Engineering Mechanics Statics and Dynamics by Ferdinand Singer Solutions

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Publi3wtOittbola.lt:

'

I

REX Eook Stoir

t6t Nic.d e.v.., Sr.Si. Ll- tlo.. 7al{9n6. t41.49.20 197tC,M,idroas^o. Tat,Nor tat -a9-5€. 7:rl -4t-57 M..il., Phililpina '

TLo

book sntltl€d

Loarntn! cutd6

In

Ensln€6rlnr

fo:r" o . lpl :r :o s o"a:t:r n ,t r r r !l€b o6 r sp r ttn6ctlrp,l/€r,; v r . , e . r . i r r , - ' p " , p " i i ! rtrd concoDts or

Etrlrn6€rrng X€cbanlca ltr e vory b.!lc and rpproscn to nelp tbo itudsntt und€.!tand

;;;.,:l:j":;

,ii;li;;

,",, ,r,r

uy;to!.ttc anO re"."

d6v6rop rher. ofdo!ry

Itllh ttro pre.€rt€d toptct, rhe u6r, wttt trave r vory cotrpran€rsrvastudy o( th6 aundr!€ntat prltrclDl€r ot li6ctatrrci,htch ar6 tppltcrbr; to v a r r. eE(nys ronre 6prrtancsr 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; dl d 6 b! te€6 In rtrolr dr' to ddy rcttvttl€3.

'*pa;a:paat*

Jojo BiIrM

nBsfs I4.t

na'i

-

The rotborr stslr to {crno,led8€ lb6tr lndebtedD6ss to. ut.nael Slongco, Jettrey Bortongan, Ron.tdo Catlrdls, and noreo ld.tano tor tb€tr ".lu.ble tn prep!rlna,nd irttlnA tbe o"nuscrlpt.

forulc@4'l

Bor As.i.ti's

f'&d[sdig_

Etlra staort rrs s:erted !o lbat ev6rythtr . tll De presented tn I vsrJ pertecrty understood, bla tn r con.ra€ tenaurge. Tbls ,tll eltDtnat€ or :l:lr :"" rrtrreu te dtddent's attltude or h.blt ot oelortzrnA ttr€ concopt rttt ou! under!trndtng.

A56diai!

pErpu-g..&*tr-".(Af8t.l1Hg=ffiH .f dle ftntlPiD€3 (BDAPT thililP

'f

Asociatim eEPA)

. "

A5id ltdb6tiF PEPA!trtE atioo.l Bd& /t*i{i(G " sd'rh ao.i'ti' A.."d"d- 6PPAI ;;e-P",ts.hh|;tas iii G* ntu.n-' osEAPt lrrdl'tr5'l Arraieiim PA) 8+86P ndt'tino StPrbr4dbr n rE( Fi$ltqco4rryic s- u*i fildrt " e,,"- cl'.Tds'7r2.al4-7r2'ar4t; Pd no-?u5+12 iri

. ACIC{OVLEDGEMENT

ctqifu

o: Ucrs e of lrirlio

C}+l6rip: ncaiF4ao- Tnar6l('lb Oroglir rt : G.,-iti.!oo- Trqr6loli'r

'

&-4r x5-n u*,2r3 ?t'N

. vtt

I

l1 '; I a& lba.

coii;Aar tE aoob h' -+oo cr,a
--:1508L@, p,- 3@;65 Ps- :e@ 4^*":P-b-

. - so42 lts. Ts'.-a@ €i" ad - -257.12lb€

l\Y

,17".,s'eE

cotrrr',",ntsof cdt

of ftE to(€s

ewvn in FigueeP-aot, congido. lho 7221blood,

r,=-nz(finr)

-j!@r+_tD6co'isidc,r lhc 2e,b loddt P,= aoo co. e: f-Jg@ Pg= 2@ s;n@' | l'73.2'tlbs.

nb 4+€b bodl

Fg- +1t

(*l'

is ebj@d 7dE) ltu ritorgld@' btoch ehown i Fig' P-M f t\D=Sh\Dc=6'L, lolrE loods P'1@br,tF-6@b-

resolro coolt lood inlo coopr;le .conei&r

ru'md \ lcgcnlirl

lt,p i6oo lb lcod j

sinc--L aase-+ h- +-'(16co)' t26ob' h-

Ltl@o\

= S6olhc.

,&- l6';6i ' toa-

2

8

lt

i'r"

n.et r -AA \ -Ar xz X'1.rc<1)-12,s7(q)

onounl k, posi{ion of lhe lhe Fink true6 .sh@n h R= zcb+ te+ a4o | 'aa +..n t zooa (d i@t€d dodn*o"d ) B-a39]!

- P979.!b , R'- 2.ht tsoor aal |eoo r 2oo d@"-d,t L - ]4!@,,s,ta4

"t- ?9,41fr-lL_ d = .:ryL - ?49 !1, a e|*I plola 2+o) lhe shodcd oreo in tig p-z
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

t2

)

aMc - 14oo(5) = Toooi] lb, Rdc
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)

-n

;''',

(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 jhe to ihe s,ien couptes compuie lhe "ol'o of rciing ot lhe )he 6re p)e. A)so delonire

l4

e)

c- 3oR (4
25o.) The conlileve. lruss shown i\Fig.P-2eo cor.ies o v€rlrbal lood of 24<)c)b. Ihe lrr.:s,sle s.pponied by beorings o) A \B which exenl lhe fbrces A-,Ah,\ Bh.Ihe shown con|lule adple€ which musl hove lwo fou. forces pnevenl oppoeile momenl effecis lo movemenl oflhe lruss. Delermlne lhe nlognllude of lhe supporling foecee. rn o.der !o corelilule o couple

o

&:ZtpLb

epwod)

+ ) . + 2 . . T - p t J) P-, "ro

l1'<'

t s) p-6 o 6.tr6lcm a/f (d@ .E ]]vc(F loo aowc ,Iri-F\vorlicol ot-r@ b lhuugh ^ ptu6 o counld.ctocxw; -frrceo qD

canPv d b-f' .re .tr q'I@t€/l}

lho sr9t6

-tu?F,dfte effei Aj:@.b

,bve

lhol w.,ll rro.

downwad

a@(+) -eo

r:2JL

-

aqtt

ridri oFo

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
3-t-:

sqqlb Mn = r4o

_r: :d. l:y

lo lhe |,aft -75o

=eoo(4)

oy

:99]E

G,.,E'b

bor,w o)

"*t oo'nF€cs,o., membef, oa-r|s I P = a@b_ eil-uolea z n_ fmm lho orie

o€ €r.own ;

l6

= 4ezlelb-(ro ho rirhl)

L, - ao _ ?pllfr aane o xrz6 it =-:!@'-+!l= t t1 ot o

lvb'1ao(1) =-2oo ' PG) P=:o96(do*nwo'd) ZM^'-2oo -a.4 (+) -t G) ( uPword) t:29pb

aa?re ot-

"'o 5 xt' --:-la- (uP*qd) M-c- F, L,

2400(6) - bh(+) Bh -Ah = 3600 tb

2.e1)A vertlbo) forcc. Pol A b onolhe. ve"ti&l FotB in Fig.P-zst pr,e4"o" o reswitonl of loo lb down ol Db o 6€Ba+occlocl.wi.ee aauple c of zo
corEisls of o cbckw€

- 2ao @5'

B'-F,

B"t 'Ft

I

i

.rsLn

p]',:.o 4{o r! rcrc. aicled r4 lo the nghi lha,+ trE o.-dn of, r*,Y oEs ol Ot.xt- Recto
R: l4 b dncoleA rcrlicatty LJpol A B do*n oi B.

i,

A tircc

F4.I'-2ss-tn

on eooen h-E of lhe rEmbef,.

sl"ens,th of moloFtot6 il iR

tz

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

f l i '

tl l li i

2s Rcpbce |Ae egolcm of foroee st'4n oqu;votenl forEe lh.oJqh OV, o coupte o

;;""jii#;,...':i',X"":;3'::"'e:::.:mi: zF, = |a1.a(rka') t 22+(46) - t61 (r/JB)

wi)h lhe oadi|bn ofo poir oi oppositc oriol loode eoch equo) io zoolb )we ae\ F= 2oo lb ldowoword) c'2oo(z) - :@a]bjh cw

: Pt4.Zg-b(dot!.

'- ; // "

lhe bend'hg erre6) ol porn) A. l'

lw,st,noefrecl - 1so(?)

1".

B.nft.bn o"na'"qelocl - lso(s)

l

= 9oo fl'llr

h

E?) Reptaae )he syelem of lo,r-.s ocling on ihe r.o-e in rig P-2sr by o ros"rionl ,e o) n q, o coople oc);nq ho",%"lolly

lh.r'4h B eic.

)o lhe nlght)

0r. lad'zoo, f@,os gj|: !L99' ol C =
a farce P - 1@)b. Force P ie perpe|dioolor 1o lhe Plone conDeleffi:ne )he iwisling etfecl at Pon laining poinls A,B,%c t f"lDO tD

:

lherighl)

fuaq4r!(lo

try = ,+1.+(1k ) -22a(/8) - r61(./JE) €F-t =:3oo.s6 G, ^e"^e doanward ) ^ - ,/(10a.o0.+ (-300 36r

zso) A ve"licol shoft nB i6 sfl long h boited loo r;qid sup' end 6.re ollached ol l i)s r.,,pper pori a) ils lowe. end A . is 2t1 long Al whrih bor Ec ihe end of C ie oppl; rizonlo)

lhe €hofi .^8 \

in Fiq.p_2ss by on

b) +p= 1taa1.l P: 2993 tb260.) The effecl ofo ce"loin non_concc,nreni fon:e egelem ie aofined by )he fol)owrhg data : .x - +rJorr ,
.-T'l' ,ix-ao l.r"*

-so tb (6)neons do*nwo'd) R= lMa =C

6oG) -r,ch) = r(2) f - fo tb ltu'u B \C

l8

oe shown

zy

=.F, Ly Lt - 360/90' afl

belo|9o

2or.) ln o cenlo,n oon.
L, = +ao/46o:-:4 n;ght ol on,gin

t9

li' oc252) Dc\ermine comPlele)'J lhe res"llon) ol )h€ lorces '|ing in Fg. P-e62. on lhe s]eP PuIeY €hdwn

@

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

1ft . z!,o cos.6 | 2so -: q994zb(lo lhe 'iqhl) strl3o' ' r25o

4f:r '7@

1,*!arq('

,6a.) Complele)y dclcrmine ]he resullonl wilh reepec) lo pi. Oof lhe ft.r,e syeiem slnm i^Fig. P- t:A.

meons doMw

= Gs9.e2)2 | (-37s)' e - Q5+.Ag h dorn lo riqhl '444t, - loti' 81s/oes,52 12so(<,5)-2eo625) Rd- aMo " ztu(|es) poe€* ihrq,eh lhe !4:9::4:ojs'R

fis. P-263\

___L

o7* i*

- ."o .t"'.

t z"teqe) - zz+(e/s)

= | o n' 1 257. o3//+rs.1s

9, zMo-

o'le in ih€ r€sullonl of l}e 6rce sy6lem show^ t}€ r 1 v inlercePts

,

R " \EF7-+aF7 -'@Ai6Y I Gsri.F t!(up lo lhe .,qh)) B_-:___sst9_A

,bl

R.

141.1(1/.$ )(a)t eawc
d' zMo/A - J!19!p- - - 3.27ll. 44.68

?e) Cod,pola lhc rcs"llonl of lhe llrcc ,;!e€ sh6en in Ftg p 466.l-ocale t)6 inicrecolbn wtlh lha r ts y ores.

the."iqhl) :-ll9iq(]o zta - lt co3s) | 2z+(t/r) - 361t4/r.)

1F,. ao(%s) | 72.e48)+d (Eh3o) - A@r11 io lho .igh] zrr - a@(..,L) - 722(t/,Et

,:-t94! ruPwoftt) R- IEFV-IZFV

:,:gOacnEdn6

t6rzrl' . - ft@-eEY '-l!.Ab

-e.r-+an

- ss allae.s

sa.61/149.9

2 M; - : o a s ' n ' 1 2J ' 2 2" ( / n ) e ) 3 " ' G / ' r . ) ( t - -L,r,6 n 0 (- neJ.s co"")-Cw/ - 1 . 6 7f + r ) q h \ o f O 'Ly -1oo6/1+9.9 - 0.67 ft

20

below o

9,

do*nwdrd)

R- GF? +zrr.. .,/c1_-+rgsloEY E::4231_doq. 10 nsh+

GP io lhe 'iqhl )

Io"ev - zrt7ar,

a

. lon-' s1o.1/01o.11

9a:=A49'

lMo = 3@(1,1a)Q) - 3so("h)G) + 122(2/r,')(4 - 3oosineo(3)

=&: a4.91 j1:lb cw

Lx - 1121.97 - 4LD,

righT o1 O

ty = 1121.q7- - 1,3en. obote O

uo.47

2l

ili r iii li

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 bioeeAb. Far s6>a desiqn, thie r erseolion should oc.ourw/rh lhe didd)e lhind oflle bds@. Ooes l) ?
iil i

trl

iil

,i; I rii

iill i

l

,,/66atf;

267) Ihe Ho*; .oof l..,ss sho./h in fig P-2o7 cotrie€ lhe given loods. The wind )oo& o'e pgrpendiculor to ltte inclined m€mb€Fs. Delc"mine ilre mognil:de of lhe resu)toni, iie lnolinol.ion wllh ihe horrionlol, \ whar"e li inle-

u lo llo

llo

ltoa

I

zt"-zo
lb.z.ia)b.ldblb

^[email protected]:o.)r R

!

i

Zr' - Rt tr , 11ot tso e/s) - o Gmea"€ lo thc lcfl ff-:lqqlg

CeTaad"

) Ztt;A = -uooa0t) + poaa(b)'bo.P( = -228.cea fl lb (- meons ccw) ZM6 = aFlrb the lcfl of E \ xb - zzeao/2zoco =--€.t]tL(from nri&le hence *ilhin lhe third of.lhe bose)

i

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

€F.t . RJ,

R = 2?424.02 lb.(down lol ri-qht)

g, - Ion'zrt/ara - lp.,' 2n P/[email protected] +"* 2s,91'

ir

- 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 +,

- 1A'278.17 lb rdodn )o lho rrghr I

22

Fr -12or 1Eo(a/s-)- o _-L

? '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 d6lm to 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) {E_:j6qlb

F | 11oi 1eo(3,,s) (1o lho n,'ghl)

Q1 ' ZYy -reo fr'F) . Fr -12o +rco (1/s) aeo Goq^wora) =t=:=:P. R-F - (60)2 + (-tso)2 i :_21-?.!?&(ddo ro nishr J

+2Fr2

23

- tdr-l

-ga - lE1zJr/.t,

'

@l@

-+r::19-

ua'€No n{*'E't"l, n{'olu)t2) l+:,fli:Di, = ao/po - Z4!L ir - @A&o'

z@LL

-11o(+)| rfuk) rtrt dt rtgt'l or o eo"B

o

ro zo) IfE ll.Ec tuEca 6l|'m i\ r's' p-27o o'v r€qt'cd tf F= A' poinf @ti.g lhrorgh .€artd't a lgia,lol ote sr6ID, &l€.niE lhc volucs of P ! r- ,tr. ' Applv UR-€'lt p. €:llF- [hR, lhcn ltn- €rac lo fi.d 1o dclc.fia 1fi'ollt

-'&, (',/h) 6) Bt (./e') &)' 4 Gl R.* +gg-6+ lb.fio llE .i,|l.l ' lk {va - e*(.A-o)b) - z*,(r's)@ +t-aG)

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@) rb (da6word) 8:,iqqJ tth. -€llb

.:@.+eti = r e/&>(.) - r (.ftY1) L:-Ec'?,b' P(.A.'tG)rGE5.ae)O/ra>G)-a'e.ai(h)G')'aoo.at(+) !-:!tgY

Choplor

3

Equilibrnrn of Fore Syeloms

The cyhM€r C ;^ fiq P-3o2 weigh' of cyl,ido. c q of rod Ab. *a)

looolb D'aw

o fBD

("i'"F !a)

ol!& o FBDdf pullq/€ Eq D 3 of lhe bor n D €h4n rn

P-.oo. nseu-s

otl hinges fo be sm@ih g n€loot

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 besfuoth thri:rnoes of lhe .od b o56u-e oll @^lool su'{^o€s to

Tne fiv-e che*n i^ f;9. p-3aa i6 surf,orled €orb Per fl Drcw'o 3p. Eooh membor wo,ghs

i^ Pivols 01 FBD ofac\'

a+)

th€ w6,9hl of

.<

"-Kv".

eo€) Th€ cable q boom shdwn i^ Fig. p-tsos eupporl o tad of 6oolb. Deiern1'he lhe lcoslle Col.@ T ;n lhe cobte b, to comprEssivc ,Ale C rn the boom. r Mcthodi (usinghorizonlot\vc.ri@l ^"".) r@se'

I6'n2o't

- C.a6ast

Cst^aE' - 6ao @

eb6l. cq r to2 t.alolo I i. tcms of T) . soo 1 6h 30' + (1 es.d/coeq.)(srn4s,)

J,:!!!=?9:4

s
t.

r,F

G-@lh

g

heol€o{

lfe

ee'9hr

of

eo' h

c - 1BlE Go*tVe.

* Melhod-I(using tulotior oies) rrw-o. cs,n -, ) ,2" '.'.

l@

l

26

e.

rb.

S:!4.%s

-

-c

27

O

c _ e!1.aazllL

r cc6,zs' l- 6oo@6,6d . a coset + saz ea6(coeze')

ztn.o:

FBD of +he blooK

Method I (udrg '

-E34!4-]k' r Melhodtr (u6hg Forcz l"io"gle) si^B-

ii\v

orce)

300 - Nsin60'- Psin+s,

o

P.DsL ' llao.6o' P ' tl cbs6o/c.,.1s'

e 6o-

@

Melhod r (u6ii9 Rololed ,a'6) 3@ - nEi^6o.- H@Edho,n *,J

A

cylindo"

woighing

aootb i. hold ogo:n€+ o sl]@lh inrod AE,n f''s.P-3oe.Det. Pqfl c.-

11- 1@. 7 lb P" 212,1a2 lb Method [ (us;"g sn.E

ll.4n6o'

l

M"thodr (u.i"9 t{\Y o'*) t8 of aanido. b

.Fn-o I P . .q @.6; + il co..o' p -.roo 6 66' + 41g.6os @1 60'

/-K

rltdr e-

MathoJ )[ (u5inq Fo.c€ r.io.gb)

)d.\'1

-ih.Ot

- .oo .t rs'

Pc.6&'- llac.f P - dc63r.'//@.t'

@

dsin!"

* .oo @

P= 4@,el

(6k)-

[N...a€ (.'",{r/@.F - ,+oo- l:3!aj6glL

+ n.i"aa

;.;-

nl) If the vdlue of P i^ rb. p-e1oi6 18o lb, d.r€rmhe iho ongtc 6dtvc il musl be i\.trhed w;lh the. Gmooth plone to hojd 3oolb b6r in equilibrium. the

:;.c

P = n @*/@,e'

- 4e.6os(,o.a4/-. P?194 lU

z.' r.l6in9 sih€ l.w j q = L

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 bv e - ?s' dcl . ltc volrc of P b lhe nomal p.s.6u€ ^t eqlcd

2a

q:d

scb@1..

P'r@!

_g-

.,flor


l

Psins'r

Fo,.e1i.ongte>

29

!ir).

Datcdinc lhe co@!ft.i

to k@P the nogniludes o' P \ F he@ssar/ p equniL'rrum 31? In sh@n in Fb For@ .r'Ia6

3oo4^@'+ P-

P6 -1t3

4'

' 2@ st^lcb'

.oo6in!o. = Fsrn€- O

245 to

F ' aa/2 a'E 6tS I Pcd

7 '.uasao'-

z'; - 2@ @s 165'

oa z* (cszo)- zo <'x'*'

F - tu,87 \b. fo{Ee €v6lar e}i^g ato s1a) Fio 3€ rcpreechts tlc -^cu.Ent p k E fo m'nj6i"t of o bridge trus€ Detcmine tho voluos of to;. e{ullib.lum of thc lorcee u6ihe Rotoled

!1..) Ihc !1..J aoolb fon@ lhc aoolb fol% q & thc r}h a@lb firrco sn6rn h Fig_p_s15 otE fo b6 held in cquilibriun b^/ o lhird fo.€o f
Are

Mettod

3e-a@@a.. I r.a;a_ @ ro .4. O @ \tn = aao coszo- +/+@6ta6d\ /. -a)

4b6l.

-@- 4ao c.E o' _ co6s _ cdl6l ltoo 6'n !o' -e.- - -76.93s. 76.93s bet@ F = .roos'n3o _ aooEna. stn 26.t38

\_oai.

r . 20s.315lb '@ 6ih16.+ e 6i^i/5' = ao6.'nat F - 412,439 tt) P14@@"a{-

2@@1E:

{ ?oo si^l

t 3d?4;;

v6) Dete.mlne the votqe6 €|1-fhe o.st€s o( \€. so fhot cca EhoM in Fs p.3tb w be n e4ottibttun

ihe tu*

I Fa'*

P- 1@'44tb' :*) the fwa 10l@6 shown i^ Ra P s p"le $e "ou€e of Pt-/-

ore i' equilib'ium Con-

2 Go)(14) co6ezast

'4t'r 3@ str@' '46

s'n E: t FGh&'

-o- - cos-' o,ezs -e'28,96'-29.

F--i4633lD ZFh= o t3@@!d' | 2@@.60' - r@ra &b.lilulo lh€ volue ol f

P tad@*"

= (aao')

P,@6sF'to@@e"t% P=

-€3'12€

30

r roe:o'

_29_

=_L

"n* =t"o("nzg,)l/n

ll' '

3l

ir: I

ll , i


dlt?a^ h Fb" P-trz e'FPg't l^ndlc' cire ./ :r7) Thc ayslcm { lavile fo'Eo i cdrc,,n' lhe indiootal $/€ighls' CtnPute tlE

. P-

u6hg rotiz

22z.or 6tnr..

t.todgle

.

-s----9---2--

-g-

Et 60'

9,

.i.r.d

- _-L

.tn$'

D' &7lb

n I R)A stD,g . Boo t7 - 8oo 4oo6t.e)'

i

l

ecn.n''aoor;canat' B - 36+ .ao(stn&') I.

tl

l

| 9..s15' A --cc66 - a
11. 463,6 = 4s4 tb.

v -d^;i- =

914,162lb.

#i.

-;1_

P = 223.07Gtor, )

p'C fdtu) ot ae) lhr€c barc, hi,yez ot A\D\ a ur-linr ncoroni*r' Dolxtte in Fls. p-318,6o of P lhafwill Prevonl rDt'on' Fototcd

,tses Malhod

a' do$a ltrtd*

P = zo4,7t9 tb -,1, --.

""

eeh

?t,rd6€ayer P ete

toqcd

[email protected]

^sasrtnq

o 9tn6tt 6po.e.

a.po6t,m

4@tb q ;"",,

".'il;r";;

lwa

frictto^b{s ,ou 6,s ta |\e; q h t + o t ? o o t D , \a@tb. D€re':n^: jhe oaebo\rhe nordot pro.€!,! N t4t. the o7tia. de.s \ the sm@ih raatuhtot ^urttu

.d)an*'

s6,'=

i

= 15t2rs

b

qb
A

tFh=o c- w.@+',

A46o'

33

ca ec.:t fhc FinR l.us6 €holn in Fig P'322 iE 9"@o to lhe nordol ore loads gNen ler oi A t') o hmgeaI B llg Ropaotronc at B lkl: A\ ^"^o.' Detc'd,i'e trE i-'i""o plac<.)ho loodc b.}, fh€i' reculiont

32!r) TI€ l.iir66 e,v,'*n i^ Fb. p-32. ic cuplo.'ted q o hi.sa dt A b o .olfe. dl p. A lood oF 2@lb ic oppbia ol C. Dol. ttE €oofione ol A b S.

zMA- o .ona " eao(e'"eo']lat) R^.451A,Alb= a62olb,

Rsv r Ra = gooosin6o' P,a<

- [email protected]'

Re"'23o9

161A.e

Ilb

P-ah- 8@o ct'e' - (E
+o.O- - 2309,+

4000

aoRb - 260 (@Eeo)(is) RE . 6s94,76 _ 30_

Ra.2tgg.za b * zaoo n

R^\ = 2@ C46so' &\h - l7Bz,O5lb

R^v = Ra- 2oao stnaa. R^i - 1199.8stb R^"- R^h. + R^.2 rs -,/ t11t4,os)x t (fq9,35)2 R^ = 2106 tb lon€--P^w,11q93s HAn 11a2.bs '6 . lorta {99,3s 1132,Os €-

e R6 ",+6zotbs ot 3d" w;lh +he horizontol

l4

t aa(etnza\
= z4,aol

R^ - 2106tb down lo +te tefi al -6 " 84,7'

a5

: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 5-h cenler which rs neceieory ta slart lhe wheel ovc' +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,eswrfh +he horizonlol ;\ lhe reoohbn ol

tsl Dol.;rn;nc t'hc o,,ount q direct,bn of Jhe smolesl forte P ftqu.tn b E,o.i lhe wh6et ^ Fb. p-3es over brock. whol i€ lhe reoclion al lhe bt@r : ,

the blooK

casq,\y,

Z M a .A

p.o)p/(o)'a ,aco(a) 26t(t.ae)

.t e = o/41 - elo =ae ")

"^t..,",.1.X"'l,r''riL1,l"

Pcos- h.6^ F6,"\/tsq,,a (d6+) r p6hq(i.6e) . iTso

Pd{ (o6D P('6i"q) l 0,6+jF a"q

c b . 7 1 4_ %

"

,uit,.

l 1.se p coe< + 1.sede 6,nq . o

o.

t,q.

#1"**" *".", "_,.,f,",",-*.

p--,7

,439,

d ' P * 1 96 a p a ^ q - r . e e p @ la4@64+izqdrq.

\

d4

Zr4d'o 5P - 1o@(locos3at p' 1732.651tb

Lag C@s- - a.a+p.,n-, = fod< = l€1 lI1 o,6+

?. Pd .rs3o. -_ i32,o51 Ra = 2@Olb

o,64 <-71.29'+71.3'

P i6 miniduh if il will be -L to Fa hence, -q' 60'

h( W

10 pnin = \oao(1o.asso,) P6\^ -- 866 tb

.;1s.,1'

P stnso' - "o- 1.tn n, o" '

Ro cog3o' = Prnin cos6o

ps -lp^;n1nsaod/castt

P = 1es4 h ot /.a" w',h Rsthsd - z.co (€D1s.r1")

- laeo Gosao'l/ cos to R- 641.6lb !

36

37

6+4 Ib

o

i I r l lr l l

i

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 .

tsro) Two wc;9hlle€6 bors p;nnod togelher os shown in Fig ps2o supporl o lood of .sotb. Delermine fhe fircc p\F octiaq r.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.

erl1b41ao'.R6 a6ra@e d - P6 FeQ of Enall c-/litdc.,

zPs.np a [email protected] - sso(Io\ 2P(ane6.a') | 2P(caE66.t1)- zsod p= 901,39tb 0c .t6)

Ft .
j

2e'

E e.) Iwo c.tti^d.re n q, 6, wc&hjng lootb \ zootb ,€dpcclivcty, by o .igd r€d cu.vc, po.ollct {o fhc anoo.lh cr 7". ?'"-"r"d lnd.icol 'urface Eho\'^ in f tb. P-a2e Dalcrm,hc lhc onato" o< thol danned the poirtr'on of equiljbn;m. \e

P.r.stn.d

e.cd'-< P |a-f

@lir,q

lodl.4s< - aoot@e loocoga . .oo @(eo-a)

lhe rj'ore eto*a h fig. P-327 Delernhe lhe votue ol P \F

oldg

@

rcoa-<-m(-so&,.".an^\ loo .G4

$(r) aAsti - 1so(6) t ae82) f - 390,15lb

l]!s-i

t6<

- ,oo €nEo 6'rF(

- rod 26a@.

ts(P)snsz,+ - twg) -dha) p - - 1a7.6,4 tb (- @66

- ,o - 26'a3's,4.

colnptce

10 Mrl FcG

ea'l-

P@6t4

zso ra (aseai)

- t6.o

- ( 1.'.6,)(@E6a.a)

38

- a
39

&orb-l I

€s)-The .oof n I b. p * ,s [email protected] b./ o mlk, -1tu6s o ht gc al B Fnd the 6jues of lne rsc rrorrc

-a,ltu-op

ot 4 !,

.{€o(a)roo(+Xe) +R, (1o)- !0066) - o Pl= Feo lbs

. R1I R, = 3oo r rood4) r .oo RQ- s2o b'es) DelcFmlnc lhe reochbre R,\R, oT the be.n inta P-#3 looded;th o concentmled lood ol rdoolb &) o lood .oeling fnzn .e@ lo on inle4sil/ of 4oo lb pe. n

3a R\ = !ioo(10)1600(eo) + ea6s) R^ - 966.67 tbs.

.

1M^"a 3oRe,- e<,r(1e)| 6oo6a) +soo eo) Rs" = 9f3.83 lbs. €Fh"o Rsh.o

...Rp _ 9si,39 the. beom shdn h F,s.p-sec is burft hlo a rcrl lhol ,l roale oeornet po,nl
| 4F1r1600(a) t6R.' 16F.2 r5R, =1600(16)+ soo(a) + 1600(3) R4= 2loo lbs.

r\trr -l
r, {t*o("W\- ea

R1tRz'16c,0+SOat16aA R1 _ 19oolt\s. fo. the tlem

looded c

$Rr -Mo$+gQA.)

6hown h

zRa.e@o(1drtua(12)(6) R 6 : r e 6 0 al b s P,^.Re-z@a-rbGz) R^ " 1s@-zaza- 12ao

tP ** beo,n ,h F,o p.ra2 iq €upec.,e<)bv o roaL,,on 1'l -*. n whioh_ 6epo.ore€ ,hc upp6r k^**rowe;lb€od6.D€r"-ih€ .:: : : ,ot lhevarus of d;;i;'*"

+ 60(6)(6) 1dR^ -ad(14) , Faa(1) .o

R, - .9.sslb6. P4i Ra-12o I eo(4) |

1149) €oor19ao=R^rFie

40

a

tM?.-o loPe- 16oo(t+)- 1o@(4)'o R4 - 3a4o lb'

ss) ;;'i

toF,l+ 1600(4)- lo00(6) 'o R1- 1760lb z-4o oi lhe Poge @ 6c Thc lwo 12f1b@tns dl('r.n n fQ tood ho.' zo.lo / with r€ePeol hoooch olhc' 9 ;-J

tiiJ ;';;

a/4 (D/4) ^ yr(d/r) r p(o/4) 'NDA -w{a = PV, wA @-d) - pD/2

t' CD so ihoi oll lhrcc reoclions ," " "^" posi:t;o,, qilt P ;;;; i."r *,'r "" q n' nen bo? Ilot tor

be from D?

aa;a,

p.edb

w-3L (o'd)

F . 34O' R1'R,

tto)Forlhe sy€,@ of pu e),e €rfrn h Fb.p-ero, delch.inc the ratio of w ta p to rcintaia cguilibiuh llcaleot orte fnb_ I'oa L th€ weighl€ of the putlors

qRB

co.sn4ring

th€ 'rPPc.. b€om '

zF"-o Rc -Ri rRs

PG) PO) ga r. |

Rc - 6ro lb

960

R6 (Y) =Pa(12) Y = 320(12) Y=6ft.

