sonc@la. \y'c \e sa'/, eficie.l. rvhol ls lhc pa.?an a.r+pulin Kilowo+is i
A.qa | tu||t ollpulSa)i .
P.'c. . 8Qh ' Fv
L - b 2 7 [ n C ^ t ) ' t ) L o o a l = t t e t . o t b
""/zq . acar . tr/bzr)G<n) - 16o,6nlshp = fv - [F6,1x6(16a 't/ssa
hp = 3e,7ts
206 207
e - outpjt /tnp,fo,9 " hp /3e,73
hp/iaeatrla - 3s.rs hp.
o 9+ ' hP/3s.1sh p . 3 3 . 6 r h p
p.r!o. Onlpot . a3"61 (01+6 Kw) ' zs,1 t<w.14.1) \Nolar e^+crs a hydrcult:c .cacl,:o^ lu*;no w/ a \at<itff of 12f\ pa" 6& q, barcs il 3n bwor wi.th a lato.ily of a fl F.rcd.. IfM.t&ab olwolar lloa lhrclgh +la +u,$.tne o&h,*co.d,.ahwtcth6 ho.sopowdn dulpul Aseunc th6 lu.b;nc ie w,/, effii,cnl .
Oi"cn :v t -u f t / sv, '1f l /sc - aol.
h - 3 l+ .R.qa ' Lp orlp"lst6 .
u7,s = Y'Vq + b+ntp).ftGra) -afuoz,\ r 3 t,,
.H - 4,9a76 f{.Hp.*"" ' trH - too,to"(+,setu) - +ggte x,o. fr-lV
Hp' asa.rcry3.N, thp . go6.U np.-rsd I+-!!e - p-tp,tt
/c;r"+
a.B - p@to,t /so6,ba hpPu tp "1 ' 725s t rp
$iIl{rt,t
i
ChaP+or 15
lmpulec \ l t46monlum
208 20s
1e..:') A Boo tb bfoch i.s in contoul wilh a tavel plci c lrhoso cooff;oroal of hrhelrb fi^iction is o.to. Jf lhc btocy, is aclrjdupo^ W o ho.izbnlal . forEo ofsolb,whol limo will olopgo b€forD lho block tuochcg o vato;tfy of 4g,3 ft pc. €ec, s+o. -ling f.om rs6l ? lf lho.eo-tb fauie ltwo ncmovcd, how much\ongor will lho blook anlinua Io nyxo?Aivon: ; goth:w-:oclb, F-.eolby'L.o,1, ' , r= 4e3 f l /e,QcqA: tnno Zr, =o
lso-3do(o,1t t - 3oo/32.2 Gs.z)t 2 2 5 s c .
z.t(o1) | - 3oo/32,a (4eB)| - 19 eac
$aa) ,A
horlzanlol fora of zoolb puchos o 2aa,tb btocK upon lndlno whoso stcpo is 3 ve.loal lo horiz.nlo!. lf {*=o,2,dalarninj +ha linc roqurcA lo inorcoso |ha "atocily ai Ihcblock f.orn 1o tu50 fi porcco.6i ton: soth: - t| .3o.tb. N= 2oota . .<11,.2-m-/+: / "-o.z st*yff,e4;u1= toft/s'h-sofi/sp.c4d | tr"tma lzoa tza , uo(oa\] t = zaAzz (scto)
1161 - 246,4s
t .1,60 aa. .$$) AircoI contml tmpocl acans bal. a ro,lb body rrcli^S1o thc rlght ol slt pc. ad. v, a aadl ol *dtqnj i ..'oin;,orno rct r ol 3 pc- ,,cL lhc traLcrcol ol rcsl i l" I ion a_ o,s.I\,n
,aDo:,| thc 1oa b tbdy rcbounds io t^o tofl at 2 fl/6atU^el.,rn're l'. \\c'ghl N ol lha olnor booloNon gdlh:
W^V^TWBVA .W^V{rWrVEi\^-.511/s.yi ' 2f t /s 1@(b)- 3w = 1&(-z) t wvewE .w , vs - .e {l/sRcqA: \Noighl
7 O O = 3 W + W V 6 ' - . . - @
e. vs' vx/v^ vao,E- ' , /s ' re/s-L<)
"/d - 2(1/<
Eao.J A qolf ool E dropwd ft.ma hcghl ol 2ofl vPona horaon&. slco ptola thc cocfftcienl of rcslilui'on is oee
frind lta hoiahl td which lho boll rcbounds on lha lr€1, 2nd,
slhsliluto Vi 10 aqu<rliot\ 1,
/oo =3wf w(a)W - l a o l b
8\ lhird bouncos.
