')t
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<o'
--: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<o Tepre*nle
of uniform ihichness A lole of + in diomele' hos bea coi
in the plole Locote lle cenlec oasFa"ifv of lhe Plole Hini:
The weiehl of ihe plole ic equtvotenl lo th€ we'ghl of lhe
origrnol plofe minue lhe weiehl oflhe moi€nol cut owog
Rep.eseni lhe orieinal weighi ol lhe plole bv o dowoword
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 <uc
dc = Taco/.14ro - 3-o6!!.;st.+ or
i) ' 12196tl. r)g|,t of A
za,) Find the lotue] of p c,)r @ thot lhs ftur
fb.ces shoal]
n.Fig. P-z+e pr-duce on upword resutionl of w tb oci;nq
at + (1. frcm lhe En end of ihe bar
zMp= -f(3) + 2cnG) + i.he) - aoo(z)
r= 2oo tb (do\9n*o.n)
.MF-.c'o(1) - pG)-1oo(s)- 2@(2)
p- aoo ib (upword)
-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<b-1oo)flab - (412)R
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<X*t*
@)dc
of ra
tb' n
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<jtb-n. Find ile magniluoe
\ aireolbn of lorc€€ P q F.
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<t lhc
a."en eyslco ty cn
srnqre fo.ce ! canp,te lhe nlercc"t€ oi ils
3c"":bil
linc of clion wilh lhe x 3y o,e.-
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 =<Mo
3F = a61(a/r3) 6) r 3o1( s/J:t)( i r ft1 A
(1/.rz)(2)- 141.4(t/E)b) - 22a (2,/.rs)(1)
- 22+(t ':t")()
3F - 1AO,1
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
,<y - _6otb,ona
zMo=360lbfi
counla-o)ockwi6e. Dele.mine ihe potn)
olw/c
lhe n€sulloni rh)€.eec)6 the yo,;s.
.-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.<nocunecl loft.e
b/.te!n ,t B fau^d
lho) +x..so.b.?y-,teb,\zMo=aaob
f, Ino oounle.c|oot.
uere.h:nF the pornl o) *n(n
y,*
)no ree.,lonl rn
T.::
lor6ects the )l o),;.
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<iG)
+ ao eina(+) + ao(
- 2tto (9/'{-t.
)G) lil9.19 rLtLcw
d' zMo/A - J!19!p- - - 3.27ll.
44.68
?e) Cod,pola lhc rcs"llonl of lhe llrcc ,;!e€ sh6en in Ftg 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) ?
<rr. rc,ooo - 60(b c'o€to'
. ago:.!a
tb ( to the
.iqht)
-6o1co
-24oOO
5t.l3o
Zfyneans
do*n'
t 27)jA(
*ord)
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<tot++u(1/r)
' +oo9,32 lb
rca -<+d",!t)
4s"--fi-f666:--.9qf.93..b-(- mcons down*o"d)
lb.z.ia)b.ldblb
^l@.seiz-tTiffii: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/4a@.es
+"* 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<z) A tuotb lood is supponlod by o coble whlch rune over a pulley b G fo€le"ed lo lhe bor DE in Fig P-eos 0m*
o l6D of bons Ac \DE \ of iho purlev Assunc oll hrndp.
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
<ft =or fi€ink''BoosrnTs.
d - +oj,ao1 tb
<fh'o: P= ri co6,rE'-ioo @ 7s.
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 <ntinq ol on unknown a.sr6e with lhe ho.izontol_ oeta"-ine thc
votu€6 ofFqe
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
<F,. a
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<n(a"a1 t q+ra(a-1€)
A ' e16.11 lb-
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
a@u.d
^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<t
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<
- A@o6t.6o'
Re"'23o9
161A.e
Ilb
P-ah- 8@o ct'e'
- (E<n 4)' + (4aoo)2
6e'= Rev'rRen"
-t(2aas.4)'
I uaq'
Re
Ra- 461a.e lb 4 4620 lb
+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\<a)
= 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 aP@.p - sso(Io\
2P(ane6.a') | 2P(caE66.t1)- zsod
p= 901,39tb 0c .t6)
Ft . <o asto'
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<to . o
39
&orb-l
I
€s)-The .oof
n I b. p *
,s 6up@.rea 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<A\L
rh€ beoh i6 rz.
1,, ",n'o. ons \ h€lgh6 jootbpeFfi n concnltuted
tood 6 2@a tb j6 oDottet
aI the tree c'4. Comp"l€ the
n@chbn€ ol ,t kS.
336) I}E cont,h'@
| 4F1r1600(a)
t6R.' 16F.2
r5R, =1600(16)+ soo(a) + 1600(3)
R4= 2loo lbs.
r\trr -l<ooQ)V
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,
<Fh -o ; R^h = 2c'b t 2Z4a s.2866" r 3ooir€ rbc.
1M6 -g
ao p,^a - e.,.'rAo) | rc6 (6a)t z@a(ao)+ 3a,t (b) | z2ao(@s 16.
