Solutions to FE Exam “Dynamics” Review Problems;
Problems are Online at McGraw-Hill Website
Prepared by
Stephen F. Felszeghy
CSULA Emeritus Professor of Mechanical Engineering
Start the web page for the book: Beer and Johnston, Vector Mechanics for Engineers, Statics and Dynamics,
Ninth Edition, 2010, at: http://highered.mcgraw-hill.com/sites/0073529400/information_center_view0/ .
Look for the “Online Learning Center” box on the left. Click on the “Student Edition” link. Select a chapter from
the pull-down menu. My solutions, which you will find below, are for the online problems that are associated with
the following chapters and topics:
Chpt. 11:
Chpt. 12:
Chpt. 13:
Chpt. 14:
Chpt. 15:
Chpt. 16:
Chpt. 17:
Chpt. 19:
Kinematics of Particles
Kinetics of Particles: Newton's Second Law
Kinetics of Particles: Energy and Momentum Methods
Systems of Particles
Kinematics of Rigid Bodies
Plane Motion of Rigid Bodies: Forces and Accelerations
Plane Motion of Rigid Bodies: Energy and Momentum Methods
Mechanical Vibrations
Click on “FE Exam Review.”
Solve the problem, and select the answer from the multiple choices at the bottom. Click on the right-arrow to
continue to the next problem. This process ends when you click on the right-arrow for the third time. To try to
solve other problems from the same chapter, you will need to exit by clicking on, say, >Chapter XX> at the top,
and restart “FE Exam Review.” Now you will be presented with all new, or a mixture of old and new, problems.
After repeated trials, no new problems will appear.
As I mentioned in class, some of the online problem statements have errors in them, and some solutions and
answers are wrong. For this reason, I have prepared a separate document that lists the errors and corrections.
You can access this document at: http://www.calstatela.edu/faculty/sfelsze/FE_Exam_Review_rev2.pdf .
Although I shared the errors and corrections with McGraw-Hill, the company has not made any corrections on its
Website.
The online problems are not numbered, except for being associated with chapter numbers. For this reason, I
downloaded the online problems in no particular order, and numbered them consecutively in a decimal format,
XX.X, where XX refers to the chapter number, and X stands for the sequence number. All the online problems
numbered this way are included in the above “FE_Exam_Review_rev2.pdf” document under the heading: “Part 1,
FE Exam Review, Online Problems and Solutions.”
My own solutions, which you will find below, follow the problem numbering scheme I established above. I include
sketches in my solutions to allow you to identify the problems to which my solutions apply without necessarily
having to refer to Part 1 of the above “FE_Exam_Review_rev2.pdf” document.
I wish you all the best on your computer-based FE exam!
tA*i, /l
11.1
aJo
t
(,r-t
T-
s-
'
-/o4
--c
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(@LY,,d
t-t
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t f rad.
=
ra.(
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= Uo* N.t = -
u.=
J
A.f t,=
-.{
36"
-o '{f
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t.=
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?r = o-o (ca- e)t, = Zsob-'+t"fse'.04
11.3
u tlt
= l0 n/s
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fr
A
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es lin e
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a
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t /6os-
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lo n
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= /.zst
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uthen e-= C : ,^7/(1t
g
1
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ts
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rt aa/ B rez,a in "lxed
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11.4
.
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11.2
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11.5
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ft B fo a rrire a* C
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n qe-fn cby
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=
5'o
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'
iz
{s
12.1
:
KD
L!EtX_
4t= % +at = 5-4.?A{ t
,f=A ,rrhot= 5 = l.O/As
v.16 fiz-l'1pq
J
&=
-
sin 9o=
?,
lv-, Q.