6kcn th- zo t l , a= a ,e94Reqa: h1,h, \ hs
solh j
)(o,adi'6i.ne
h4 - 12,7e {7(o,asa)" (he) -h3
'@
h3'1.,21 {'1.
Ys'= 'Fgo ) h- I-c11,226 - {4?44
c - 4,61
h' 6-4,61 - 3,49f | .
cos+ - 3 aq/B -0,4237s
1/ - 65"
" =.F,,i, .J-tu/r . jb/*
o osl ' ft/zo .- hr =losofi
ts.ls) Ih; bolls A&,s 'n Fiq p 1516 orc allochad +o sli(fof ncgligibla wotghL Boll n G rolodgod fr-om r€sl &. allo$€d1o n1.166 B lf tho cooino,cnf of roslliution ic 0'6, dalarnina
tho onglo e lhnough which boll B will o*inq ll tho rmpool
lrr.ls lar a,ot saq. alsa ft:nd lha a.oruEo inpd fotx
h =€f l . ; b - 1o's =,ef i
v^ -{-4h -F66G . n's+rik\^(^V^.wAVi lWsv€'3a(i.sa) = 3al^1 | z'Jv
'
s 3 4 2 . 3 0 V ^ t 2 A " / a '
o.e .(,r/ v' ),/6t. a1 o)to,1/ - vz v^ -
fra.. 2, v^'. 16' tu,7)
s36,2 - 3a('/a -1a,7)) I 2oVB'
5 3A 2 = SAVa ' 323,1 1 2ayB
861,3 = saVB' * ys'- 17,226 {l/s
2LO 2r l
!5aa),Thc sgslom shown i.) l-q p 'l..ir ts Lscd to.lelcc-m|nc.rho c@f i lcront ol resf, l , l ron l l bott /1 ;e 12lsoroo 1*^rast.\ boll D s,*ings .lhrorgh 0. ss,i aftac A";"9 ,tr""n, Ll
Solh: cos 60- hio ers s,,1' . h./gh ' ' + , s l l
C ' 8 4 , s - a t t !vs - F@4Gd) -A,3s#/s
W^V^ .W^V^ I W9VA'3o67.9a') - 3ov^ r 2o(&,re,
ui " 8.37 fl/.e = &s'-v^')^/^ -vB) - (+.ts - s,zt)/<tt,o+,o)
o ' 0'333ts+2..), A bo is lhrown ot on ahglo e wih jhe narmot lo o s_-mll l ,w: l l
os chowo in f ,b p vsz ,L .et :ouno. ot on oo,xte1
*lli l: nornol. sho6 that tt acflnetl ,f .*,r",;;;:axPwsecd by o= Io e/bns' .
. _yi cose/,r1coget r o m t . V " \ . s , . e / 1 r €
e,Cy,:s,:9(:9,e_) . tane o,t estno \ vc.se l
c . ron) /Lono$as) A boll is lhrown w,lh ̂ . .-,^-.r. .t .A A L^. - , ._ , ,
. . ,_ . . * , , . u "aoct t / o l co l t por sc. t : . d t ia : , ,
h=" f tb " 10 -s .511v^ ' . t2qh ' t rzo2 .21(s
- t?,s+ Ms
:1 !- !. * t\ thc hor ua tt a, .r"; ; :;;;'' ";:":7":r:t*thc tatl ie rat.,a.cd (rom s p6si,on a6,t,c ta".t a,o,^i;, ;"",," l; ;:.,;",' 'rT.J""rii""J"l,1!,ii,of rcalilul,on bolwocn bart b\wa| i6 a,6, Ho* far gem t6o wollM tn" b"tt elriNe lh". qrcund 2
: '1:.,u whcn thobo,r st! ta. thc arouno
iIII
Iii..
i '
ili
ili
I
i
il
:'
I
IiI
jIIIIII
I
Il
7 -iosnPt ,'/tgtl
34,07 - 11,1 statt c.l | 161 l'
16,11r | 821-a4d1 'o
f -vo snet - h ot'f - Ea s'"6o(1 d - '/, G,'2)(1 6)'
f - 2 s o 7 f i1 . 6 r 2 8 , 0 7 . 3 . ' , 0 7 f | .