- tk 62) ' 6.062) " 6a.62) . 6ao4a-)

x . gFl. .. RriLR6 ie 6ft oPo.l. P,e

42

afl.

ta) rf_ aah purlg €br. in Ft. p-Bro wei9h6 36 rb \w F,hd P lo ooinio.h lho cauilibriun. r,1' 2s.2b

p- e6 | 262)/e

l-rc- O

43

.7zol4

i!1.--

!€)

Ihe *tr€el toods o^ o i@+ orc.gi'o " so thot lhe reaotio" "t ,Of.* ol Elni@ oG gFAl ..e lhc Eootld

s.r) --'*

h Fb P'ea of ll'e bao

U- 2Rs GPe'ltcA

oel5' al A rs

boom AA i6 9uworled r;r o hortzontol posifirn h/ o h,.se tun6 fton C o@- o smo puite/ ol D os A x*. o cable $h,ic\ 6hown in F,ir' p-ra€ codpuJe the leo6,bn I th the cdble 1^ ihe ho.tzonlol !^ve.irbot oomp@ehls of fhe r&otion ol n. n : the.jEe o{ lhe putte/ ol D. lql

.aii+ion)

tsr.a= 6oaG) + 2aoGt+) - @ .5p.6- eaor +eoo

RArRe ' 600t 2oo 'vA-e@ .R6'e@A

2oo(z) | rca(6) - r(s663a3')(+) I = 279.s2 lb.s.

"@

Ph = r.oe63-+a" - (r7e.ez) (.663.ai')

b GbVa) " e.ot) +aaa \c 2oIo s dit'g o56to"^ aa!)ihd we{ghf wof a l.o"eri"g a6ne (tn.lipPtnq 'o lhe r'gl'twh' the @^e l '^ i,t ,- "nu lo p* *nt

-

l"*.ttp

,r'q *t*t

il;';:'il"r"";;" f*-

Rirl6i^€a,+ts'-2aotrco

a @,r P af 2a t''ac'.o..@^td*'ts1 -S,: ::i ,.f oo'e*rrr re#'n ine4uirr-

ia^ *i*

the @'imum

P.! - 3oo - (21s 62)(6n6a4z) Ba - bo,a6 Lb.

the

taad P i' opPtied t" wfEn lhe loa

zal.) R'paat pftb ea6 ir +be aabte putls {he boo,.1AB in{o o po6itb^ at whjoh il is t cl:ned ol 30' abde +he ho.,z6+at. rbe lood€ retuln verl,bol.

Limilinq Condtlio's, r P.2'o \thq P'o \rh€n P'2o ) R1'o ztAq-o (*ton P-a

6tne'

4(x) = zrG) q' = r4oTon6_-O aMR,'o ($.6 P'2o) q("s).zo(.)teo(ro)- -el qi i\{sl = 22oTons 4t .1,t{z).,tet

q = 2o +ons

| 1&(6)@ao'

Re+I6h--. = a@ r11x) R! - 3ab- 216.. (etn6d)

- 6f1

Fa - 1t2.5o lbs-

45 44

- V4

lon€. - 6/4@ao"

ftorc

etos

".;ut " soi p'tfi

B Eooh "*"* n

i6 tupPot'tcd h pr''ot6 oi A \

P 4+s

;^ f b

d"p"le

t " ho.,zonlo! \vaticol

*

Rsh - soolb6.

thof@'r?io:T'-ol lhe

oo"poale

r p@(eo) - se(^d-

a@(ao)

R^= toag,7t bs. {fv

.O

PlNrR^-6o0|12co+soo Ra? = 12j4.2e tb6,

e.E- GAAiGTGAF

l!.'bl) = s&Q) t4l6) 1'8'h') lit' ' 2455 67 lbs

- Pa4.?etrB.

.. e - 26.12' tang.;p1i.ee/eoo i. RA a12so.7stb6 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

nh . Eh =?+66.6?lbs. &r -^ao+s@r@raoao

is oPPoriel on re e's ol The teuse. shryn i^ f ig.Pia conpo.'€n+6ol the reoolrorLs &-o hinge ot A solve fd. the

rrg)

A ft(Ra'\ - a{t<12)

KB -Yflgo)' t (3oo)'

Rsh - z'to lbs'

q--!4

21R^ | uo(15)'dL) R^= 71o tDs' 24R6! - @(12) r uok)

Beo)ComFrle lhe lolol @tioas O

ol AqB

Br Rol.o \ Ptuporlion, Rsh - r R$- s,(1/.)

r '+46(56)

- 4b62)

R^ ''Lrr..-ziG'jf t6(FLw) ' +oo(i)

fo. lho fruso shom ih Frgu

/t /t-

1. ,,fr>E I 12@tb

rU

194

ln^

46

- Bo ,, tb6

A pulley ,+ft. h dioreF. \ sdpp. "r'^g o t@d of ,@tb :e @nled dr € on o honzonlol b6n Gtq p- e.2\ Thc bam ,6 guppor led b, o

!6r)

E

./ t/ | "l/ ,1,/-/ c

- 335.+r lbs.

47

A-R/B(r6e,b)-#\tt #E

rOD of lhe beam,

12 t&_

P , . R / B ( ' 6 e / d . t g l 1 1 s t ( s € ,-l . : a o w . 1 19

3E+JCdnprtc the fotot reoonbns ol A\B in F(t . Prn5a.

on the

Pc(s) = 1co(a) zF! -a R^v r Rc ' 1oolb6 P^v - 1oo- .eo = 60 rb6. . eoo- 2c6Ginao) R6- loo lb5

5fh-o:

R^h'T@6&' ' 4oo @6a'

P*\ R^-

' 113 eo tos ' 1ea27 tb6 @o)a t(18.2o)z

lo"$ = soy'tz.to ' r'1o' ', k^= 1oo.21 lbs ot 16no'uPfolhe ngnr . sf@n in sse) The forces octing o^o r-f1 ledshl ofo dom ore on Flir' p 35j.The uptlo.d qrou^d |.@ction vo'es un;io'olY ftoh

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,
ot p, b/n. at-A lap" lbA or B Delemrntp'r p"\ol''1i.n"ity

| 224a{€,n "6,s6)(1a)

so +heho,-,2r.'lol' re€ieldnoe to €lidrng' R4,Bionce

I

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 ) -e.4 e- 9

48

lonq

' 33u-o9

€ F . + a n _ 13 9 7 6 , 0 9 !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,ss6 h Fig. p rss Mehbers CD \ F6 arc re€peot&ety pe.pendic, _ br lo n E \BE ot thet. midpohl€ .

= 0,56fl -

49

35t

The unilonm rEd in F,!t. p-ae7 wc,bhs +2o rt \

of em"ib,ol d. Del+mineth. t.";-,;;;;ftX.:

bo6 ,ls

tione o'l lhe 6moolh_eurfooeeot A\8. aM^-O

-. '> Ao BF 1617/cd A o " B F = t o , 7 5t ] .

ton+ - 13/tat+'26t6' ' ts/cosze Ee' ac =sa r'lc- aa' $17 f)

iX!.,

^

2Ir 440(6)- afish4o'i 6rt@€. b!l, stn lE - aosa6. 2T .r 2s2o - t6 tlstd.'.

=poa(as\l ao.x)(a2e)++ao\et i

T - ad@sa5. - 1260 . erish+s.- t?6o sub6l. d1z ia1,

, r -dcoe.E. @

-e6a n@94s' - grlcD.+s' -7n.*16.! - 1260 fi - ?s4,sd tbs.

Q^ - 536i 27 - 6360 lu€

t!)'r]" ' -""n.,

, ""*6ets)

Rsv = 6131 67 !

26) t
6130 lb€-

Rsh = .ooo s'n26 66" R^€r^3o" . 5361 27 stnaa - 4oooatn26s6' Ran = a92.Og5 lI$

2R^ r aeo(a) - d 8ha.G) 1 n@*.f6) RA - 6dsn4s.e+o

pa - s (2.+.soxsr"+s1 alo -

2!}o tb6.

js in €quil;bf;um unden ihe @lton of Jhe fve Fis. P ess. Detemine p, R \-r.

in Fq p-a% ; suPPricd-bv o thn '.i Ihe c,]ntilerer 1.u36 6ho'n oi A h B , .tt,r BC Determine the reoolim i;

R(16)i r@se(s){ r6R 1 9T66e =Fw -o

{l'""'u. o1! 4 e6.a7.

-B^, - -!999Ao ;a:

- 39p9 s,.ed

Q^ - 2ooalbe lP

50

^ -

$ (6c).- Ioase) ! elco.+t 15(6@_ roo6 36.s7') 1 €.r

f 6ro@

R '6
T- 12es.7.t tbs_ R ' 6oa- (128s,7) es #.s>' R- +2e s7 lb6. (!p*a.!,)

r6nef6) - 6co(4)

t@6e

€6@0 + 6r€,n !6_s7- . 6o00

| 4ao(s) _ Eooo @

@

?6t.> Referdrg - 1@

P +1.,t1+

4'o @.r$ols't=P^@4'Gz) - "r"^1'*' -1 tuo |,

,'*

NeeP lhc

bo'

r( r - 3fi r .r6lffii.!€

be ,rc|';€d

l., the honzohtat

" (!4fr!e1sct, " t-*.ffif4d)

#'#

ftvja b tig

34 ,-'F f = ?dttb

rl is in o poerlion oFegu;librium.

ez' o -
*",',^oii-*'i'

Io tM

agle €- ol wh,ch the bo. *tll

o - ae.afrE A-: = 1'e 2" tE llF

or as.-'who' .{o\re

'r ocrirq or '( =3fl

Us"9,+brlb,tu@tn, " ,s, - n(l-,') fo. &, !-o = lof.(6)Ga)

ft. 'he afd;"ales r 16@

d pl-o

= D (caee + 6ns-) -x

x =gGseCt_6'!9)

3- , 16@-. qR^. b Ro, -g-tzene = - lqd i'-"a,*e) .tzGne+e.\e) -\-..3pr. J =

I * fdn@

fo-

a+ p^.

3 = Pta

at (cast

st'e)

horrbrtlot

nl'a"*t-pL | l'l..a'

& . , 1 4

A{

-tc's;79fi' caad - fr

Ita-6-1'?,=4'61fl

a") 1 6 61') = a@O 1 - 60'3 b€

52

e.t i 1tl@ao

- 6&e

:: og+

t N-+.3e

-oo=+ 24-.'rnll'

-'**1

I

- $q[ sa6€"- "(,..e, er"o)l .l.t^@ ] L - 27.8e

- 6o(@cJ eno) 1+ aon6o

= @ cGe | @ 6ne "td.6,.o 1ro"@) -@-l -

3B@€+6rlon6o) a6€fal(r

[=(r

- a,(@.+',na) 1r+on@

**an eo) - oo] = 6.6. = A@26279 ldtot -O- - 26.6aE'3A7'

53

(eo)

tlp

-

'1{,a)Joiat b of lhe lruss sha-n in fis. P- ao2 ts euajecled to 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.gle of+ degreeswilh 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. t€ obo zelo cqs ;^ mSdb€. cO'oE EF,FI,HI.,HKI,\JK 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

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

ChoPlor + 'Anolysie

p.haiple ddeL'ped in Pnb to2. cE-cF-o

ol S{ruct':rcs

P - cDdn@'+ aeet 6o' 6'i!€ r CD=OE P - 2cD e t^e' co-o,577P=aE 1C CO - BD ! o,gj7 p

BF = BD@s6o' bF - o.67aP coe 6o" Br * o 617P (o.s) BF-- O 2A9P -f

54

.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^vr RE^/'160-. .O FDs - 66.6|b.

Brv

@pt B.

zry -o

@pla

sa'2a9-

@ Pr'A 4,.

a--

bc.966tb.-. c / @ pLC

R^v-oeA6-@

lF"'

Ac' 0.A6 AB-@ gr,cinr.,', AB.i^N; '1oo +1e6&' o.5go t o5y'O'1cDtso po+so' ts(z) 'ta-@ F^v - o.e(.oo)= solb.
'o,E6cje)

' E6 6lbjr

@ d c

AB) Id | /\b ' 4') ^6.1@b -b

o,6(2F@)

9c.t.6o' -pD 6.nao,. rooo r AB sn3o. o sBOr o.g66Bcr .rc,oo+2oao(o,r) o.eaDI a.e6ac = 2ooo -. - a
CD6t.6v"- Pt,E|.60' I loco co- g6sfos66) +iooo

cocos6o'+ Ac+ scco.6D'- CF &- 2o2o(o,a) | 17t2+ 86{'(a9) = s1ru ib -. . _ C

+oz) In lhe co^lileve. l.uss €ho{o ir Fg P-a
,,. E,o- /.E+,loo,, 2ootb - c

- ftoo eo,5o. A a = 1 1 3 2 1 b- . , - ' t

^9ana6 .

,Ac - CO ! 46,5 lb, -T

@PI B 8C.100jb.,.-T

.06) Th6 coniilove. l.uss in Ft4 P- 46 i6 hi.€€d ai D \e lhe fucs in oooh tnemb€r '

Find

@Pt^

u6,19 F.otdt,b^ of Ax,e,

i ee.rrsiro l- r

1 AS6neo' = 1dO: ^A'ao.'dtb' ' A E c o 6 s o '
l"e lL€ . 'L$7 {"

bp . 1.?,12r 67

wor.en eoch nember of lhe .osJ computc ihc fonce i^ 6hdnn in Fil P-'o€

trucs DE6tr|@' , a1st

R^e ' 4240

lb

t so@

DE- s+94.2 v s+€otb c

coneide.ing the wtd€ nborc: =ME'o t L@l1a) | R^t(n\ - e@($)

@' r etd

DE- 2o2o(o.e66)

ai1.) DolermlrF thd ftrce in n:E]mberc,,a, /c)BD,co, qcE of tk)e coniilev€r lru€6 sho,n in. rQ.p-411.lf lhe loods were opplied oickE in€l€od ofol E\D, €peoify whioh memb€i6 *ould hove thoir internal fo.ct ahooged. ton6-- 9-

@ pl. A,

ZfJ aot

R* = ABs|n6o' A6-A!9_

ZF .O

@ pt B,

r.f,l.Fa3,as'-1d)

-2OOa rc' -4s11stn6d srn5''

lrc A3 ' asoT 62 < 4910 Agco6so' - Ac tc-
A1s;n6ci - aa@r

AB - 1eo,2g lb

rc.2@tb-'-'T

,,

BO. /\6coe6o'r bc.a66o' 4h.o: ED +e1o(o5) r 1600(45) BD.3755lb- -C /

./\B@za.@' .eDa44.@)' AA - ao - 1eo,29 tb -. :f

@pI c

ta o -94?

t*/*.

@ p i .c

lFe=O: w6n&'I caen6o'' +OOO \EDok@l r co&'06f)' aoe ''f, co = eog94 + 4O2DIb' ZFh-o: Bccoe6o'r /€ = oDao6@'ICE 2b.o(o5) r 2ass = 2o2oGs) | CE ce'1war24s5-1O1O Ce'Lr+s lb ' -T

58

PL- A: I oE'i..e4'

co- aso)b-.-'l

/

Ce - CA.:ocsol2| /\(a - 2g)< 6s3:12 t 190

ct

= 300 lb-..c

59

=Fh.O AC-

Bcos

r'.c- lsotb

aoe) oelcrmo€, lh€ for€e in m6nbat.5 AS,BD,9E,qDE tbwe rof lruss ehown h Fb. p-4o9.

of lhe

A" (ao)- @o(3o)- €oo(2o)- ..o(ro) =o

H"(1o)-,ro(€o)- ooo(ro) -6.()(4o) =o Hv: 9r5olb.

a.

A, +De - io+t/6(12o\ ... 2OJ = 12or e/s(12o) 2Da - 192 Dv-96|b.=Av

lnta.tonsnq hinge k rclr6' eppo.t *tll not chonqe ltE fo'ces in cocl' ba. e,.oopt {ir Ac &' cP ac"q,te/,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 1D :

€

*- \e6-t

sEsh6o'-6oo(Eh60).o BE - 600 tb (@.nprsi6)

[email protected]. r@(@.6o) - atoo 60- rsoo rb (cepr!<,ir,) t'a) Oelermiie the liJr.e i. €och nerba. ol ih€ pro$ roof lruse ehoM o, E, 'Y /@ u5iae d* ^c, ze".o &=1s&bc-F6 ,Y' 4/ l* a lhc at-,s,rcto,6 .aS-ED=DF- asoo tb-..-C

at c. E aM{-o.

to,.c.

€oo(e)

,6oo(ri}rad(€)t = AY(3")

Aa- adttb

'/,

s--+

l^w Bo " i6o tb (cdnpc66'o^)

&=4q-_Aq

co = so(slo) -oh

_,q-_es_ g .ti5

:. co= 463.3i rb-.-T

DE=O

6l @

" DG

Ac - 2/r-n q) t cE cF . :,64)0- 7A (ztee.az) (F = EA . 2400 tb --- T

AS - +s@ lb ---C : FH AC:6H - 366tbr-T

b q t ,O h ' 9 6 | b .', Co '321b (la5o'r) dt C: 2?r-O AY TDA ' BC gC ' 192 tb0€'€ion)

f.d-

w-.E

6hownin a1t) comPuie lhe force in eoch rn€r'be' of lhe lru6€ a'e shlfled vecticallv do" f,A.p'+to t lhe loods o{ B\o -o.a lo oaa io lhe loods dl d b E' wil\ lh€re ba on/ cho"gp o in the.€oohbne ? Whioh membsrE' if ohY' would underyp aho.gB In hte.nol,

6rce

@ p l E ,

@ ?t. F,

'

Rw' YEcF

€hown in rig

oonsid6.i.q

DF - [email protected] 161o1b,..-a the force in eoch m€mb€. of lhe crsne

lhe i?hols fi?u.e.

02 |ca - ?occ@B b. - 6. t e. - z.G>(s)c.E126. b = l3.oab'-

- 4,o t2@r2@r eod P^w i Rry ' 1600 lb -O

p,y rp'd

@ pl. A,

1MF.O

tn | ,

A" 22,Epl

9^,Y (eo) "4oa(4o:) r 14("j,o\ t ^blao)

a bo=LAe,

+ a@(?a) ' eealt)

bD6D5o'-

@b61. lhe 6l]3 of R^v in 1Rt! - 1@o - ego - 12a la

+eo++,/b t ac t {nGe') k1e8, a"a Bc- 7o'o+ ='7@lb -


^ 3. B^,-A,Bs,a

-C B - 9 s 3 . e r{ 9 4 e l b
@ptc. tF!'o | 2oo bc'Gco 7oo \ c0 | 2oo ''

-'r

5 C(,'


62

,,,!a = 13O9A 61 - 131OOfrr -. t7 1Fh.6 ACc@2aa9'-

6 ,'\D- 1t1oo'(6e2.6q"

tzo"o . o.eor(ff-e6) BC = 6c0c'26 !

Bo'=*ad - 12o23.4g tb

tB = 12cbo tb_-_c/

@ P l

l.* / Ca'lfeo' - tlto)b --c

Bc6h.ir'

o,560 - o.s66Bc '-ta

BO . 9e5Z' -4e2.5 <492tb-rc

= 4'.ote.

l-.

62 -@-os)'t s2,.G.oaXqc.FA

,^6 -eo@s& +Bcoa6o. 12t)Ca- o.a66ao r a,aBc -a

63

+ o.sac

6000lb_..?,c

= rcsg2 rb

?,

+ lAlAAtb-:.-C

AB'BD'& CD of lh€ aft) Ocfc.mine thc for€€ in mcmbcr lruss 6hownin Fig P_a14

+1s.) Solve lof th€ fo.ce trusb Ghown in F,i?.p-4rs

in menbe.€

Fri, DF. s, 06 ol the

atA}..',

co.r6,cren ng the whote, Rav I Rhv E too 1n@ r ocro R^w*Rnv! lsoo

K-,

T

@

"'T , 'l q' u,

sblb

coo lt

h

tuNfr6) = aao(e)r 3606€), - 6o0 lb. R^v = 15Oo-9oO

4Mq =o. A"(36) = !oo(27) t .ooQs) r @G)

Fr = 1274.19 a plo

tb -. . - C

@ Pt. f, \k A8= Goo --"C Ag. 948.99 lb ZFr'o AC - ./& AB AC= qJotb- tr t &taao ol B,

7.r, FH - 3//.tri6DF

or - A@]li) (3' tz

;e -E-c.

n"

oF - 9+c.6 4 947 tb_.._c @ pl. 6,

l"-

& $/a rst

-C CD = 125 lh --

r/tio Bo - y'F ^a

)

B A - 6 3 2 . 4 6l b - " c ' '/It Ae - l/.Fo Ao I ea Pa - 4.o li) - _-T

4/5D6+6tt)-9c,0

pa - 3ao (s) D 6 = 3 . 7 5t b _ . , _ r

64

@ F, /,tz FH - 16 | t/fi DF t/E h2io) - 16 r Xi baz) F6- Eee. 4 6a'tb

lhe fo'ce In meddele'oi'e u6inq fho mctthod ofGsctrbns, in rl9 P-ar7' the roof lru66 6hown be.6 BD,CD' \ c€ oi

ru)

..28

con6deri.9

,l{s

lhe Y'hole fiqur€

-O . F^w r FFw 360

Btu p^eG6) " ze6.)

or(2o) - R6v (2o) D F- S o O J -b, - - C

9C-+47.21a++Ali'o---C

cE("o) r jooo(to) r R6r (2o) " R6.,(eo)

cE"4oieasfu):_ogacsl cE- 100tb-.-T ap) u6e the rethod olseclionc to dele.mire ED,co, \cE of lhe wonEn True6.

F*(1D 'ao(s) bo - eob2)

cohcidenilg

po- $alo- -c

the to.ces

tfE wiEl€

in nenb..

figurc

,

RvF ("o) - rooo(1o) I sooo(F) r b.b(.)

co - s/. Azo) C o ' 2 o o l V- - c

ri ".? | \

l/a\"

.,"-'ro =. e- a.66 n.

- -1 cE' 3zblb

41s)rfE wofco lruss rood* -06:0::l ' i ::j-^:'":'iffi o1 A ar 1r'e n a1|(d of oe"lios' .

- -^,,^. ^r r- \

-..r-

rh6 {^.ce

a I'nqe

in lhe re-m^e

w

w\,5at

ooosldding 1?n-o'

3o(s.66) =ooo(.)+ also (ta) BD - 32E.o/e.66 BD.37s2.e1b-..-C

lhe {fEle fEu€' p-6A ' 6aa ltj

4W-O 'aobOb)1 6@ Oo.l+ 6@(0) i Paabo) P.d (a)

cE - 231so/e.66

RvEas) - co(1o) - soooco) +4o00(6) cD- 412s9,4a cD-212stb-..-I - cD(e.6a)+ 31s. .s(e.e<). z.<,o(.) co = I sooo_ (:zsoo., r+)

cE-2742.etb,._I

CO- 2O2O.Alb .2o2a lb ---'f

67 66

lhe focce in ltt6 ndnb"rc aad Od6r'ino P'+b-' tb$,e lrure €lto'"n n fiS'

of

Df'06' \Eo

:ir_o **r15B]o.,,[email protected] F,F- fr,6 | *rten)-.,t'Idil BF- 2@tb --. -c r,|.lrEdof g.olbo , @

aM.'O|.r'.o\=a@6'2) '-c Df = 40cD|b' @ot t/to6- A@ 2r!-oi 1fh.o'.

DF tu+

3/sBD-BE

t 60- *a6ao) ao= 4@tb.

EF - 1]E l0+ 21@11,6O EF = a'g(,db) r 2& | 1zd): 2@

Pd.

rJ6-76.Db"c -e6 r./to6 1/'4s@)'Eo E6'a
.aa)ro-rherroesiEm:'q €t'€cr i-rfl'ilff,'fiff rhe r msltEd oej.ints \ ltF/'

* - q+16,fE-12@'1 gF r 45OOlb -. .- c

t*",

b,/ llt€ se''l;orF' fir't obbin {h6 n-t ' 6 opdl. 'e meltod oc Li^.. \oloe of EE bt iftP€cr|oo whol6 f.gpc, ^,.. cotr6t,-,i,q the

{.6) In lhe hiL t.rr.e nr Fir. p-a€B, lho Gb momb€r€ ct'o.d I't tF o|c F.perdirlor lo ttla irlctirFj r|lsb€.s al lhej. midp
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
--

'

4F;v *a"

aa{a(rd/+

(126)

!9 ^e/2

..:E--i6 try.

f -r4'5'

68

- lrara+4.r1 -gB.

F^y-F6v;4x lo_:-i-

P;o'

'5-

EG.E )n(a.6) + t('e.s) - Fe! 6e,.) !F -S.e|!9 ryse4 Fip. _.._ c &f-o|. +lbllE | + - ,|FDFt a t1 D E = a r x J i E- . - - T

00

zilr -a

- EK(rz3a) | roo(ao) ) .e(eo -LB) r 26('o'1s) t @(a.-2..6) ER - .9A,94 ? 699ltt - .-r Dr, D6, q E6 fd' }hc tb'r€' Dol€dinc +h. ft.ce in the lne4b4s

R^v(,) {rl)

tb'connot determine the lA Fio P-4?5

Then use

force- i" Uo"s fH 6ri,\EK

6 pn6ta

rF/ -o, con6id6 rhe *fde

ol .s'-

2<).

fiaurs,

K Rr = R^v = 1Cr5

2sfuoF - E6 r 26/(t6eD6

6=.fu(6.)-ryt;@n E6 - 1io.7 7! 1t' Rrpc-.-T

PNtu>ao(@)' e(d+ rfglA + 4-e+ DF(L') -c DF -161.67 +162 ktqs p^,Ua) t NQ,

* r''\' tn Fig.3 en3o'--PE

D E= l o '

'zb('br'' 3-2o\ - Fn($) + 1.t(@)t ! 'oo(4o-1')

R^\ - 30+60+.&+ Dr t lkfu D6 D6- ia/Ilo, -4=o_ 3t6.+o6')J 6-

r i = 1 1 o 4 l b-

-c

-4".^'" ^'44 *Vi

"*(1.\'i aeo4 "' 6H(^E') ;,;.', r 2@G" aA' .eO'') \zqt'z1s) zs2arb 6 t 1 ' c . 1 96 .

70

'*.. -r 3a.61 =sa.., r:7s

'-f

<€a.) u6e lhe 'nelhod of s€oiioE AB,AD,BC,\bo

lo edpu+e lh€ lor€e id of lhe lnuss .shown in Fig. P-+32.

.,*o ' zw'o

"!

p.',!(2o)t.,b ^8(i6 = gk|e ^sQ6)

e=,L

l*" lr- \ . FxG4'zao&i

lsor,ot

[e(o)_D6d]. AB . 7o.7s = 7o.e klpe i.,_

R1v66I- a,1; ^cdel ta = 6/+ Go) C - 46-02 -i€

xip6 ....-T

| .d16) eG.,). vQo) | tc(o)r tk

4@r e6ao' W r\s BD- lck @4-41@J -T EOr5oo1-Or' + 5OOOrb
-c

w'tr@s1o)t +h(@) !E'6a.Dtb --'c


€a) lr{.c

c

€ME.O

-T

co.npdte fts fo'c6' €hown th.. FriJ'P-a!''

AB,^c,or, \oE of ihe 6'i6sa-e < t-O t2(to) e.x <@) '12'(.) 1ia(a) r 14O')t e(1o) I R^v - lox

/t

^?

l"'

6,/"1.

^1)

/1' <{ .// lr/r'

^--6-

oF (22- 2a)

r y@ DF(a) Df - e3s

- 42.s k?e-..-C

'lho melhod of ecclions lo compulc lhe forEe in lhc a2r) Usa desc'rbed 'n mcmbers DF,EF,\EO of lho conlilever lruss Prob.+11 q Fi9.P-/r11on Poge 92

Fv(so) - 4oo(ro) r ?ro(ro) r soo(!o)

oe. ao/3 rS cEQo). 72b
^-;t

F".@rb

7eoe4.)= z@(r,) i eoo(2a)+ a/.rsbo (ao) BD- 491,93tb --_c ZMF -o (p-@t \^S CO dIC)

rMe " o (Rd6olving OF ol D) 3/rE Dr (ao/3) - rco(ao) r 2&(^o) OF 'a6o.56 lb -'- | .MA'o L ft

ff

2aa(adr eoo(2a)- 1G coho) co - rn1a.a3tb ,-_c 42.) Use the helhc, of seclion. to detcnmtne lhe force ooting in members 0F. EF.8(E€ of the Howe irues dcgoribed in Fis. P-aas a^ page91.

A\ (i4) - a@(4) \ xro(b) r
(Resolvinq EF al E) ,Jo) | 2.to(2o\ Go) - zoo EF = 335.44 Ib - -1

rME .o (R€sotvins oF o+ H) l"(ra) = .oa(1o) + aF(en3d)(,o) DF = 1€oo tb - -c

Eo (2a) - @t(ao) r qno(qo)+ ca(rc) E6 = 450 lb _"- C

page a2, t\ coma22) fe. Ia ihe desor,bod pute tha fo.c-€ in me.nbe.s BD,CO, E(cE bY

i" (,o) . Eo (io 1o"3o) E6 - 16+s.4s tb --*T

.+2+) For.thc l.ves

?i-ry ]Y 'ne me r L cfllt d or

she^

ZMH.o (cccotvinq FF al E) a$(1o) ' EF 6'.b' (2o) FF - roo lb-.,c i^ FiT.p-a2a,

dd{erm,ne thc fo.€e

E ihencheckrhlsrc€u[u€;ne :f io,nt HilI. lo

sec'idq

oppr, thc _elrod

br, hsp€l,on.

Ocf,a.dnc lhc fdcc in trr.c BO,C,. \DF of lh6 nocotte .rt lrui6 €ho'6 f FtO. P- 4z

tMo:o At (16')- 1MG.) r ,ae(91 Aw ' zaOOlb *'

&-aleAa AE ' 25oorb-'-c

AC,cF =tg.o tD-"-T

c"b.)|

r.ID(6) " @(2a)t cw r t6oo tb.

fe(ta')

r/&

oE ,t 1@ - &et @ oE - 512.45 tb -"-T ot Jornl D, Zli6 -o (?.ov6g co ol9)

1/ft DE60) = 3/b ez)(co) co = s@tb-''- T

4k co . r/tasD| y'{ooE

[email protected]!5tb-..-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 rob l'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,n 26.e7.)+

21.o(d | 1t@Gr). +/s sF (16) gF"2@b---c

A,(zo) - [email protected],.110, zo)+(E^ %,sf) (z)(er1o) + ot (1s) tW. o : 2:4.(.a') = -.(a^ *fi.Xt) 6I - o_,rseKip3_.._r - ,(5'n?,.!"Xro) i oF(6n ,..B'XEo) +
76

Ay i 2.+6 Kipg

F6 - 2.24 N

dclern\^c

l.usc shc^tn i^ a9'P-429

0F, FH,Ft,6r, g\ ro.

e+o) For tho lrono loadad o€ shofn in fg.p-44o, &lor mirE lh6 lbrizonlal \ vorjiool compcnonts of tf,ro pi" pros. 61,.Dol B. Spoc;fy di'Eotion"s(vp o" aou,t; l6fl or right)of tho lorso os il oot6 upon member co

2l G=o, s/@ or@4)- 2$'@r) \ ,.bGo) r a@Q.') oF -- 12564

lb -

ar@\ - 24(e,) + ab(6) EV. 590 tt) :Mr .o N (.r) - 36G\ - 21bQ) Av = 360 lb

.-T

lefl of B-E

at^t.'o.

5/R rr!o)=1e(4o) r 14o60)\,!t(@) + 4+c1=4
'B00(6)

8n - t€o rb (lcn) bJ - esatb (dorn) 8r-2.gO-39O-a

+
is hin96d ot A &,c. Fidd of lho hinqo lbiE€ ol B8..)