I t s; n 3e"=.-1 ?OrC
4.2G5
f
@ 6!=1,o/Q r
: i{ = rrt o at=
/, / l.eosIl{iq)n
L =2u,{{a
Z G)(t.aa)Ans.,/
rN.sERr
12.2
I
k9
Q
5
r
FED
1,4d.
z. ra.= ir<a
-t_
ftcar'4{o= 4a
6L = (!,3t)eo=4{"
AFTE
R
@
12.3
Nole
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t
I'
On
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in- p/an e
atV
folee{
cocyl < ar<
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hdn
.
KD
- Ln&n L cp's Zoo
M - *g L sln Zoo -- - in (afL sinZd") L co= Zclo
y''l (r)p.rt)(2 s;" 7", - (r)Fa:24)*(2";, ze) (zeo"
=
"c)
N-tt
14?-/42-7
G ZU"
=
M = /42.7 A/- t?,
*
7
fr*
12.4
E:,"
KD
f = tma-= (4)(ts) = 6c A/
12.5
Nt.
'6a"
*
Ant'
a
*^5
FBD
ZF^ =C +
T:
12.6
It
,,L
bl
>-,
.// \,
a*
^g
T-
^geetCc'=
6c"
= lt-7LA/ #
co"r60"= (s-)(?.tt)c.p
Ann
,
ye
<-,C
fu&n
tng
FBD
C
KD
(a,ra
nqt fry")
7 F, = - lv1drJ -T sin 4 = -tud n er
TF^)J = O 4
Tc.o-€-kact = O @
Elintaa:fe- T- be*uzea O V @,
tam 0 : /b{ah
4J
o"LL sin G
a
?.8/ -ntsa
,a ad
c6"v=
_T=
6*4er
/
\ 6'
t
A = 56-0'
FBP
10 '7
12.7
KO
trv
m
.l/
7nC.n
,147
:zr
= hen
n
,Xor.g
7r
=
n€
f
4r-= (g
G4(q.tr)
An'"
rr= la"/ ^/c
=
13.I
cA"+. rs
13.1
=
4
Q = AT+ AV,
it" -:
=;l+^,f" !%;. ^,LtJu,'
AT=
Jl* {.t*+ *to
10.t1-+ rc (t);J
= 2L=l.tt
Z--\-t
AV^
d
AT=- 4V, +
:
= 5.s?
- rn,3
alf
=
a[
ut
+ - ^,,-j, ::,,oo=(r,")' ) o 17"*i) ( tl
S?"
//
2
0r=1,37/ %=0rl
=
4,3?f 4
C"rrt<rra*r'au ,f fota t
13.2
/
,44
@+
^ox
-2c0
-^
/0q +20.6 A
/{= -t5'+t4' @
_zee =
* 30o = /0%'* 2o4'
3oaAr3
cA'=
13.3
fa,
q,/
^u%'
i:?
'"
(tdyto)t- (zo)(-){)= )7orot+ zo.Tu'
= 3'-3r,*
e=?'-3'*0.,
{o- {s
lo - c- ts)
o-
en'/*** :
o ,t1
tust'3 = tuAo)'*
-+- //-
-ru-
ln ear
* {o0
- /6, t, + */+""
Cabte. /eng+h i.s caxsi" TAerefore-,
2xat frs* consf. = (ansf,
2zxn ^ - A*u
c
2*n- - xB
I'o
FBD
Fso
ry
na9
'l,
Mej
* ei^erg1i
Heg
lo"o* 2trAro
=
.<
I
A^axn
*BjAxu- F AxB = *^r*;
@
9^/tl;fute Q ,rto @, a',nat @ ,"Vt @rano(
add rer otl *in9 u?fut ron r
f
LI
W,zrk
@
**siz * Hsl)zxu = + Ar*n'+ ws4i;)
?" s i G ,t + "to) (t u? -- (,t u 8o) to'
G
i; = Z{eL, rA= t.os+ J"'
13.4
zsa n/s
--+:HA
rva/roo "f ht"/ l;n ear kle n e tt*u v
J'C
nn rn + ry{% = (^o+au)rr'
(o-os| G,so)
4/,= lnA !A
Coare
r
ha4+m6 =
4rt
:
/. tZt -A.