\f - (sa @s6o)' = a
\vt - vor" 2o, g
,r' -(so!,'"Go)' .,hG2,2)(28 01)\ry - s'2 fl/s
,,tr,t.,Fai6,z' = 26:1 l!/e,x'- lon-1 b,2tt'zs - 18,16'
x -\o c.sft'1 @e 28,6b (4 222 )
x - 18.a11.
e - taer /'t.1^0.6 - \ t62 ̂ /26 .31 tLEts .L '
24,51st ',t6,1e- - v6zf' f t2f " s,2f l /s
vs, ' [G-ia 2"
/ - t o n 1 b ! / : s
2122t3
$.4,) ns shown in Fb.p-16ag, o ao-tb bo| movng hor;zonloltyto lho.nighl wilh.o vcto.'.,
.ol g fi pd. ec, ca id.L obt;quatf w/o^ 30 )o barl.^movinq up_ to lhc lcfl ot 4' to tta tori:I/oiol ol ro
lt F,r sc. tl .lho. co6ltr.,ont Of rE6l,tu'ioD ic 0,6, &t.'|rlioc lha
.9:Y \ d,.€ct,bn 6 tta wtoc\ly of qch bo| a,i" t ini,ait6por_
&Vr rm,{r ..riv;, r m,Vr',14(d - *(1ocd$ , +v,i, +*a{t60t2 - ao\tli + suL _..-@c -(\h; -\;)/!,,_w^
a6 .&; - yrt)/ s, $cas'to =vr i v, , , - . . ,@
m,rb rnuq/ - r{il + r',rrv,'y6(tos^ztt ..flv| *u.; -6n/6
fro,n z, u,; -roirr' .u*. r0,6o,a - aov,', teo(ao+v.i)60,2 - 4oy, i lere\ i-239,0 - dv.i
vti =-e,+a fl/s
e -Ian-1vtth.l - ka-t s/s,57t " 3 2 2 7 ,
Ye " &26 fl/s qlo righ+ oI31 2r' \4/ lnr b\zo^+ol
--!- i M, ) fM.)- l!-
M,V rMrV - M,va' lMrV.'K4 - th Mtli + '/, M2v2.
\^ =8.4a I l/9
Yt'-Y+a . 3 aa fl/s to that'flf.oa:L]r; .10t (-3.a3) - .,5.rt1/s
v . .JY, '+v , i '' u, .vs.F-a,s. . o,ze n/"
r.t.. t/r uN;' I t/l^.ya''c ' ' t2 ' -V'
Ii
r) A rigid bor CASD s'Jpporlcd 06 shdwn .,n Fig.g is c,cloctupon by lwo cquol horizonlol foroes p qppti€d ot c \o Oal-Oulolg lhc r€octions lhol. $,ill be inducod a'l thc poinl6 ofuru-
PROBLEMs
Pport. AqEU.ne 1'.rf t , o.3{t, b. 2f lAn€. Rb " -Ro . o,zgP
2) Owinq to thc wcight W of the locomoliva 6hov{n in Ftg. E, Iroacibn6 ol *'e lwo pdinlc of 6uppo.l A\B wi[ eochb,e e-q@l lo w/,. wt'cn tkE locomotivc 16 pulling o lro:,n { th€drrh^,bo. pull p h ju6l cquol.lo the lolot friclion ol fie pls.c,foontool A \ ts, deto mine lhc mognlludes of lhe vcrlicolr€@l ions Ro tA Rb . An€ Ro" ,+ -g r ,Rb .+ r# .