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' $17 f)
iX!.,
^
2Ir 440(6)- afish4o'i 6rt@€.
b!l, stn lE - aosa6.
2T .r 2s2o - t6 tlstd.'.
=poa(as\l ao.x)(a2e)++ao\et i
T - ad@sa5. - 1260
. erish+s.- t?6o
sub6l. d1z ia1,
, r -dcoe.E. @
-e6a
n@94s' - grlcD.+s'
-7n.*16.!
- 1260
fi - ?s4,sd tbs.
Q^ - 536i 27 - 6360 lu€
t!)'r]"
' -""n.,
, ""*6ets)
Rsv = 6131 67 !
26)
t <aoa(+t zs\ +oco@e6 56'(+1
6130 lb€-
Rsh = .ooo s'n26 66" R^€r^3o" .
5361 27 stnaa
- 4oooatn26s6'
Ran = a92.Og5 lI$
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<b6rs,no.
@sr'e)-
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 - <a- Gz*z)'a=s
'P
' 37,.qz tr,s (ro rltc lefi )
*",',^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.
<fh-a: Bo.tE,go'=/.ba6io't 1@ctag'
'
&- Ao oe65(AB)
bD = ^6 ric'l-*@
tfa'O:
'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
<Fh *o : 60 ccs3o'- Eccos5e.{ AE @s !o "
0,466ao- o.6ga + 2oaa(a,366) ___.@
q , E l i m , n o l i d nr r \ t
r.a sso + o a66B. - 2@a) o,5
+
( o , e 6 6 s O - o , e a c - 1 7 9 ? )o _ € 6 6
gc - ioo.
o.25 BO *+ d.rqi
o,25Bo
d..+€3 sc
looa
'+ o?s
Ao
o..!e3-bQ E lgoo
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<r, coip-le
foroe in m€nber6 AB,BE, \ DE.
@ pl-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
'
<Fh-O I AC
t\c - 2@.189'
/
c /
,.C'1-ft2lb'-
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- <qto Gosao)
/c' 2459lb--'T
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)
BorBE@.o. 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 - i@a.924 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 -
<r.,.b
^ 3.
B^,-A,Bs,a
-C
B - 9 s 3 . e r{ 9 4 e l b <Fh-o
Ac - .^a @€6s 43'
- s e 6 @ 6 6 ?. 4 '
/c
4 4 o b e | ^ A t : ' t b- - 1
@ptc.
tF!'o
| 2oo
bc'Gco
7oo \ c0 | 2oo ''
-'r
5 C(,'
<tn-a : /cr Gco 't F
'! 1740lb - -r
cE - 4ao+4G612o)' 114a:16
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.,,t2@rU.rB
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<t@tt"--r
.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^!c.
l,rco thc drelhod of, €ellon€ lo dst6.ainc
th6 fo.€o in rcmbecDr,
DE. lr C€.
,
R
-
R^Y +Rry r 2a@t14oo
n^v l Rov - 3600 .-O
P^. (16 - 216G)
+ 12@62)
i^ r, c(i'v -9O'2@=1e'b
BE _p@lb.
-w=
24<Xtlb -
--
'
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<Ftt-O
ec - +/@ ^b + 1/s 60
Ag ! 5909.31 i 59lo lb'
-c
w'tr@s1o)t +h(@)
!E'6a.Dtb --'c
<Ms.o
;
'tlb AD6€)
!
^o(c)
R^v(e) r ?g
D-30@lb_
€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<a.'t
cE = 1440 lb _,-.t
:Mc-o (Rc&l"t"d Bo ol F)
^-;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 <a1o)
de = gso lf'
(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
BO=3@.5!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) - 4@s26.r,.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) + <M^ " ot
Fo Oo) - 2(as 26.sa)(.toI 20)
z(@ e. 6, ) (b). e (@ 2E5't) (....J
+(z)(d 2GE7'.)(6no)
DF - 2.s Kip. -..-c
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<r:,<2o)&@(1t)r'.(t(.6o)
-c
AI='t166.67lbzF,.ot 6\ | 5/.l6iFr = /giFt
f\ =2aa.27tb---C
tte(go)
-T
F H = 1 5 6 4 6 1l b "
:Mo-O
,a(a\- aso(a)
gn(a)
rcfl of c-c .
zrt^. a : 60Fa= .k]x(6o)+a.a(ao)r 2.t <2r)
f6 =.733-33lb -"-T
Fig p-a3o o'€' in
aeo) The lod& cn ihe Po.he. 1'u66 et)o{n in
"r-lb' Delermir€ lhc lorces in menbe's Bo'
^t". O"" ^t *"r"
z?! -o
Av rJv ' 3o(7) Bul Av'Jv
'B00(6)
8n - t€o rb
(lcn)
bJ - esatb (dorn)
8r-2.gO-39O-a
+<t Tho strucfuro sho,q
{ho hori&ntol e^ vc.tiool
is hin96d ot A &,c. Fidd
of lho hinqo lbiE€ ol B8..)