J
!-*
' la'oi{
fln"
;
)
3,5
13.5
SUV
b/s
ro
_>
Mn{A
tr*n
Ftt
I*{
Inrlial
?u
at^en/at
+
Co/lrb t on
Tnpotl se-r
O,7
Coa
=
= ab'- 'r' O
lo
wu{i
4*%
L_
L:T*
Frna/
l^op, en*a
terva,/ i*an a f to*^ / I to ea,
y/-\
c
r^
4a
e
nfup, :
-l
= tut rrq', t na, t2'
6u
(aooo) (t
") = 60oo 14'* lcoo
Or
/0 =
"A'u ?-u' @
Mn% + */q,
t7=€-o'
/+//C(@,
*b'= /o'z n/t
Af f, /y fnTtr
h e n*arz, e? - frr E ;
F 1jt = )* *tu'
/te'
p1o
f = wet/
AT
)2 /
13.6
= O m/s.
T"= tno, ttlhen a-=O"
2
X, = O.o2 rn., %
{t
l/naonpress9/
JT
'
Ax
-ftKz= ^,
{_ - (tc)U.st)
pas),t'_ten Of
sPrt n9
*
o. t
J/U/
L-
n- (rew)
C = AT+ AVo
C=
*-q:,*
4/ln.ri="-2 f
lO
L
<-Ant '
/s6-Lt/
= @co)(to.z)=
o"3
a^7
(ro)
+
lc"
= ??.1 x
trrs
*r.
lo-s 1.,
AVe
3, - r,) +Ll. (rJ-K,)
.j tot (o.o z'* rF.i'*
Anr.
Aa=2,087L
F.x r)(a.oz -?8.t x rr-s)
1r'=
-mLX 4.36 =+
m'Y
+
-S
ro-P)J
p
t3,n
13.7
TG tr,,rO
h,l
Tr.
lL- d-_att
?
n(r,',,*.rq
w(%),
I
= W,*,.
6a,
O= AT+ AVo
/
+
Zi* [(-;, J :
'
-tL
*9h' O
i-n [(';)-)* = ^7ot @
a^/ (q"), , a^/
Soire
C ano(
gabrTr lite- in Q-*,,(-r),
b7." belit^t t
"a
)4.14.1
t
L'h
=
Ac
U+fl-x
Lln-'-tlt
3w
3tn
= lp',
Yn
u
'e
fI
2, ru (za:) + I x 2m (t -)
6w.d= c())(t)= 3oM
t
t4.L
14.2
S're ;rttddle. fr.@
'/Z/
A
fue
*y
An.r
0.8?1 -{-
Ceater of nass : /.
,z/- / 4
7s
(u;)(v;),
Conserr, of *olal lin€dr
r'a
i
huur- %u,
= *rt'u*
^y-,
(o. i) (e) = o.t-u; * ( 0 {v
o = q, t'
%
taaa*t
--<=-Ant
en/uv' i
i
e=-ds '*-i
i = €r':aE'
+
€
Q * C.{x @ :>
qr' -4w
J
HA = 3*'Hyn'= 3x(t)(4) = l2 /"4'
r-r t
6 = l,{<t7' -
"
@
T-
<- An''
'
.
2j*{4,*
y--3 L + 2i-s/, w/,
m=tlg
I 4,s
14.3
H=
f=lg
f X pt4j
-o
s Jl
\\,1
to-z{l
I
t
3 z -r[
t [ ! (rc -/o) -j (- s6 .- t,t) + 4 k, *, ))
3Z{"5' + / 3a 4, -&A- thL
=
/4-1
14.4
.