214 216
s) A boql i6 movcd unilormv olrf\g o aoft)\ bv lwo ho__
se6 pul l inq with f i r rrs p'?oo lb hQ '24olb ocl ing und€'
o^ onqtc a'@' (Fis ,\) Dclermine lh6 oogrirludc of lhe
r€€ullon{ p'rll on lhc bool t .' lhe ongle p \-Y oG chown In
t h e f ' g u . e . n r € R = 3 s 2 l b i p ' 3 a ' i 1 ' 2 7 ' '
+) For lhe porticulor poirlion srwwn in Fig C +hc cat\'*E-
{ioq Fod RA of on Gnginc eqrls o f6.c P" 9oo lb on lha
cronkFi'n ol A. Re6ol!c 'lhis fa.ct inlo lwo rgal(''p,vla' cofi'
ronenl6 th -,-FL, opling hori:.nlolly L' venlicallv, ol A''
n n s . P h = 4 f s l b i P " ' 1 r r l b '
216 217
.t f\ vcrticol loo.l P j€ cuppo.icd trl o t.iongutor rrrack {os shown in F9.6 F;^d lh€ lo.ccs +.!nshi+tcd io thc boltgn \6. nsGume thot lhe boll B flts loosely i. o vc.liool610lin lhc plotc. nns. Ro.1.2sp i Rb .O.7sP
Choplcr 3;i) A w6ightl€€6 ba. Ag tc a%d-led :n o vcrticot ptono to hingo of A ,r o lie boir 9C, o6, g]hon . Dotedn,no, gmphi-collT, llr€ otbl l6tt S 'n&Jcad in lho lie bor b, thc ocltirn c,fo .t€liool lood P alpl:€d o+ R.
S = 2P (t(,|€an)
:
l
2) A rorlsr of rcdio. ' = t2 t^ \ *c ohl q' eoo lb i6 lo be PUF
,.a' *.' o ** of helght h ' 6 in b't' o Y\orlt4n{ol fcrtc p op-
o':.i, *" "- of o j"i"q w"'"a oround lhdci@-fc€ncc
.f thc rorrer ' F,hd rhe moqn'tude at ' reqi'rca +o 6lo''t the
rorrer .!€r tf€ curb A^E P " 260 tb
3) A bol of wd,qhi w rc6r upo. o sdath hor,3t:l *T^-a
i1.""1".i" i.- 'r, cr^\ar \*o elr;'s< \s t* Ao Yeh''h poss o
"J fi.*tr.'.* purbro al 6 tr-c tl. -'ry r"d'^p '":' ::'::'1"
;;. ;" ;" ti rt'e .ri"g A6 'q ho'-'zorlor' F"d t\eo qe '*
il";,nJ;;,"" ;; .o-" *''n rho Fb'rzontor whe4 rhe Et'rr is
; ; ;; i;" .r i"t,;".i,. A16o f''d rhe P"€s"e R be{*c€n
lhe boll 0,, lhe Plonc.- ' ' f , r " dosn -P /q tA -w
- K=Pr
2ta2ts
a) oatcmi,ne ttrc o>bt lcrcra q &- Sa induocd i. tho borcAC la Ec in lho Fiqvr. doe +o lhc oclioo of the hori:a^lot op-pl\ed load ol C. Tho bor€ orc hing€d togolhcr ol 6 & to lhc
d n n ebcl.io 'liqht fiitu.c of wcighl q-.orb 's supporled os6ho{n. DcieFmine lhe }ensile lc.cedq -riq in the wi.es BA &BC if lh€ii ongles of rncl'nol|on or€ o€ €hown
Ans 5, '2s€16 ; 52 = 2a7 lb
tu^,J-a 1l:I8ffff; lhc rcoclio^ ol A \ th€ force S h ltre bor oEduc
ro ir'c oct,on of lf'" Uods P t'! oppl'ed lo lhe crone' oe srowrt
n-JJir. -",gr'r of lhc crone ( osEurnc idcol hinses ol A' q
q e. a+'"-' thot P'.5ool:: 1'.1:-.o.:s:i
-o--.1 Anc. Ro = 11'{o lb i S r 1ei95 tb comprc€ion
,) O€la.mir€ ttE oriol 6.€c6 in o bor€ 1'2'3'4'L' o'f ihc plonc
i** "r"**ra Llood"d ot sho'n Ans q'-P;92'+Pi
9,t- -oiaP i 94' o142P ,9e - -O'333P
d Det "niie th. &.ce s in lhe bo' As of lfp Plonc true€ lood_
cd \ slppo.ldd 05 efrM Atc s = o+3P
220 22r
aJ A plor€ fiqure-f€ur liorne nBoE i. @pporred on on Inor,necrplone E\ looded os 6hown. Colculolc lhe ot;ol lore indoccd in
Ans. Sbd " .106.7 rb, tension
s) Two b@6s AB\BC, joined ioq€1h6r bro hingc B,o,€ 6upF€r,-,cd bt to!- bot.. h,ngod ol rfE,. ends Dete.;,ne lhe 10(6 p,odu-ced in eooh ol lhd6e borE due lo if€ octio^ of lhe toocr p = soolb.dime.eio^ o{ ihc €l.ucturc orc os €hclM. Ans. Sa' 1oo lb.codp.;ga"s. '26e lb, Cbf lpe.erof t i g ic=62rb. tenston.