CE- 97.22Ki?6---1
'o
<Mollhe inlc6elion of Bo \cE
z?ft;-'s+or(16a)r :o(rss) = rlo(roc)
'
BE = 63-gg siPs_ -T
@ft of b-b
:M ol lhe Inlerteolion of ooqce'o
rco(a) \ $a oE , 30 ($5) =1oe8p)
-C
oe - rc'873 x.tq.-
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
<Fx-o
ZFl-Ot
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 <ro) -o
Ev' 26'r tV
-o: Er-AJ'24O'o
-24O1EY
Av At = 24 tb
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@<r)
CH- 2SOlb.
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<dtdL)t.p,,A2)
Dv= g1OrD_
:F
;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
= <n!2 .,
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.
<Fa =o: r - $o(cos.n)- zoa(snaa)
F . 246.+1lb.
l L - 'F' A = 2 4 6 a 1 - a 6 6
,tJt2i
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 <noffiopnl of fnr'clion \e o.z unao- ea>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.
<rj-otn
FBDof BlooNb:
II,
5L
<Fr.or P. F+Wdo&,r7.
p . (d4 (wcos!#r) +
w (enaa,er)
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
<F!'D: d'soa cosrb/' = 24o tt '
r = @+)(24o)- s61b
-o
: sP = w 6h e6s7(4)t \\@€36a|'(a
zvA
sP . Pao)bn36.ef
O +.,'za b1'O))
sP ' laaob
!=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<t
i f s fiPPin9 i-Pends , deJe'rnr wrcWcd otaund lho alide.
al fe'cl(:n
na P\ the aoffiaienl
e'c'' f c:oaoo'
1F^'o: Hc'oe
't+co€6o'ttta.s*'
,/t-
--@999-
"o6773
fBAof b,
€rx-O I w6rns. &sra1..ar | 8.6n1+.o+.
aoo6,ns .(Rj '8.) 6rnl+.o?.
. (\+R4) . 8e1.+.ha A
<F3'o I Ra a<Efi-o+ - R1.pq daf - Wco6e
(qL-B') c8la.oa - 2ooco6e
R4-fu ' ao6,2 c<E+ @
1'@1: Re - o2+.4sne- -R1
>
a24,16too- R1 -R1 - 2.b6,2(jo64
az4,+€ioe--2R1 - ao6.2 c.€d
: tut nj. 1N;7case- 8a4,+6;ne--2(1zazote) - zo6,2c<Ee
6244 €ine- +s3 6 @4e
lon e -ElEsr
zo. ez'
prf.b.
s'6.) Reran;.s to
il fha coc"tirirbnt of f.;ot,or
sts,
'rs
o,at V, o- =ro' what farca P apptiad lo B aoling dowrt
\ panolrai Io lhe rotine wi,l e{orl rnofion i whol ic tha
leneion ti the, ct t dfiaor,ed la A?
<M." o
q ( 1 )- F ( l )
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
<f!'a:
hzcc,saos6- z.b@.ao' 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$,95'
7 0
s.z+-o+'
c - 201,9 lb\/r'
a
aOlA
w^ . s98.3lrt
of friot;c,^ ut\aer A to p'ucni
w-.e
t'42
rnolion-
e-113'
tF,.o:
.ln4.r'
C . 2 J 7 .S + l b
<t"-o : r-c@624'
H -4Ct t Cen.o'
n- aoo | (2s7.s+) s;nzo' F -Ui1%
r
/ - Er " 2 0 6 a 6- o- . i e /
l rr
o|ocr,on,.rr
ihe bdl,e 6u-foe
szr) r" fis e-s,o \f J.a 1 urde. both bloois \^ wo6he aoo
b.rhd he. nor' *eishf of F thdl cnn te 6lo.leA oP lho
irottie b9 appl)nq Io A a e's6l wo.c r'cnzoalol tcr<:z P
y'.!-.o.a
at b: t-a.t-.
FBO
z4-o : tl - +o3 I c6in3o'
zJr-O: ,Ko. Ca€e6' I F
stc -caeao't @,2o)(+,xt+cs'"zo')
rb-.(1oj6)-C-374oztb.
o- 16,7'
wa . or+.a"(.'o*",i)
wa = 263,7 tb
g4
Vtt te+,e)(o,ca)
P"@z)(712.a)
r zs1.2s
p- +a-7tb
's
t":ot 4oo tb
";ffi
rhe purb,j shown in
l.*.)