CE- 97.22Ki?6---1

'o
1@ (ba) ' 30125)+ s/EA bvr.z ) -C BD. ,143-41 &tp.-

y''rr" z,-zf 8Br = 1oo(e)+ ioo(6) BH . 125tt) j BH.AH - j75 ib At - 166-|,46 =a Av - 2OO tb


Cd=B!=175lb

78

79

bor CE cv + EY -Dv -O Cr - 36a - 264 & = 96 tb {d@n@d

Co.'cira^i.g zF\Fot

,1r .o*pr*"t.

cd-40ro

i{^za zf!

bor 6D

o'@\ = 240(3> Or = 90 lb E"G) - 24o(e) Ev - 19Olb 16olo1ing bor DA

=M^-o g! C6J- 240(4) & - 160lb

xo9\- s!(6)'o Bv = i 20 rtr{ upwo.d - / *p.ol" u". rc]

80

ro Ac J

aa5.) Thc frElne shown ln F9.p-+as iE .eupportcd byo hin96d oi E k, o rollor ot O. Computo iho f'orizonlot \vcrtiool componenisof .ll-Dhinge focce ol C os il ocis upon BD.

j 42c(1\) - Er
2ao(e)- a, G) - o O' = 360 lb

I'N1 i;pkr

BH = 4€ rb to tho righl

of lhe h'r4o 6.ccs ol Bg'c os.ihev ocl

,p."."-P.ry'

t

zN,,\-o I Bc(4) i cv(s) - cH(b), B"(z) - o BA = aoAo) +a2o(2)- (e6)(s\

tho wtPlo Gono i Av +e! -12O 'O E ' t2b'to E! = 6a lb

aPA-o. e,D(3/s)-AA-o eo 4'4)AA 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/ohingod oI A A' o rollor ol E Compu{o +he horiz'nfol \vo'rF

*i1h rospedl to

^r1 "-' :[1o=o:cf(5)rc,€) r,tz) -o Cr. 2.4(2)- @>

lzo(4\ " Er(4). o EA ' 12Olb aVr.g.1 l4t- At-o E$ 'Aq " 12olb oi i6olatirg bor A_6 zMa-O I A!(O)'120(4) = o Av -- 60 lD.

Zt ^=oi

zMe"o (6)}.v-

24o(2)

AY-€Olb

CA(3).7oG)t@
8l

+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'6ololeoocb ltu€6 o6 o frcc boaT

AaOo) - Aa(b) - 24o(1o).o /*-AA.12o *@ 6q. @ &- @, A" G) - AH : rfi<)

An - 32o to zF" -o Av -B!-24o-o

-laLal-:4eL

N G.) - .6dct - 6aoQD) 'o A!' 42o to

&r.

tsA_ - 132a Aw - .katb

-' ".,1

44o- 24o

Ba= B.a + EH2 . (m)z + (e2o)2 b - 372,+ lb

.t\A-P,w-120

= 4a -124 /Ad - 32o ltr

a<€) + A,A(3a) ' o A"Go)'3@bd - a@(@) - +2o(4o) Ai(t) AA - -32o tA = ;. AA 32o 10 Iha .lgl\l

loro rc -;.7i ) /'\'

\

A booh (ar|ig +ta loods shoM n rig p-+aa i€ lh.@ ..sma.ts t{ i€ suppo.icd rt br vee_ 7*,W* { 1tc.ctt:c,aLto s \ jo-oa 6, b.o f;cl,o^tace nrngc€ Octc rmirte iho votucg of lhc rDoc+ion6.

. zFf=o a2D /\,8.\n 36 s7. -o c ,LB- lao\o zF"-o: B2o- Ac - Ae @s 36,6i- =o , 76- 326 _ 7a6,(cos za,az.)

-.._1 /c_- _ 24a trj. 24o tb 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'Dpo-onts of lhe hjngo {b.oo ol B tN. }ho.' delarmino lho }/p' e, mognlludo af forca n bors BO e'BE ,

z(.'o ,.o.b)

.n

*,e

c. cf r-'lo I o t-- -t) ---1 at!2@tb

wl = 100(6)

lofl

lrusc gr

lG

f

lR+

RaG) -.6c8 (z) R4= 3a1tb=Cv

G

+ 24o(zc) r AA Oa) - A" (4o)' o Av(a) -AH = #ao -@

l6.loting

a2

@

RzOa) = 2o.0a) i 2e&(7) 3ca@) R. - 2120lt) R3Gd - 2s.n3> + 3&(14) -4ra(4) Re= lleo tb.

83

lv'o o'd Tho bridgo sho'{n i^ Fb P'aag ocnslsts of ot ofgrovilY oonlor €oolion6, coch *oighir€ Ctn' tone 12o wo;gbihg 6, hingod ic o unifo'm A, B, E, .',\ F.

.s9.)

"oaa(e)rooa(6) | FN6). r, g2) Fv(s) - F{ = g2so --O tc@(s)- rcca (6)+ AtN(4) = A" (12) N(3)- AN - 22so -@

@ nanb.r

co

CB(1o). eooo(s) ca -1s@lb. Zl''-O:3.xA-Ca-BA-O gH = looo-1silo

o" (@) - 12o(:,c') | 6oG4) Dv = 1OOtong C,Go)'tzo(tdtaa(eo) Ca= Aolo 6

i

E"(@)-Qtbbo)r(a(lo) e\ = 26A *o^a zlr\E - o ' lctt(2.' ) F" (@) - zaoQ.) O,.r(i,) = Fe C4) F{ - D{ .{sootb zF =a: e4 -Bao-19ca.o Ec = i@O lb -O: -F; Fr.tr 3oOO- AH -o AA = asaatb

:ME.o:

N Go) - 2ca(2o) so(2a) Av = ae tong zvl^. a e.Go) - 2cp6o) t s>(1o) w = 212 lons tc o 45o) A billboord 8C woighing {ooo lb is subjccicd Fig P_aso Ncawind o.cseuro ol 3oo lb por {l os shown rn hcmbors' doiormrno locilno lho wdrqhls of lho supporiinq E( F' 16 66-penonts of ihe hingo fo'cos ot A wnd PrcEGu'E = 3oo lbl{+ . 3oo lb/${ x lO }i

@ 1 , Fr i3) = e2so + 15ca Fv ' 32SQ 1t)

@2. 22sA + 49cn A!(3)Ar = 22sotb.

- 3OOO lo

84

85

= lsoo lb.

s@ lb

Ea'21A -O E'l,.21ob

EaQL)-sko)-2ao6o) E! = 2sq tb

Choplor

- e@G) /v62)'2440) AYF5olD ' @ .nombor t.rht=o tc'

c ll*cn { ot-Ho

Fr icl ion

DH C4) - 24(o) DH= 4€O tD

zrio=o cica) = 2ao?) CA '24o)b

o"G)=e
;O: Dll cBH:a6O

lb

EFr'o 6! - so+ 610 ry Bf = 9o tb.

8a'A' Cr'56010.

86

5

87

w ,o " ,"11^if,";"jjll""l", ,05)Abtockwaiehine

r ie(o)gr.ore' 3il1l,#;ir'1?:;"d"i''lioill l h o n e loe.Ic) lc€E thon e:(b) cq"o'

lhone- ih€ bloch wirl not siide down )',l ii,i' l. aiter ihe f'rci'onol i,i.,""j li *i,, reloin ils poeil'bn be'ou6e

IT'li"S jit. i:1" r ;ff ,:\'ilJl"Jl'*, ?,n,'; ta'c'l:ll^:'",11;i: iir fi.'iq n",i"ther'aro^ot, " j';* i"x',;-" ?iii:.: T;:iJ fiil"[,:,"';tl:: i,"' il :.T;:il#;Tf ::;::;i,z * #.2::-i,:;^, mpc^d 'f aP" tpt tr y ta \)4w'

il

;;?

,.4'"""o

5a7) Ihe eoo)b block gflown in Figore is in contocl wilh o ab' 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"{ prcvcnt molion down thc thc bloak up tha inc|ie (u)j"gl (o) Il P-aoc lb, whol ie ihe o-ounl \ dr-ecl'bn of inojine. thc J-.,ct;o^ fb.ce ? > P - COOIb 6n6o's6' ;nseq' F.n

-'l*\

1 wilt €lrll ba in o_

mation la

'" 'o""u

g'*i'tl':lji3'#;::L:1 5 *lrl,#,i.]:*':t io etort the molioA

P

=
P= ftatb

P -- +oolb

ql'a2s..s-fta4' 11 .-r N

p

. t c.) ^* e,+at4{P

'&^"

T\ b

w

^ 2+:o

P^:- - l10 1lb

88

.

5oottr

-"-^J-"il,i"'r'

*{ 4K",",J41\!\ t! A\.V

P :4oa(Los15')t f

r ' 70lt tb

Isao\l@sao'\'o

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 lhe conlac4 €u.foce6 -

zfu =o:N=aao(stnno)| zoo(ar.ao N'37J.21 lb.
P: 239'2E

#*E-#

P - o.,c.br)

t___:g,a

5Oe,) fl,e bloak, 6hown in nA. P-@s are cnnacnled bg fldib inetlendl'to cord6 possihg ovor fi1bt'bnla6s putless. Al Al]rrcnefftoienl ot frrclton ore f. - a,oo \ fk- a,2o whils ol B Canwte +ho nog.;tudout d;rcc lhos orc f.-arc\fk'o.@. i,bn of tho friallon lorca oali"g oi each btoo".. oro) Whot weighl W G ne,coe9arlJ lo 610.l tha .essJcmof hbakc ahow^ i^ fig, P-o1a novirg lo ihe F;ghl 7 lhe cocf-

89

frbr'cnfof fiichon ie o lo, \ bo fnrolionlese el

..og.

r

lhe pullege are, oesumen lo FBO or $oaf, Al

M ^ L ^ ', *''21'*' i*\"

*rl-o

!nr) trnd the leosl rolueot P rc.quir?A io cousc lhe sgs_ lcfl of blooks6how in Fig. P-sr1 to horo impendirg rraiion lo the lofl . flv h blooh . fbo of block^

F(

n^ - u*,-" ,..n',

nol"9

11^.24o\b.

'' r^ ' f. N^ " (o 2Xrao)

I

F^- 4b lb {f-o : nr- 2oo(cos6it, t16.12Otb '(o.\(11o) . F.' f,tlB Fs a6 lb.

ldc

-tx-

, A . o . 2 .. e . t . a 1 '

W

Fr,Dol ElooKJ :

{Fs.o: li:roo- Psrrq = 1oo T slnrl,rf sin7r,69' r {Fx'oi Trf-Pco6a -O 62", r(..z)(w ps:,r"\)_p6q "o !!Z99l!_ - A2Pstn\- P(aE<-o 12J.O2 p= 12z.iz K".zs'a"r+cos"<)- pt e2Ib."o -s!L. P(o.acee.s6.<) ais,,- ,,-r" 'p- 124.0lo. o . 2 a N q- a h e . o o.2 E \trnq - iorq coso<

, :f!

6 6 . 1 ^ 6mArd =,nrf

l^' 6otb =fg -O: ll. ' JoO co6 ro' HB' O'1,6.+Jb

o5Y" fFD of ElazY,CI

l*l

--T--

arz.) A hoingcncous -blook .w,. irvgr,r vof r wejghl w t Y rresi EDr u upon Pn rlhc l ) c Iinnor'ne l9tlown in Fig.P-.et2. If tho aeffioicnl of lriclion ic o3o, delerrm o lhc gleic€l p!' aletel h.,iah+ hA ol ^l *,hi-r ^ for€o c.haight whioh o porollel fo tha incline "at "pl;.a 60 {hol fhc bl6'ck wirls_ tu6 uP tho ;odt;d w/o;t lpp;,4 ove.


FBDof BlooNb:

II,

5L


k-@1)lra4t60rt@

v: ry.!:-l!:

'Fl'o 'tt - 204.6+ lb.

80

{M^'o P(ti =w.-€ 16.01'(t)+we'^ e6/(.) oofnalh) . ,.\f 1.6y( l_ h -

9l

fig P-512, lhe honagenoous cne,fftoteni of fn'alrb^ ie a 44 f E6) h

focoe P ta,q"ce \ rP\l,

blook we;gh6 'too lb \ I lhe n'sitr ' dcleti'na

nol@n to rmPe"d
!=1e!:

s1+) Ihe rco tb c.Jlinder.shown in F's P 51a i6 hcld ot rcsl ftEn a 'tt'd or the .to' 'noline bg o weighf p 6uq6de
--@999-

"o6773

fBAof b,

€rx-O I w6rns. &sra1..ar | 8.6n1+.o+. aoo6,ns .(Rj '8.) 6rnl+.o?. . (\+R4) . 8e1.+.ha A a24,16too- R1 -R1 - 2.b6,2(jo64 az4,+€ioe--2R1 - ao6.2 c.€d

: tut nj. 1N;7case- 8a4,+6;ne--2(1zazote) - zo6,2c

Rl st16

p=ttl=F Z F ! - t t : t 1 6 h t aI F 6 n b ' - P ' 1 o o o..113)=1oo N(stn6a'I o sln.tBd ' ' 1@Z 173'22 tb i w\r

P -l,l =(o.s11i07a'22) = loo tb s15.)BlocKA ir\ Fig.P-s1swoig'r€ 12olb' blad< B weighs 2<{jlb' cord ic po.ollel lo ihe ino|i e lf lhe coeffcic''l \tho 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

, '12o 6h6sa+.

,1etb fu - 121
hzcc,saos6- [email protected]' r R1

R.'32311lb. 1F\-a, P. B2s;nao.a6 t fu 6tnaae6P - 1 2 6 . 6t b . s1s) JF lt1 Psto, l4o bjoo\s ore .b^^ei@ bs a sot.:d slNI oi#oc.]ed to eoch bto.t, w,ln pjo6., lrrcl;onte€s

[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 preverrf Irotiort . 12A

;^r.*'

.

R,1 -"'^(a,'4>

R1- 1237 sin (4o - e) p1 - t u,1 (sin ga'cose-- cossa'€n e-) Fl - 123.4coso-

92

93

lL.A26

:.O - la,O+'

c . 2 sn$,95'

7 0 s.z+-o+'

c - 201,9 lb\/r'

a

aOlA

w^ . s98.3lrt

of friot;c,^ ut\aer A to p'ucni w-.e

t'42

rnolion-

e-113'

tF,.o:

.ln4.r' C . 2 J 7 .S + l b
r

/ - Er " 2 0 6 a 6- o- . i e /

l rr

o|ocr,on,.rr

ihe bdl,e 6u-foe

szr) r" fis e-s,o \f J.a 1 urde. both bloois \^ wo6he aoo b.rhd he. nor' *eishf of F thdl cnn te 6lo.leA oP lho irottie b9 appl)nq Io A a e's6l wo.c r'cnzoalol tcr<:z P y'.!-.o.a

at b: t-a.t-. FBO

z4-o : tl - +o3 I c6in3o' zJr-O: ,Ko. Ca€e6' I F stc -caeao't @,2o)(+,xt+cs'"zo') rb-.(1oj6)-C-374oztb.

o- 16,7'

wa . or+.a"(.'o*",i) wa = 263,7 tb

g4

Vtt te+,e)(o,ca) P"@z)(712.a) r zs1.2s

p- +a-7tb 's t":ot 4oo tb ";ffi rhe purb,j shown in l.*.) ,!:.':' | tl",pi,'? ie p-etenlea F.on @tdt.:rso,j o ta:: P.opdEn ly .-d cf the brotf- re,e.. rf ,he @el .:"

e1oo7

I

fi.112,itb. p_F + c .a6so" "

:,-)

A

:"o",;-:t",.o-m

is a.eo,del

the,alweofp

. ft_ r//rL= zog, iMa-o i. rcaob' P(4b)- h&\- F(B)- fioa(.to)- 2oo(a) pGi) = t+too _ p_ zcoto. r.,,re a bu.h:^g2,:^. ton2.,q,,tippez:)

, e ^ t t . . a , t @ . o r 6 h & - . n F : g u - w .t h e a.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 1rF derqnl

95

\ ? a - 1A l' 8D

2M^'O

w(L-1)t r,@) - tib)- o. al$Fl t o.2(z)M-2Y - o o , 4 -Lo A r o A - 2 - a

Afr-o) N1'Nz

mo,e€on ..st. or L. y,1trJs,o,.a. u.*

Y^*:' f,-yt,ir

^ o t6) tb n a1 o l s t p p . o q 'l h' :e" :a"r-' e

.,.mb b-fd_e lE I , fGt ', .o^ -- d - ,, o - ", .

;,?""ll":,.'.::""'

L--L

n',t 1-o,zN=o,/tt.

.,, e oI j t o r c + . , g n e e b i j ,6,q .toda6 at grc,t.t! lfF rDrof^e bdda .. p.o.4J oga.re. .frtn a "erti

L-ein

,

w-- Flt F.- o.2\ (a) W= O,4 l

@{. di 1b * u.Io.7s"x

. -r, : aJ ,,^,

, i,"-,"trl.)*; \"lz A\Z

Lon

v "?

[^"'"

.o^ '(^..o)

Tanzs'\ '1t.tz . -Ion1r, r tolon.re (to'z''

tl

' 1o" to'', ' ,o

.ng-ec.€ad).$a(x-s) x -sft. szs.) A uotlorn lodde. 16ft lotq V, weigaioq wlb i6 Ploc€d V one ed on fhe grcund \ the otne" hond ogo,hst o ve.trcol woll Thc orgte f footbn ol otl cnoloal s"nfoces is 20'. fthd lho mrnimum volue of lhe onglee ol wk lhe 1oC.

160x - e40 + ^ _ 5.2s 11. 52r) A. hon"gncaaG celincrer rfj. in

''*'a,, n i,.q"" i;; ,";,"_ d o";i::'";J.^l"lf* or f' n'oi G w"

to. on co. t..t I eb,,o.ps cad.l

! .!',.?et6" noq^l )de ol the cowp,e pllo ' rat e1u'red dq rctolrs """.k-;";;.""

"lr=4,t**t".,'S \ to td tvnro'

O g.rilrb

wqr'3@lb I

ot cg:Jilibnun

qr '.\lJ

lr\R\"

Jl___,.,

4!l\"

.ffir:= 4,t\>r4;rr

I

(!-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

27on 20' L@6o I zLqtne - L6.t (ron7a'ttoh2a') lLst

e'L6the(ran ld t ron2o -

-srr9 =2,39i2

a.Ion zA-L
O
+-:Po:

Ton2r'!od
'L.o.r+

{Ma'B

o ",r. (1c)r r,t.s) .

B l 2 o , a ) ( 1 , s( e) to f t ) ( 1 . s )

9t"

:,x^:-T:::?, cuti^der;c^*z counte.ciockwise-

t L6nt+

r-"o'-

the citi'

d, o6is..

D, @67s,

t1,"i'c^s::".

n7 .r,'co376"


-,,J t""rc.) ",,o n1=2os,7e b

... n.,tz6stb

. E,at.

_ 0 : : f U 6A n sr'.) l-s1tuo

,-

l*,1

\n

@ (!,d__h(1-a)


Io sio'l

..t,.ph.

=(to'6)(%s76) = r"tis.Gt,ts) n'77,41b. f?= zo,s tb. dFl-_d,n- lhe m,n,mud h c , r r z c n l oI

ronee.liolrs ro thajefl or .i rh" tha t";;il;;, ropof rho ;-,;""";

,:-.,:71' ' the calind-

ro+oli.

M

2

m 96

97

ili

otrJle q al whi.h

Ptrd' r;fttd. F,{}FI P(r€l = ,o 6(1{} r z6(t€I

€htrng

"(^ffi#:31*r.*.)." - ekt^< t 2Xor1a,@6o. + lo^q.1,46+ 1^d.

g"-rrb U- Ionrs'7 @b..lt

..

: n - -I@6a'(x-2Lbs") !rzL.ti< -t(tane'tr6.b,) - [email protected];,ft<

r "ooe.o'O" o'gaa

N

-

9j.!9

_r " . o .

X' 2Lc41fo^6o-- 2L.;n4 fo^1.. tlan6o.

p{tr) = w6) pU t o t6b)- 12o(6. 6) P = 1o..o2tb

o

(s-g),--{:-z;)

tb

@2)

In

td

fuo

Fig.P-!€2

j lwo

btock4

eaah wobhing

t.b tb oe

ca .,ae-

,itfo.r.n ho/'zoofat Loe whrch wdghs lcotb.If lhean_

gto of f.ioltb^ ie E u.dd coch btook, nid p di'l>+ea rs.ol to lhc as' i.ottio thct w)| ooueo impendlnq tution lolto |.ll. iEdoti^g ba. tho O

e.1{

../'.o.26a l

l

.r__J1

-s<;.

_9_ c q'Ion6c7 U-o)- r6ad ('.lo) J- la.r€'7 (t-o\'-'^.d(^4) ' -Idn,f.a t ton.(it, lo^bs'7 = -1a6L')1i1ctan1d i",s\ ,Dtaooo' r (ro" oe-rton+o)- to lan ro' r.(tonzo' tlo"rc|) 'l= 2,81

< M . - o , p ( 2 , 6 1 - !-)o 2 4 14 ' O

3 . 2 +- 1 o r x ' o 83418|= 0-76tL LdngihzL i€ totol "tl ,;6.pr""K of wctsht W \ 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

:n. tao6;n*'t rocqn+' zn.o, r" +a-;zs<)o-o-*+s. p n. 2e2,8+ tb. (o26s)(.rr.ei t o - p

rii,l

,,y'a.,

p:Zq€A bo. .^8, wa:tsh:,as a;b 1i€ ro6tq..abe .1

lrlcr'rnlfs6 p:n- lo o aloc, *e,gr,,aq zoott 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.

99

a h ' O I R r c o s a s '- F , c o 6 7 s ' 0n.a2) cc &' = R. - 3e,6a tb

t " r-l!_f,__ i Z F g ' a t 1 1- 2 o o I A r d. jo1.6 tb .O: P=AAIF

'

1M^'o a24(b@'6) r r. ra+E'dB a"s-L'a

P- 2a64| bz)(1o1.6)

-o tt.\@.+s' | (o.t6t)tt6\.b4t6'-d'\s'na6 ftg.q = O,s1gflo Na-2894lb ' " Brt Aa 116 26e'4 ' (o %6)(2Bs'4) Fa /^t15

.'.F!"o : Ar - +2+tra - so| 6 h WED6ES 53s ) A *.dge

\ts . B, s,nrs &s,n4s' ws . (as64)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 of fr'otio^ ;s 20' fat otl aanlo;ctsufiac?,a

r*s -

, t€ bger'r ta .Pt t tog.

81.".!19.4b,

1. a rt e )

Iho angte ol frialla nor ' ongl'< ollho

lion br}t'ean lhc \ldgL\lhdlaq,dd

!::!rJ!=

s38) ln Frg.sst. aelo"mino the yotue ol p oct;ng b te 2Rq.| - 'ra1-P'**'

,

aF'-o

'

tetl rc4u;.ed to pult Iha \eadgo oul fmn urae. tE 4<>otb

61tt)'P

'i'"'*P]"e

aP - ,Rtd.|ttu"4&) ! (@Y.Y+).al!a cos Y.&EQ 'st^P st'"{' cas.t/2 - et.d st "t/2 coeq

Ia'/ - &1"1/' s.6) h fiqur-, delonninc lhe nrnimum wa'ghl of 9loch B lhol gloohA uP lho )'clino $ttt heeptl ol 1.,61o forco F 510116 eurfaco ol F lltc weighl al A te loalb \ lhc ongld of fttclion lbr oll surfoces in oonlooJ is ts F B oo f n

iF'

LJ--l I

l$t 100

,*F{'

L?

--EL- ' 3L

'-f={-

_L'

-P91:L

-

p - zoej

Ib.

$s.) lf the wedse de€aribcd in llusteofton hod o wdghi of +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
l0l

*"':+n"" #/ I 'i--)<---l vtnr.

dngiE of fnbnb^

' 19

-&- -_:99-

$a L./1 V o, - +aa -;"1or -;*'

wb

Re- 1og.g1lb 1Fa-o P Oos,b1)c.e't lE.4.ni p. - 91,Etb

nW' R 1' 6 4 1 . 1 t 0 .

!fr,. 'p-

= ql's' 2t.2 P^ - ft,t Ib

s+i Detornirc tho forco p rcquircd lo €'to.t thc, wcagd dron in rhurc P-eat . fhe @"4a of lni4rbn lor o svrtocos n ca,lool ie P'.

A*


fOD of b

P - + 1 6 . 7t b tr\- a : ?nsi..' tW @ts' - o

R, - :&_e:::


F.@6'

afr.ot R..os r') -w

(-€inrs.

_L btoars warllri€ z@tb\Esls+o) ,4s 6hown in Fig p-'io,l-o qfoae bo P!€tve orrjl b4 a tc' oft lo i9 cr. a ton:anlol ic 1s' fo' dll ,@ioot cuFloco6 w.age' lhe ongk' ot l"ial'b" p ic rwqoirea td €to.f mov€hal o{- thc blo'k6? wroi nr"o ol t1o* woqld thie ohswr be cr'd€cd il ihe wor'ght ol oe ol fho

s..) whol lorco p nuel be rypiea to thc wcages snom rigt o P- s+2 to 6lel ttE,n utu a- +t1o t',och ? lho ot.Eltc f.,,itoi for olt @^l
ar/1y

. 6't A. R, . 2aa 6€ a'4 .aol;/

Rt"t"ztv

aFa.a ! zPn'sn'' 'P P. ..(n e)6,^3o'

3,:::3 e

to2

/

- 11,5s.1 p-g1a.+lb

lo ts@tb ?

V

eooo

R" (costs' .
Rr(ce"'cnc'io"rc) - +oo & (o e7a)'+ao R l ' 4 1 1 . l1D .

;a.eaecd

' -R.6nni ,

I R46D,€'' +oo

a,ryc - 8rslrl/..

htcrc*< |\erc

1 6 ' .@

&. A.coslo'-s.rb

P

-

ed,q

_f_ '_le.u-tb

103

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'own h figuro p-gaa . Octo.mine thc n)rco p ncc66cory lo clort thc wadqos if llE anglr, of fiichbn oi ol! surfoaee is 2a'. Ncale.l lhe (r,ol@ ot lhc FolJc.s

G':,o'*'" - -..'"*\ (et

,r'@s1

,

1 +

st

tu'@-@b'6'aq

-6'n2o'@6q

j

a,ee-e.q)

(sDo.-G-&J

o4"

6,n<

. (*-".,

*"

Grn2o'-€ra2o'

_

*) ", "_ - o+66r

= a.446a c< 2s"

Io^4 gS!^RE

P opp)teAol Ihecra ol a Ie.6 zfl. to^g which witl €+o.t I'rling o *ebht of zbns (b) whot wtue or p wt| yc-p tE

__ L.__8_

jaak tu*

(a)

P: !9PLLL

|o.hids ?

(b) r^-o.to ta^ . o.to t."o --p.z 4 6-btf -e -1a te:*) P '{l t"^ (P ' e) o ' Io'r'6;'@'

y'." 4+-

s+.) In itlue. P,oa $+ lf tha atgto of fniJto^ G b' ol illrel@+e o1t sa.fbces i^ @ Iac+ dolarnae tho mo,imum wclgc d.glc. \

lnor will grve

lhe ^edqe

o

ne.^ant.al

56]'EW

sas) A s;Bte lhrcodcd jootca@q hoc o piloh oF o,s t^ a meon rcdius 1.a,5 ar n. Iho creft oiaj \ of elaj( trtctbr of 0.1s,\of Alhetic f.iot,o^ ol o.1o (a) Deternine tE torcz

R - 23aS.4lb

fBDol B i, ..N

THRE-^OEO

od"anlo7e,

ft"a.1e

P' 0"4)(,,') u" (.,t t ".2)

p,.6s lho" lh- wcrqsl w or Inc tlo-|.-.

:.e,6",<

l'as" P"+:Lro.(ote) n' Ge@hn\ b" (.ata.*')

t
j ' sj +JbE 6a5.) tho d,Aonao bot||$ oalo61 lh.cdds o^ o ,.iple_ lhrcoac4 oou"** ie 2/.3in Tte, h€o^ Mdius i" zin, lte coemotcr,l ar ff,ot,oa o.ro wtot toad con be roised b9 eae.lirg a nonvl ol zaoo tb- ft ?

- 1a&. n1.a'

l'l*

pilo6.

€rbltllleP,

taaa_

-l srPorq)

6nO,-)

(s1ntu';.(6'n .''44

- f_1t

'--

P

en@'T ::) "

qa+,s

;;G;;'4

,,6-

paa

€"1&r<)

-@1;6'"^) hab - @s'o.6'n<)

-

2/.;^ .. Pilc\ = 2;^

I baa

l"

(6,^@ il j6 lnpl.

10^6. ?;Gi . o lee lr - g,a3' zFr

lfl '214.

r-wr 10^(4le) *

ihedcd

f r " l i i p r 9 r i c _ p + . hb

f -aft -

- a66itl

2oootb-tt- w(o.ft67rt) ton(srfie.ot

2ooo tb - Fl . w (o.o1E6e6u ^)

r04

to^f . oaa f ' "'tt'

105

vb

o"s;.:r c t"a ic G6o' e4 - .'eo'

- 1, . 2 ut . 1"o;"-,{*"k)

:-.;tu t"

tb f, - 'o 1"' 1+>- 11s7 ... ri "-j1eLb.

bll l.w

36t ) n ropc "."tppd twiac o.ouit a po€i {ill 6uoDonl a w;'?hl af aooo tb wh€.\ o tz.c€, o/-,so tb ;6 s*led ol ,hc o_ Pilor. . o.zEi^ (;,

@ d1lbto

nEadd

@tliPrSbs 2) "-19j14: - o.os31 lo^e 4('.s'lr) € ' lanr (o ossr) ' o oez'

I - r,t. ta^(0 ra)

- 14U rgF\jf^) ro^l b.sz', " . a - ' ) " T 102,3lb-fi srn) A 6i^gt? ltuc-ded 6gua@ s.Ef t'x. zvzflraae / i'+'ie ein . The lt-.odI atanolc,- is a,6;^ \ tte ootElda d'2rt* ',c cdff'ot^l { f"iol,i'n o.ra. Detcmi^e tho rp:r6l r*,<:zset'rg io €to.t lill;ng o \"t-li.ral otl'al lod ol
r E- w . r n ( d ' e )

.
B€LT

'f,E)

I-""'

nq/".ti-z.e')

!h.. o d. tulu:f,;e tte aetr,otc l cf ftroljon. ongEof co^l&) : /2o. t.rorb

,"+-Jt-L^€?.t(,*.,tr")

r\_-4)

L^ so - | (lr.s)

laat,tb

I ' Jt-!! t2..7

'=> Ylo e's

%,) A boot .,ert6 o pu| ol +oootb on tls hoween Vo is wtupPc.J obaul o copelen oa rhc dock n thc I.o.3o,ilo.^ no.9 lu.116 mu6l lh6 haa,sa- rckc [email protected] rha o;taa @l|Dl lfp pull ol lhc olh€. doos ncl arccal srto_

Ln-\-- tp

L":,4a - !t4e'_. oaa t | 1yk = e31j' .11,6t g^a.)

tnL.

P

A

loftlue

of zao b,fl

+

t+,ot -a.