t Whot i€ the neccesory cocmiccnf of ld:.i6n bclwccn tirc6 krEodwoy io enoble the lbo. wl"€!l drive o! tohobjle lo c|tinb o 30 7.
r ) A emoolh c,rculo. c/l,.der of waqht Q 8i. tudue r 16 supPd'-
i.a u, *o e"*;,'.c"ro' c.'rin&r eoch of lhe qdme rodius ' (we'q-
i'iOi", "" .i^- 'r *e coefiaienl of oiolic f iciion b€tween ffp
flof locee of tL" g€mici'culo' c/li'rcers &' fhe.norizonlol flone-or
2) lrc bloc( hov'rg weqhlr w' !' wz o'c <h€lcd bv o €lFng \
*", ." n- -"t, pL*" "' "-*" l[ lhe onere ol l';cho^ for
"". io ' ." ' t .9, F' .d ihe roe' i ' lude t . o '"ecl ion of l t 'c leosl
i.,* p "op',ed to tl'e uopc' brocn thol wirl ;ndJcc al'drnq
An6 P-i" - (wi rw') srn{
;;il;.r -"t ls + = /2 L. fncfion bet*€en t'c c'lrinderE lhem -
!;et ee E neg\e.lcA, &lermine lhe molihunl diEt'nce b belwcen
the ce.le.s B 8(6 fo. which equilibnum will be po6eibl€ qoui
lhe middle cyli.de. iouching {he ho'izonlol plone
t ' nna b@* - 2 e3'
a) Re f'rine !o lhe fiburc ' the coefficiehb of flic tlon arc os fol-
6, o* "ritu froo., o 3 o+ the woll,!( o 2 belween blook€ Find
fhe minidun ',olue ofa horizontol for€e p opplied {o thc lowe'
block thol will hold ihe o/slem in eqlilibriud nn€ p-in = 81'2lb
iiI
i l
, i222
223
Ii F) A sor,d .qhl cirarlo co€ ot otilude h - r, h. k md,u6 d:
bo6e .=t'n. hae its c€nterofsr.ov v Co^it6 E€otrctrio ari6olldi€lonce h/a - 3 in. obovc thc bose . Thic conc r€sts on oo |ncr Inedplone n g, whah mor,es on ongte of 30. wrih ihe ho.izonfol qfo.which ihecoeffic,enl of fFiciion isA=op.AhoF:.ntot Force pie opplied lo the ye.iex O of th€ conc &obi6 in lhe verliool ptoneol lhe fraLle es rhc*.. F,hd ihe morimum t(rrlioimirm votues olP consisfenl with eqrJtlibrturn of ll-rc ooire tf the wehrrt w-
Ans. P*, - a.61tb ; Pm,n = o,sgs lb.