,!:.':' |
tl",pi,'?
ie p-etenlea F.on @tdt.:rso,j o
ta:: P.opdEn
ly .-d cf the brotf- re,e.. rf ,he @el
.:"
e1oo7
I
fi.112,itb.
p_F + c .a6so" "
:,-)
A
:"o",;-:t",.o-m
is a.eo,del
the,alweofp
. ft_ r//rL= zog,
iMa-o
i. rcaob'
P(4b)- h&\- F(B)- fioa(.to)- 2oo(a)
pGi) = t+too _ p_ zcoto.
r.,,re a bu.h:^g2,:^. ton2.,q,,tippez:)
, e ^ t t . . a , t @ . o r 6 h & - . n F : g u - w .t h e
a.e 1 ot t.ato.^ ba lhe tu6i9V
lh..ad E o.iq CD^p.te
o:r^
A oi *y' {.,eh, ^ @^ be pto.@
ta ptll"a\l
:: :,
6|pPn9 cb'v. thc rcd ,)er,ar 1rF derqnl
95
\ ? a - 1A
l' 8D
2M^'O
w(L-1)t r,@) - tib)- o.
al$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<bEetLetae
Ion1a" I Ion 2a'
O<M6.ow(x-5.e€-)_o
+-:Po:
Ton2r'!od<e1L6,ns
lon
'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"
<rs.ot 1116t.76.|tj.6t
t6..rao
tl,q_e t/k,@,..\ s,",.. - 3,\,
,
rrt,r.^*.+
I
.
-,,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)
<r:.o:
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,)
- 2L@6q.toh6d.-21;,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<icr tho d)o*.
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*
<t'-o:B'.,1;-W5
fOD of b
P - + 1 6 . 7t b
tr\- a : ?nsi..' tW @ts' - o
R, - :&_e:::
<Fg.o,
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<yl €;tf.,.rE ie tO'.
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' .<i €) - sn.-t is' - R. s.|.d. tu )
RzGoss'<al€- stnrc') . zoe I soo @! E'
R. (.3.a+d) * !666
R. . 7lts.4 lb.
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<tL6).a. \)
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 <o,o<n lb. wral
rnor"eol ie rrrcasory
lo elorl. toa;ng
lt- tood ? .
P-L--L
P - ' D o - t' - ' ' 9 a " 2 , 6 i ^
tPr 3'si^
1 .- . , n;n
-ne .gL
'/1a+
|
"<e
216+)
E-^.i^
'o.u
f
lane " o.x€t
l
ony'o1 '
'
4
'
6
'
e-
r E- w . r n ( d ' e )
. <oan n ( + *!) l "" (s.z't z.; )
Is = 6e1.82-b:fL,
' w. lan (C *e)
T@o
- 4<,@(1i
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 o@.d
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<rarg wcAhl. lf lhc coe(o
oc''t
of f",alro^
ic o.+. whol sagl.l
a.^ bo @p+r+n
bg
c,cofi^g
a 60 -tb (bt@ al tv oll*
o^d of ll\c .+.?
sso
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'
<r\'o:
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 bdck@.ds,
i Cr=r41-l.. iCz- -Aa.s7
<r - 115.24-118-23-113.15- -117.1+tb.
{ uprio.d to the left.
1t - - 1S3.CS| 234.49 | 141,41 - 226,2+lb
22' 2.a.+2 - 29e.o6 - A+.e7 - - 152.46 lb,
€o1) Dolc.minc tho mognitude oflh€ rcultdn{, its pointrng , ond
ib dieclioq cosines lo. lhe folto*ing s)€tem of m.-c.pto.|or,
conorrenl forcos, roo rb(z.3,a) ; B.btb(-3,-a,s) ; 2/btb(a-o_a).
Fd.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
<y - easo, . skoseo') " z.s
zz = Rcose, - !" (@sa6') = 3.sa
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)
<lY1: r - l:06.2 tb-ft.
+-++-*
:. 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$orh shown in Fl9.p-61e con€ists of thr€€
b6.€ Ab, Ac,q Ao whose tower ends o.€ in the some ho.ir6._
tol plone.
horiz.tr,tot fo.@ of 1@ lb oclinq pono et id lhc x
oxi6 i6 opplied ol A. Delcmine the forc6 in eoch nedbc.
= -g.tO) ' 7..)(1)
r1't - '17oo tb'(l
- PaG),p,(1)
- s@(4- 7.b(+)
- -8oo lb-{I.
}'4/
zttf
d;
6i+) Ths sheoFleg derrich shoxn in Figp-61a suppodso \ic.tical
lood of zooolb.opelied olA. Poin{e B,c,\Doc
in lhesa'ne norili
r.ntol plone A,0,\ D orc in lhe )(Y plone. Delermine {he
in cdch menbe. of lhe dcrick.
a-1r:of +<crf r (o-<-::)'
a;/.3-oy..(o-f 4e"ol.
*,
'(o-o)" ' (5o)'* (o c'5)Y
Go,,ro) da
d^b - lS.7oo fl .
drc" . @' o\" r ks- o)' r (o' o)'
d^c'20616ll.
di - Eto<-zal'*s-o)'.
'Gr)'.(6af ,@o).
oN. s.a67'
lcolole Right Sidc vi€w,
lsolot6 F.onl Vicw,
;
lsololing Top view-1@(D, rcf(3) ,o
cr.62Slb.
.r{oa. r. o : B/G)-1db(5),o
as-, !L.
c/ 't @(.t/$
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 | <a-o)?+ (+-o)2 - b.n.
a ^ o . , t ( 1 e a ) 1t ( 6 o ) z + @ - o t . 1 t 6 '
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 Ac-@9.ollb-c
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 <o4)'
d.,b - ao.7zotfl.