6z7.f ia6d

oci6 o^ lhc

= _?:EJe!r--.

btukcdtuh

€hcM

rn ri

P-s53. Jf lh? brcN. bond h in c.nta.i *ilh lhe b_Ed.._ lhrcvg^ 2sc' \ ihe coemc,al of lnctron ,s oeo Detah.,ne lrE hfta P ol tho e.d or the bmN€ tcv-. f1 - -14')L@'\ tu) L

JL. e.,az .. r, , T r 3|a

l

FRIATIOII

,/\ repo tuttg I v+ turc orcu.d o 6rolio^o.j ho^rnloi dF.h i6 ue.a to s"rlt-l o t
t(Xi

( r-r2l(rar-fR) Tr..L

.q,6otb

ft (o tcoo) . aa

ru

. 2+o tbfl

-

rt ,4ee.2ab

il

plre^- c*) . r, l?,:^ '+) p(1.333fl)

. +qa.a3 (o.l/,61)

ZMp'o

(9T, r rz(z) @n" Pttt -5 f 2 , - 2 1 3 - 3 1 1' o ,s (!/,t 2 (a a41)w

P'617tb ss+) Jn F,a p -sE+ , lE

acetficjtql

G o,2o b.-+qae^

of fnot;^

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,-

- t,at

o..(r4u*)

''

,

a(2.ro)-o

6e 1tw - 6& w= 7047\b

ft'1A7Iz d1 'wo636,57'


Iz -tu " w€i^36..)' 12 - (a,.) (q @ 36,6, - w a^a6.?1' 12 - o 16\tl

T'

4F3-a | \2- 1o3o.@e6,6J.t i1

rl2 ' sod I rir .€rx=o 1 Ir r Fli f" ' Pao 6i^ r6ar' \ | 1t:ti t1t t1- 6aa H . . B o o t t 1 \;

= 3oO 1.+2W I ot6vl t a, | 6w' 4oo - 16?t

v,t.z92.qL s's.) J^ F,s. sss , o fler'ibB bctf .un6 fdm A d€^ rhe 6pe^d purlca 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 rhd T onoxrhurn weight w lho/ oo be eopr.fted vaal mloling

tho putle4 P or etipping lhe belt on to

p"|eg

i !z= ut-"'"11-"t'n,'."

h.

12

1"

butI'.V2 I1 - 1.6+e(Y'/z) l l

108

109

€o2l Dclcminc thc mogniludo of lhc rtsrltonl, ilc point;ng, q ils 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

-a1.4-_4!--3 a

o!r"yrr!'

o

- ?n/3 lta/r.rI ... A. - 1ls.?4 lb. 3.4/7.e1- Al4 .'- A' - -1:.2.55tb. zao/ral 24.17 b. d6 .' . /e. gL-,L-L" -LlAA

- I1zMea.oo C.t6e' -a/R " 0,34-9 aGo, - 226'.24//46.00

6.71

:. Br'

Choplcr

6

Syelome in Spoco

.-119 a2

; pr'

_L"_q"_Q--L-_@ z

236.46 i Bz- -29A-06 D

CGet - $2.a6/2s6.

,'a7

.'-C\. .-r1a-1s .., porhl,iq [email protected], i Cr=r41-l.. iCz- -Aa.s7
Fd.ca 2

to gpl lo) uso ot - x'ir't _aL=^L-,aL-lq z

t2

-e!=cL"SL

5,345

:.Ct'a;C./=OiCz

,'. Ar - 37.1+ : At - s5.7 i Az. 1a.2g s,,/r " Br /-/ . Bzh = 366/z.0-7 :. 6r -'

rl0

z

1 2 72 , 9 OI 8 1 - - 1 6 9 - E a B z ' 2 1 2 . i 6

lll

- 2e+ - 2OO

- 3r.14 -127 2ge 1 0 - -9a 1E6lb - -111.02 tt1 - 7+ zB, 212 46 | ztA ' zre6 44lb.

<' 4/ 1t

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;l noke-s wi{h the reference oxes. 6at ) ftr@ oonc"@ai

s" = e/)' t(.r)" r(+,)' = ( sojso)' 1 (-11a,a2)z t (aj6.aa)z . R - so7,7 tb. pa;hl;S f..*ord \doM absoa zt//F\ = gaiEg/s1z7 - afiB cosor - tr//a - 114.o7/sa7,7 - o.z2s Ii)6aa - az/e - +aaA+/s.rJ - o.s3e

6('J Dolcrdino th.omognitudeof the r.osultont, its point,nq, \ itc d,-.r-o" cosineslor the fo ow,ilq sy61eh .f ,,-,,""pt-"", concurrcrl lorces. 2ootb( 4, s, i) ; 4ootb(- 6, a A F.r. tb ( a,- 2,

3 whee

p'elb.,

!!--L'lt-=

- 4 . = 6 0 ' ,6 | - a ) ' e z . . s . :

z

3! 4,5e

:. px=8.r3. pf - +,37 i9z-11,ra

' (' 12 4)'

q-4L.-44'_?e

| ( 6 26)' tC n 6',)

-9

. . q r ' 1 6 . 2 3i Q / . 6 . r s , q z - e . 7 + 1t - Fseax . s(cos6o) = 2.s
roge+D veeI D2. a2rr',ze L-AL"!:L..<@ ^ r z 7 0 z l ,'. A" . 113,15 t Ar - ,t.+i,44i pn - -s4,el -L= !:-, -EL - -@ z

F, . 2,s - +,37 - 6.19 -a.36 tb \ -

o,17

Fr. 2,5-16,23- A,73 F\ . -22,46 tb.

,'. Br = - 27s.46 ; B) - 152.4 a Bz - - 22P'05

L-

-q-SLz

pq

Fz - a.6+,9,r+

s,ag

Fz'

." ca = 222.63 t Cf - -111.32 t Cz " - 166.A5 2t - 113.15- 2t3.66 | 222,63 . 62.12 tb. 2l . 141.1++1A2.+1-111,A2- 21r,..6 tb 1 z - ' a + . e 1 - 2 2 9 , 6 5- 1 6 6 . s O = -17s,a b. R " - 4 " " + z f 2 r < 2 . = ( 6 2 . 1 2 >r"( 2 1 2 . s 6 ) . t ( - a , 7 s . q ) " R - g2r,5.B tb. Cas+, - 6212/s29,s3 - a,118 case.r - 212,s6/s2e.s3 _ a.+a2 Cosez . +a9.9/s24,se . a,gaA .'. poinl,n9

bockwo.ds,

t12

\ lpwards

- co€122Aa/$-6s -6" = 46.2' rj, - @s', e.a6/23.6a el

- 7s 6"

'+e=cos'23.67/33.66

.'. po'nl'ng

bockwa.ds,

\ do*nerd

1z+a

23.G7lb.

60,.) A font ol (n tb i6 di@1ed f.om A rowdrd a in the cubc 6h@n in Fiq p-.p7 Deleffiie the rcrcnl of the fole abo,+ coch of lhe aoord'no+e o.ds

1o ihe

tl3

t!-'

!r-"

!L'

6td A fot@ { a@lb i. di.ecl€d frDm C tor.arA E in lhe Eubs ctn i" in r,6. r-aro Dclc.'r'i€ the hamen{ of }he forE€ obout

ig'Y

:. F| - 62.5tb i Fy'4 4\bi Fz'626 1t , . Fr (1-) - Fz (4) ,,- aa,eG) - 62.sG) tur

= -62,4tb-fl.

.t$

- F. (a) ' 62,t(a) Zr,4r- 2so tO.ft.

a\z

tb

coch o[ ]he coordino]c ores. (a)-Fi(.) iMx.F ...5(4)-16?9(4)

. -rz(a) -- -62.s(1)

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 eooh of tho coa.driold o)las. rMr - F!O) - 1,+8.6 lb-fl. = - L8,6<4) llh--394.1lD-n.

auz.-tu(r)rr'G')

t -L"EL- @-

- 7-+,3(i) | n1,4(4) 4M.- s1o.Slh-{\.

ri - {1 i tb.:,Fz- 140.Ftb. cos) A for@ of:"oio ieai.ectea Fb- B loenc D in ihe cubo 6hown in FIi]. P-6o7. Dele.r,he tfte Frornenl of thc J?rrreobout drLh ol the a..di^olc o'es.

.M'-

d - a.e fl-

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)
+-++-* :. Fr. 1@31b. tb. i fr. z26,sbi f.- 1fE.a

611) A h@ P,dircakn ftr6 F ta*otn I in lhe cube sho^n in Fig.p607, cov.es o momenl My - i6oolb-ft. D e l c m ; . e P q r l s m o o e n l obout lhc x hz orc€. -!L - !L.3 2

d - E,36s f'1.

tq !r9.5

:.4=6aotb.ipr"4aotb.

4M*--P'a.)+ryQ) = -aoo(a)r Foo{.) M) - -.{ro rb-{l. 4tiz - -Prc+) . . -Soo(+)

P/'g@tb PL- !-

.., P-1o17 tb.

61.) A fot c p is d;ructed

Mz. -32oo lb-fi. f.om o poinl n (a,1ia.) io€.d o poin{ S

(-3,a,-r). lf il ccusesa rlomen{ Mz- 1cootb-ft, Determine the monl of P obool the tt &,y oxes. - -z.to(+) atAr -9@ tb-lI.

-E-'LL'-L=4 .'. F, -o lrt- rgol6lFe-2ao16.

zMr- tu (4) - r€o(a)

d . 0.11fl. -La

q,1

4M2 - 72Ob- fl-

Z-

!L-

lL

... p, - 7p/s,n j Pl . 3p/s.11i pz =sp//eAr

tMr-

ztA,-p"(\)+WG) teoo' 7/sr\(p,+'&)pA,r

244 tb- ll

P . 9'll lb.

rl4

ll6

M

iliii ll

d

fi {

I

I

pt - 7elb i ry - aootbt p2- s@to zM,- -PzG) P' (1)

65) Thc frona$orh shown in Fl9.p-61e con€ists of thr€€ 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 x oxi6 i6 opplied ol A. Delcmine the forc6 in eoch nedbc.

= -g.tO) ' 7..)(1) r1't - '17oo tb'(l

- PaG),p,(1) - s@(4- 7.b(+) - -8oo lb-{I. }'4/

zttf

d;

6i+) Ths sheoFleg derrich shoxn in Figp-61a suppodso \ic.tical lood of zooolb.opelied olA. Poin{e B,c,\Doc in lhesa'ne norili r.ntol plone A,0,\ D orc in lhe )(Y plone. Delermine {he in cdch menbe. of lhe dcrick.

a-1r:of +
'(o-o)" ' (5o)'* (o c'5)Y Go,,ro) da d^b - lS.7oo fl . drc" . @' o\" r ks- o)' r (o' o)' d^c'20616ll.

di - Eto<-zal'*s-o)'.

'Gr)'.(6af ,@o).

oN. s.a67'

lcolole Right Sidc vi€w, lsolot6 F.onl Vicw,

; lsololing Top view-1@(D, rcf(3) ,o cr.62Slb.

.r{oa. r. o : B/G)-1db(5),o as-, !L. c/ 't @(.t/$

AE.lll€

Ba- l2t'ooAo)Y$

aw..r- o: '!r$(1a)-ot en) - a a/,= laoo )b . L. !L' !!-"!r a Dr . 2cballl ; D.-o

e"9L'L'92. AC.1!?4,s

_4_

e- - AL

@(z)

Df-alEtb.

-6IL - __9u_

Ac.76s.olb.

Ao - s22.91tb.

tb. i gry.5ootb.

616) Refer.ing lo Fig.p'61s.r-Jpta.nhly-looo tb jarca ta v€i,licol down*ord locd ol ea@tb. Defemine +he lorce n eoch .tE1i1*r rnda. {bis rc/isod lood,ng.

tb

d^a.,@Gioi4o4Y

-&"

d& -r'G;F ,G;f t Ga\61ArY da " e36r ll.

ll6

-o,(oJ -o

tt7

leololo Righl Sid€ vi&,

610)'the un6./nmel.icol contilcwe. fftrrewo.h sho.q in Fig.p-610. suppork d we ical lo(t of 17@tbol A. pdnl€ C rt- 0 oE in lhe bodo .dlicol plone whil6 g i6 3 fl. in lron{ of thi6 ptoi€.

fi€ nnce in eoch @mb€..

a^s.t@-ifi6:F-,|77litr' d^c - l6al;Gzf-aB-Or

(2a&-tuaoxs)-c,G) .a qk) - 2a.oe)'a

d^o.

DrG) - (2ab1o.,aY.3>. o

. 6.vt!. - 12'

"/(s'a)'I (+<)' ' (o' e))' ' e,16r'

-4C-" ,9'-4L,_9L

AO -

D.

AB- 1r1O lb-."c A O" s 2 2 , 9 l b 612) The poinle B,C,ir,,D of lhe oonliteven frolnsv?orx shown in Fig. P-617 ore olloohed lo o v6.tical wolt The aoolb toad id F|oro llel io the z oxi6r\ lhe r2oorb tood € veriicor. Compute lfe lorce d4 "446.)2 | (b o). t(4:a +)t2 - 101t o^. .,t(1o or |
Isololo F.ont Vie*,

,; t:rz

,l; c,C1o)oeG)-@(a).o

lelole

1,@(e)-B\(O -e/6) "o s | (1o)t 6/@). 12..b - " -A i6 . g, - br .gt 5 Are

Ftunl view,

'-t\

1W- a .d*

ot/.6) - M(4)

- +o.(1o\ ' o

_6q -,qeq A g ; 1 6 1 5 , 5r b- . _ c to.o (4)- Lo(.o) - c, (a) . a -lL-

-jL.

_4aaq

AO = 2382 tt)- -I

--lr-- . sao AC- 53A.3

l.l8

;. bf ' 6/68t

- 5,b.,lo

I

e,(d) | 6/sB,G).13(a bt'Qa,tb,'.Br.12.alb ... nB "r7s5 tb,.-C \

A C - 1 2 6 0 h -- f fteG)

s.16s

-

- 34d(.) - 0, (1o) "o

T

A O ' 1 9 a , 3t 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.619 d,^a - a.i|s l+., d& = 12{1. d^o - qfts fi

It9

lsololc Frb.'l Viow,

leolate

Top view,

zrA.ro. -o,(te,) + Rf l4).-o W - 6.6./aot - -@ zMa- o, 2o@(1)- CrG\ -D' 6za) at(4)|q02.41.

lsolole Riqht gidovic*,

a,46)- t6{E\ r.@(t) - 3e

q- btb. -_L 6

,'. sr = 6/59r - s,B.t& 1ou + G/eg'G) - 6@ 13,6 8,

AC - 120lb -- - c

a6g@

- o.(1d)-a/i es.G) +1@@)' o U(to) " -5.,/c)14o(3) | E@

g-5@tb. iq-@tb: /\e- 8-/r,3 tb---I i B, -aaolb.

.D= 4166

O" r21otb gL :. AO -,1,{€6.+\,. 0

i....'a)

,..

AA

i Ao-6.1c'6lb-C AA -ros5,3lb- -o I [email protected] in 62t) n ve.licol boa p = @tb oppl'pd lo th€ lripod showi codlp.esgrle fiq-Q-621 @u6f,s a lorcc o[ 2i5 lb in leg AB \ o cornpree.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

.((-t-1))'t!o4)" r
d,'' - (6a-o\2 +ka-o\' t (o-(sr' d^o. r+,i+ ft.

r20

=o, Df(') - Cf (1) . O

Cr = 56.-2l'1b in@, o' = ,15 G6..25) - 1$ k) = 9eo.7,t4tb. |'rO, q"8,G6hGE) , _95O.r13 ., Ac - W.2S t _Lp_- _jEL ^o 1o &fio1 10 lara

aro) Thc fmnc*#tr sho{n in Fis.p-62o suPpo.'ie o €.li@l 2ooo lb. Pdnls &c,\0 oe in thc sdE ho.;zonlol plcne l.Dd of Delcrmine lhe fo.€a in ea6h nEmbec. d;-

-o -@.

Dr ' +/3 cr - -@ .vb.. +o@ in @, cr<+)t 4. c./(12.c6)'oc.o Ct O+.Pe\ ' ada

o -.co),g,,6;r &(r) -.,o{n)=,

9' 6.,) | B"t@')'Iloo?) - o I'Go)+RrG)'6w--A /\B.Ar-8..Si f f i E s . +

l$s

a c < t >-

t2l

lsolole Righl side v,ew,

lsololo Fronl View,

-i' M c . Oo -0r(6-2.),@oG)-W41) -o 'aoo(6'zo')| as@- 21e6.6 -o

-&-.L'@

;8t'19e,attb _9-_q-29L

q Ls). c/(., - 12(,@t . o g/ ' 6
) --@

- 2100 + 4co7o . _2001 .4 Za . 0,997'

:. C-/ " 2oo1 lb

6dro:cr6'\o)-qG)-

-PL " -01o.t.t, 10

ot | \999..O44-*U-O

Dz' 3s,s6tb

q(rd'qG) -o ro . [email protected](6U/4tb

24@

-Cr(a) - 2a
o''b$bes'Iy'o

4'+ooto

trO = '(aOf , qa' ttzs.6e.f AO - 432.7lb -.-C

Io _.t' - c, - 2a3 _C" tc 1.n2 6' 1+t+2 B Cr = t6o,alb. Cz ' 12o1 lb.

lltlo - O I C, G) | 12@(2)- ot Ao, . o S./66)-qG) - 2.e - -e) subs.@ro@.

l

l

Cr+o,ta./-12@-o 3 2 O +W r & 9 - 1 2 A C , - O '

-4L= p.ea6

,l

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 t7oZqY

dM - 12,$6ll = d^c "(o-o)' r (1o-o)'+ (6-o)'

d^a = 1+:1+2 fr= d,a t6'14)Y t1aifa d^D = i1.3s6 fl

- -?L

_lqcp

A - 471.31bC -/\D = \.aso

/'C- +sz.E tb-C 512 40

d."..[:7'TG;F,G_g do^ - 1.aw'

eeY

doe' 6i'tf qu.6,n7

,G-o\\ PIi|'

Cj06.6,C62

dva-"6-o."tcarc (+AoJ

t22

t23

I

1

0 = s81.5 tb -C 68.) 9elcr'l'ine the nroxrmum sofe verlicol lood w fhot can be suppo.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

)

r

o.o= 7211

* if. M" 24eb., [email protected]=AL-1q ,.103

2

t*a,r(s)-r'-(o).o

G

Aa" 229,61 tb.

., A, - 6445lb i At- 19,:+,*tOi AE.12s2.C1lb. Isolole R,ahl S,ae vi*, leolc,te

ahec'. \f g > za4otb oA 73s.61 D.\ ' 2 167.25 tb. .. thiE @nndl be o@pl be@|s lbc I'mll vhich i. z{.ab. ,. sae

dar. vot.e of w

i.

tl witl eo6ed .sigg.S lb

EQutuERtuM roR ofl.coilcu^RrNT SpcEtoRcEs

A'(1) -B/('>-o 192+..6G) - BaG) bf - 1539 '@ dEcrK \l Dbr24@h DB = 153q.46o

Ee.

6-

.'.DB- 468.561b . ./ tl dclol crd

(srt N\z -G/G).o q - 2(t 4.p}t

4)-

q . 1.731,e2+ tb. jf dt ct. rc >24.r.tb *pL - 1731.921tb :. qa = 241.4a trr a'211 5 "/ildoetu)c&

n(4'at(A=" tif

DE '2.@ |

62c) the Flole 4arn in fb.p'626 aoti$ o load c,f loootb aoptiei oJ 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

,&-(1i21.s246)- srds.etb t tl DC'2e t

,

#'+'T-+

2 1 O o- C t

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 tb dv:k 'f M> 24oa

_w. -22122 DA - 27s+.s tb oo totl .x4t tti6 \atle bd@E il er@&s za
-Ci

^C2

ct ' 1q6,9 \b. C.'O

6l-r.L-!

_-.]

W.-4,4.,0o(+)rcio).o C' 4oo tbT

-6G)r 1.,60{6) - B(s) = o

s'-3p@\i@@

A t A I C - 1 a t A" A - 4oo 4oo A - 1<>
627.)6oleeprob.6 if,t^ add,l,on1oihe loootb,the plo{e w€,bhsj

'U@\@t" Ue)qt)(e,/.\ +'fG)e^1qe) gr'bA.h) j " nbll.

y1()4@t - 't G)a6)(61 ,/s6)+ ,/l@(d?/e.6)

t =5 n .

t24

125

Topviow,

LVz'o O - Q(a) | G (+). o 02(.).0,(6) o'/+ ut: O! t,cr-G (D'/,')Gt- o'l.o) c,G)tc.
o, ts ;i:::=-" ,i.'"/

nn6g,otal , .m 6) - c6o). o

ebG)1.&o G) - @ta) - aLs) -o

.V" ""{2.

c' " s.2so, -@

qbs.@ b@ ,x r s 2e D' 'eoo 0' . Solb F.N@ | Ct . t.Lt. 12o tb

g- g.o tb .T

c . g @ l b ,- f

ztr.a -

,to.fu(c.rcsl/a

-A+ [email protected]'g&'a@ 'o A' 600 lb"l 62c., Refe. lo unsynrnetrrcol conlileve.

Ac.kao0z):L/1 lc - 126blb.

Go'r€wo'h

dosc'ib€d

in pnb.61g on poqp €6 q rep€oled heneosFl9.p_62c.lf lhew: ibal\lood of 17oolbi6 shrfle, b ool o1 lhe midpo"l ofmem-

ber A9, oomptrl" the componen{sof lhe ceoclion ot I E lhe lb* oes in lhe bors tC \ nD. dn -.[.e-af,O+ef '6aY ' s,7" X a"c- .@$i6 -ofi@-of ' tzfi a^p- t6of 'Gaf ,GEiff - sftaq. I

^ c - c _ . . c r. e r a./' A c''cr/2 | C, "Ca

AD . O' --9t e,.6s g

'02

Relcninglo FrD.t view, zMo"o 0" b G)| s.e) - e(.o) . o ax(6)| azG). +r.. - -@ z M c "a 9

ino, .eoQ)-Be(z)"sat

BxG) -62(3) - D,G6), o 9*(4) -bz9) - 600 - -@ ^oD (, L@ ar k) - b{e) - @a ' +aoo e, tn) ,2.6 . b, Go) soaa B* - 5.b lb.

j

ri

I

6ao,) Ihe b.f,,n BE of ltle sf,fl". l% de;|cl(. €hawn i^ Fig p,6so k tuloj€d bNo.d jr' meogurcd in o honzaolot ptone lhe nrasl nb 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.ces

in the lEc Ec \BD

l

ii O, s@(.o) | 6, (!) - e3so br = lasa tb.

l :

t\ lhe.conponenlsof the beoring reootion c*

Q c, = otlz 1 az'D./+ sub.@q@ lo @ (o,h 'Gh)j '(.^*o')la +a2so 6,50,+gsc^'+2eO D "r c ' . e d o - . - @

9,6d+6/(')-ne(6-2') . a s,(a)l qb)'$3o--@

dao'dsc.tr2tg I

@t , ct)e)- @, to,)(.b)| noo(z9) . o (0, . c') (i) - (., I o,)Go) { a26o - o - -19

t26

r27

R,!lh{ Side Vi.*,

- p;? ,
lsolale F.rni Vrew,

aio'a, N@)-'[email protected])"o

Cr
." E: - 99L

zw-o o

q(6)twG) - s.,Oaa) - o A(s) rt G) ' 4aaa b q, v/'ae --@

q 1o1's66

n e4.4.

oy = t63 [) - . -A o

-A,(.t r (c'* o'X.t r soo(s66)<1tt X')'o -o - @ ^" 6r , (Gr D")Gs) A,tst =(,r,7 i t1)t14 A" = 2ag7 tb oz . 6114/s_- 61 tt) Cz . 227a(s)/i= 22a2tb.

. \91

i a -

4''2d9tb

ZM^-o. r o @ ( i o-) E 7 ( r o ) - 0 r ( $ ) - E r ( s ) . o BUI: E4. " E,lo :- 4- 1.5Er -o i @ < 2 ) - ( \ 5 E / ) ( 2 )- o ' ( . ) ' E a E at 2 a , . e . a o - - @

Or - 193


6-PL

Refc..inq to llbhl .q& V'bw, + cr G) o/5)'saaG) "o zMb:o: ^z1't(hiaj)(s) t61)(1st633(s)r la3ci) | 2w Az = - <2271 Az - 166.7 ll).

n rOP6?1 63r) The boom Bc ofthe ctiff'lea de'rich 6hown rg.s-lsin i6 conto,ned in the XY ptono The mo€l AB ls "e'rtiaol \ ' o soohel ot A PoinfsA\D ore in the same horiuonlol plore the Points DkE ore in lhe.eome v€rlicol Plono Detormine

foroeEin 1r'o 1o9sBE ?^ BD \.!4ryw"""ts

ring reoclion oi n.


ol Ihe bea-

Zt'/^ -o . D'Oa)'E G):Ey6o)-o o/(L)'Ez'E (.).a -@ e4o '4hs ,,, Et . to/tsE/ '"6'" Dr(t- 1d$E, Er(z) =o q(r)-aoA,E/'o D, - 4o/3oE/ sub..to @ C) 2E,tDr-1do 2E | 4b/3oEr .looo B!+'4.t.bE) 2*r a,bo(1bE) - a@o +8, ?1o.o ...E,,2sob.

.'. E,=(.Eo-o;)/z @&.raA ar/'a -O,ha .'. Or " o//z -.Dbs.1@ Be/@s. r5/1o .'. BE-58.4tb. 'e<'otb -@ | A"@'r, AtG) *!'rg Et "tse, . a,s12ta1 Ar (.)t A\ -Df/2

. 4.)&th

El ' 375 lb

- aaa!) ^t (.) ! (@;!L) N|+)t1@. w.Baao ta)Ar or ' Totb --@

-A'(Q.A,(")--B^=

-{&.a

t€a j_3g)

6doo

usn]gq . 4944 - ao/eo Gas) Dr ' soo lb ' bo//@ @/aa . , BD. 612..+ lu. uahs@ NU)-Df "7eo Ar &) ' 7c!:4+s.22 Ar . 7@r/4 :. A-/ = t61stb U6ins Ez ' 1./16Er .4y'6(379) . 2so1b .

oa'l6e(ot/za

' zso tb.

rcGming 1o tujlhlside Vew I tF: =oAz'E -Dz'2. .'. Az'o

t28

t29

25a =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

1.10.6,.0'.

rolt.6' - b/^:6 .\n6o' - 6 /.o

a.@tl.

:, ft -.o$.'. 6 . ir.32 n.

1ar,@.. 1r.r/6^ .-. A . ro fl . (Ge'-$/A,.'.&.20lt. de -,GoAfi a.A:ofi6'i-Lry ".a 2t{l L, 10t a 5' - 'e '6 rt @'aoton@" 11''att' $r.2e.2. $ ae.6il6;f'('+. 3lo "2"'" 9c'816 "' L'

Choplor

lnE4O q .

'

q

l

I Dt'1132 .fi32'3173nA

8o - 11e4.6a+ n A T

'15444lb

Coniroide \ Contors of Groviiy

-'.go ' \63tr lb

- Ai Ga),2db60.6c) L o

ot'!91e.L9,

zM^'a O

c,'-trzfi@24

C',o)@- rlro(s..6) ' o Al +O, - i7z2 - -O loble Right gddview,

ce .199.96tb

02 - 1t9a 6a+G1.32)

Dz = g9.ec lb. P.l. lo Qbhl Etdevie : .F-'o O.-A,-Cz-O Az - 939,96 -199.96 Az'saott)
Cr (.1.a4) - pegg.z4l&

r30

l3l

ihe ccn{fti, of lhe shod€d oreo shown i" rg. '|6 by barrdcd lbe l( d'.i€, the line x ' a q th" pd'

7o7.)Oelehine the cantroid ol lhe qu6d6nt of lh€ ellipse 6hown in f1:9 P-?o7 The eauolion of the eriipse * !fu-, *

c7b"'1-\7o'

G,b) k- e% - b1a

'

a'.- bay'a- u- blr&

d

-

,t = b/aq;n-;t)

n-f, aa,-fi ary*a^

^r =f iG;,) "f,,(u.e:r)a^

t.f a' =f w.F:ta, .. slnq='/d LeJ r=o6,a dr = ocdsqdq

.8"1-,^.wd"-:,l{i

- Va[ h@+y,o.] Ai - !d = eEI i 7 - &/'\-

ylJ7.V ac!s-..Fi:F

'chgud,)- hr e!d, A,a -f h,ll(*4) a^

^. rt*")("-"-" ) -u"l!!;.a.,,^a^ _ .obL hL11@atd4

_o,1..1a.,_t%]:

-4f"r€r3:l" 7 = 3o/s

- lle +

4t 7o6) Detffiir€ lh6 (btroil P-7o6 whd6e nddius is n.

'N'r" .1.

l.; ^f,\

"l "

^':ld^.('(adl

{'*'"'.,".. )-h.%G'-'")-L

-'l t'{i,v";l

ltt

of the quo.+e,'

- n.'

-

oircle €ho,n

in Fs.

A- fed' -("$.+ U' _,/. ...6,^< .,,:;,".

e J;"+ N

'9'=b/8

p,.l$qd.

^4^

t.t!'-*?.-""e-t*":e ('" f -1-a-(fl4,-"""1a,

' o-'E J ib lrh tt'PL

A - obi/

14,tq"4

7oa) Cfivlle th6 o.eo of lhe spondrel in Fr'g. P-7os bounded by lhe x o,i6, tho tinex .b,q the cuNc g=x,n wheG n Zo.wlEt ;e locolion of lls c€hl.oic fr€m lhe line r -u ? prepo.€ tfe lobke ot o.eoc \ lo@tion of cenl.oid f6'- 6iues of n.o,1,2,ta\e.

r"*=G-F

-+t-''al: -+l'^'"d" #1

a'h\Yb^

^.\1

Ai'l,"a 'hJ'!ad'

' r,(: (" ") d' - t'l'"' 41: ^i _;i," ^Zl - ".2

edx.

^--f,,(dr.f,.(#)d" ' h4^f! t" a, -hA^t#7:

t'4+ai '%.f,1.Ji "%"i++-"-l-!\r --L lu--'r1

, hr."T-hil: - o'1 = rt" r =!Gd nr'

A - br%r

t32

- s_uZ,

133

ut l'i" r i" -tf.*a r.(oo)

;.

-t-l en -' {

7oe.) Deledine Problem 7oe

n5)

- b(nrr) - b(nr1)

b - !ltl])

Dele.fiioe the @rdinolcs oF t|€ c&t#d in Fig. P_715 with nespec+ to fhe eiven

st'ovn

C c ' d l- u z -

, [hn.,]-l# , e] I xt x"t , y,r r't] s -Lt^Gxqora:'

the s coorditule of lhe spondEl

deso'ibed il

^e ' [: '/,eQd") - af' e"a' ' Y,l: h'i/b- d, ' h:i4l'L+"'-k - t/-*^ l.tl" - of ratu:<'':s) ) 2(tn t') -:b[

.t

q - ".+r i^ al:'+t l/r(.\(e)(k.6)f tlkr6'O1 4-11i

= h(a'l)

[6, rrd r €l t . 6(rr s(4'nr)

-'/"f"u'a" ^6-!:'/"eed'

r r(*{:d)

5 ' 2.+a;n = -6(+) 1 e a4@s3o'r 4 ) - 3s.1ee 25 st

26.@t

uf = a's,nn,/L

:

' 96.41 , = 2,31 in-

n6) A slendor homogeneous wire of unib6 cross sct;on ie be4f inlo ihe 6rope shown i^ Fig.p 115 0et. lhc @rdinoie6 oF ils @n-

of lhe o.eo bounded bg the t ot'6 lt) 7,o) L.@fe lhe cstroid the sine cu.ve A= ognayL fiEm '=o to x:L

9'an^u

- 30723

41j44

". --t ."",'1b

:!qa

of fhe d€o o)(ec.

i'13th ,17') L@Ie ll}f @n+K;d of lhc b€.+ *i€ €tan 'F hon|oq3h€ous q of unifo.n orc.c 6etion .

t --rq!: <

- 3:r-eg:

in Fig. p- ti7. Thc w;.c

, ae65 ; .

zo,,/tu

","u'- B/e".; -t. n. 1.4ts, l, (, E^ (:4'^ 'l&.)) +2f s -[z(axzr(zo''4o)'t(.plJ A2Az! '8996 .g-=1.o36ini i-o ttE oenlrc;d

of lhe shoded

ol@

slEwn

in d9. p-rle.

v'GYq1t.f h6*4@n .6)'] [Gt@\(t)t v.(6Y.<\t | | h @G)CA.<)']+ 'E tha o@^troidof the or€o obow {hebo6l shown in F1b.p-7+.How lor

L(€) r 1(6t E = [1(6)(atl, ] [1(6XosI 1+a - 4: t - 3.o7 i^

t34

t'/, G\kr(%'c)1 i26

- $2

4 'u,".

a27 " l,h 6.2) ('/' 4Dl I l,/. Grdch -d1 \ f r{.)@@'. 6 !.11 t=5in.

r36

t,:

,o) Dele.nr'n€d lhe ce^lrcid oF ,h€ l;es rij of fhe €foded ored i^ Fia.P-a1e

thot lom

the boundo-

,!)