1) ln thc coseolthe t.ipod €hown iherc is no f.iclion bclweenthc ends of the less E'^ the ftoor on which {hey.est ro pre,,en}slipp;ng of the lcgs lheir end6 ore connecled t gtrings otongthe li.es AB,BC, \AC Derermine then +he ren€ite lor€€ S inedch oflhe6e st.i.gs iFeoch teq mofcE 30. w;lh lhe ve.l;cojPG o "e.ltaol lo.ta
2) Deiermlne ihe lorces prcdlced in |he bors 1 fo6,itlctusiye.ol Ire spoce tru€6 ch@n, owing io the oction of lour ve-i,catloods p opplied 06 eho*n . ACpD ?\ A'C,B-p, one lwo Gquoreswilh porc lel sides of te.91h6 o E! 20. .€6p€clrve,y, u<^ lhe
l
224 225
O A pJlle/ A of mdrirs o is guppo.led fnom lhe Foce ofo\€.trcol woll b/ +wo brocca nB&AC logalhcr wi+h o fre ba.a6 6hown. A flelible cord EAF i6 losl€ncd to {he woitot E,prqs_ses ove. thc pullq/, &- c.die6 ol ila erd Fa r@d q. Find thela1!;le fo.pe S pradu@A ri1 the +,e bo. AD lf e, botb,a=6irb . 1 l \ c - z ' / 2 f l . A n 6 s . r 3 r b
Chopier 7 jr) n ho.nogeneous slende. wi.e 12in. tong ,e benl in lwo.ri,gnt ongle-s os shown Det€.minc 1tle coordinoleG of ilsoen_
z) A stccl st€fl oi c,rculor croee €edlio. ho€ o cirEular sleolhub prc66cd onlo if os shown Fo. tho di.hcns;on€ ebown in ttc
flqure, dcle.mine tho di6lonc? xc fron ih€ lefl cnd of the shofl10 lhe cenle. of grotti l c of lhe compogrle body.
Ans N.- 624 i^
3) A hohogcneouE body consisls of o ciccular cvlind.icol Po.-llon of mdius r olloche-d io o heoispheriaol Portion ol rodiug
r oE sha{n Deie.minc the heiqhl h of the c/lindFical po.tion lf
lhe oenler ol grovily of the composlte body lieo ol ihe cenlc.
C ot fhe citculor p..lope lice of thc hemispherc. Ad6. h'r/,{t
a) A honrogcneous body co€lgls ofo righl ci.culo. conicol por-
tion oliocfled to o hemlsphe.icdl portron of rodius r o6 6h-
o.,n Delermine the oltllvde h of lhe cone l| the aenle" ol
9o"i1y of ihe compoeife tlod/ cc;no'ijes w,th lh€ oentc.C of
T
ih€ aroulor roso ol lhe cone
% r/ i \ , l
K-i.jfi---w
226227
5) Delcrmine the coordinote yc of the c€oier of gft,vily ofo stel rilel hoving fhe d;hcnGions shorn in Fig.H. As€umclhe beod of lhe rivei to be hemiephsc;"o|
chopter A ir) Fr.d th€ poto. momenlhovioq boso ir h\ ott;lude
of inerl;o of on ,soscetes +.,or.,,teh d'lh rcspe.l lo iis oper A
Ans Ja - bh3/a t hbT+e
!) Frid thc polac morrrnl of incr^tio
Ecclor of rodiuG. b- cenl'ol onglcof lhc onco of o cirtulo'o( wllh ragp€cl +o i{s
Ans. Jo ' o.r'/+.
a) Calculole lhe mor"enl ofincriio
FiC. B wi lh fcsPecl lo lhe l -oxr€-of the shoded n r€o
Ans. Ir = 26 e3 in.+
228 225
d Coloulote lho momonl o{- incrlio of l|,c orEo of lhc onol!€&tion hohng llle dimcnsiong €fEwn in Fig.A wilh r€.6p6cllo o ccnltoidol ol.ic po.ollcl lo lhc x oxiE
nne. Ir . s,r6 ina
Choptc|. 10lr) A bodr storls lo rnovc, vcr+icollyupwond urdo. ihc in-flr5ncc of gmvily with or ririf iol vclooily i. = .ofps. Fird(o) Itp moimum he'qht to vvhich il will rteo C\ (b) tE tircq'.rinod for''t lo roium lo ilc iniliol po6ilion. ToF! thc atrolting point os tho ongin so {hoi )b.O \ ncalocl o;. rc6is*
Als . (o) )lrcr - 6.2 Cl ; (b) t . 1.24 6co.