- (o-o)'+(io-o)' + (o-(+))'
d^c . loiro3 fl.
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$s
a c < t >-
t2l
lsolole Righl side v,ew,
lsololo Fronl View,
-i' M c . Oo
-0r(6-2.),@oG)-W41) -o
'aoo(6'zo')| as@- 21e6.6
-o
-&-.L'@
;8t'19e,attb
_9-_q-29L
q Ls). c/(., - 12(,@t . o
g/ ' 6<bo -.'(t
) --@
- 2100 + 4co7o . _2001 .4
Za . 0,997'
:. C-/ " 2oo1 lb
6dro:cr6'\o)-qG)-
-PL " -01o.t.t,
10
ot | \999..O44-*U-O
Dz' 3s,s6tb
q(rd'qG) -o
ro . L2@.1(6U/4tb
24@
-Cr(a) - 2a<t
Q@'q(a)
-C/(e) - - 96@
q _ 32otb.
(32o)(B)
: 8/. 6@
. 36s tb.
o''b$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,$6ll
=
d^c
"(o-o)' r (1o-o)'+ (6-o)'
d^a = 1+:1+2
fr=
d,a t6'14)Y t1aifa
d^D = i1.3s6 fl
- -?L
_lqcp
A - 471.31bC
-/\D =
\.aso
/'C- +sz.E tb-C
512
40
d."..[:7'TG;F,G_g
do^ - 1.aw'
eeY
doe' 6i'tf
qu.6,n7
,G-o\\ PIi|'
Cj06.6,C62
dva-"6-o."tcarc
(+AoJ
t22
t23
I
1
0 = s81.5 tb -C
68.) 9elcr'l'ine the nroxrmum sofe verlicol lood w fhot can be
suppo.t€d by the t.!'pod 6ha'n h fiq.p-G23 Arlhoul ett:e*d _
lng o cdmp.essive l6rJ 6 2arblb in dny member.
w
)
r
o.o= 7211
* if. M" 24eb.,
2@.-L=AL-1q
,.103
2
t*a,r(s)-r'-(o).o
G
Aa" 229,61 tb.
., A, - 6445lb i At- 19,:+,*tOi AE.12s2.C1lb.
Isolole R,ahl S,ae vi*,
leolc,te
ahec'. \f g > za4otb
oA 73s.61
D.\ ' 2 167.25 tb.
.. thiE @nndl be o@pl be@|s
lbc I'mll vhich i. z{.ab.
,. sae
dar. vot.e of w
i.
tl witl eo6ed
.sigg.S lb
EQutuERtuM
roR ofl.coilcu^RrNT
SpcEtoRcEs
A'(1) -B/('>-o
192+..6G) - BaG)
bf - 1539 '@
dEcrK \l Dbr24@h
DB = 153q.46o
Ee.
6-
.'.DB- 468.561b .
./ tl dclol
crd
(srt N\z -G/G).o
q - 2(t 4.p}t
4)-
q . 1.731,e2+
tb.
jf
dt ct.
rc >24.r.tb
*pL - 1731.921tb :. qa = 241.4a trr
a'211
5
"/ildoetu)c&
n(4'at(A="
tif
DE '2.@ |
62c) the Flole 4arn in fb.p'626 aoti$ 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.
$q...tb.
o+ the nbhl 6h6 vi*,
zw-o,
Ay(1)- s, &) -o
Ar ) t/a (17a6.rc).2232-1 tb
dv:k 'f M> 24oa
_w. -22122
DA - 27s+.s tb oo totl .x4t
tti6
\atle bd@E il er@&s za<Dtb
-Ci
^C2
ct ' 1q6,9 \b.
C.'O
6l-r.L-!
_-.]
W.-4,4.,0o(+)rcio).o
C' 4oo tbT
-6G)r 1.,60{6)
- B(s) = o
s'-3p@\i@@
A t A I C - 1 a t A" A
- 4oo 4oo
A - 1<><b
627.)6oleeprob.6 if,t^ add,l,on1oihe loootb,the plo{e
w€,bhsj
'U@\@t" Ue)qt)(e,/.\
+'fG)e^1qe)
gr'bA.h)
j " nbll.
y1()4@t - 't G)a6)(61
,/s6)+ ,/l@(d?/e.6)
t =5 n .
t24
125
Topviow,
LVz'o O
- Q(a) | G (+). o
02(.).0,(6)
o'/+
ut: O!
t,cr-G
(D'/,')Gt- o'l.o) c,G)tc.<i'o
o, ts
;i:::=-"
,i.'"/
nn6g,otal
, .m 6) - c6o). o
ebG)1.&o G) - @ta) - aLs) -o
.V"
""{2.
c' " s.2so, -@
qbs.@ b@
,x r s 2e D' 'eoo
0' . Solb
F.N@ | Ct . t.Lt<eo>. 12o tb
g- g.o tb .T
c . g @ l b ,- f
ztr.a -
,to.fu(c.rcsl/a
-A+ 12@r10.o'g&'a@ 'o
A' 600 lb"l
62c., Refe. lo unsynrnetrrcol conlileve.