5
-
=
L
-+t= 4+
,yi O = 4T-+ 4V,
S-. @ boltom +
c = {o - *^, (-r)'] * *r, [2-- iJ
-t.
z *KG)- r 0,8t{n
9'= %t
3'
F-
wtB
.S
14 14.5
Yv
Coi/r s r'o,
b"trl"u,'oi;LuP
/
ftns,
ms3
H
wR
4f,-_
vzo/z
5y.
s
ru"
=*odn
hrcr
mo%
--
!n,r{
L
fup[*
nf
K U.n
11,?-
Co//fsi"n belween ,u/
*y
twflo+ q;o
i
1r{, a\
'
n/rn
ffi a{n
E
D
^rny=
m*fi
'/v
hy.r=T= w.+{Y= T=t.{f
Z
Ant
<_
'
14.6
ZF = d^ /'o'
L-s -o--.,
-A/
At
ZF*=ffi;
= Q.125
.
(o"t-
N *ry
/1t J- . tf
LnP
I
l.J
?ou = /6
15.1
u
*AB
=O
G o.es;n=,1)
?(?
.f
farl
-f
9"= too *qo O
: a -[a.
) +/'a,
)
1-e/B/n
Ve/e/s
-B
eB = -fnm = ftol'(o"a) ' 6C r./s'
lsing ICE o7 BC : bu.=.*E = %e -_ (tqG.t-)
o"3 c,3
o,3 =2oC
to"/r), = o *1 il' = ed'{E* 6IVeJor diaTna'^ cl @:
= 268.3
9*ln
,t 6
(%tu)"= ttu{ c/B/n
3
s'
14\3
'Jz
6
N
15.2
536.7 b
53 s.'z
F.= VMS
\n
(&^,-)
L c:/F/e,= N-B<-. Bc
= $co
r,a--l
,a,
-^
Jt-
fr"'
-1
ft-- 4t*
frR
-TI l0cru -!I
r.!
oo.
A
n'r
'
15.3
r1
Usin3fc? o/ Ecr tur" =9pa,t d
v7
5e. bnfto2n of @
4O=
*AB 9r^4f
'uu' =
u^o R-o.t
'$79-r
fu.o = u*B ftE
g"e
o't
UV
.?r =
rEO
lft (a,2")
=
15.4
6ear A , Ca = Zoen
Gear E i
4s = {-p
ilA = Zo raoL/:
= 4 'od/s*
At poiot "f eng^g er-ent , dn G = NB .B
dA
NF = *uE= 4
eB = /G 4c_
15.5
2lz-x4f
E -rel
-
-+Lo_
(- %",
=
2-rz,
=
2tz=a;,(i"-!)
)"
(#,)
V' '
!)
e----/
&
2-rz-<r
E iael JL
-
Anr,
-<--
15.6
O = 4Eo
Qos='Y#*
4nu=,0 # -1.
Using tA e ZcE
&ut
"f
fs
BC
..
@t
tau)
&rPv = uotB= Cl o't
=
lE
lQo,l
= {r+e
,f e
= ilno'l= O,{
4rc
t-= Q.p
d.v
g.
=
CD
- (- r^e
O.g
o.L
= 98 + e4u
J
(e.)*" (t.),= (g)o o (es),* (tru)**
@")n = 40.; TD = F.s)'(o.zo)
=
l, Zr
-V
(t.7), A
^/s'
(a")r = &ns B = (to)(o.t4t4) = t.4l4 */t'
(ou),-- afi AB= cs)'(o,t+tt)
(o-/r)^= doriFe - (fl'(ol) = 2. f -/sVeetar ilingr^,A "f O t
o
(a.),
(o"/u)r
(a)"
r-
(o")t=tP-rw
- 3.ts{
v!
(ae),
=4
Cas)t
(a"/u)
"
t?
lx
Q,-=
-C-J
l'414
,/s-
ttT
- 4!- l,z{ j
Ans.
*(oq)n
'z {
,7,4
FBN
16.1
T-d
cL
mu9
GZ
Pto=
ln.Q-
w,drfr, * r,d + wLaLoZr+I.x
&,= 6,*
&.= TC.x
m-j7. = .fo &
(za)6o s)+ f"a;l =
GW)'a/;trJ**
3o
--r{ =f.,g?<
'}.