2) A {'oin is ho;€ down o slope of oocra with o vclocitY ol
:oolph. Al o ccrioin inElont thc engince. opP|b€ lhe bmFcs
1t p.oduceg o iolol r€.6i5tonce lo tolpn eq.nl lo onc-{enihof the weighf of the lmin . WhoJ disionce x witl lhe t.o;n
tmvel beforc slopping? Ans. X'32711-
i
a) lhe troin tr^ovol ie liom sjalion A to stojion B which ls1 Km opoFl ;n e minimum l ime of onc minulc. I f thc lminslo.ls frbm rcel af Gtolion A,&. occcler.oics at 2.8 n/s&,,contlnu6s ol co e+anl spepd h. decelarslee al 2.s 6/." u^-til lt 61op ot stolion B, f,hd lhe moyimum seeed in rni/nrHow long d;d l f l rovcl oi . lh is 1op speed.
A^e. s - 6a.76^m/h. ) t .763gs
e) rhc nof;o^ of o porliale is g ven by +he eqvalio^ s- aLa-31' i5 i r O wher€ s r€ ro {1. &, L ic in s€c. Conpulc Jhevoluec of v l^ o whcn i, - 16ec.
A n 6 . v = i n l s ; a = r c f l / s z
2gl
Choolcr 'l'l :1') A rnolorcyclc & ridee of tolot wcighl w: sc)dlb tr6?el
in o vc.licol plone wilh c.or'etonl spocd v= 49 mPh olong
iha circulor 6r:rve AB of mdil/s r ' 1ooo fl' os 6hown Frr'd
lhc rcoclion R exe.icd on lhe molorc/cle bY tllc hocK os
il po66c6 lhe cresl C of lhc ouruc'n n 6 R = 4 9 2 l b '
l2) Thc cocfficicnf of frrclton bclwccn {cl ocpt|oll
\ the ti.cs of on oulomobile i6 folrnd lo hdvc lhc Yoluc,ra- o2r. Al whol conclonl 6p€cd v can flE oulornobilc iro-vcl orourB a cu.!e of (odivs F eoofl /out s\;ddi.tq 1f
the rood ]E lc.,ol ? nns- Ymr : 49 mPh.
232 233
-r)-.f n fig,.rrc bclorry. o hoorrcr ol wcqht w - 2 rb siqls leomrE6r ol n &. slid€s do*^ o rcal for which thc caff;;tcr rf-rcr 'on $ l- o.2 Ftdd lhc disloncc I to thc pcinf ,whcrc tt hils the gcound
a) In whol p.oporlion wilt thc moximum rorge ol o prqjec-lile &, incjrcoad if lhe iniliot vctocily i6
'irl(a<l€,cd- b,
1o F eal ? Ads 21 p<jr ccdl
s) fn lh€ f'gurE. ikrc pitol ofon sieptone ftyng hontzonlot-v wf rn con€lonl spccd 't 3oo nph ol o^ cle@lon h.2@oI
oboye o lcvel ploin wishee 1o bornb o lorgol B on the 916-und. nl whol onglee below +h; horizrntot shoutd hc scethc torget 01 thc inslont of rcleasing lhc bomb rln orderlo sco.e o hil ? Noglecl oie r"";n1o,o" A7,s. e - 22.12,
-- r--&A.i^ --I \ \
Illli1l
t
Choptcr 12;r) lfro ormo|.rno of on oloclnic molon hos on onqulorspcod n= laoo rpm ol illo lnstonl whcn iho powo. i6 clrtoff. (o) lf 'l comos lo rosl in 6 6oc, coloulote Iho @.qulo.dacalarol\an c< oesuming thot lt'rs constonl (b) How rr,o-
^y cohplcilo rEvDlutlons oocs lhf orrnoluni mol'ir du'ing
lhre porjrod ? nns (o) d = 1or scc-'. I (b) so rcv
, Consido.ing ihe syglcm in tho fr'guro, dotormlno fho
vol,.,,o of & for which lhc ncgolivo ongulor occolorolio^O of lho bor OA hos l lE moximum voluo Ans. +'30'
244236
lho blocK C is rising
i A slcndor b'rl .igid €ornicirculor wirc o{-rEJius r icguppoilod in il6 own vorlicol Plono by c} hingo ol O & osmoolh pog A 06 shov.n. lf tho pca 610.l€ frorn o &, rnovos{ilh conslonl sped'to o\ong lho horr'zontol r oxls, lrndlhc onaulor volocily 6 of iho wi.o ot tho inslonl when e.60' . A n e . 4 = v o / c .