Locolc tho cenlroid

o.co

. tl'. r,ttt (,..tt..')

. (1.d' (.t(,.4) - 1'w (4+)

| 24.4a112. 4..s X - t.o+;^.

ao-aeii = 251.322 F'526 tn

g\&A,4rr.,(9)Vd,.fr,(WW.n) .4e.eiq'1eG),6(.>+@f

2+.1a112E - 1.*> 6) | ('h)(t.r)@(% n) 24.4a1+2 I = 63.5ee

- 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

lh€ shoded

.'Jdt [h(.d(G\, +b@

^ = 1r@ | I6(8Eb/4\(,/r)| W(r,/")('/E ltz,7-eo r s t.F4 +-.tr-!,-l +{nX h"z)('/tr) | 6)l

4A,3e7 t

of

the coordino}ee /9. P-7.a.

5'26e;n of the oonlrcid

- g) +2-*G

of ihe shod€t

?\- k@O-%6r&) -!ktJ' - r(eb)-ge) Q/,Grt',) - !!{ G\ -.!F @ - 49)

s7-[h tbY6rlr3 d t'aGYstlty'.

t4,rs3t

€s.33i in' = 2inb'? bt = 42.666s n2

- hra.'s1 t . z.ra in.

'41eaa1, '2^.t(.)-/e(d(dr"rt tp'6a ,21) Befe. ro the I_ 6€otion of prcb. ?t+ shown io Fiq. P-7r4. To 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) ?ora.ib-4+o.6b ' 2b -20 I 722.>t@le

lE

b_10n.

@a+rcid

of |he ehoded

oreo i^ Fiq. P-122

by cuiting o €@icicle of didmeie. r frod

o quonler c,rcle of

'!#("-#)

ll;

l[|1 a

= rl

--i -gL 12r

= 0.6.7.

s' ( /,Y,'th'(-"16)(/,)

o"Zj -.% - \.7ts - 16t:: str'

r,%_s- 6 5#:' E'-e!]g-r-

, l:!t@ - n ctuelr=ly@k)(E',\[kbtu"X% aq 12, - s7.6

r36

t - +.€fl.

n i .[.h&doe/a..\ - lh a>o)& -d

,t2q - 3€ 9-3ft. zr) Locoll3 lhe lglrc;d of the cutvenl st$*^ i^Fig.p jz1 tlnl. ln tog.a{,bn ie onneceosd.g tf lho o.€,a i6 €ubdiv;dei into the eloment b be fdrnd in foble vr-1

, -'+

1.o-rs(+Ydt,fa&)1.\')(./') [r(kJkx')t r /.it't') - e/!)(4)(1.)(ye.,\

7/A_t o 3aer

- {t)

1++s93 E . Ea,a6e J'5o€in. z26) tr:.afe lhe @l.o:td of the .sho&/ dr€o eotc\se! b9 +he cutue lhe 6frc;9hf shos l,ie in Fi9.p-1t5. HinI : ob€€Ne ]ha{ U..o' \ 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.

=e?X!.,r,(IlL. X-ei:) f+ +il' .r".; -,2 #7,"

o.€o

I

4 - i,6ft.

t37

rrd wifitul usitg ;ntogef;nfhe )( o'i€,ltp li,.e 1-t2 ,i.ltg A . (qd: ^ "ii 1.^r,'/6.t/fla)a,

c!.nPulc i foi lfE 6so b.u'dod o.,rl€ g'a\ t t/s-a/ao ' ,"'r

+- ., A . Iz" +\i6+ rlr'1.

A-

,.e)

A

At.€Ad' - l: (af ,'7e- ^'/e\d,

252' = 1q1s z I ' 760 @'ts ' ;. divided

!.t/*..

_H,r | ,.h, r7...1"

292 ttil.

rcclor5j:B

|t(1\1)!j,(1\(o,) fiO r'(t), la)Ol g . 1i,|,tr...) .o, - i11 . g -o;7 in. - 1(.)(7,e\, (t\ @)O.cs) zW

b/

iato

two Porle

b' il'c

E.) 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 cenhoij of lha uppecpo"i B i. t(rolea WtB-/,iA\Eg"24^..

Two 10 in.- 15.? ti

72,+ \nl

chonnolc orc werded

ioge{hdn

os €h@n

h

fu. P-7:1. F;d lhe momeniof a"ea of the upre. dhonneloboul the ho.;o"lo j @^|rc;uJaloie rroof ihe o{rro ceul,o. o@

ol roi^- E,e lb - a,ar i^'

2(aaa)6 - a.+a(e+ rrc) ' +.+rG) e.9t5.67seG1

-b6'to rhot c^ *n erAhbl^

g- ,.86 i^

. b(.rz)-b

r^.644

FD-*lr"=br'

\-E{,1

f F{s. p-72r. Rela lo Toble vl-z 0. +t? FoPe.+ies of the o.9t6s q b.-te,.!"e cntrcid ot t€ bu,n-up cal,;n

/r&'

\16rit/

bhni, -)L-EL

6,8 i.ft] [e(i)r r(E) t

=b."!nti;?b'h. S

2(e2)

#Bt'=bh("'4)-(*)D#}l

'F-5"- b##r

-*ilE".W 5. , h(nrwri .. l. .2rA

138

" ale.ra1s t- &'sa'^'

r-a - b\,&'-r-o 16 _ lod

,ir 7,o) A b@n hae lh6 oro€c eotion shos fia moft€nl of o'€ of ihe sked Po.tion an+rodor o'i. xo of lte *lire €e,lion. (flole llot th c E€.lte t. laa i^ €ht df -ol;ole x,itum cheonrg sr"esj.

xa5

5 . €^n@!.') r (i4)t.) ..,s(.-otu) r s,sGrs)

enlrcid of lhe buill -up solion €,i,bn €hadn ;r to lobb vn-? ftn lhe popo',tic* of ltc ebrcnls.

l :

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

F9. P-%o,Cc'nFrle abo,t tha ho"iantol , tt ic e-t'o.. i' 6llqJ e n@cr'P'li'q

r38

l l

ri

t6 rololed oboui ondxte 7e6.) A riqhi t.io.gle of sldes b\h coinoid'ng wiih €i& h lo gerP.ola o righl cl'culo' c'r€ ' I

v ' ? r tt. n a - A r . k b - | A b r l 't = '/'rb'h

A .,"1'\

At=Csba,)-f e"d,

'f- okG'-t)"

v

- ut.l", i'"1\ - b/""|d - "% , ""

-"*.:+.+ =;fr"u.

Yepune- st 4-A

"/f,

A4.bTll 4421

-,1ij""1*-*" -r-*ion6 l; the 6v.fo<,eio@ E vorumeeene€ iod b/ rololing o semic,rcle ol.odius . dboul ilq d;m'ie'

n.ab

"r

u-or'4.^@of horro,rcre

, kho

uW

. Ai - t"r,'a./

v '+/er"'

..L

- l r"l V

t o . ' 4 7 b . ' 1x ? o -. 1 - t % "

_ { . { , r. +

- 2t.2/k.'t. A - +r.'

I

_"t/b,lbr. /%l:,

+r'.^,'

..J.:.th-"%id-

/;-L'o. j *"i:: #r: #'ft1i" iq o'.n,.{+" +. - -i. ,,j""tt_

"

-

'{;t

. _

,.,

A ,2 ^ b h + ; . + _ + --!P

rPi V f F b b d l d d= d r ' i A =Yr.li.4bh

_.i

t

v - +ro,b

at . a74[+a)1] rcht "

["

.ft' ?):.

-"*'F'P

. o'/b'[bt-b%$'-b%]

73e) .sfbw thdl the volure of o Porcboroid i€ eq@l 10 o€-hdll {ha oiccumecn,brg oyllnden , i '. 1)a' A; ' r A.J-l4 'r\d,

1-^.,i

o"/6"(t" -5") vdqre

' l',"/v'(t'':')av

A=2t i L6alh of ("-e

\

t''

+o'h

i - 9 7ro) ,A oille of -a;,3t" t;'" 'r lhe xy pronewitb rtc oaltr oi o d,6+dn€ o obovc the x-o:is. Royolviig il oboul ih€ xoxis will gene.ole o doughnul-shope ri.q aoiea a torus, poraea o '. 96al*

thon..

Coopule th€ €urlo.e

a,b

q votume of

-*b

{ 2 3

't

h bQ.h

Delamlncd {he vdluBe of the cllipsoid of ^€"dluiion qcro€.,te (c"olote ottrpaid) mia'a'ic q l6d rolotihq oo ellip6e obout o) I b) ik olnon oxis (oblaie etlipsoid. Toke the lo.e{ s@;o'h o. d \ thu smoll+ semi-or-'s oe b. 7e.)

,7b"' ' 'Z'

r>."'E

f .q".G'',)

140

,a1) A 6a' ptpe eibow ho6 on inlenot diome+.f, oa 4 in. lAe .od of cu.votu€ of ihe pipei oontrt,re ie ain. F,nd +he inlqnot wl. v.Atuo x hrrcid

rd6io"* +"..*ed V = 7€.e6 ih:

t4l

. t(4)4- 6 _ (er' "r/.d;)

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 -r

v-_rc-

z,+!) Tl€ oreo con.loined tEiween h^jo ocicenldc €€oioil.cte6 of roall t.s;tt q.;n. iG .ofor€d obout clrlo:,s +rn.owou,i\ porallel- lo lhe boee diooele.s oF tte eemio,ote*. Co."putJ lhe surlooe orco 1,)votvhe geoeroled bg o complole re,olul@n

,

A- a h . a y i . f t a 't., A- / '

Iotot Lufh6

.

^eo

A'i +r."

lthk'

'+)f q ' u,!)tl(Q1 r/-/taYfa^.d1 16-6oat ' 1A- a.25 to,6oig - 1s.75

, 1,,

\:

.

t-1ass;n.

V - 2I . (1.+se14). 1o,6e.z

@.lo.e ole 5 volude 96€^cled br rclot;ng Fg. p-7€ th.ough one bolulid. oba/l l6cx.ot;

246) Dolerdn€ lhc €u"lo@ olg B votume qe@Folcd by o cofrpt resul,bn oboul lhe r ori€ ot the €hode, oreo of ptub7is.

,

t-

t'o,n

|'fltf,*l t . "t +tt4?,4,^l+.11,q l

t =!in

21.E6.9 - t32 132

4 ats'n 6 t e . 2 r . 2 ( 21.s6.) .' v . v.

A - 2r. s.a1.(1,* | F;A

th\+ ,t a.[flF t 'rC)(#L,4'

,@ t 2({r;t o"cs..+)

a z . t \ - 1 s de 6 ! - e't'" -

,f. tP.T

i:

z+)

6-p"le

@olullon

?i+) The rim of o pulle/ hos lho cros6 s@lion shdh {.ishi

, ,V;e)

1 6 6 7i . t

6odoar st@t wc;\ehiry aeotbp.. -

df the Flm ,

h Fiq. p-74-l

. 1.61i^! trc).11.. V.2T.(1

V. o,aessll' W . o.ages
t42

A= 2'

fi. i**f--t"e }h.

14,n, (.,;1)7 4, a(a\(.L), (!+2\(+- /a) 11.e 1 . 18.5

lh. €u.jo@ o.e \,.i"ffi ge@rcte<) b/ o @mplete tha x or,c of lhe 6hoded ow of prco. ttt -5.oe ,i. 3 t/z(c)h.d \t .2r. E.os v@4/+l l+.s(dt 779.e2 ;n? v

ob,rl

g. tangth ol c;N,rtvibina

Arca

A- 2v.3.erfa('N t e r. ' 6., ";l A = as2.szi.: r fo" t6elh

:lt " 6.-,.. -t". ",,, J',.,rp.,.r",,5;;,( t+\l yr,.) + tt)4(6

19,Be7 E - 7e,,2s .5 =3'e+ ia.

143

: t : ) a)

F/"@.(n)-t(.ft4-17- \/{.ftdlu*r.o1-[<*tGy-",

7si.) gctenmine tho crntnoid of o hemisplrerc of mdrus n' tching lhe otis of egmmetng os lhe z oxr€'

.

".

tlr':

-rl-I---l

^r.?

$''"1*f 1 '

(e*rrdre)r = r(+)(+)rs(er+@'o) 2..s4t = t4r'elo i -c.5+ in.

!

7!6) Dol..ninc tlE hciqht i of lhc cgtindc. mountcd on lhe h€mi6ph6.icol bo€e s*'6^n in hb.P-7s6.Eo lhol the conDasile Dodgw;lf be h sloblc equilihium on ils bose. flinl: y',e tong os lhe ccnlor of groJlg doos nol lio obovc the I-x plono lh6r€' will ori€f o rcslonhg couptd whon th6 dq ;6 l;ppcd .

r

p-76? zar) A u.ifo"o wirc is bal in'lo lha shope €ho{n in F€ The cleoishl s"4@ols lio in |ho x-z Plo(6' \ thc. e.in l4elh s"grnar.a o" o"qtce of 30' wilh the r orjs. The .enic'"culo' w''c af lhe oool€' of menls is in thc x-Y Pldne Locdte tho sE;'lv

'

1.'2-127 - ++4..2c i. -11 it. frcm opa

;r65€ag " r G\(+) e6,s6cg =32 g ' 1 2 0 +i n ' 26,s662' .(!) + e(aetn3a') 26,66.2 - 3+

z-r2ah. 7e+) tocote the ce.iol g6wiis of o st€ol .ivet hovinq o cgI'hd.icol bodg I in in d;onclo. b 2 in long wilh o hcnispr'e"riol hcod of 1 in,bdiue. Uso lhe.6url of Prob 7s1

r("/h(h/)-\trGfW4a) h' - 2b't h = r.4l+ fl.

?s,.) Fcpaol Ptub-7s6 if lho cyl;d"bol porlion of tho bodq in llq.p-t!6 G raptocadW o r,qhl .t \t:cotpo.l,o. *ilh o 2 ft rodiuG bose q oll'tude h.

A,

\+/

lk efh(v) - 4//0f(//@) h"A=+

h-3+64f!.

7se) sleel ball ;6 dountod o" l,,p ol o Lrnbor c,rtincre. os shovh in rig. p-zso Sleot woighs +eo b po.or n q timtc. *o,qh, 1oolb po. c, ft. D6le..mino lho pos,lion of 'ho ocnlo. ol qovi

w,ra a"rrfv: r (+r",dLJf Gx "yrr"1 wti"bd" - [r (sr^, lyp^)'(ra^" Wr = tog.o9hi

ae) A bodg codsi6+s of o nqht ci.oulo. aonc whoe ba6o i612 h. ;n. de.p s in. in d,bncle/\ who€e ollitudo i6 16 in A hole h a 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

tbhf)

(rc.o2+te.oa)g = rc.oz(zet/1e)t ta.6s(p x /z) 1a5.1g = 2a6.$ = 3 r.es fi frum boso

tusuli of P.ob. ,{€.

t45 144

*\(60

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 porollel

to the bose. Uce the lrsneG. lcrmulo \ P(& soz. l"- bh'/$ t = 7r ' Ad'

th€, rBarll€ of ilto€ .

' bh/r6 | bh/, (zbh)a

' bv?/& t 2brP/s 1 br?/4 60!) Def6.d,he the norcol of inerlio of lhe guoder onljte in FIg.P.8d9r,lh r€.p€., to th€ g,sn orc6. tt J- lp.d^

Choptor a

r- f,-r(4/.di DY*']P1 . L+/'4p \, l/r . r.

+/.)" +".

j

' i' ri, ' r'76 r, . t.V6 1r - n../.a

Momon{sof lnoilio

' 1, +1,

8od Dete.n;B lhe dorenl of in€rtio of the €ed€Fcte ,h Fig p-ooq with rB6pc.lio thd q;6n ot€c.

1. --! red{

.gfy'^"vyaoay

=f, l' /o2^"+ae

= 1" ./a C a.'ede

[

P/* k-,ed.)];

. r./a C y. r.coe,6)do , t%re - s^,e/a: . r'/. f(l-o) - k'"ry - qho],7 I'

" ar/6

I' 'I"aa .f ry.J;l:p'.nbldeal t: p'dp.e\-de. ( *+(cs.+aelJi . li ,./, (^,.*ae) - fl+ !: h,e.d de - "/o lc _aAe]l . e1e frt-ot - (qstr

I/

t46

. trTo

r47

- ao\1

I

r €o7) Sho"v the momenl of ine'tia ofo s€nicircb of rodi'Js the dbd'etgn is orira with respecl to o ceo{roidol o)'i6 pomllel lo

sla) D6{em,ne the morunt ol ine.lio \ the redius ofg7.otioa,V respe.ctto 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

nr'-/rr-\' rc' . I' +--u-'\3{ r-. i, rAd? - --z ' o.921ra ' ir I o 26Lg4(+ i, ' o.\og76ra* ot1ra qr'roclercircle €oa) Detcdnir€ tho momenl of rnerl'b fo" lhe sho{n in Fb p-8os wilh respecl to o cenlrorldal X-oxts

r-/"Cfd^ t d .rd,

t

= -(oa) . a

rf6r"-,.4)d"

\'La'(A- f/A: \

+(4t'\e-of- (,-o)'/4

- ("/^)'h

^'frd, .tr'(..")di

t-

32/s -t2//e

- 16o-

= S*-'+

A 4+t - t'h l-

rr'IJ

^ -iy<*a:t -ttl

#=t"*(*f

' 8 ' s / - - -2 + ' 6 ' L A i n r

+ 0 . 1 1 1 4r71 01 3t-7r = oo549r+ = oo55 14 It tfc mo6€nl of iner{ro with 'especl s€e) Dele.-irE *hoee e4"olioi foc lhe o,.e.a e.eb.€d b,/ the s{iPse

,l,lecdeler-i"e the@iis ca gyrclio"

"4 , + , ,

:.,t.1W4,V6.h)=f,6 o11.)Dele.mine

ihe mmenl of nealo w/ r€sp€ol lo the x ax,s PoroLlrlo q8o shadn in Fi9.P'€11.

4.*'' - "'-l'"&7d

,

, - "toV1;

,'i,-Jy,d^ =J./.ardy

i,. +f,f (otow ) at

b= b6'r'e Y _bene e'e4 - a-'7/2 dY'b.ae€de . a b co'€- dd b".ie @/b) (b'- b'"."4) \-+f = +fh o'o " a"+<'x"ede

- is (''r"a ,*n)ca\(, , cx*"")lae

. ab. (t, ex.,e)da l/ - lr(-. ' .66,t de ob"Le ek - 4^'a/s1: (t ob, l"' = ob'5B./+o)-6n'?!-5nolol - "6ii-p - ""*761!"

?,.p-

.. t,.t*rd, -f t'"X"*) a"

>

" =Y1t14"aiy.r atf t,,'(bZ)'

- b/L

148

I, -{faa d^- (a-t\ar ; t -x1" *=x1r" 't/'G-"/sr')d' t -o/b'r' .a/b' . ('6v'- &'(t') ) at

i,'[;;1 - "/t('%t .[2,<"-r"[+utfiuoll 1r. oF/" - ob% - "b%"(s-e) . 2ob/as . e.2) De+smt^e the I/ O. the €hadeJ pa@Wrttcotta of fig.p-o11. rf'l,.dA Ll-\t'bl4odt

'f, ott cu o,

.fo/.art,y'n! - (26\o/1") (o_ o),h . z/, (b/.td)G,e)

'r./ - (E.Ydb) - 2osbl

149

8'lo) A rEologle 'e 3in. h5in. Do€nnina *tr poLcnrtrnanl of irF,r.tio\ firc mdiue of gTroiion *,lh r*gccl lo o poldr Q(i' throvgh ona dner

l-f/,///) 'V,/) P

1

6i9) DaLrrnine the monE 'l of ir€plio cf lhe T- 6eolion i^ Fb.p'8@ d/ (f,,rc'i +o'lc cenlddol oxi.

n

r,=!, rAdr t. - Iv+Ad' +.('xe)t ' ar6n1 ,|'*l

rr

. L(6X2r1) t .
s7

I ---f I

shdM

i' - 4Ol | ,(6X..'r'4&f ,z
2

I/ - qFf + 6(!)( 5F ' sa inl

1, - 2so,6, in!

li.r@Ya).3an'.

82o) Oelcmine the rrc nenl 6,f irrorlio of thc oreo etrorn in

- 216+9+-270in1

^ . F 6 . - , @ f f i - 3 . 6 ai n

Ar = 6(l)r{2(r)t€(r) = !oin?

srz) 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. ,.,,::;f"it* A'v+Q.'-df) .t/+(eo-+;)i

J - r/2(ta-aa)

*'6

-@Fn

\ '!4t

- 1o2i 'n.a

= z s s ' ^'

1" =i r,^d'

I c61.s),

= 13es.a3 r\34s,93. 2730.66 ir.1 I .Ix. llr, 272.33i^+ I.^. 4G)' + 4(i?rjF

^'w' Jvn

K : 6,73in.

Jz " 7rttlv. = at,g +zttA "ss+,ee'n1 h 'J.-Jz - 2730,6c-5!ta,6c'21'6n1

t !9t +kE 12

l2

- rcain!

e21.)F;M |te dD.nenl af, irerlio oboui lh€ irdica+ed x oric fon the shoaed orEo sho{n in Fig.p-62r. \ Ii.ixr^d?

r" '+9".

' 2er,6 67 i'! 06oX5)"

I'" . o,l (+la r n1+f(o'

1g))2 . oao.sz nl

2666,az- trco.6a . 90c11 in1 e24 F,nd |he
r, - iZq)". e(exat=rsee33in:l

r;, .- 7.-a-f * +G)u+")' = 27733n'

12

_,

6(o)(+t = r?65rthl

150

+i6)(1.o'),

t,, _ ess.e inj

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 lhrpugh one of lho q4e'ile oomers *ilh reEpeol lo o z oi,6 Po*iig

Ii, -gg!*

i, =a{;)' * r2G)t'.z)a+ilgt +jgf

- t/zGa'-t)

A.]E,r1\n

- 4z(i.)(o,e)+ 12(1)(1) | 66Jh3.r)

et

^t

.tut6)(6/z) - 72 na

i' -lgf

, 'rzcaxoxo.Sz +eg3

+ 6&)(a,s)' t" = 19g ;.'

l6l

lil $i.

ii H fii

ilii

8zd thai

- ds6h h.JE-(&Y i,. b(ae6bf - ru+.lo-'ba

i I

I

i

An aquiloh'ol t iongle hos ile bqso b ho''tonlol- srx ltp centcot&l rornenl cf ire"lir x'lh 'espocl tot'o'i-

12.5GP I h(i2,5J&)(6

ofL\Ir.

oea) C.actprtr-lt'e n'a'srl of rls-lb *ilh reepcci roan ox;e tetqrl pascir€ fh'ough i*o opPo€ilc o?crcs cf o .q'W 6 s;de o .o-- aao/6 - G.,. e.ob/o -@cVt b-,y'2
Y.E:6hvh

h - aL/2 t of* (ott/z)7z +

,4p;sqon,tfJ+

t oa!a/*

r- dr'th

42

"'-v"

\-;'f

tu\$r1=ph

":."';,1,,-

= 12.5h. ^'\/smi.fi' . h,/A cos 25.e7' h=c..36-sr(1J't=61n.

, s@i^'

7b.

,z.sG)t r n-t(.)(a)2

l'.-

12sG)a I y. (i2"61(6t(vt.6f - 22!.i,f.

t52

L - e(i. 'aa')

i

- a/+G.f ,l:..o/af F 'G,/+\(a..8)'I2 -"1_T-

7, =z(1' +^d')

'72 - lerfut t t*,!Pt +a/ae.s)(1't$

ir ' rs-+r in_a A'+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. DeLmiftt the rnarEni of inc.lid vrith rospc.l to ihc cenlroidol X orie.

-sj'o+

ruoezd Caipule lhe morrp-nlof ire.t;a of lhcroh.b,.l;n x rl a''.whrbh is lo oboul n FiT.P-Bzs the torqb €t'osr . sn41/sHinl: R66o[,e the ffgur€ ;nctird d 61 @sb-o hlo porl6 A,B.lq C.

t 1b.6)2 - 2a7s in!

- 2ar6 +22s+ g& - 3coo iri: i1 - L^ri,".7'c er25.)lt|c cross seclon strown h. Fig.P-o26 i6 thoi ofo 6t tuEf maobcr Nr'"wn os a z Eeclior,. Dctermine the yaluas

" ryrtwf =+eo+''rieb+

,'449',

ui\y!x \11!\irz

ib-

Ar-f.(r)is(rt2+r2(.r) " 3s in: a$1 - i2ttk) rle6r0t.e)t s(1)(s,5il2 | = I.sf n. +Ad') I!.=(t =-T 1G2\t rr2(1YLsll b.

I f$ax.szl'Jz

,l.r?' | 1GJ@'a1)'-l2

a1€;'c+n.1

U.ins Tobla vllFz Propc.ti6. of St.rralral Seoli.ie o'r."r' : i,- r6.aha' i -i.6E'n.i A.r3'n: i, =l39E I r.
1' . :z.6.s,ml a29.) l*o Qnt. ra7 tb ch.I1(fili arc lallic.-d logdhc. lo forrn llE 6cclt:cr €hom i^ F;q.p-s2a. Del"-r,^ir.€ how for oporl lhc chonrefs shajd & plc,
163

ir ir !

i

Dclo.minc lho voluog of

Flld Tobla vrrl_z Prqc. of slrucluEl A.olys;s GEher S,ze Areo i, L t t e'2on 6ot 12s13,9o:ro iAd' Ix'f

' i, - 19?a+lel;49-"| $A.zs\(e.tsl'f z '

-

leii;I.6Gtd,.*ry,FS8, .(,)(.E)l a

+ILQ]E +rax+.rl+ t, . t$tt1,tz,z-g4atlz t l
L -(12a.tr2

1, "fes t aa@/a +ot)'f z

i"=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€ctongr4 shown n tiqP-s2s should be spaced sol|E/, i,-T,.

I,,-t'.Ad.

r [39! , '@)12.i,

L-Lt^d.

lf63t!

z -i, aG)@/211,s)'f

17- *te.ee th-t U6ihgTobbv r-. P.opc.ia. of sh,,ctu.ol s&tion€ s;{'i" : A'€o . fi ,i1 ii, = 11:6 F tlr. 6s.6inaj r. 3,aEi. \i.. i.os i. | tla1.6 nG.2)Ia +k6?.25)z)lz | .ts(2.26)(s."1e)e72 t"'fit*llJla i, - 7661,ag-n!

t fcect tG'r"'l+ ,E z.reOB)aU|@) i, - f*G>iJy'z

1t ' 3oz1.1in! a3?.)D€lc.miie thc cdnt.oidol homenls of iicFtio of lfre bJrll * up colurnnseclion sho{n in Fig p-6a2.Il ii cd p$d of {wo ro',r'

l

ptotc5 nvcled

l

lo f,o

121^ 2o;1tb clbn]dla. F.DrnTobte vttF? Prcpcrltc.

i, . i, ; [:-
i" ' 5/'6.k3 sf .l s15., e<."t<,t,sfl+ , To.5(!.e)! r 0.6(r.5)cc.Ef la

1'-tur*;T U6hq Toblevnl-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 ei r i, ' [e,: t+,rs(r.oo'.J+ !{'/1GGzs)')/12 i, ' zaa.as tn? €€r,) A plale x\ odglecoluhn \c conpoed ofou.ebr46/l inon9le6 w,lh lhe sho.l l€gs connccled lo o web plof€ 1ain by 1:. plu6 two flongs plo{es coch {g;n W 2r.;n.E

154

6lb*^

in Fia.p,gsi.

d

si.!,cluml eation6 12'-47tb ! ANo - c.o3tr'. )1,.r2s1,

1 r" 3 e i n J ' t . o q t . o T l n $d(6.s)'.f 2 7' -Q.1(2) tW+

-*

'!:'""o

1^. $1o.s,n

,l<{l t, {.e,".ozO,fJz

z

11 ' 9s5's7 in: siri) Fou.Z be.. eoch hovi.q ihe 6i2c \ p.opc.{i€s dclcmined ln prrb.026, o.€ nivot.d bo t2by 1in. plole to Ontr the scolion shown 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,'

I

1

l I z/1(e.sJ(612d'l+ - ir - ss1.6in: 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'crofl hcigh'l of r+i.. onofto ol nqt in?. \1, of 339'2 ini Conpule

x oxrs ' 7 q the nodrenl of rirertio obo.,l lfr ccnlrpidal

Fi@ Ioble vDr-a pEpe.hee ol s1.lEluml &cli l,r wF ro'-re,!lb h- 14rnArco.4.4zt^L ArEo'loino 1,=6c,6n1U-l./'a.1inl i Ar'1or41t - 1147ir'

Far,

' 1o(1) + a +7(13 6)

t'go+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. lhich F.or. ToblcVlll-2 ro'_'i5,3lt) Afto ' a a''.2 )1r ' 2.na t^J, = 66.9i.a t - o.6a;^.\7 " o -zAr - 14r(2)7 - aa7(e)r a a'(e 6) N7

r

7'73\^ 1 r =6 6 . s+ 4 4 ] A . 3 ) ' + 2 3 | a a 7 ( 2 . 1 ) 2 7r ' 116'4ia 2(44a)7 = 4.4"(s) | 4.+1(a.6a) t - 7.82 \^ i, - ea.e+ +.+z(zaaz t 23 1 a +1(2 e2)2 I" = ro9 in1

o6],) gl u6ths lhe +onefer ardulo q the .cEult ol prcb.sqdetcrrnine 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

I = ./z Mr. prob 862' g. &5) By leinq fhe lmnsfitr lormulo ihs ree,rll of dcld.minc the momenl ofincrtio ofo homogenearespherc of mos€ M \ rodius . $lh rcspeo+ lo o lo'rgeol l.firattt'da 7 ' 7/e rkL

e66.)W 'JEinl tlie l.onsfc. forflulo \ the resull ol Prcb s63. dete.diie the rnomenl ofinerlio ofo rod wllh r€specl loonoli€ through lhe cenler of goviiy peependiculor 1o the .od

F---

I=,hML2 t-

i ! t4d2

hML'.--i

4 r,4(Lt.)z

i-r]!t ase) By usinq the tronslb. lormulo h ihe resuli oa prob s6l'dcierhine ihe monenl of inerfio of {fe rectongulor ponallelepiped stlown in Fiq.a-2e wiih @cpccl lo o aedion lme oflhe z facelo.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/avc. = I Uz t^(b. r 4c'z)

{he md"Enl of 'her'iio of the |^%tohgulor po.ellels6e) Dcle;ine o. F,9s_29 w]{h lesp€cl to o^ or,e [email protected] eop€d chodr in Fi9.P_€6s

6e slP r.rolbl lo lhe Yoris | (c/r), r " M6, 1 Mdz = r1, M(o.i.,) t M
r

t57

gr2) DclcFmina lh6 rno.r'cnlol inortio o{'o holbw 6t.ol cyli with rcEpert b ils georneiric orie. Tho 6yl'hde. i6 r{1 long q hoc on wlddo dioaelcr of sfl q on in6ide diomeler ol2fl. 9lccl v/ebh6 ato lb p€r fli v.r(i.!'-i')(r)

- 3.e2t ll!

f-

Ma" =va@zgs)l@fiX

sf ' <,11

'I-gznlltb-scc' s7r) By ugrng +hc melhod d,icuc.cd in pr€b. sTor delc.hii€ lhe nloli€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 radiuc r. Oer.ole lhe n a6s of the rca,l+i.g hollo./ cyliaCc. by M ' \ +he r''as€ porunil volqme by Y. \q mi for th, cvl'ndar M "I V t,r (. \ v,'rRrh - mi -brR'h .n ',.' -, ro. n r'4" Vr -lfrrh - ftr = lrr'h

e7s) O€lc.m;ne

M-dv M-Erh(R'-.i)

'

t - Yrlm,f -mcr'] : r', fErR'h(C)-Irr"h ('.'! . ,t b,rhI Ra_r.] , =Y2 Erh
' \/|M(e'+r',

rcd 6{1 long n lolcs about on o>,rg perpendic 'Ihe rod y.€i9h6!alb. C.oinpul€ z ft . lrwn oneend. rne,.tio obou{ lfrc orie of rololion.

i. y'r, MLt uz(%ez z)(e') +(ao/zzz\(1ll " J +.97 ft -lb-s..' €7s.) For o houo* cost-iron sfifi. ol 2p in oulsdc dio.ncle" in inside diornete.. morr,enl of incdio q lhe 6smpule fhc \16 rodiu€ ol g./.otrbn w,lh rl:6pocl lo o drbrnct€l.. Co€l tron v.ebh6 .€o lb per cu.{l. w - aso b/lla 6iven: tr6.2O'.'. R=1oin. p; .16"... y,. g in d-Ktb.