Ac.kao0z):L/1
lc - 126blb.
Go'r€wo'h
dosc'ib€d
in pnb.61g on poqp €6 q rep€oled heneosFl9.p_62c.lf lhew:
ibal\lood of 17oolbi6 shrfle, b ool o1 lhe midpo"l ofmem-
ber A9, oomptrl" the componen{sof lhe ceoclion ot I E lhe lb*
oes in lhe bors tC \ nD.
dn -.[.e-af,O+ef '6aY ' s,7" X
a"c- .@$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;?
,<ao-yaif
a". ' u[-a",c-Y
"
ago ,6<',o)t'Go or i6Zo-' ' la
lGolole Rqhl 6,da Vid,
lsolale F.rni Vrew,
aio'a,
N@)-'e@t6.6)"o
Cr<i) - ]6at!/l) -o
c, ' 6a3lb
." 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
<j:
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.
<M' -o; {oo(ro) - Ay(o)- Er (s) -o
A y ( 2 ) rE " . , t o o o- . - @
AAE.O
D(E)ro6a(?o) ^ytu)-A,(!)-o
t\r@)t A\<s) - 9,<5) - 2ao@
A,(4)iA,-O'-.t od - -@
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)
<Mo-o: -382 <1rt2) | c' (21.6+)|2@Qr..1)-o
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<asa)
W = ztB lb.
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 .<o)<i)
s7
I ---f
I
shdM
i' - 4Ol | ,(6X..'r'4&f ,z<ox..!).
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 <lJnlra,dol morcnls c,f ine.lia of lhe lrapczzid
s'ha*n ;. Fig.P'922.
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<a)
tq?o
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.<i)Qc,)'z ,lt6.o + 11h3e)if 2
&
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,<pd a oe to more L eguol tolv fo"
thc eccfri:n. (liosl6t
lhc lollicc bo.s which ore rirdicalcd b/
lhe doeh€d linee.)
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$tt1,tz,z-g4atlz
t l<P+ B(rX,)._l,r
L -(12a.tr2
1, "fes t aa@/a +ot)'f z
i"=i,
€a.rfal -\.[s.s +sos(d/z. o.r)'f
d? 1,co tn
a2s.)Del..r.'it-F-fhe dslonce d ol whrch the two s in. tsin. r€ctongr4 shown n tiqP-s2s should be spaced sol|E/, i,-T,.
I,,-t'.Ad.
r [39! , '<a>@)12.i,
L-Lt^d.
lf63t!
z -i,
aG)@/211,s)'f
17- *te.ee th-t
U6ihgTobbv r-. P.opc.ia. of sh,,ctu.ol s&tion€
s;{'i" : A'€o . fi ,i1 ii, = 11:6
F tlr. 6s.6inaj r. 3,aEi. \i.. i.os i.
|
tla1.6
nG.2)Ia
+k6?.25)z)lz | .ts(2.26)(s."1e)e72
t"'fit*llJla
i, - 7661,ag-n!
t fcect tG'r"'l+ ,E z.reOB)aU|@)
i, - f*G>iJy'z
1t ' 3oz1.1in!
a3?.)D€lc.miie thc cdnt.oidol homenls of iicFtio of lfre bJrll *
up colurnnseclion sho{n in Fig p-6a2.Il ii cd p$d of {wo ro',r'
l
ptotc5 nvcled
l
lo f,o
121^ 2o;1tb clbn]dla.
F.DrnTobte vttF? Prcpcrltc.
i, . i, ; [:-<er''oj ', -[QG)"+s^@h t t|)'f\
t2o = 1B| 2a<d/2 t1,r),
d'1.29 i'
TIE
tege
aho.l
of fou" 6 b./ 1br./2 i^. ongles orc <.nnecled
83o.)
io
lo o *b
plole P h
by sl6n. to fo.rn thc plole 8t ongle si.doF
rho o,ue of i,.
Eha6 ,n Fig P-e3o Chpdtc
i'12'..
i" ' 5/'6.k3
sf .l s15., e<."t<,t,sfl+ ,
To.5(!.e)! r 0.6(r.5)cc.Ef la
1'-tur*;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 lh@.gh
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<o/2),
. u, M(o,+c"\+ Mlr@. I c/.f:]'
- U, M(o"&') | M(o7a+cYa)
r - % M(o'&'1)
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<R'-r'\(?'+r')
' \/|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<n. 1.1\(n.ftb)z z(zftat) - t,"l
87 qlodbf;c
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 in@nd.- (,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 =+<z) = a ftfe.