= /'c, si ra//sw,3 E, *
-&'')"
,
- h'IQ,- tu&.
"):O,r^
m,g - wz g = - 4ot - ruAz
J
os = 20 +2o * -g (0.s, t0.39 + t,< lo.s?)
o
?8t\
Ann'
=8.24N #
16.2
Pa=
U Jg
0'119s'/-A/6)
FBD
F
*) zrl"= zo&
(rz- F), =lnrudL
64 Haaalbaok)
FefuTY/z b {o,
zGt,!(?i_'"n/1, t)
d = zr(ep*rr/z-t).=
(zc)(o
kmr
kmr
: lCz.g ra-t(/s' -ea)@'zs)
Ant.
P=
A) = cJo:
dt ,
co =
o tuf t = 9= # 6a loua
*= o'{/o'r{
16.3
,/*= O'3i
\2"
nJ
-5 zNn
=*/6t7
&t2=
FBo
fn
=
KD
o<
"','
r3d=
@
rc
-j - 2d 0 / il = O u|<n Q = 4
-, tuo- /aa*rn\-t
2e
:4t@
@-@
J"*
Qr =Znx C
Fo = '/u'F G)
@+(e:
ar/r,t
@
ex
)I
l- = L6&
6
:
16.4
=
,/*r
31"4 lV
\'ra 1
ZFV =
(
TI
-its) (o,ss)'4 n
(o. ss) (o .s
A
.!--
FBD
#
:
s)
nr,
KD
C+ N=^9 C
f= k^a @
F=,4tM 6'
FropO,@(6,
d-=
*ftll
= Q-4(?"st)
= 3.q, lr.
#
A nu.
16.5
.V
')
[s
FBD
t<P
rug
c
&=
r,/
t ZM"= tnar*fe*
tn g l. S;n 9on =
cL=
mar + LFar"*
2q sin 3o
"'
Z
(?,gt) s,n36
)
& = 3.Zz m/s16.6
A
+
KO
G
*
!na-L+ ^=iS
@-A ^ 4, n/j-,^u= tAX- 7*g = ?
/O/4 = Z.e N *-W
=
L
Q= z
-o<
fi 4 *mg=-tAaQ2
l -J
knA * + L-.,x
Ze
yt4a
?zMa=
,oL
\'/ L = w&+r-Lr^L" 4
L
tnq
,l 2 =
nt'
J^x
e
lnA,
qE
12
o
chp*.t7
Feo
sl
I
)7"17.1
KD
d
{
\ut
+
fr'
rnl
A
ZFl:
i'd- =
G
mq
F- ta9 = ha.
F= ha * hq
= tffi(e { tqooo = /1o/q il
ZMo = rn*
T-Fr=fon
^
T = Fr + 4 o/. 1- - rdius of gTraho,
= (, otr)(o. s) * @,{)?o.)C,)/o.r
= 57O? A/. t^
P
l7,L
17.2
A bo,re
=
g -- f,7o?
W
Anc'
P= /'?C'Lt// n
= Patun,
--
T-at =
T-
f= nj
P= F<r
fig^"u
= t og-'- (tCI,o",e)(#) = ).67 -l-til 4
Comserra*r?h of angca/a.r t'r1e,+-ten*otp, a-beu,/ O:
17"3
17.3
witr/= (^a * mn) @ t)d
(o.o ss)(scc) = (soa" ozr)
wA
t figu{e .'""6:2;
' C'onseti of
: dr*rtng merten/,-n
inpacf./
Sa.,)
(/) = O"O4Z0 ..//s
E>--+
1f
17.4
('O,
u)t=
&-)
=
<
Aot'
t,ffiw',| 4z (nrdqL
i
-
(,:c;30")
'+
Z
-Z? rwLls
lr1o,o3{)tr= (3zr.oii1@,r*)
:} nt -
/6,32q
^/,
<- Ans"
17,{
17.5
i\
I
I
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