+) For {ho fiSurc shoen wAigivd/G i o(^= -1,5 rodls' 't!
2scc6. Fird thc voloclly \ occalololio of blocK c.nns. vc= 125mm/s i Ac = 3zs mm/sz
s) For tho figur€ chown, c( = 6o@a/sa '1g=6n. Ho.r losly6- r+t m/s
llL
tilii
Ij
! i
i
Ii
iil: i
1lI
f
I
l
z) oclcroino lho aynomiool dcflootion 5 lhot wll bo pro-d,uccd oi'lho c,slor of o 6i'nply slrppoilod boom by ollo-wi.g o .+ooo tb woighl lo drop onlo il fro'n o hoighl ofain. Whon q.odually opplid, lto .ga'io locd prodv@€ oslclic dcnoclion of o.1 in. Noglcof tho rno.6 of lho boom.
Ans . 6 ' 1 '@ in .
256 237
3) Whon o ball of woighl w rcst on o spring of oonsloni K.it producos o stotio dofloclion of t ln. How much will lllc€ofro botl compro66 tho6p.in9 if 11 lG droppcd fiorno l-aiqh " 1 fl? Ncaloct lho mae6 of tho spl^ing An6. 6 = 6 in.
a) A qrnoll block of wcighl w=lotb is givon on inifial volo-cily vo-ro fpe down tho inclincd plono shovn in Figr-ro.Iflho cooffioiont oC friction botwoon tho plonc \ lho blocK
'tc ,tL = o3, F6d {h6 vclocily v of lho blocK ctl B oflc. rf hos
lrpvclcd o d€toncod x.,5ofl. An6 . v=29 ,9 lps .
ll, i
s) lf lho 6y6tom in Figt.E iE roloo6od fra,m rocf in lho con-
frgurutrbn srown by solid lhoE, fi''d lho rnorimum die{oncoh lhot fho v{ciqht p will bll Nogloc+ lriolion \ os!6umolhol lho pr.tllcys A t\g oro very smoll.
A^6. h - 4PQt/(4s2 -P2).
Chople. 151d A locrooliv€ wbigtrirg eo to"s hqs o wlocily of 10 mph 4bocke inlo o froilht cor woighing 10 lons thol.iE ot ft151 on olrvol lroc(. Aflpr couptrig is modo. w ilh what "olocrly vwill tho onliro systcrr' aolinua lo rano? Noglccl oll lriclion.
Ans. v = 8.52 mph.
2.) A wood blocK woighinq glb roEts on o smoolh ho.iz.n -
lol s',.iicc. A .cvolvo. bullot wcrilhing lz o. ie sl:ol t.it -
z:,nlolly inlo tho .Eido of tho block. If lhc blocK olloins oealaailf of rcfps whoi woe lhc rnuzzlo lalaat lof l|)cbullol ?
An9. v '1610 lp6.
238239
!) A no. wolgh;ng 15o lb .!ns h jump6 from o plor into oboot with o horizonlol volocily vr = 10 fp6. Asgumir€ thol lhoimpoci is cnlir€iy plo.slic, fiilcllho volocily wilh which thomon Eq bool y?ill movc owoy flo- lho pioc lf lho bool wci
nns. v -.4.3lps
+) A golf boll droppod from roe'r onlo o comoni 6idowolkrcbo,Jnag cighl- lonlhs of t l le hcqhl l t -mugh whrch l l lo l l .Nesicctlng oie rasistancc, dalarn;nc lhe arffbionl of
II
5) ln +hc fis,rro shoY?n, o smoll oor of woighf w 6ta'ts
from .sst oi A \10116 without friotion obng oo inclinod
olorc to B whc.€ rl i6 sl.lKcs o blooR olio of wolght w'u.
rn, t io l ly ol rE€l ndgum;ng o Plastrc rmpocl 6l B' lhc
co. &. bl; will movo f.om 6IaC oG a^e pontclc tf tho
coeff ,Zieni of fnrblron bctwcen lhc blorK \ Plono iq, ' ' { '
tla,6alcwlolc iho dretonce x to Poroit who'o tlio bodrc6* - l ^ r ' + A ^ s x = ^ 4 2 ( 1 '
1,fl