- 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<coieinll
por ecc" k v ic h ft po.6oc Whcn t j6 za.o, €=6 (y -o. F,hd lh€
rololioo! batwcon v kt, s&, t, v\s-
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<t W llr.lixt
in d stroighl lne y{ilh oh oc.€L,rolion wrrich varice unifrrty
{roa zoa b a ll paeea' ia e+c. Ctt .q'ta fle irnlial wlocity {
tulanol A*c
l\o danqa in dieptacz:inonl durinq ]tu a a
(tlcr}\E.
uaioq
br
n{tlon cuNcc \ .}Eok
6
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.<bla.oIic ?
a. qfl/e'
Roqii : o) prcE€uro ho 6rcFi
b) p.oesulE iF cldd.lc.
is d'x@'Jing V lhe Gomo
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<F
*i,) f* lbaLt A t-B anr r€looe€d Fo' rosl o" o 30'holino
llD, o'r,'ofl oporl. Iho cooffioic.'t ot f"iclbn undor lhd wPor blocL^
i6 o,2 \ lini undor tha laio. blook B i6 a+ Compulo lho olopecd
timc unlil lho block louoh. ,
|a5+)
O' 6.4, 11/6..'
$-B in f6. P ros4 o,o
lwo bod'es
'Ihoi..olion
ecpoelod
b./o
(;pri.g.
down tholnolino iE ros'6lod b"/ a lorca P = "a)lb lf'a
@om;,cnt of Kjnolicf.rollon is o30 undo. A !.. o,1oundo. 8. Do lcmlno thc lorco in tho firng.
A^'a z t\fz'a7
R.qZ : I'lho lo clapcod unlil
golulion I B6ine' - o,+8ut4'
*'o bLrks talch
- e22.4 at
qB - a.% f)/s'
a,2 A ctbts - if..2
A6i.e'
<t^
a^ , @,n fr/ee
3-'/aaat2',Y2(1 ss)I"
5or9 -'/ea^L"' k (Io$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,<a-A
x 1338.s3 tt.
"t - rsa.c - 1s3.2sm3dI - lz G2.2\ L2
/.f
- 2 s 7 , c- 9 c . 6 1 - 1 6 , 1 I e t. = Ssoc
.
=vo
1932 coeso'(B) = j338.s3 fl
coset
X
pob.1104
11tx) Ror:pl
if iho pmjocl,lc ts I,'rod downwo,n ot&"
hor.i.ontol
tho
to
so\t\: '/ = ro6iet I '/29+.
2sa6 - 16r.2 eB.j t I tk (az.z)t2
xst,l - 96,cLr 1a,1lz
srluodmlio
-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<oso mrrml o€,al.rcIio(, ol sgfipa.€,C. Dc{crmrhothc
rcdius of tho loop.
t6 a. = v'/.
an-sq /Ee
s b2. e)r- Fa x szsot 1/s661'
r - flal.64ll.
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<i4 r.d"& of
' 1 <9e
= qA/so
Oi.\l?furv
lone '\'//\/*
-o'.+2,4"t'
E'olh:o,.g"e2,2fl/6'
a -\o.ospt
On .Orcos€ -et si.b
.so; rooco660'[
a. . 32,2o)s+7.4",'.21i9 fr /e1
Or"v'/.
I-i6c<
t '8t.gq)74ts
\\ -tr,.as6d - o
v! '5o fl/E
a - 2so,64n.
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<!
.t,- r.@(./s) - -12(.)
on ' oy co6t-, o, ch+
- a O . F O- 1 4 6 t d o
Y\'z4fl/.
q@(4/E)
.b(e)
vt =
a. - aoft/s'
,tr.o , !-zlfl/s
= z+/26
-r
o" :v/"
. - 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^
<Fv-o; lsi.t,it rlsin6o'=w
r-<a#o'G)
ara'o laa&!; -t1<.'6o' 'W!
O
l=w
'
w
n3in60'
wsinio'r
ll - w- o,5W - 0,9774 W
o.ga6
subel ulo to t
-o 511arf ./Js6o' = v{r732'G)6e
/@sa.;
,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$cA 4a2o
rc5).To aha€k ihc mdius of o 'oilroad. "Fvo'
qt'la
susts)dd
lb wo,bhr is obcarycd laLJn 2a7 6n o sp'iag
.frclfl'
al aodph
of o. e/pcnocnlol @' 'ou'di^g the curyc
tro Jf
Whol is tho rod,irc of +hc cuwc 7
@s6'' 2o/ao1
Aie.'. v . a. ./lpt,'€,86 n/s
',\N.2alb
a" 14 9+a'
I . zo,7tb
t?r=oi16;^6=*n'7sr'2a:7sn1+'sta'
RaaA: rcd;is
' 2o'7s'o t4'Q13'
son ' zr1"o
lut<o' w,teo)1/az'zr
r +a,s fl.
Tcoso -w
i ot'o "t(b)
186
Sol,n: str''D'- d/10 -
6i€n:
d=s"
( . Ett G'
v-orn.zr(o,r$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@s+iIAE@...j-w
+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-<z'
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
a@.lho 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
<trla - O
i. (a,ttsa)' 32eo.zba(e,q1)| 3a7o,7
sto20(z,4iz)t zzzo e,azo(s)
'39m7 @< 2o'(3)
ll4 559,81 lb
'
F4' 6.sg,O7(a6) s36.92 tb tmc^ whacls
l1n 3a,e6 - 2,a11h
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.<lz
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<L:
'::,.)