158

-

162 (111)(22,2 )

.

R?Ztsin.

lhc rronEnl ol inc.lto

of lhc coct -iro.r fty*frect

5t!6^n in Frir.P-o7s wilh rqepocl lo thc oxie of mlolion. The hoe sir elliptr'oal spokc6, 3ra il |n crosg gection .,vhich mo7 be onErd6.ed os €l€Fdo. nodr. O6l

iron v..rghe .tso tb pcrcu.fl.

w.-Er(R!-r.)L j rim wh =Er(R.-r')! r hub Ws . drobL ; ftf, on€ epotes xf Qgla(v.-ze.) tz = tlss.ge tb.

r"'a"o'

\'P-" -e'

K- wfr

I . 6.2 f1-lb-s6c. '

w - 1924.23 lb

elO A 6b.dcr toil ot o@rnt thc mor.'€.{ of F.+'+-! --,1 F

.N . 4e tb/frd(tra1 ,O = rrr2,astb a2.2 | t42) J

w -.9orblfl. (v) -qob4 Gs27X,

r. /z M(R'rrr) . tu\*e)ltt

* .l.,a" n.,

u'%F:9I

r'tb .8gE(s2

-2a)I . .'\-aatb.

w3 . G94f.(r.5X2)(23) = 56..4e lb. 1725

ij

il

II

L = y2 rn(t . tra)

- * (aaze,hz.z)[*' +zd)l*)

1. = 2a6.9 l1-v>-sa.2 Ih -12 M(e.|r.) - Y2(32ah2.z)l(s\ 2'Y 1al lh = a+29e fl-lb-seca Is-n(lrMd') "^(!/,.Mr' + Md.\

" e z(sc,. +s7tz.z)(ttTrrf+@a.+y32.zl @,e1Q' f lt^

I5 = €,n

fl-lb-eeci ' 2O6.e+ o+29e1 a3,11 .I * 230.3+ fl,lb _5€c2

159

I

roor) O'j a ccntoin slrctch of .trsch, tr.ihs cun oi oomoh.Hor foF boch 01-o €toppcd l.on shoutd o qo.ninq taryado ba r,tog,J lo cignol on on coming t.oin ? Assurno thot lho brakes o.o oDpliod ol once \ Etord thc lroih ot tho unilbrm rola ol'efl poreool \I'

W " 2ae , to - @}EBg- eslvsc.

-Ee'. -2(2)s s = 1936fl o. 0.367 mi . lhrewn vorlicoll/ upwo.d q rctums to oo.lh il ils niiiol vobolly q how high dij it qo?

\o. -e.a1(10)- ee,1n/s

Cl''opIar

10

Rcc{ilincor Tron€lolion

-vo - -32.174(1o)= 321.14f1/s s-rrgIa = hb.s1\Qo)'- 4o6.sm. t s - '/egI' " h G2!7a)(1a)2 - $oe:t fl .

rcoa.) A boll i€ d.oppcd lrorn tho top ofo lowor soft high ot somo ihsionl ihot o socond boll i€ lhmwn upwo.d i..om +ho qr€ wilh on inilbl volooltyof .aofl/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 - y2ba,2r{" h = € 0 - { € . 1 ( 2 ) 4 . 1 5 ' 6f r c n l h o b o d o m s'= 60-15.6- 6aa fls ihe top vh = ao - 32-. (2) = - z+.< f\/"oo vf1 - 3a.2Q) - c+.+ (t/.e, Y " d4.4 - 24.+ - 1o fl/soc.

160

l6t

r

I

rl

; l'.r,rp6d do'i| o riol \ 5d: ''Gloio' |lb 6oud A dds rG) r@ eI wt'6..' ' |f $r olottfr d soro of $E splocf ; L.rd ? *|ul j. lho d@lh d lta"/G[

bdlfPod ti = fi.c trtrbdorl3 _ i{'odtd lobo hcotdiE G. ud t^-t -

Crn.=r--

d =!st

Gdtd

a=:F,,o(s-h)-@

a=fg6 d'h(!,''dh'

\- as66& E+ rd' d d= i6r({ €er5)'- as.3l ll. of, |lb +b6h ffrT@l g.&- |6 if ftlosd'rd

ErSd-L

''€

lE'd

dfid'

d'12 dti ' Y,(6L2)\'

6- rro(+-r.) ---@ r lor: a&4trtdt ' l@(+-ln-, - r64t ,rrao - tnzol. _ re-r lt'

-b 1lF E' q.E*44i6 trq ' \= , a

..e

r@

qDl

\b. = zaa|@ "

rd6-h = Jt (")t'

n-l"er.fi

h- $'a-raL'

i- *' n-**t'L. i-z't;rc h. w au"lvp tw

tA. lho 1.1sl@o

-'"-@

z+at aa. $ta raL €6o, = sr21

3*.+.

153,2 t

Ey luodtutic

*.'5s6-

l6s

;h=rd6o

t6(5)a = @

ll.

3 e 6 . 4 . \ a ( s } s + , 4 ) , 1 61 ( e . 4 r 4 - 4 ) 2 'Ja . $e . 6e fl /eac

16,1L2

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 snc slono [@ ]ho lap .f o 6cr, ld*e. ,f ]ho rwo sro^oc orc ro poss ooch olhor 2oo tl fmm tho top of tho io*cr :

too. Y,6a,e) Ot.na - L')" 2
ca

' n21

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 1s3,2 ft 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 lho firEt boll i66.+ ft tlon tho grcund i

h- 8 st|'X- v'(a47(r 42 h= 24'6t4t* -1&r'r6F;t-'+-'-@ *{=

ae.3t-pi/. 12}.dl,!6.da 112.7= 6.'' L L - ra soa. h = +€.i (1,+) - j 6.1 (1 .a) ? h = i6-o6a fl

t - Limo li)r fhc rsl boil t-a = l,mo Ln tho 2.d bolJ

€/''

\-47

= 23r-6. [1d= r."tb$a)2 at on oredftdr of 16r) A slFn o'uppoa Gbn o ood;io bo$dr ic F'dl66tad 'dl;@[Y uP !.r'Xd ofaltla'€16€ ,* il L* ."*"r' g-k lf ez 24€ e' of ft Pr 6@ 116 $o nd *-$i Jc&rdi'IY rod "-*' dto' *i$ ilio6la@6s F* -fcn" \".se"6 fl F €'"

g-zen^!-.'

L. tioo f6. tho ict€tooo t r - !,8 fb. tL 2".t etdt

h- a.3t - 12G2.2)r, h ' 1 s . Bt - { 6 . r t z , - @

dr(s ta) : rGr t t @-flrolr'rjui

i.d

ioo€) A stono is lh.orn vorlicolly upwo.d flh iho qmund wilh o voloc'l) of +s r fl par soc. Ono eo<.nd totd. oortor stmo ie lhro{a v6rt,@lly Dpdond wilh o v6tocit/ of e6.6 fl ponso". How fo. obovo fr6m lho grcund will €tooo bo of thosono l6vot 2

L. 1?.$e 6a. 212.. +7s6.1e s* asr, a %j I, 2 9' . D :4s56"sa sss4st,1161ti" ' 1 6 d d s / q u odmlia t 4+ rN ga\, 1,8,e66...

163

q, quodm{ic fomulo you eo{ vf - ,ao H/. b,, el - 66 4/s rea ar go+ sal1/1 86fl/,$ " ElgsC " -4j19. ' eo -ph

.o11) /, Ehip boj^g louirhcd €lido€ down tho wo96 wtlh o con€ianl occolorclion .51rc lakos e €oo lo clido jho i"sl fooi. How long wi sho tok! to €lido down tho v.o'le rl th;. longth i6 62E fl., Gr-| - '/a(oa\%)(r2) I - 2aasac n 3hi^,2aeaa.

c. I fl whon t. e 6-. s - '/egL< - 12ot2 t. rz a G)2 .t o- o.o.12s fl/sq:

roir.) An ollomob'l sto.t,;g f"om .6i spa.ns up to aoll pcr wnh o conslont o.a.la@lta^ al atl pa. s&,, tuns al ihis €pcod o t;mo, L finol/ cdno. ld rc.si w'ith o docclorotion of sl\ por a:1 E tho latot d;sloocE{raolcd i6 loooft, fhd }hc lolol tima rcqU. oivon: vo=o soth:

'::;"';:.

d-.1V.2

o' Bnl'

\-en/e

ffi*ffiG+

vf-v, - ati

o-.sft/sa

-t4-

40-4\

Rrrid: tolotI;nc ..

1Ds@

q- Y,6)dq.- 26(r. ,t - s./ra _ s. . .aot, v f _ v 6' _ o t 5 --{0- -5te*+e-

s!= a.l!,i

v,6(6y *1eb

6ee = $oft

.

9+S4iS: 2tb I s. t 16o - ter * s2. e44 €+ cao.4ot,z -+,2=16e@. Ti - ij +t"+tr -1tt,16t6=3+se.

ro4)

A t.oin trovot. botwooh lwo €tot,b€ th nite od.r+ i^o mlhihum iimo ofa6cc lf the trcin oc,elo^oloe !.t do&toE+o6or a fl pa. 6@" , slo.l froi rc61 oi ihc rai olalion ,\ ooming to o siop d It 2d elol;oq,wta, ;6 its morihum cpoed ;n mph / How ldng doo6 ri iroyol o1 ihi6 fop 6pc€d ? 6iven: d- ,/z h le a"ofl/.' sathl n-u/'. o1, - v1 - etr tt - al eoc Foqtl

, rcr.

€p6d

in hfh

\ distaooetm€t o.t lhi6 lop apaad ta-i. i

-v{ = -6t, s'=vlta- 12@r,. Sr.S.r9e

- o,5 hiie

26tu- ry', vfL.+,tt\ - t4 164

4646= rl (41-!L) 2cao = avt

vt' a

10rc) nb ou.iotubile mo.ng di o coneionf vclooily of +s fl pon ccc po6€as o go6olrn€ .6lotion . 'lwo ea<.ds tqra, ohotho. oulo_ r l,i{e leavc€ }ho gosoli"" slotrbn ( occolomros ot thc congldnl naio of eft ponsocz. tlow eoon w l iho c.cond ouror,obitc do._ 6i$n I y1. +6fi/s a'6ft/s' R.4A: tina

€oth: \1=d/t

-

4st=d *a d-t/zo(r 2), *@ atL - ,/a(G)(n ,+rr+) tst - ta _A ta 1 9 t . + , 2+ , + L4 1si t+ -o s/ {uoarc},; t - r0,7esoc I, " Biq _z = 16,1s 6ao . 1 o ! e )l h e n o t i o n o { o p o , { , o t e , c g i v o n b / t n c c q u o l ; o ^ s . 2 t + _ 1 ' r 2l' wncr s € r. foci L t [email protected] (,onsaa iha "or,ee of v \Go

C)r6t s-2ta-L%t212 l'ze"o Roqa: vx\o

s . f t 1 ]d L " v = B t r - + oL \t" 0/,6- eg:

a L =o - , + t - + , 4

rat

+ +e) =zon/e

a ' a + G ) " - z J p - + +- s e r + 7 " o

to2o.)-A po.}]eb m6/c6 in o 6troigh+ hno ocoording to ihc tow 6= 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 ath so@ads. (c) wrE , rf,c po.i;ole 6'von: .g-t3-.tot

ogain .._os

to .e6t, wh;t

is

-,te

R.qa: o)vol. b)ovo vot. ,( c) oocorcrctio^

166

solh: !9-v dt

Aa -socad6- + 1'c -t'rfe**r-ol

- I ' | l E , + i= l t"c

-3t'-ao = ts(5),_ao-e5ti

t = t. !{4t9 }qu i_'=-

b) c)

3lt

v = 3 t ' z- , + o o = slz - 40

4!=o'6t ot

r=€"+

--6G65') ' 21s|fl/sc'c2

c" =&'-g)"

c"=l@-r" |=36s1sd) nrc $22) Chc.A tho ore{oFG to lll!6 Prob io18 b/ the followrng bv ouccoesi'c thod rr';,le on clprccsion rclol;nq ' b-'J'$

-ao^/Jfle + aifforcntiotion"n". ,n"v '1u' x|tfiFiV v- oa h.'t^7,!1,57r3 conpu+evBe- oa frth rhosor€lohonc lon Fr-- -'t6/./^ .ginc. vs ts doMwond Vs = -v^{on+ xo+ho=zo ; | ={'z;f + h_Y @ .=v"("a+h"\

$

1 z ,4 t \, - 4 t dI

-dr =vB

d:,=v^

=v" ip1e.-o"

r"

.tl

* ##"& ri$ .iffi'/{(Hh{rtxd^

t

h"Va,?

'.F1iz .{G1na"

'/e-ts 6dYf4*e" = 6t1/. o" = le (iyJ-+,a' ,[ o" (o'\'/('tT,,x)" = 6c7tt/s2

'd?iJ lllo rccllllnoo- ,'t:t'o" ol o pait'c'o F at'aqb/ -''te-e ro, seo\v'3 whd'o s G in Fot *.v in foct P." €c.rhd. V\4pn t

fl por *r

Flnd lho s-t,v-t, 9\ o-t sr9-v-

t=o;s'o ;v'3 FEgrdI s-t, v-[,qo-t

+

!'=.lsre

*

a-k

_n9

$-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'Dtulolirs*s bofrrc..r {\i"s\t,Yr-6 s,= zl3 +_L +3s=atrz+r .9-| V-' t-t RoqA : Y-i, 6 i, v-<

s)tk: 6{/4L - 4 ',t=4:,c''L2ta tL'1

c=oril '!=21-'

=

3

us =c(r9(tf .s=

+'t

r(.v)3 1r

x{-

35$!L+t

}rf

-L-{i}G

(ts-r).{r -s=2f+c

- *e:s,!e

aE - z6,oo'e de

167 166

ella =t

dorota Th6 .,olocilt ofo pd*kJa $odg olo'rq lt|o t 0'66 is -13; v'16 $*Eo p6.6€6dtd r f@l \t( fii*d i"r=tt-+'2+6x x:zfl' $tEd vd,6 ooc'lcralm4 of lho li|o Cs'p,Xo fcol+ 6(.) s.ilir: ,t=ei'-44ff d.a'. f-r"-4'+6r ,t= +Ftlw r=a vdv = adr Fsid: o o =ydt/at dYdr-3"-ar+6

1=z!):+c s==lo.s

-

z d{y'at__ o =+
- y<\./;6.+r,aB6r)

q6=

t v & = d e-aE .te

= v{

1026)-lhaholio. of q po"licle'r. g6vax'ad t't tho oquotic.,o'-s+' {hcro o i6in f@l Ftsa>" ksiEinfcot.Yv}ant=rsco,s-afl t\ t=a11 pa'acc. Dolodninolho rclol;on botwc€nv\t,G\t,v\s. \- 4/- - nt6i"on- o'- e7s"

lo93) rron +hc v't cu.v6 in f ig- p-1.E3. dctarninc lhe d\€lotyo l.olalad in a 6ock, olso la66cc. Aleo skolch ihe o-l &, 6-i curvo6 opproximolely lo .scalo. Vr' _14+60 S,- ,et72 | at &, s . - & . 4 a t , .+ 40=-5G)'t6o(+)+c2 cr - -12O s. . -5Lz,6o1,-1?b

L! 1.C.4,v-4

Rcid : ! r, s-1,,Y-., !,olh,, ods =,tdv \dv - - s/szds 'r4l - ::As\ +c

rc +t - 29Y "'/' (*)'/" 'c +=

y . - 1 5 s - .+ c 1l s-.+ kv.2 .: c =o

at = 2h s'e t(-1h) 12t-2c!4-+ Qt' = 2 (t%)e/'1 -a P T = Q A - +

s _ ta/].

s.hG)(.o),4oll

s. Y'<.)(.o). ,a{1.

1o27.)Iho ^al;o^ ofo porltolo'Eljtaa bya=avvz,*no
dtia . eL2e-9l'+c

RqA. I I,s-L r-s s o t n t d % L= 6 ' t ' / " du/clv - dt

air,y,. " aat

' a ' , t v- z6 t t o if t.o\v-o-'. c.o zvrt - al

, f c ' 6 r < t - -o . ' . c . 6 =:t3re 5=+|:+a

n -.'(rl')"

,e

s={ya"c E@ gs = vea +s+

v.5t g.st% tct q 'sL'/t

p3a,) Thonolion of o po.liato elortine fron rr^sl ic Aovornod bf lha o-L cu.1o ehownin Ftb.p-1.Ba.5r{o16hlho v-t. &,s+ c1.tvcd. Dalc,nni^o lhc dEploccmonl

6l L.g6cc.

c.'-e \4. -tlbl2 | 2ot - 6a

t, . '1!/a 1o2b) tha rnaliatl al o porlplo i6 qoranad b7 lho "clolia", a.+1". '16 in 6€0. Whon I\.zcro,\"211./s whor\o a r,€in fl/e, i( t !^s=afccf. ftho lhc "ot"cc of v q\q whon I ?ecc

2-48:&-a-e:.v=t\lt2 3 v= ah(e)1'2 = p.zt fL/s .'.s=4t+Zetzt14 R e q i r : vk s w h o nt . ? dshL=+tZ+2 s-+rhz+2Itc S o t aI d u / d L .+ t 2 e-ae)%eree)++ \/= +t7. rc if L.o\E.4; c=4

168

tl t..O t\l.o ,.. Ct-ta Y1'L' =62'36fl/s Y.'+/6t'raoLrc.

9. b./3tq;\| s1.o t\ 1.o...a.o s1 - L'A =@f/s- 72 fl .

B6 - -+/. (.)'r ea(6 t c4

169

\h - 2/314 | 2oL- 60

s.= -z/st + 242i. ,@a t C. gr-q- 72 rt, l=6 72 = - ./s (.)' | 10<6)' - 60(6> t c2 eL "-t/oL, | 1oL'- col | 12o e.= -t/s(qt'| 1oA)'1-@(e) tr2o

9' 22o n luo) An obja:l ofloins o valocit of r6fl Ft's
st&

AE = Y(L i,) + Ln@" \ -T" = -6 (c-o) +fJ,.,)/'7('a-.)

ro.a) nn oblolo. woighinq s22olb 6ia-ls G6m.?sl \ ocouirDs on Lrpword\cloc,t of 6oofl por min in o d,slonco of zon. if tho occcloroiron i€ oonslonl.Whoii. lho lonsron in tho ololofc. aoble? Eolh: lr (,n/6o), = poAo) f\,

a'2..fi/e' | , llr w7e(o) | | ll r uv

s.2o(l

1 ' i+1o h @4€.) n mon waithing 161lb is in on otdolo. moving upword V 6r occolorolion of 8ft pcr d.'. (o) Whol prossum doos ro oxcri on ll., floo. of lho olovoloc ?(b) Wul wilt lho prc.ecuro bo 'rl' lho olovoto. i6 dc,scondinq with {ho cono o.
a) Tr w - V/9 (d) I - 161 = 1a/s.4 (B) T=401h. b) |-* - -Yq@) I -161=-(1'/a2.i)(4) 1 = 1 2 1l b

1ot) Thoblock in Flg pr1oa3rooohoeo vooolv of go fl po- eca in €o{1,slor'ling l?omrtsl. Conp,,lol1-ooofitijoni ol Kholio f^io{on botweon lh6 blooK h lhe ground.

C =- 6

\o. - snlE \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' initiol 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'tol-11 if 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

Boq'd' cocfl,dBntof hie1,; fr,;1,;n

' ' t 2- L o s - a a ' . -

2o&,a) o- 6 tl/e'

P-r =no * 60- 164(lL) .1.14e" 6) y'L =012422 1o47)Dolomirno tho forco p thal will g;vo tho bc,Jt io Fig_p,.to+t on oc.olctul,br of 6fi porecc. Ihc oolloionl of h,nol,'o l-.icllrl ,so? 6i!a^ | o=Gfr/szli.-de @)h, r-(222-P./)a,2 = (322 - 3/!p) cz

p/ r--

--

2"

t'*!r.

4/sp -(ve 1kp)o.L -re4y'e22 (6' 4/sP -G4.4+o4/eP -ho

" = " :"". .^

.2>v,,7|'7+2-

l?o

t7l

a rc.r€) A tugnolio Po.liclc vdqhinq 3'G gmm€ i€ p'rllod lhough ooloroid wilh on occolom{ron ol o nrolo.ePonsco' Compu'lolho 6rco '4s496m6 \1h '2'atcii in pdlrdc dolinq on tho porliclo llo{e: l b

1 z A O - 1 . 3 7 1 Q- 2 d y 3 2 . 2 O ' . pa1e2 2 tA rco I a lrcd @b6|tulo.

6io^l \l- 3'6g - 7s2s3rtri3lb

- 7.*z95r1o''- 6s.flt) --Ezn

2 tD,i

t,u(rcarstto\-otto 2AO 117 - 4,261a - C.21A

no

- 19,c9flk' d- 6 nlsa - 236.22in/s2 F ' o'o0443tb Fea: Fd
timc unlil lho block louoh. ,

|a5+)

O' 6.4, 11/6..' $-B in f6. P ros4 o,o

lwo bod'es

'Ihoi..olion

ecpoelod

b./o

(;pri.g.

down tholnolino iE ros'6lod b"/ a lorca P = "a)lb lf'a @om;,cnt of Kjnolicf.rollon is o30 undo. A !.. o,1oundo. 8. Do lcmlno thc lorco in tho firng.

A^'a z t\fz'a7 R.qZ : I'lho lo clapcod unlil golulion I B6ine' - o,+8ut4' *'o bLrks talch

- e22.4 at

qB - a.% f)/s' a,2 A ctbts - if..2 A6i.e'


a^ , @,n fr/ee

3-'/aaat2',Y2(1 ss)I" 5or9 -'/ea^L"' k (Io$ta) sa! 217512-5.2asL2 1 4 23 s''' of lho bodic.e in rig.P1os2 il ltho occobroibn @e2.) Doio.mlno grnoolh \ n is hoovior thon F' tho fi'xcd dtum is .'

su64. 2 to1

w^-r =w^(o/e)--A^ -<) 1-\\b -N6(4/s\ T.w€ tws(4/9)

w^-r't6-vae/d '\'/^(qs) awA-w6)q - o \t^rw6

ro.e) Rofiedng lo Fig P- 1oea,ossu'nc A woighs aoorbd B woighs 1oolb pol. lhooo.rlomiionof lho bodicsrf lho @fnbio"+ of tu.otic fnotion ie o,to bol. th,coablos- thaniod drum W^- 4oolb J.o10

r^Aa" "fr .,(.r) rt/ta . e 1 t . 1 , a 1 1 g-

2oo- f^ - 2.144.. (o) - O Is - 1oo- tooAa,2G) - @

O

l

J^'o,so 5a'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 a zte -s - B.ezq --.9

a. e.e4l7/s. s - 1e"42(6,24) |g = 1se.4 tb. cAofli.ianl &8.) lta of Fnolb f.iolion Dfttar bto.k^ in Fig.P-tost i6 o,3ol\ undor blo'k I ie o,2a. Ftadlho ocolorolion oftha eyslon t( {lr lonsronn c<[i ctard,. al ct at, -12 = at/82e ot --O (o.2) ^l O, 1^-11-2e 6tn3o'-2e @6@"

c

' a'gtze a 1n-tn-ta1.c+-c,zto -- @ at A. 1i - 14 c'.e' 1e.zt4. (oe). pfu _tl _7s 90 = 3,110 -\ 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

t72

i1

12+2o146 f r c t r ,1 . € 312- 12,42o -86 =1s,63.a sub6Liulo 16 2, 296 - il O9A

t73

-o

ea

I l

le- 2tdc2l9,a2a gubet,luio lo 1 z& - 410,621 I,aza = 3oa/4iea 99.39 " 146+a a. +,e tt/sa : 11. 1s.sbr 3'11(1'c) - 9o.s1lb 12 - 210.62I 9,t2 (4'b) ' zas 3c b.

I]

,

il1l

I

Choplc'^ Crrwilinoor

il

11

Iil

Trd'glolbn

ll

il

j

u

i

li

ii

ii

iii

l

174

,75

ii{i

ti

d

60 to tho slono is thrown froa o hill ol on onglc of {o2.) 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 uoofl. Ho* hiqh ie +hohilli

--98".

-I- , '.'l

r =v6c.eet

'I

y -,!o 6,^et - y2gl2 - "@ s'"6c;60) - Y262 2)(1o)? / - za3,s7 f7 - o. 2a3,97{1. sholl tcafts o 6a.lar */ a nruzzlc vctoo'lv ol sooll/x': n@.) upwo.d dl 6o'wilh lho ho.izo4tol Dotornih6 tho Pos;lton dirEotcd How high of lf|] sholl \ it€ r€sulloftl volocily 2o€oc oflo. fi.ing

il

rj

4

t - sa ,xa'G")

| _ 422o,2st1. . -soocasrn" -9f * =o -v" zsol|/. vr v-vo '1/ - sdst

e'

= -3..(.a)

9 " 21o,esfi/s [;qQo.rr.

b - v,is,"ls -

1=na3.9Ata4791a.sh2 \100a.9x- 447914,
-I

\h91'z .t =\a6tral =s'ast u; &o) -Y, Gr'L)(,a)z |

v =J*';f

*.(&*.".)

= 2(1sa.2)'?c6623a'

soo'sda6o'

- 2911,5 ll

R-ffie(^F,t""e) Io.P-s1,

y2gIt o-voEt^et 'to6t4 = hgt * \. =Yo(ce(.'tostne\ | = Yoastr'zo --T ' ' s ol('/e,h);t 't,/2 J

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€mo po;r} 257-6fl abovoo tovcl ploio Whol honzonlol di6lonco will 1l coron boforo

co6(=t/(

R=.lE-;t-

176

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 }ho honzonlol dislonoo corcrtd bafdt lhe projcclilo rotr:rrr to lis origlnol lovol. n lso doio.minc lho lr|]^rmurm hoighl o oit)@ b/ lf'o prejociilo &s,d)

- 3,.1e i/s.

29

it cl.ltos Jho lo\&l ploia ?

Fo"murd

rr=v"."e _,hr(ya;41 fav"ere s,nzg _ vo,s,n16 h - v'o-z T --{

h =-voi-erq:q ta

177

2,to 6ihe I

.roz) Tho oo. shorn ln f!g.p-11o1 is lrrl to cloon tho wqtoi-o{T volocitv v" fillod gop. Find tho lok6

-f .\to etno-l -t/.g|.

€blht

h -r/a 3/ - r -..O

h=Vo€'not- l/.91r ' O at 2 -',tost^tdt ' Y.(tt'2)It &za =vo.t"to'l I - za/to subcl;lulo ctol.

-zz.a - $snto (n7g

,( = Vo cAg Ct -f - 1@ !,intc,b7I - 1a,1f _7=61,zcL-rctle_ @ ^ = 1@@6tO,O7I

-. -@

- 16.1(4ok)e

,t'a\ot '6440 \o " 11,14ll/66 o,* 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 vclocrrtvollho bo f

t=tz6ct-.@

yo - a0,+ll /sac. rlos) oolc.mino lho drsto.co s o{ v.hioh o boll lh'own (o \6loalfyYooC rcofl p6.6a6 ola onqloA-ton-r3la willsl.ikc lho hclino .ehown h F&Z.P'11@.

ailont uo .16flls -e . la^'' 5/1 n ' 3A,A1'

RtqA; distonoos

r?8

s=

t@za6f

{@ 'tl\t, el - 77,66t -2s,991^.@ s, +st.z fl . )'l 11io)In Fig-p-t1og, o ball thnxrn down lho holinoetnk6; .ilal d di€.la^@s- 2s+.5{l- If +hobolt ni€ca lo o .no)(imumhdrghl h-o+afl. obovclhc pci'olof rolcaso,oqnp,rtcils i.iliot voloctly Yd\ anolination +. 6rvcnr h-6+.{fl. ta: sinp -A/s 6.aei.sfl.'/n.rl/qs+,s -{-Ao..efl. 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 L9

5{]b6lilulo €di,

h - vo ,tn€l - t/29I' \o-e - uo Lt^a(l,aho) - 16.1(trg/,r.)' go,g Y.t . zat1Etlo

2\'1, - a6,gsX . 6 ?-14l - r6i ( tr = s'el 6<,0 t - 726. (s,4) = 449.ll. '/ . 48,s6(8,61) i4.,sz 1.

-61.4 @

-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/s fltlJ Rofor lo Fig P ilfr r+. find "( lo ..,-ea lho W.jc<'tio lo polnl 8 ih oretty a soc. \'vtrot is.|ho dielodco^ ? n -u-

I

at - la'q1=-ro -e66hq((4) -x,1 G) {

stA4 - 0,404167 4 : 24.a. x.voco6qt . casaa,z.(a) 6 x 3sot7 fl.

t7s

I

1r1s)n portlclo ho6 suoh o cu.v;linco. molLbn ihot' ils x cco. _ dino+cis dofinod b/ x =st3 iost whcrc x G in inch€Es\ t in,ec coid6- whon | = zeac, Ihc ioloJ occolcl.dirb. ie zs n pcr Eccl lf thc y conponenl ofaccole.ofibn is conslonl t\ lhc po.+i €to.ls f.oo rcsl 01 ihc o.igin \^?hont.o, dclc.m,nc ihc lolol

x= v; co3s,t= a.1 . s66cose(6)

\clod+f |\han | "a6d.. 6ivcn I x..str-ro5t I- 2saa. a'?s ink:

€-'33-08'

r:29!!!g

' h.Vo.snet - '/z(s2'2)t

t-,

'7s' =60'iarz a -J n T i a V ar 4s ia/s,y,.

h " 9 6 , 66 ' i e a s 6 ' ( 5 ) 1 61 ( 5 ) 2 h - -133.25 Fl.

grocn flf.) Ji iE desi€d i6 piioh o golf boll odrDssa 1mp lo o volocrty iniliol rcofl owoy. Whoi is t;o besl olLrbto uso il lha dcod ofbollsloPs lho thol p€rsca: nss'rmc of lho U"U i" 6ofi point tho lobcl os 1,o.st.;hinq iho groon, which ison tho€omo sroPos hovo Iiorn whioh tho boll i6 si.uck nssumo lhc clurJs qroduoloo ol rntccolq ot 6'so thol o no 1 rron hoe o locc In"4-' cl' davn loo cltnci ol f{s' io thc grouno ihc tio 2 iron 01 Ho.s irgn inolincd ol32' X - vo'srnzd I

e'cast^24 E22(@\ 31,72' rl.€c llo.9 rrrr\ F

111a)n €iono hos on iniliol vclocrty of 1oofl Poreoo uP io thc riqhl ai so'wllh lho horizo"tol Tho compononls al oc'a)c-.u+'a (jon' -2a tlPo's'<: o.i cc",stont aI a^- +f1rrr scoa a\og= rEoohos pufo tho hodaonlol disionco covcn'cdunlil tho €iono o poinl 6, f] balow ilc oflginol olovoiron 6i!c^ | va - (n lt /€ r, -roco.eI I Y2al' +-3a', ox. -afi/s'. x. @ocasaa(6)I VzCa)G\2 at=-zot\/s",y-aoll t = +47.62 fr Roqil r ho.izd.lol d€ton c '/2 gth: y = Vostne'l Al' -Eo . rcocF za | - t/a(2o)L2 6/ Quo.ltu1i. )o" gcl tfr Y o t u co f t . 6 € c c .

'tt -- 1s(+)2- ios 13s in/6 Vf - arl - 45(4. fto in/e , , / r 2r Y f 2

,i r.,-.16; n18-) no.rul occaloftI;a^ af o rr,.ticto on tho rim ofo puttcy _Tho @fl in diomcta. ic con6tont ot socofl pc.€co2.0oio.minc thc€_ tE d af lhc pullcy in rpm. 6tvenI d=1o{t

o^ - a'.rt n/€2

Rcoil

spccd ;n .pm

=rd o" =-vl - eooo ,t -2@ fI /s

v - nori 2oo =l Go)n tt = 6,+ rps (60) - 3e2 .pm

nig,) nl lhr boflom ofo loop lhc spcod of e,d'rpnna is ao.tnph Thi€cou
r8l 180

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@ sotht !E. 1zt' - 10 "t 6i"a" . r. zofl at ',t= pG)' - 10 - Ba {1/M, s-4t.-1ol Acjd I o

4= 241-ot 01 or= 2+G).a,fi/e

a, -va/r - @a)'/eo o^ - 72'2 Il/sa aa.6t1. toh' - (46)' i O..2)4 o - a6.7 fl /6ca' 1l?1.) A porliolo i€ trro"/inqolong 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 €Ko1ohhow +ho polh curt69. solir I o. =otcdea - o'6'no 6t:f!^: O,-6t1/6' O^ . 10@sta,67' - 6 stn ac,ez" o7 . ,tofl/s" slopo - o,?5 6" _ a.+ $/ca ' . q =G;167 ' .[d'-1F =ar..2 o- lon'' o.rs sl ez o. - Qta t Qaa RoqA : or qq. . (11,.o2)'. aLa| (+.+)' qt = I 1o'8 fl/s2 lze) 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 posilion. Y9-1oo6n5o'-322<1) Ai\e..lo=1e'f11. \r = s+.a fl/s P.60'. 4'safl " B as fl/s v..l-so-:;46;T Rc
taz

{.r) n slono lrcs on rniliot velocily of 4@llp(,. {i,r'. Lplo. lho right ol o slopo of ,i lo3. Tho conponont€of occclomlion aa. cor,slo l al o'' -r2 flpor€c6'\ 09. -zofl po.soc1 Compulo tho ftdiB of cltnolu.i ot lho stort ta ol thc top of lho

Porn 6t:vct1tVo.aeft/s d, - -lefys", o, - -.o fils' R.qA. rodtu. of auNllv.e soli: tt -vo's'"'/ ---ed;- - k1r\'(a/d' - 6aon. 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
. - zO,6Il po.ticlc novds on o cir€lo in occordonco with tho oql.roli?s) tion s " t.-ab who.o s i€ fh6 di€ptoaamanl in loot mccslr.bd olong lh6 oiroulo. polh B, t i€ in ooconds. Two eocords oflor Elonling froin rdel lho lolot ocaatarclion ol lho ponliob ie 48trT ll por *" Compulo tho mdiue ol lho oirolo . 6Ncnt s- I+- Bt , L.aet.

o '46.1vl+k2

Rqa | rcd;ue of lha OiElo s .t+-8t 6tir

vt..+fl)'-s'

40. = (21)r-1211.

46lys. OL=1e(4)'= o.- AL.rOna

(roJ?)'-&O'ia'" ot'

46ll/e'

l89

t l o ) ' e - 2 . +f 1 / e

'trzz.\ Sot"a lllus Prcb 1146 usrirq lho ff : dolo: W-loolb j V 'r':aB L=tsin. u ' v c n L l e i n" . l l w =loolbr v=8.b3f]/s

solh tone =vu/a.

" -r:9-

-t

@4?er 8 o3act69 -1 =a + B/q{,od.olic at.2L1.5)

\2

t = 2rlr/d-1a.d 1 - 2 t

-o co6F,= as348 ,e, -, s-1,67'

1".s,.< r

'

2/zz.zIoazo'

1€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 rcvolul;o^ int/1Ee. Assunl;d9ld g= 22 fl/6@a, frird thc tonsion in ltx ood q lho fo.co on fhc conicol 6h6ll. Al whal epa€d in no'n will lhc forvo o.r lho 6boll bc.od,o :orv?

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 €ord3ft. long. Eoclr cord suppoele o woighl w. Ccinpulo lho 6lbod of roiotio.r n,ii rP'n lo rnol;ne €ooh cond ol 3o' w'lh lhe

t-n/1sacj 912filsz RcdC I lcn6ion \ Fotuc L-sPocd who. Fs-O

n - sa,2alb r -39t!]99!d

= .t Einso'-2t1 n rtcyrl4 - 4h rps ! =2afn = 2\(2)(4h) v - 16ll/6

far n.0 , da6cl -9.54 - 20 I - A3'1tb. - 2ov',/2G2) a.sl i qt&n = c,6(,31) o.avsYz

fEi^so rn<.6{'- w"7qr .o -@ -o,st|=2o \.1* o GI

o,sr +o.s.€ti- ao66Y3e@) E2fion1, 1 -(zat o.sr,)/o,B6c - g01ko)

n = 22 rPm.

t84

- s7B tb. 2.

Tcae3o'-n6inro'-w= o*@ x =i,5{1. f . t.5r2 -3.511. Io^e = lYgr 'tonzo' ' ,ra/3zzG s) | - 8.a7 n/5 - 27k,5)n V-zlrn

- 8js621

\ = 2.q6rvs . o,so1d/s

r =o.an fl

- rco - Ta.cs1 61' I '187lt) - r261sll f - tst.]e = rs(st sz61)

= etf.t-fi"

Ione ' \2/6r +onad ' 'r/32,2(o)+11)

Solh:

*.Icb6e

t ' zt ['79t""e

tho \€rlicol Aira . l-1sc!:

- u/qY"'"6'

st 29- - va.ite+/gL voasa . o t aca+ 3L c o z o o, t " a e e gL

,2s) A waighl ca.@^ltrtlad at llt a,\d ol o cotd fo..n o.o nrbol Fondulum O. wh1ch tho po.iod i6 1 6c€ tolo.ri,nc iho voloo-,lyY of tho wcght if lhc oord rolotcs rncl,nod ol 3d'V

o , b ( 2 o r o , 6 n ) , d o 6 6 1 1- A O t l , s s + O , 2 g 9 l 1 rO t e 6 6 r-1 g a

r85

,t -6,o7s lI /s \l -4\an

o.ofi "le\k) n7f o n'29r'pm-

l

l il

l

t*g) Whol colrnlorwoighl wwiu moinloin tho Corlics go,cli'o. in lho posilior' .show ;i f'b. P- tt:.5 ol q mfiorrolspaod n-rzo rpm. fr'ch plybollwoighs 16.1lb.NcAlcol'|howoight al tho olhor I'hks.

w r'6616 o.1lho smoolh Inclinod sur's|'"*,' ,11.) 'fJ n';-ilbody of tciqhl

io I is p- 1'a1A ws o\l&heA ta^ f--o \c'tic'r of"'.-" tho bodv fo rofolc V.il oboul lho i'' tho iil-t--" lho spccd in rpm ol whrch lho lcnsion .il i.f."-t." ard

\e qual

to lhc worlhl of lho bcd)

n,wrp^


,1- 8.stz ft/s \=ztfti - 0,912' zr Pca'ao)n/co n - 19.19Om a 20 ryd w^orqhs6a'aD fi32) Tho hamricr 6f on rrnpool ldsling moohlno

i, ot*roa io rhoond of o I'i?hlrod ; i;;;-;i'o"t ;-;; o'ie ot A (alwhol is lhc+n L9 ',v'i"l'le p''aoa bo horizonfol c', lho pi'ol on,^stonl aflor boinq nolcoecdttrn il*.'-".';o. jroocl;on l'd boJo'6i'nil l'rf [u.o"', ot *hol rE lhe b€cnrnq e 9 fl p*t

" if f r,. veboilt of lhc to.nrncr iq thcn

'

Io'6ccr

-w solir: a) Tc6ea

r.4fl.

\ 6eto

' 44"+

T-7+,36ll'*R

bl T- w twv'Zr ' c+ + tlc++(s o)"J,/szz(t) =R' T=81'8lb lha a$cA 4a2o rc5).To aha€k ihc mdius of o 'oilroad. "Fvo' qt'la susts)dd lb wo,bhr is obcarycd laLJn 2a7 6n o sp'iag .frclfl' al aodph of o. e/pcnocnlol @' 'ou'di^g the curyc tro Jf Whol is tho rod,irc of +hc cuwc 7 @s6'' 2o/ao1 Aie.'. v . a. ./lpt,'€,86 n/s ',\N.2alb a" 14 9+a' I . zo,7tb t?r=oi16;^6=*n'7sr'2a:7sn1+'sta' RaaA: rcd;is ' 2o'7s'o t4'Q13' son ' zr1"o lut
i ot'o "t(b)

186

Sol,n: str''D'- d/10 -

6i€n:

d=s"

( . Ett G' v-orn.zr(o,r$N ,- -."o,e'

k

" Y"jIl.'/lD\'' ncqd:wlzn.lhs\\.#-*ffi .;;;il' (6)ABgh76'

l'c'.an/s

- 3€,.r66'n6o'(ro) - r6,r

AB - 45.1 lb. Aa@[email protected] +s.rco€'as'(c)'w w - 63,-rg1lo.

-Tho sico .od ol tha onqirc i^ fis p-11"6 i6 en lonq \$/oighs rcd aro of longh'l ..rsin. \ rolalo ol3oo {olb. Ihc omnKs AD\Bc rprh. 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 ol lho rvd. colh: 6ivco:w'r.?lb

(,"fi--1.71

.--j

"',*.o^

tl.v!-Fa@)'l/o

. , r si r \ L - s l l M. rootb-l{. Rcqa,M rc7) Thc€camonlof rood possrhgo"on thc cr6sl of ohill ;c dofii b/ tLE poEbolic o'r"c y ' 11, # A .o. ntsh;Fg 32e tb l..olds oloiq tho n od ol o con€lonl 6p-d of 3(>fl po" ecc Whol ic iho Frc€suroon lho *hccle of tho cor whc, il i6 o1tho crasl oflho hill whc.o y "afl ? ,t thc whot 6poodwill lhoMd proseurobc zao.2 (d//di'l* fiht: tho .od luEot cuFrol".o br yp "Gt/d"Yh oivcti: f +fi. ; v-3olve Rcqa: prtcauroR \

6pcod {hon

i =# -#

- +7ro-ztza/noo

Food

e"t'", + - g-r1

Yp ' 2/too - /'sotl. 3+ ,a"7s( =w a - zzzo -fazu bo\a)/ez.z(so)

t' - +o, t +oo- o .'. (x- zo)(,- za). o

187

if R.o

tri ur"'4- &

6ivon: Wp- 1sorb

- 32,2(sa) -$16

v - aa,12rl/s

9.

rar.) A loy running d fool mco rounds o fiol cu'w ofsdft r€d './ lhc wniicol wll if ho runs ol tf'o roio of rs mpn, ol whol onqlo ho inoliho his body 3 ("o) tu^e -\/s. "[a tszaoftfi'/zz z eiNcn i n-sofl

l

I ilI .'

i li I l

I

+a.e - 0'3@6 -e =$73'

v-rsmph Rcaar€-

1142\ A dorcdaril drkes o lnolQrorcloon ond o orrculo.Vo'lr_ i€col worl l@ fl in diamaloeIho f uol liroe \wall ls 060 whol ? woll lho mlnimumspccd{}nt will proYoni hl6 elidioo davn +ho Al whol ooglo wlll lho nroloroyclc bo inohirod lo lho ho';zonlol whot ls tho ;lfool of 1ro'cli"q al o groola'epcnd? solhj 6;@-,.. d-@ofl. €* - lon 1o,o * ts1' f - 0.6 'zzzGa) 'oevz to^d'qthz n.ial v.i"t+ ,t,s.b tvs " s1.bf3cao/5zoo-l'ss.a -p6 lrock is thc numbcr ct r1a3.) Tho gupc{.clovolianfogiltea p'evcnl sldo ihrust on il rorlg€d 16 lo inotlo( lhot iho J6rdo roil (ic sPaad- Oalonn,no whcol {longcc ofcors roundinq lho o,.!c oI ol lho euporotvolrtn o ftrolrqok boeng o qouqa of afl8'/2in a@o (1. r',dittsv"o rolo.spcod of 60 mPh. Whol ie tho flongc proesrr6 p on lhc ,l{h€ol6 of o too,ooolb co. +hol rounds lho cu.vc

ol u nph? 6iecn: r=1ottuft

tane =f/qr

+fl 8.5in - 56,9 n Rst6: lho eofr.rdqol'on e for o ltwcK '

'feo'::q'"^: 32 e ( 4oc4)

lo-|e = o 1202 -o- " 6,86

lane = a/t o,1zoz - e/sa.a e 6 tqin 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

Solh:

V' 40O dPh

lohe '2.g2 t. = 71.ol, = n ftso';4t\-

32,2 Cs280) = z,qz('r.o) - +3oA. 3f = 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.o6 whcn lho co. ie lmvolling ol 60 mph. lho cooffioionl ol f.;o|irl bolwcco tho tr-roe\ lhc raad i6 o.so. .golh r 6lvan. W'32eo tb f -"oofl;+.30' - 3872 tb x!1-j3.1gof39]%;t 3' a2.2 (2oo) !"6onph /,-o,go RcqlJi fnirfion Fdrco lo"f -o,9

l-
R -/6dddfi6ei4. sinE = f/k

- scss.so tb.

+s6a2' = f/sors.ss

F - 336a,s7 tb.

ra6) Ftid lha onqlo of bonkng fcr o highwoy cur.vcol ea mdius 66siqn64 lo a.x:a,iodola cors lmvoling ol roo mptr,il iho ooffibr's'+ of liolion bclwcan lho tircs q t. @oa i6 0,6o. Whol 16+l-cmtod epccdof ll,o cu,,a? ONc^ | f =9@fI. A.a,6o

Rqa

robd .wd

solh I IonP - 0.6

q . e.sc"

ton(.EI e) - uU lo (ao.ec+o) .Lto"!239,_"d_ 32,2 Goo) 3.,96 | e - 65-82. + 'e4 66"

16,6 o = u.%. (3@) h^s+,u'- 'r.7ea.2

'tr4 " s2,t (r@)+o^ 3+.A6' \t - 82,02+11/6 \f " 82,024\@/96 = s€nph.

188 189

,l

'1112)Iha rclca spocd of o hiqhwaY curyo of 2en rcdiag ts iomph. lf lhc coofliciont o[ fric{ion bolwoon tho lirDs \ tho ie lho dorimum Epocd al whrch o concon f t o d ' , 6 a . 6 o .* t o l wilhout eK'bding ? comd lho oonvo 6oli1l 6Na^:

t,2@fl a-o.6 ,t.- eanpr' Rcqii: moximumspcod

roa1- YTqr tone -lso t saw,/aecQ/zz,z (zoal lono ' o'3o1 'O ' 1673'

t o a ! ' oe Q' "a'se' loa(Qte)'uYgc ' ia" (.o oa'lrc,,e) v/ea z (coo) y . e+11l1/3

't - 04i1 (6o/06) = ,ez3s ftph . of firolia b€l tho rood \ lho lircs of lhc 1144)lha ./,affbianl in P-1111i. Fig [email protected] cd. woi*'s 32?olb ll G '?,Jco. €hown rodi,rs ol irurihum srcod Whot is lho rdidg lho ardo of .5q $ votucof lho fnct,Jr"i fo.co ooling undcncoch whcol i how high otrluo lta rood m,,'sl tho conlon of 4-ovily bc fo limil {hie noi';um .epe€d t'/ t|,A +.,.ncncr to o,onlu.n,' ' ,

+6749,44 an 3d(2 411)r i1sg,ab ctae(3) - r2ao €t s2'(3)

11,- 4963.|b n ./^rl - 0,6(4963)= 2S7z8lb at thoouioF*itc€lc fow high - 322)oxa?atl : o/ 11.(+.643) AAa SolA (2'a1) +sezostaao'G) | s1sg.166n34 +onl 0.6 E7sg,+6 cogeo'(3) $. ao.oe' lle'726.46 tb hn(l|o\-'t'b 'vlez.e (soo) f. "/afi"' ae (126 a4 -a's.satb toa(ao,os'+zo') 'r-ito,2g fl/6 | lhc dirlo. '!hool6 322a(io 2sY . stgq. +8tb la eo96' 241.667/h nr' . -idz7i{

4-

fl.rs.)RopoqlW.i1tu'[ 06 eho{n n Fr'g-P-lr4r.

lho nrod ie bonliod af

r =.9oofl w - 3220 RcqA: Ff".6i \h blhl

b^q'0'6 O- 3o,a6. lon($to) " 't"/gr | ), v/aoz(ao) lol (3o,e6 \ta- 19a$,aefl7c, w'7gr - zzu (teass.+q) 3e'2 (66a )

- tsgfo.1 tb 1M^-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 dl oiar fhcals


h ' 4 0 2 1 8{ l '

h.<.ozr6si

lJAa.o dlQ,6333)- Bazocosad@,+t1)

190

t9r

6va^: d.61.1. .1- 4 .p^/scc.

o - , r"/rid*,,

2rr"9 Pl

<.

o,+Zmd,/s(f,

< - or/r

aaz(1o\. ur

Choploi rz Rotolion

= t(+ z)2 - 62,e2glrt at "F< = E(aaz) Or = 1.26fl/s2

6=6@fl.

solh: c. 26/12 s-f9

yn =rtrJ, ,"u 1a2.2a)'. .za (zto) 4-

600 - (2,aa3)e O - 26b.od e. zOAtEd| 1rcy'anind O. +5.aa ray. (qo\ha/6a).2.a6bv: { - 4e.2+tod/s

tn

193

-3jo

md/saca

r src'd/s ra6.) Whon l-lc o.}Llo^ dac"tl ofo rfi o'omolo' pullu 'a'' Dcla^mF lha lalol Br-Dptoltan .Jta po'l on rle .im is 3o 0 Pc' no lho onryla. ac'ela.<^Itb^oflhc pulleyol lhi6 inelont: Rcqa' < 6i'Ent d-.+t1. I " t8o I]. ?cq'atL^- ? S.'? whons^..a. fl .

a.30f1/s2 a^-r6" - 2Gf aa.18f1/sz

b)+^- z-f,.1zoMa

at = 24 fI /62 Ol - r"( 2a'z< * q=12ft,a/€z 1206)Oolorff'ic tho honbnlal ! r'c'"fioal oompoic'rls of Ile oq'ela'6 loroiion of poinl 8 on tho rim oflho flYwhool shr"Nr ln Fb At tho qworLposrlion,ur'+ 'ud Por€€o\o(=rz 'aC pr ecc'' bolh

.-3fl

P.,tA' nofiao+ol Y of

aL-r,^ - 3 (12)' 3,s F!/s2 an. ",r.a - 3(a)a . ab l\/a.a

+ibb - 20^ 1j^ = qoftd

9^'rO^

so " /z (t)t^.

\ 19 in.

Roqd, dtonale,.

rc" 'ed' \ 6a"

too - gt2 t w"

"o-"r7,. - zll d-1lI

194

-eo - tzx"r"

- /z () (zzs),

- .3 (.o) - 16o fi.

vas,1 r., rco; ol pJ|.t B (,d:(rr,ngcd ta3.n.

b) +)^" s^/. - ,L/Gah.)

a) u-,a" - 2<.. <^.

2.67 Ma/sa

s^ - | s^ "t 1oO= zylrt^

a- 1afr/c'

+ pa = y!(a)t

L' 7.76€d.. -&o'@Md

S^=18ofl ta \so whon&-zro'

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 lolaloatda'd'an ofo point o. lhe rrir of tho Pullov i' ro{ porea>' c;onPla lho dtonat.' al tr pull., - r(a)'. =ar s.olh a.'rda Ot'r"("r(3) =3r 6Na^: .<=itoc,/c" af -erca/s ol - af ! aaz

o"/2.
G=nOD

t"r)-Orr*'Proa

( "4, \:r'

c<- 12 rd)/€,

vo.t'ita I c@pdionld

6<^.2(2).+tud/s'

tla - Yr"\ctz ' 12k)k.4e), so = r€o sD. 3(71,91)

g^"'/z
'::,.)

e^"'/2"<^1. si = t/2(2,6alz

rala:. t o: M 4 t a f o ,

at a auic, .. dct,n"6 6, ,L , .a, an s.zt,. mc.,.ur.o n.oa,r.sj t n,eaLo.de Gnp-lc a' qr'o' /'o ,l s orct-to- occc e"ol o, or ,he .ng

,: l::,.fu-"

:

t:* 4 , . . f, "

7o).t.

p@a

onqu,o- ,cto
195

sotht de/dL' ur' sLa'6aI [_ be)a-6oLa) =2i2t d/s ,)d/dL'a'2at"'60 a<- 2a(a)2 -60 = 321tod/s ts gota'ncn 6/ tho cquol;on ur121a.)Tho reloiron ofo flYwhocl 'n ccconds e' ?od wk ".,f ," "h rod'onE pc'gocond \ I le '1qon{ wh'n t 3€c( lhe volucao[€ co. ol I'e ,i' r*. *"*o €blhI rr.4Jt t 6r\€n

ur=.+Jl

de/d'lr'4{, de ' 4L't' dl

o ' 4 Lahe/r)lc if t'u rod Dhc. t'l€co' 2 . a G \ ' . ( 2 l e i)c

Rc4a1€\c{

e.

c=-0647 = ah!* -0667 8/a@)''out e "F.2rcd

t' - -'/: ^'rt/)dl ' 4 ?),:

,' n. nr"t''''

< - 1 , 1 s 4 7r c a / e a

o( - 2t ' whc{'€ c( rzt) A body alqilos o.cad'og lo lho nolouan = por sc.ond \ i l" i'" 6oc.Mc d + ;d po' scc \ ; ; ;# 'ts ins a ztttu *ha. l6 2c.o ADputo lhovoluss of ur \O ot iht oni ohon t -26od' SolhI o('?t 6kcn. o.'2t

e16.))elcrnino tho number of.ovotuirb,6 th.oagh qca putloy will rolalo licrn rcsl if i1s ongDta. ad:.cltaraltonie incnaeod unilormly fam zcft lo 1e nd por scc'du" n .qa.s€c \ lhcn uni6rmly decftosed lo + rod pt ea! during lhc rtrl :s Eec r t.* -,r,-=

'.,r\^'

swc ' !.!' 6/" tz ' als l. 1 34,t.-Ar1^e r q - 0 I+ 6 s < ' : 9 !)1t r6- c! c 3

L l "[ a I

"5," if rdo\t'o.'c'o ut;' 3/4tM= le9b 4-sht

trt.aL"krc 'than +,od/s il lr +=(oztc

o-+ 'f l '28c.. u:,I't1 ur ' 2t 1+ - arod/6at I - L3/et 4L \f Jt" 2eca d a / d t- D r . l " t 4

g - r'/z ++(a)

;f ej -e4 \r.4 3 k @ 3 . 6 s h @e. f u 6 ) ' *, . ' t l o t + c ft,.e/6

. Gtopc E+--1

dtf/dl - a-I f-bL-L"hrc f-aa t a.6 a2 - B(d- 67a ra c'12 tt.oti t.o tt - 6I -l'/, r 12

de/& - 6t -1'z/2+12 A.4'-t"/e +eL tc if o=o 1,\t.o .'. c "o o.7 il.6 4 - +(e')- 161"/e +pQ\ &'194rcd

+.1bot )4i

+ : I1h+at tc t l t . a 9 < t = a. . o = a

196

c:6o'++z rz e/.a13-16,33t | 6a.4
" 5 e / 3-t \ l a l "t c &=:\t-l 11,.t[j t\1"4 O,.6ek(7),-Blb(1f a9sG) t 6a4n3 l?t . eeTst+t- e1c4+1' &. - 146.a2rctd -a5,33 -O.144,a2.tdr:lL c" - 23,2rir _ zf rdd\ tli ' 6Bht - ek( - $,33 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. va le.ily ib a2 tud Fs sc:. Coopvle lhc ntliat or oogulor ,lelo.ily \ lhc numbo.of rEyoiuiions modo duflrig the 6scc in{ee"ot.

dtn/dr- n' 2t

RcqA: u/( F

"a. ot ' 3!' o. -t,c C ^ r rl o q r' 0 ' ! \ rt ' oo c ''do e dt/dt , 6aht, a/61, 4s.33 o a - 6 e / . 1 ! - e / B f - a & . 3 3 tl c

t97

- za,6s(.v.

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' i

p,3e9,ea - so(o,2). so(rz.s)

goa)-[a(az.zl/ez,z 27,, 1,- rp6

P - 4.'4,2o tb

Choplor Worh

\

{4 Enorgy

,a- 6s,o6r [email protected]&'(ae) r aoosiag -[uo Qz,afl/alz It- t99,2+ lbt
, (td - 12.42a\\). e@t sae a^ a@- 24.940,\ - 3e +g,32o^

^trt l'@

[email protected],ft5a^ O^ - 2.a3 fl/c?

\- a'3aar/az.z

A +-:ry+3'o^

- It

v|'$!ae)@\ v^. 7,csfl/s

I r/ I to.,24^ I

i N-1,\*r;= o

sr,1

-l! t29t m-1, {?n/3e,4h.)

It - 20b - 6,2106 '14. zd -6,.1(2a^) l.- t@ -1L4zO^ - .-@

198

\rF lb= ze/+ 199

Irl

I il ir

in laoa) Th.ouqhwhal dislanco wlll bod/ A in Fril P- 1ao0 ma/o 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- 12t+2o^.3oot4,cGA^ .L J

I

J l@

160'17,OOA^

S -l e-@ l

, zn -t, -(a/to zt o^

\-

o^;sa6fl/s" v|" -u^i - zas^

2 o o ' 6 . 2 1 a ^- - @

4 |

ll\4 \{.

s^ - 9.8 [1

21\-1,

l1e b_aaa.&%,.,)o6 @ h-.Lnral'a6. k- 3oar e,32(o^/t)

2I..e4rf,44a^

.

{-Qq

',i Afru

l,.zr, - -6

tl . ro,,

') 12'Ma. 24o1oo(o

p" .2(^aa)€^ S^ = 3a,a1{1.

j Xla\ttE(td) L- 24 - I,a2Aa +(tPt,/ f4.2.4 - oB2 (rd\)

-.-
tm,n rc€l ;n lhc pasilrbn shon in fb p rarl

0ot.''ts "atoo'|t offar il hoe ^awa $fl oto q i.c {n.r,o.,6aa un foca

'| \2

Subslilule Y6 lo \t laoa - 3,11(0)' | 4,66y^a Y^ '17 .. FI/s

2L-3d4,12.+2O^-':+ z(2o+'b 6+a^) . ea4 t 1..42 oA

+2 o^ 4aa 3a2aa' 3'|'1112 'o4 +s.i ci

S"< .)Q(.scd)

rr6dlr i)

o^. zosfr/< Y^2 - 2ac

T. 32n(o,L)- 24o -6oo/1..2)a^

'!^ .

11'a4 rr,+2o^ - .-o 06 ?o. .,X ^ T,'?r. - -@ \1

[rdalfr4) y^, zooll/s

-rI4

%i."at*)

,&&'4'

-O

'\)a{ 4 \3 )S'i'c'-l 2(2oa fl ao,)' re t,? a2a\ vsa.,t h s2o(6,2) + 2ao 4co,37,20a^. Bo.4! 12,42 \
t22 6' ' 2(5 as)s^

P^''11'a^'zae

v

fo.) ln whoi dl;loocc will bloak A,of Fiqp-nas dtoi^ a eeloirty of tz (l paree, elonlinq frDm16€17

2".!E*{ . n' 4. pia" - 6' 2.az/at

. 2^dr/dt

p:N - 10/4g (y',\/"2) 2aa G/, - a) = zoo/61.avs' ! atb/.4,4u^z 14@ . s,r1\/8.+ 4.6V^, -.. O 1t12,)Fi:ndlh. \clo.ttr of boar AinFiq.p,1a1of1e. ll hrs |rolad, 6lartirs i.am .asl ot thogNon ryvitior,, lor gltdong lho lnollonlos€ su.la.c 6hrwn

t"a-no(p,) v=Pa/et a\aa 1a'|da-9e2ae

200

201

Rw - z*/ag ('t'-\"') " 2d(0-10)

= td/6++v;

b & - 1 , 5 c ' \ t ^1t t , 3 3 V s 2 , - @ 1 lo I, suh6lllla b(). t ee Gave"/r.) |,.3.,ra. ',t6 " 1g,ea l|/q

| 1'o/c+aY^

fir,/.) A soiq, | ;s a aPad] lrcna poei''on )uet atn"a, brl nd @rching, a 6pinq. thow tl.a hnrrmum dcbrnoltbn p.odrrood will bc f*rco lhat rf fho samo worght iE g@iualtr lowd4u/n,ll'. cpnry,

6' 'tuv40)'- -@

' 4'66v^' frcn'l, l,+@ 3.1.1'1.'|

6ab.$lvla2lo1' " t 4,eevt rroo " 2.11(6v"/rc)4,ro| o,tA'la'

'/ekt, ., 9.

v^ - 16,66ll/€

+cat t*o "t;a"*',cc,^"d'li V"Vt'+'

tiqP lho fn.l;oalo66 quidcs sna,m In

i;,i;";"

.'in

'isid link 1ofl ldng' nalc-i^ 143 Daicrntnc

ltr- \ctel

bcro{A 'r p 'r'"" lrdm'c€l whcnr'c'lrcorrt

= qwc ''eo lb Ascoflo W^-We 10, lb @o -- \..GU^' I l,SavAz1oJ7CVt' ' -@ sao. l,rEV^4, 4 e1ve2 s@ " 1,66 (36'.^/61) + 2 33'/ e' Yl'.125fl/e.

ak,.Ava4/0,6""

6 - 26" waighiflg 46,6tb is dto$d lron o hcighi of afl. whosc modulus is loo lb po. in Whot volecilywill tho blook hovo oi tho instcnl lho spnnq ie dolormd + in.? 6lvaa: 50thi T=W- 96,6lb h -,+fl. ^. 1& lbln

t_

6" +in PoAA!'btoc;ly

/' 8tl | 2fdrhro 2rd/y'dt 6v6 " - av^

u^,,1ev./e)., _0

''RN - 2tt/t4 (!'-,k') ' ta (.ct .i) r soe\ @lac + t,' ',44tv|

'sn/"aavj

'o z/dt/dL t 2ldr /dL

*(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 stidcadaffi an incl;na having o stopc of z '!arIi<:allo4 hartzonlal. 11sloris lrom.csl \ ofra. noi.q af@I, ElrikoEo spri.g whoso modutuEie ioo tb po-fl tt lhe aalficinl oi i.rnelic iricl on i6 o,lD, ltnd tho morimum \ctaalf of tha btocK. 6i"cn:

14la) Ropcal Pr,b i1E whon r'6fl ' f. 6f1 f ' . 1 b ' -b '

-U v""(oYate)''a.) *N - z\!/2g Q" w)t3a-4r 60@)=1d/c41\^' r@16+a\{'W,

_-H_ g'

d.4fl RcaA'

[w?/s) w(4/sYa.r))kl I -'/zxs' =wvfq 6cb?t6)P/s- vs@,iil- iu)/1E "(at/64.1v. 26a6| tus6-soog - g,z2v"

s@= t.ssv,'t t.ssre': g!::A

202

203

i

diffcrEnl;ofo voloc,ly wrlh rcstr..l b 5,

%a-@s's'uktd 6 - z.e+fl (6 aat. vatoaily) 6@(4r 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 conslon! i. ahongaatu s blh

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

lcng1haf lhc ep",nqic :f1.

| . Fi?