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<t,t ,
anouta, 616,4.o_,.on
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<e
" 5 e / 3-t \ l a l "t c
&=:\t-l
11,.t[j t\1"4
O,.6ek(7),-Blb(1f a9sG) t 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 2@.a&'(ae) r aoosiag
-[uo Qz,afl/alz
It- t99,2+ lbt<t) Fhd ll€ wbd'|.1 of Lod/ A in Fqp-rot
oflar'i hos nolcd
to0 fiom esl isunE lt putbrt tobo {,crghllcsc&\ fr;ct,a,tc€c.
, (td - 12.42a\\). e@t sae a^
a@- 24.940,\ - 3e +g,32o^
^trt
l'@
1@.31,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\)
-.-<q
fa.20+-rc,a41^
1411.)bat ^ slol6
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
\
<a@ht.e)a^
e^
It ' zo4 r v.az o^ - 'O
b4 - 4a.7.7^
o.' 2a^
,. +
a^. z.oo{t/<'
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.<xrndaa/ spi\ngi, @ch ol whbh tr.s o nadutue oi
?,fio.h? 9
5ooll po. in. wlai lle otr ie broughl io no€l,whol will hovo
bccll
lla gralael n6tomcnl oo ? 't1:rnric.co^tooc
ol thceeaw has
oD.orlw W thc .tvt^ 6pnnq '
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"$:1ne. Thc iurbine is @1, offdeal v.,k co""a
l.d la a sonc@la. \y'c \e sa'/, eficie.l. rvhol ls lhc pa.?ana.r+pul
i
in Kilowo+is
A.qa | tu||t ollpul
Sa)i.
P.'c. . 8Qh ' Fv
o 9+ ' hP/3s.1s
h p . 3 3 . 6 rh p
p.r!o. Onlpot . a3"61(01+6 Kw) '
zs,1 t<w.
14.1) \Nolar e^+crs a hydrcult:c .cacl,:o^ lu*;no w/ a \at<itff of 12
f\ pa" 6& q, barcs il 3n bwor wi.th a lato.ily of a fl F.rcd.. If
M.t&ab olwolar lloa lhrclgh +la +u,$.tneo&h,*co.d,.ahwtc
th6 ho.sopowdndulpul Aseunc th6 lu.b;nc ie w,/, effii,cnl .
Oi"cn :
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<n)
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<rliot\ 1,
/oo =3wf w(a)
W-laolb
!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)/<tt,o+,o)
o ' 0'333
ts+2..), A bo is lhrown ot
on ahglo e wih jhe narmot lo o s_
os chowo in f ,b p vsz ,L .et:ouno. ot
on oo,xte
-mlll,w:ll
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
$.4,) ns shown in Fb.p-16ag, o ao-tb bo| movng hor;zonlolty
to lho.nighl wilh.o vcto.'.,
g fi pd.ec, ca id.L obt;quatf
w/
.ol
o^30 )o barl.^movinqup_to lhc
lcfl ot 4' to tta tori:I/oiol ol ro
lt F,r sc. tl
co6ltr.,ont Of rE6l,tu'ioD ic 0,6, &t.'|rlioc
.lho.
lha
I
I
I
I
\ d,.€ct,bn6 tta wtoc\lyof qch bo| a,i" t ini,ai
.9:Y
t6por_
,'/tgtl
7 -iosnPt
statt c.l | 161l'
34,07 - 11,1
ii
1 6 , 1 1| r8 2 1 - a 4 d 1
'o
&Vr rm,{r ..riv;, r m,Vr',
..
i'
il
i
i
li
I
f -vo snet - h ot'
- '/, G,'2)(1 6)'
f - Ea s'"6o(1 d
f-2so7fi
1.6r28,07.3.',07f|.
x -\o c.sft
'1
\f - (sa@s6o)' = a
@e 28,6b (4 222)
x - 18.a11.
g
\vt - vor" 2o,
01)
,r' -(so!,'"Go)'.,hG2,2)(28
\ry - s'2 fl/s
= 26:1 l!/e
,,tr,t.,Fai6,z'
,x'- lon-1b,2tt'zs- 18,16'
:'
I
i
I
i
il
I
j
e - taer/'t.1^
0 . 6 - \ t 6 2^ / 2 6 . 3 1 t L E t s . L '
I
24,51st ',t6,1e-- v6zf
'ft2f " s,2fl/s
vs, ' [G-ia 2"
/-
I
I
I
ton1b!/:s
I
, +v,i, +*a{t
14(d - *(1ocd$
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 <h€lcd
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<l€,cdlile &, incjrcoad if lhe iniliot vctocily i6
b,
1o F eal ?
Ads 21 p<jr ccdl
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