6.- 4,243-3- 1,24217.

aG') r t/,G,12) (1,2at)z-(aa/6aAJy2 \/ - 16,26sfl/s

r"Gr;t."ri.

62- s-e - 2fi. ao(a)- lz(sx2)(r), .(ao/6iA\(v: -16,.6s,) u2" - 332.21fl7s, v'.1b.2ill/e.

a"to1f/ z' ?Jrra-"-t ux,"l @,')-po Y.10ll/6 6 .3ll K' aatb/in

lea*dl,/s+,+ h2a.) P.pcal

d - 6 . 6 7{ 1 .

(Ftq Pw1) A waigl\l of w lb \6 se€pondct f.cd o vc.licol cPihs z1l *ho!r'. n.i,ulus i6 K lb pd. fl. Ihe *oiqhl ia pvtlod doa s fl. fnomile cquil;bcru4posil,bn\ thon rcl.a.ad. OclamJr.(,il7 latocity whcnil |"d1urd6lo tho oquilibn,umposition.

S

F. r22)

utt\6' = rayrq

"S"

\ 's J r'0fu

Iha rtqid ho.i:o.l;l

sha.o

tn ftA P1422 i€ suPTrlc4

\

2

€prings.A 3oolb 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' vvholi. rle /cloct/ *hcl rl .coaha< A? ttagtcLt{r,cl,o"\]t*c

sht of lho bor

3oor rcaG)0,) - so(1,)6 6 - o.5ft {sn/6+,40;-6'\ +1q1,r)(a.f ' ub/rlz)Cos)" \t2 - 4.161l1 /s

204

'a.2aell

: uat.rjV Rc,2d

p'?b.fz3 if thc unslrrlc*n long|l. of lbd sprtnqis 2fi. L. Fl*

= a.2+3f!.

6.- a.A3 -2 - 2,2a8ll_ a@) +,/,(s,.2)(2.2a3)'=("4/at.4)yo Y - 2o,88s fl/s 6' -s-2 - 3ll. aot+\ . ,/, (s^12)(z)2-(co/e+.+)(v,^- zo.ses") Yt2 . 299,1 \z = 16,1fi/s '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 oflooo lbpor in. lho.lyiooq'riia./ bohpen 6hrold6(b) ora 12n. *Aina aat^ ca. a.
PcqA:s e\l

206

l

e - outpjt /tnp,f o,9 " hp/3e,73 hp/iaeatrla - 3s.rs hp.

y2(ooo)(er6)2 r'/.(2)(@) 6' = 1@'o@ s@ 64' | 246r b2')r sd)6" ' ta,ao 1@06"I a2o&6 -26cxa.o 6't126-28'o

6 ' -:ztJ€dliEzet- - zin'

S L 3 1 1 ?- 2 t 1 2 = 1 4n . KEs'Y4k(12rE)" KEs 'h1o@\(tz1z)' " sEot)o . KA^E . s^a1o/ooooa 'ss'/ /" t+2s.)A l,oin watghing1@lans 1. baingWtEn up lo 21,gndo ha lnoin €.sielonco\c cona+onlaI lolbp$ +ao. 1la sx.d of the lmin k tra,.aeca tran afr per6cc toaflparecc in oaistoncaof tcnafl. fina lho mo,'mum lo.sc .o|\cr ddclopaJ 9olh: 2 .s - w/ra &'-ua"j -.ao -We rco(iuol1o,46afl 7- lolb/+ooe lr -lr,bo>s- 4bof1. .

Kcqo

fr {ch In nP.

', , " F - 9 , 7 2 6 . 7 1 | b Gafl/sso Hp.7v-le,zze,r

fr) walc.n""" ln ,n^'l *!ii"nt".

aab.a* u'ndcn ohood

ofa@fl 1odd'a a l"$:1ne. Thc iurbine is @1, offdeal v.,k co""a l.d la a sonc@la. \y'c \e sa'/, eficie.l. rvhol ls lhc pa.?ana.r+pul

i in Kilowo+is A.qa | tu||t ollpul Sa)i. P.'c. . 8Qh ' Fv

o 9+ ' hP/3s.1s h p . 3 3 . 6 rh p p.r!o. Onlpot . a3"61(01+6 Kw) ' zs,1 t
vt-uft/s v,'1fl/s c - aol. h - 3l+. R.qa' Lp orlp"l

st6 . u7,s = Y'Vq+b+n

-afuoz,\ r 3 t,, tp).ftGra)

.H- 4,9a76f{. Hp.*"" ' trH - too,to"(+,setu) - +ggtex,o. fr-lV asa.rcry3.N, Hp' thp . go6.Unp. -rsd I+-!! e - p-tp,tt /c;r"+ a.B- p@to,t/so6,bahp P u t p " 1' 7 2 5 s t r p

L -b27[nC^t)'t ) L o o a =l t t e t . o t b ""/zq

. aca

- 16o,6nls r . tr/bzr)G
hp = fv - [F6,1x6(16a't/ssa hp = 3e,7ts

206

207

$

1e..:') A Boo tb bfoch i.s in contoul wilh a tavel plci c lrho so cooff;oroal of hrhelrb fi^iction is o.to. Jf lhc btocy,is aclrjd upo^ 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. -

i

I

l

ling f.om rs6l? lf lho.eo-tbfauie ltwo ncmovcd,how much \ongorwill lho blook anlinua Io nyxo?

{r

t,

Aivon: ; w-:oclb, F-.eolb y'L.o,1,',r=4e3 fl/e, QcqA: tnno

t

i

ChaP+or 15 lmpulec \

lt46monlum

goth:

Zr, =o

lso-3do(o,1t t - 3oo/32.2Gs.z) t 225sc. z.t(o1) | - 3oo/32,a (4eB) | - 19eac $aa) horlzanlol fora of zoolb puchos o 2aa,tb btocK up ,A on lndlno whoso stcpo is 3 ve.loal lo horiz.nlo!. lf {*=o,2, dalarninj +ha linc roqurcA lo inorcoso |ha "atocily ai Ihc block f.orn 1otu50 fi porcco. 6iton: soth: -t

| .3o.tb. N= 2oota

m-/+:/ "-o.z u1=toft/s'h-sofi/s p.c4d| tr"tma

. .<11,.2-

st*yff,e4;

lzoatza , uo(oa\] t = zaAzz (scto) 1161 - 246,4s

t .1,60aa. . $$) AircoI contml tmpocl acans bal. a ro,lb body rrcli^S 1othc rlght ol slt pc. ad. v, a aadl ol *dtqnj i ..'oin;,o rno rctr ol 3 pc- ,,cL lhc traLcrcol ol rcslil"Iion a_ o,s. ,aDo:,| thc 1oab tbdy rcbounds io t^o tofl at 2 fl/6at I\,n U^el.,rn're l'. \\c'ghl N ol lha olnor bool oNon

gdlh:

\^-.511/s.yi' 2ft /s

.W^V{rWrVEi W^V^TWBVA 1@(b)-3w = 1&(-z)t wve

wE .w , vs - .e{l/s RcqA: \Noighl

7 O O= 3 W + W V 6 ' - . . - @

e. vs' vx/v^ va o,E-',/s're/s-L<) "/d - 2(1/<

208

20s

slhsliluto Vi 10 aqu
!5aa),Thc sgslom shown i.) l-q p 'l..ir ts Lscd to.lelccm|nc.rhoc@filcront ol resf,l,lron ll bott/1 ;e 12lsoroo 1*^

rast.\ boll D s,*ings.lhrorgh0. ss,i aftac A";"9 ,tr""n, Ll

Eao.JA qolf ool E dropwd ft.ma hcghl ol 2ofl vPon a horaon&. slco ptola thc cocfftcienl of rcslilui'on is oee frind lta hoiahl td which lho boll rcboundson lha lr€1, 2nd,

Solh: cos60- hio

(o,adi'6i.ne

v^'.t2qh'trzo2.21(s - t?,s+Ms

h4 - 12,7e{7 (o,asa)"(he) -h3

h - z o t l, a =a , e 9 4 Reqa:h1,h,\ hs

solh j

C'8 4,s-att!

vs -

F@4Gd) -A,3s#/s

W^V^ .W^V^ I W9VA' 3o67.9a')- 3ov^ r 2o(&,re, ui " 8.37fl/. = e &s'-v^')^/^ -vB) - (+.ts - s,zt)/
h3'1.,21 {'1.

.jb/* .J-tu/r " =.F,,i,

h ' ' + , sl l

b " 10-s .511

)

8\ lhird bouncos. 6kcn t

erss,,1' . h./g

h="ft

o osl ' ft/zo .- hr=losofi ts.ls) Ih; bollsA&,s 'n Fiq p 1516orc allochad +osli(f

of ncgligibla wotghL Boll n G rolodgod fr-omr€sl &. allo$€d 1on1.166B lf tho cooino,cnfof roslliution ic 0'6, dalarnina tho ongloe lhnoughwhich boll B will o*inq ll tho rmpool lrr.ls lar a,ot saq. alsa ft:nd lha a.oruEo inpd fotx

*lli

l:

nornol. sho6 thattt acflnetl

1 axPwsecd by o= Io e/bns'.

,f .*,r",;;;:

. _yi cose/,r1coge tromt.V " \.s,.e /1r€

e,Cy,:s,:9(:9,e_) . taneo,t e stno \ l

h =€fl .; b - 1o's =,efi

v^ -{-4h -F66G . n's+rik \^(^V^.wAVi lWsv€' ' 3a(i.sa) = 3al^1 | z'Jv s342.30V^ t 2A"/a'

o.e .(,r/ v' ),/6t. a1 o) to,1/- vz v^ fra.. 2, v^'. 16' tu,7)

) h- I-c

c - 4,61 h' 6-4,61 - 3,49f|. cos+ - 3 aq/B -0,4237s 1/ - 65"

'@

s36,2 - 3a('/a -1a,7)) I 2oVB' 5 3A2 = SAVa' 323,1 1 2ayB

861,3 =saVB' *

vc.se

Ys'='Fgo 11,226 {4?44

c . ron)/Lono $as) A boll is lhrown . . , _ . . w,lh *,,. ^ u ..-,^-.r.. " a o c t t / o l c o l t p o r s c . t : .d t i a : , , t.A A L^.- ,._,,

* t\ thchor uatta, .r"; :1 thc !tatl!.ie rat.,a.cd (rom p6si,on

a6,

";:":7":r:t*

of rcalilul,on bolwocnbartb\wa| i6 a,6, Ho* far gem t6o woll M tn" b"tt elriNe lh". qrcund 2 :

'1:.,u

whcn thobo,r st! ta. thc arouno

ys'- 17,226{l/s

2LO

; :;;;''

t,cta".t a,o,^i;, ;"",,"l; ;:.,;",''rT.J""rii""J"l,1!,ii, s

2rl

i

$.4,) ns shown in Fb.p-16ag, o ao-tb bo| movng hor;zonlolty to lho.nighl wilh.o vcto.'., g fi pd.ec, ca id.L obt;quatf w/ .ol o^30 )o barl.^movinqup_to lhc lcfl ot 4' to tta tori:I/oiol ol ro lt F,r sc. tl co6ltr.,ont Of rE6l,tu'ioD ic 0,6, &t.'|rlioc .lho. lha

I I

I

I

\ d,.€ct,bn6 tta wtoc\lyof qch bo| a,i" t ini,ai .9:Y t6por_ ,'/tgtl 7 -iosnPt

statt c.l | 161l' 34,07 - 11,1

ii

1 6 , 1 1| r8 2 1 - a 4 d 1

'o

&Vr rm,{r ..riv;, r m,Vr',

..

i'

il i i li I

f -vo snet - h ot'

- '/, G,'2)(1 6)' f - Ea s'"6o(1 d f-2so7fi 1.6r28,07.3.',07f|.

x -\o c.sft '1

\f - (sa@s6o)' = a

@e 28,6b (4 222)

x - 18.a11.

g \vt - vor" 2o, 01) ,r' -(so!,'"Go)'.,hG2,2)(28 \ry - s'2 fl/s = 26:1 l!/e ,,tr,t.,Fai6,z' ,x'- lon-1b,2tt'zs- 18,16'

:' I

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j

e - taer/'t.1^ 0 . 6 - \ t 6 2^ / 2 6 . 3 1 t L E t s . L '

I

24,51st ',t6,1e-- v6zf

'ft2f " s,2fl/s

vs, ' [G-ia 2" /-

I

I

I

ton1b!/:s

I

, +v,i, +*a{t 14(d - *(1ocd$ 60t2 - ao\tli + suL _..-@ c -(\h; -\;)/!,,_w^ a6 .&; - yrt)/ s, $cas' to =vri v,,, -..,@ m,rb rnuq/ - r{il + r',rrv,'y ..flv| 6(tos^ztt *u.; -6n/6 fro,nz, u,; -roirr' .u*. r0, 6o,a- aov,', teo(ao+v.i) 60,2- 4oy,ilere\i -239,0 - dv.i =-e,+aIfl/s vti l/9 \^ =8.4a Yt'-Y+a . 3 aa fl/s to that'fl .10t (-3.a3) - .,5.rt1/s f.oa:L]r;

v..JY,'+v,i' ' u, .vs.F-a,s.

. o,zen/"

e -Ian-1vtth.l - ka-t s/s,57 t" 3227, Ye " &26 fl/s qlo righ+ oI 31 2r' \4/ lnr b\zo^+ol --!- i M, ) fM.)-

l!-

M,VrMrV - M,va' lMrV.' K4 - th Mtli + '/, M2v2.

I

I

212 l

I

2t3

r.t.. t/ruN;'I t/l^.ya'' c ' 't2'-V'

r) A rigid bor CASDs'Jpporlcd 06 shdwn .,n Fig.g is c,cloct upon by lwo cquol horizonlol foroesp qppti€dot c \o OalOulolg lhc r€octions lhol. $,ill be inducod a'l thc poinl6 ofuru1'.rft, o.3{t, b. 2fl Pport.AqEU.ne An€. Rb " -Ro . o,zgP

PROBLEMs

2) Owinq to thc wcight W of the locomoliva 6hov{n in Ftg. E, I

I

roacibn6 ol *'e lwo pdinlc of 6uppo.l A\B wi[ eochb,eeq@l lo w/,. wt'cn tkE locomotivc 16pulling o lro:,n{ th€ drrh^,bo.pull p h ju6l cquol.lo the lolot friclion ol fie pls. c,foontoolA \ ts,deto mine lhc mognlludes of lhe vcrlicol r € @ l i o n sR ot AR b . A n € R o " , + - g r ,Rb.+r#.

i

214

216

s) A boql i6 movcd unilormv olrf\g o aoft)\ bv lwo ho__ p'?oo lb hQ '24olb ocling und€' se6 pullinq with firrrs o^ onqtc a'@' (Fis ,\) Dclermine lh6 oogrirludc of lhe r€€ullon{ p'rll on lhc bool t .' lhe ongle p \-Y oGchown In '27'' nr€ R=3s2lb ip'3a'i1 the f'gu.e.

+) For lhe porticulor poirlion srwwn in Fig C +hc cat\'*E{ioq Fod RA of on Gnginc eqrls o f6.c P" 9oolb on lha 'lhis fa.ct inlo lwo rgal(''p,vla' cofi' cronkFi'n ol A. Re6ol!c opling hori:.nlolly L' venlicallv, ol A' ronenl6 th -,-FL, ' nns. Ph=4fslb i P"'1rrlb'

.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 boltg n \6. nsGume thot lhe boll B flts loosely i. o vc.liool610l in lhc plotc. nns. Ro.1.2spi Rb .O.7sP

Choplcr 3; i) A w6ightl€€6 ba. Ag tc a%d-led :n o vcrticot ptono t o hingo of A ,r o lie boir 9C, o6, g]hon . Dotedn,no, gmphicollT, llr€ otbl l6tt S 'n&Jcad in lho lie bor b, thc ocltirn c,f o .t€liool lood P alpl:€d o+ R. S = 2P (t(,|€an)

:

l

216

217

*c ohl q' eoo lb i6 lo be PUF = 2) A rorlsr of rcdio. ' t2 t^ \ p op' of helght h 6 in b't' o Y\orlt4n{ol fcrtc ,.a' *.' o ** j"i"q w"'"a oround lhdci@-fc€ncc *" "- of o o':.i, ' reqi'rca +o 6lo''t the .f thc rorrer' F,hd rhe moqn'tude at A^E P " 260 tb rorrer .!€r tf€ curb

hor,3t:l 3) A bol of wd,qhiw rc6r upo.o sdath *T^-a posso i.- 'r, cr^\ar \*o elr;'s< \s t* Ao Yeh''h i1.""1".i" r"d'^p '":' "J fi.*tr.'.* purbroal 6 tr-c tl. -'ry t\eo::'::'1" qe '*

ti rt'e .ri"g A6 'q ho'-'zorlor'F"d Et'rris ;; .o-" *''n rho Fb'rzontorwhe4rhe be{*c€n R A16of''d rhe P"€s"e .r i"t,;".i,. ' lhe boll 0,, lhe- ' Plonc. K=Pr f,r" dosn-P/qtA-w

;;. ;" ;" il";,nJ;;,"" ; ; ;; i;"

2ta

a) oatcmi,ne ttrc o>bt lcrcra q &- Sa induocd i. tho borc AC la Ec in lho Fiqvr. doe +o lhc oclioo of the hori:a^lot oppl\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 os 6ho{n. DcieFminelhe }ensile lc.cedq -riq in the wi.es BA & BC if lh€ii ongles of rncl'nol|onor€ o€ €hown Ans 5, '2s€16 ; 52 = 2a7 lb

2ts

tu^,J-a

1l oEduc lhc rcoclio^ ol A \ th€ force S h ltre bor :I8ffff; srowrt oe ro ir'c oct,onof lf'" Uods P t'! oppl'edlo lhecrone' q

-",gr'r of lhc crone ( osEurncidcol hinsesol A' n-JJir. q e. a+'"-' thot P'.5ool::1'.1:-.o.:s:ir

aJ A plor€ fiqure-f€ur liorne nBoE i. @pporred on on Inor,necr plone E\ looded os 6hown. Colculolc lhe ot;ol lore indoccd in Ans. Sbd " .106.7rb, tension

= lb i S 1ei95tb comprc€ion -o--.1 Anc. Ro 11'{o

o'f ihc plonc ,) O€la.mir€ ttE oriol 6.€c6 in o bor€ 1'2'3'4'L' q'-P;92'+Pi Ans Llood"d ot sho'n "r"**ra i** 9,t- -oiaP i 94' o142P

-O'333P ,9e -

joined ioq€1h6r bro hingc B,o,€ 6upF€r,s) Two b@6s AB\BC, ,cd bt to!- bot.. h,ngod ol rfE,. ends Dete.;,ne lhe 10(6 p,oduced 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,Cbflpe.erofti gic=62rb. tenston.

lfp Plonc true€ lood_ d Det "niie th. &.ce s in lhe bo' As of Atc s = o+3P cd \ slppo.ldd 05 efrM t Whot i€ the neccesorycocmiccnf of ld:.i6n bclwccn tirc6 k rEodwoyio enoblethe lbo. wl"€!l drive o! tohobjle lo c|tinb o 30 7.

220

22r

2) lrc

bloc( hov'rg weqhlr

w' !' wz o'c
bv o €lFng \

l[ lhe onere ol l';cho^ for pL*" "' "-*" *", ." n- -"t, lt'c leosl t.9, F'.d ihe roe'i'lude t. o'"eclion of "".io'."' ;ndJcc al'drnq wirl i.,* p "op',ed to tl'e uopc' brocn thol (wi rw') srn{ P-i" An6

I i

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 ari6oll di€lonce h/a - 3 in. obovc thc bose . Thic conc r€sts on oo |ncrIned

plone n g, whah mor,eson ongte of 30. wrih ihe ho.izonfol qfo. which ihecoeffic,enl of fFiciion isA=op.AhoF:.ntot Force p ie opplied lo the ye.iex O of th€ conc &obi6 in lhe verliool ptone ol lhe fraLle es rhc*.. F,hd ihe morimumt(rrlioimirm votuesol P consisfenl with eqrJtlibrturnof ll-rc ooire tf the wehrrt wAns. P*, - a.61tb ; Pm,n= o,sgs lb.

l

tudue r 16 supPd'r ) A emoolh c,rculo. c/l,.der of waqht Q 8i. lhe qdme rodius ' (we'qi.a u, *o e"*;,'.c"ro' c.'rin&r eoch of

ffp 'r *e coefiaienl of oiolic f iciion b€tween i'iOi", "" .i^g€mici'culo' c/li'rcers &' fhe.norizonlol flone-or flof locee of tL" lhem-"t ls + =/2 L. fncfion bet*€en t'c c'lrinderE ;;il;.r diEt'nce b belwcen !;et ee E neg\e.lcA, &lermine lhe molihunl will be po6eibl€qoui the ce.le.s B 8(6 fo. which equilibnum plone lhe middle cyli.de. iouching {he ho'izonlol t' nna b@* - 2 e3'

1) ln thc coseolthe t.ipod €hown iherc is no f.iclion bclween thc ends of the less E'^the ftoor on which {hey.est ro pre,,en} slipp;ngof the lcgs lheir end6 ore connecled t gtrings otong the li.es AB,BC, \AC Derermine then +he ren€ite lor€€ S in

edch oflhe6e st.i.gs PG o "e.ltaol lo.ta

iFeoch

teq mofcE 30. w;lh lhe ve.l;coj

i i

I

arc os fola) Ref'rine !o lhe fiburc ' the coefficiehb of flic tlon Find o* "ritu froo., o 3 o+ the woll,!( o 2 belween blook€ 6, p opplied {o thc lowe' fhe minidun ',olue ofa horizontol for€e nn€ p-in = 81'2lb block thol will hold ihe o/slem in eqlilibriud

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,cat loods p opplied 06 eho*n . ACpD ?\ A'C,B-p, one lwo Gquores wilh porc lel sides of te.91h6 o E! 20. .€6p€clrve,y, u<^ lhe

il ,i

222

223

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 the la1!;le fo.pe S pradu@A ri1 the +,e bo. AD lf e, botb,a=6ir b.1l\ c-z'/2fl. An6 s.r3rb

Chopier 7 j r) n ho.nogeneousslende. wi.e 12in. tong ,e benl in lwo.ri, gnt ongle-s os shown Det€.minc 1tlecoordinoleG of ilsoen_

224

225

z) A stccl st€fl oi c,rculor croee €edlio. ho€o cirEular sleol hub 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 shofl 10 lhe cenle. of grotti l c of lhe compogrle body. Ans N.- 624 i^

5) Delcrmine the coordinote yc of the c€oier of gft,vily of o stel rilel hoving fhe d;hcnGions shorn in Fig.H. As€umc lhe beod of lhe rivei to be hemiephsc;"o|

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..lopelice of thc hemispherc. Ad6. h'r/,{t

T

a) A honrogcneous body co€lgls ofo righl ci.culo. conicol portion oliocfled to o hemlsphe.icdl portron of rodius r o6 6ho.,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 ih€ aroulor roso ol lhe cone

chopter A i r) Fr.d th€ poto. momenl of inerl;o of on ,soscetes +.,or.,,te hovioq boso ir h\ ott;lude h d'lh rcspe.l lo iis oper A Ans Ja bh3/a t hbT+e

%r

/i\,l K-i.jfi-

--w

226

227

d Coloulote lho momonl o{- incrlio of l|,c orEo of lhc onol! €&tion hohng llle dimcnsiong €fEwn in Fig.A wilh r€.6p6cl lo o ccnltoidol ol.ic po.ollcl lo lhc x oxiE

nne. Ir . s,r6 ina

of o cirtulo' !) Frid thc polac morrrnl of incr^tio of lhc onco +o i{s o( ragp€cl wllh Ecclor of rodiuG. b- cenl'ol onglc ' o.r'/+. Ans. Jo

Choptc|.10l r) A bodr storls lo rnovc, vcr+icollyupwond urdo. ihc inflr5ncc of gmvily with or ririfiol vclooily i. = .ofps. Fird (o) Itp moimum he'qht to vvhich il will rteo C\ (b) tE ti rcq'.rinodfor''t lo roium lo ilc iniliol po6ilion.ToF! thc atrol ting point os tho ongin so {hoi )b.O \ ncalocl o;. rc6is* Als . (o) )lrcr - 6.2Cl; (b) t . 1.246co.

a) Calculole lhe mor"enl ofincriio FiC.B wilh fcsPecl lo lhe l-oxr€-

228

of the shoded n r€o Ans. Ir = 26 e3 in.+

225

2) A {'oin is ho;€ down o slope of oocra with o vclocitY ol o :oolph. Al ccrioin inElont thc engince. opP|b€ lhe bmFcs 1t p.oduceg o iolol r€.6i5toncelo tolpn eq.nl lo onc-{enih of the weighf of the lmin . WhoJ disionce x witl lhe t.o;n Ans. X'32711tmvel beforc slopping?

a) lhe troin tr^ovolie liom sjalion A to stojion B which ls 1 Km opoFl ;n e minimum lime of onc minulc. If thc lmin slo.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/nr How long d;d lf lrovcl oi.lhis 1op speed.

i

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' i5i r O wher€ s r€ ro {1. &, L ic in s€c. Conpulc Jhe voluec of v l^ o whcn i, - 16ec.

An6.v=inls;a=rcfl/sz

2gl

'l'l : Choolcr 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 1ooofl' 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' nn6 R=492lb'

-r)-.f n fig,.rrc bclorry. o hoorrcr ol wcqht w - 2 rb siqls leom rE6r ol n &. slid€s do*^ o rcal for which thc caff;;t cr 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'irl(a
I

l

l

l

i

l

2) 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 iros\;ddi.tq 1f vcl orourB a cu.!e of (odivs F eoofl /out : Ymr 49 mPh. nnsthe rood ]E lc.,ol ?

1l s) fn lh€ f'gurE. ikrc pitol ofon sieptone ftyng hontzonlotv 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 916und. nl whol onglee below +h; horizrntot shoutd hc sce

thc torget 01 thc inslont of rcleasing lhc bomb rlnorder lo sco.e o hil ? Noglecl oie r"";n1o,o" A7,s.e - 22.12,

-- r--&A.i^ -I

232

\

\

233

t

Choptcr 12; r) lfro ormo|.rnoof on oloclnic molon hos on onqulor spcod n= laoo rpm ol illo lnstonl whcn iho powo. i6 clrt off. (o) lf 'l comos lo rosl in 6 6oc, coloulote Iho @.qulo. dacalarol\an c< oesuming thot lt'rs constonl (b) How rr,o-

i A slcndor b'rl .igid €ornicirculor wirc o{-rEJius r ic guppoilod in il6 own vorlicol Plono by c} hingo ol O & o smoolh pog A 06 shov.n. lf tho pca 610.l€ frorn o &, rnovos {ilh conslonl sped'to o\ong lho horr'zontolr oxls, lrnd lhc onaulor volocily 6 of iho wi.o ot tho inslonl when e .60'.

Ane.4=vo/c.

mol'ir du'ing ^y cohplcilo rEvDlutlons oocs lhf orrnoluni = (b) (o) d so rcv scc-'. 1or I nns lhre porjrod ?

l

+) 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

l L

t

li

i

I j

, Consido.ing ihe syglcm in tho fr'guro, dotormlno fho vol,.,,oof & for which lhc ncgolivo ongulor occolorolio^ Ans. +'30' O of lho bor OA hos llE moximum voluo

!i

i

I '1 g=6n. Ho.r losl s) For tho figur€ chown, c( = 6o@a/sa y6- r+t m/s lho blocK C is rising

i

ii l :i

244

236

1l I

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 11lG droppcd fiorno l-aiq An6. 6 = 6 in. h " 1 fl? Ncaloct lho mae6 of tho spl^ing

f

I

l l

,i a) A qrnoll block of wcighl w=lotb is givon on inifial volocily vo-ro fpe down tho inclincd plono shovn in Figr-ro.If lho 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. A n 6 .v = 2 9 , 9 l p s .

l z) oclcroino lho aynomiool dcflootion 5 lhot wll bo prod,uccd oi'lho c,slor of o 6i'nply slrppoilod boom by ollowi.g o .+oootb woighl lo drop onlo il fro'n o hoighl of ain. Whon q.odually opplid, lto .ga'io locd prodv@€ o slclic dcnoclion of o.1in. Noglcof tho rno.6 of lho boom. A n s . 6 ' 1 ' @i n .

256

237

s) lf lho 6y6tomin Figt.E iE roloo6od fra,mrocf in lho confrgurutrbn srown by solid lhoE, fi''d lho rnorimumdie{onco h lhot fho v{ciqht p will bll Nogloc+lriolion \ os!6umo lhol lho pr.tllcysA t\g oro very smoll. A^6. h - 4PQt/(4s2 -P2).

!) A no. wolgh;ng 15olb .!ns h jump6 from o plor into o boot with o horizonlol volocily vr = 10fp6. Asgumir€ thol lho impoci is cnlir€iy plo.slic, fiilcllho volocily wilh which tho mon Eq bool y?ill movc owoy flo- lho pioc lf lho bool wci

nns. v -.4.3lps

Chople. 151

d A locrooliv€ wbigtrirg eo to"s hqs o wlocily of 10mph4 bocke inlo o froilht cor woighing 10lons thol.iE ot ft151on o lrvol lroc(. Aflpr couptrig is modo. w ilh what "olocrly v will tho onliro systcrr' aolinua lo rano? Noglccl oll lriclion. Ans. v = 8.52mph.

+) A golf boll droppod from roe'r onlo o comoni 6idowolk rcbo,Jnagcighl-lonlhs of tlle hcqhl lt-mugh whrch ll loll. Nesicctlng oie rasistancc, dalarn;nc lhe arffbionl of

I

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 o ealaailf of rcfps whoi woe lhc rnuzzlo lalaat lof l|)c

bullol?

An9. v '1610 lp6.

238

I

239

5) ln +hc fis,rro shoY?n, o smoll oor of woighf w 6ta'ts oo inclinod from .sst oi A \10116 without friotion obng w wolght blooR of olio to B whc.€ rl i6 sl.lKcs o olorc 'u. lhc B' 6l rn,tiolly ol rE€l ndgum;ng o Plastrc rmpocl tf tho will movo f.om 6IaC oG a^e pontclc co. &. bl; iq,''{' blorK \ Plono coeff,Zieni of fnrblron bctwcen lhc tla,6alcwlolc iho dretonce x to Poroit who'o tlio bodrc6 *l^ r'+ A^s x=^42(1'

1,fl