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MER212: Rigid Body Mechanics
Spring 2014
Problem
Exam
II
Union College
Department of Mechanical Engineering
I (20pts): Identify the zero force members in each of the structures shown. For each
zero force member explain why they are zero force members.
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t
u6
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Atl
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te trrE rnEr\BEQ
co'ltnct*R Auo T$E,E
6F
15
cft
r;o
ePE
k*E
aN
E
Ec: 3as
Pe
1b.
tuf{rE n&rBE5t BEC|06E 064 EF
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' T$anr,
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EF
2.5 m
l
86:
16
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Nc l,rTO
MER212: Rigid Body Mechanics
Spring 2014
Exam
II
Union College
Department of Mechanical Engineering
PROBLEM 2 (40pts): Three couples are formed by the three pairs of equal and opposite forces.
h.q*8t +o.z16tl - o.r?ro3rl *
\.- 3 15.#N? | 23.?oNC - tl^cfr-|Nh
8or.r.
100 N$
30o
6e
212,1*ni
+-5"
u .u
= 3oq.r,6.ftal'l
=
m
= gt.gsN?_g1.8sN?
-/
WwrCcs
2X2.1
,.y
120 N'CO.?ottt +O.loltj)= 61.85r.ri
+
At.BsNf,
r',
Prdt.m2.t&
6
bbWhr& hhr,lft. Allilghlitld.
2a. Determine the resultant of the three couples,
8o'N.S,n.loo.,srh 3o" = 1!.68QN
8ou. s rnZoo"cos 30' t Z-3':oN.
\:
;'\
L
X
?o6^
Z1.3GN' 't
Bcr.l. Jrn
=
.iya}>
''* d.c.966'i -n.!.fr.
F
i
\
"!
\ xy''
,iYr.-4'
I
\,,
I
- 7s.1sNt -72,?,{t Nt r 13.6&Nn
= $6trr.(-o
,1sl8t- o.t1cz3n o.t?ton )
e= €*t
f -o.s
II or 0.866
h
[t
I
o oI
I
^
f,olt - C ( 0 ('o. s)l f *6' (1X0.86I'!^
6.
sf - o.gc6l
MER212: Rigid Body
Spring 2014
Mechanics
Exam
II
Union College
Department of Mechanical Engineering
Tueee frsE T*n6€ gsro: oF funrE*s TH+r frrw* coopesr
PErPrpof-6.uLr0rr N lile Puqve 'ivl!' Oar rn,
M =-( toON\ (aoor*)
+
(SoNX L€i.t\nn).(-o.sf - 0.9661,1
Lor.r.rn ?-6'??
= t?.xsN.rn
2d. Determine
PvAwst
t - (1zon) 8u.!) nn*[
= -(toou\(o.z-\t-(xzorl.(o z!Ir{ nJ
'
Ep
(Bouxo. 15ttt4a\'to,st -o.so6fi)
n.mf, '3?.Zx'm 3
(-o.q 677t-a.tsstf
-o,*oz!r)
to the fold along the diagonal
the component of the resultant perpendicular
surface.
TnE Ornzrrra. ?rnD&0Ecre
sfi
f,'f. = ('aon.mt-6.??x.mt - 3l.zu'*
= A6.11N'rr*)
Ts a
To-frll Fwfi fr/atuGTvrt- Brefrb',wL
1)' b.%6f
- o's'e')
b.W) + C'37,7x'^)(o.s) = lL,7q il'rn
2c. Determine the component of the resultant perpendicular to the fold along the horizontal
surface.
TUe CrxftEAIrsJ ?Ergg^,ofccrr4p T,1wia.D
Pt-cblrT+rE
*a*f,uta]*c
Ylln,o-n = (-Zox'ryr? - 6.?7il'r,n 3' JT.Zrrlr^1)
2b'
o
t
=
-
Es
ru
twe
t
Drneciuoxr
ME.o -- (-ZoH'nI -Gllx.mt- s?.2u.n.0)"(tI a
tsTHatwo*t(/..
6.??N.wr
Determine the component of the resultant
arong the fold.
Tre DroEab", oFrus T<t b
lt**g
- ?oN.rn
MER212: Rigid Body Mechanics
Spring 2014
Exam
[I
Union College
Department of Mechanical Engineering
PROBLEM 3 (40pts): The upper jaw D of the toggle press
slides with negligible friction resistance along the fixed vertical
column when a force F is applied as shown. This produces a
compressive force R exerted on the cylinder E.
3a. Using the diagram below, draw the free body diagram.
'e&.hh.a@id,
+r
I
}I
I
I
I
:
I
I
I
1
t{
Axt
eooN (-0.2 5 ffi t - o.16s1 3\
:
-51.?6Nt
- t9).aNf
f-
tt.*$x
t -x6.srrnn^t
-\t !
ru
tdtsaa e-o.rrsq
i)
I
{#Or}in
\
)-
F.fu.zw?,0,?6s9
i) \
f.Co.zssEt -o,%sqi)
-Nt
MER2I2: Rigid Body Mechanics
Exam
Spring 2014
II
Union College
Department of Mechanical Engineeriig
3b' calculate
the compressive force.R exerted
on the cylinder E and the force
supported by the
pin at A if a force F:200N
is appried to the handle at an angreof
0:75o.
Srgnrcr.E r,r.!r* $ DpnrE
zF,
AB
=o: - 5L,76N+ Ax + o.zsgE.Fe ?
o,zszz.Fs @
5E=o : - Lg3.lN r 0y -o?6sg' Fr3
=) Ar, rg3.zN + o.i661.fu
@
Srpcg 7$E
Qr,E5Trc
w B*wG Nuea
EMw*= e=
Ax= 51.%H
DE5 ,Vor r?eotrrg
(asom,r)(zoou)
&
m,o Ar
+
l-rr.ru,*-rrron^
f.zsas.;- .16si.is
5lp.e gC $
r,
Bg pErE\ylrr'+gD
\a l"e
o ' (200n)'(rcH) r [(2s,Srn,n].(o96g.E
) - (-o. f6r1n".)(0.28trs
o= (2sor'rm)(zo*)rsomh"Fe
_
1""
. Fs)
* E=- tjffiN=
r
-1&oN O
A Two foncg rtlrEl,,^l?ri
e=E:. Tlre rdAO
r4h.+rO
tt*i$.fi
rs
n"'rn
Frr.L'
irrr- Fbo' v€.#*. Fecccr.Bnrcrar
B+$i
Berntr,-
EE =o -- o.g6s?.E
ScBSrurr-rr^,
6
+ R =i2
rrvta TrrE 4rlcVe
Rr -o. 16si.(- IoooN I
R=
Ri urlrrc
= g6s.? N
ra
- O. 7Cs1 -F.
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
NAME:
As a student at Union College, I am part of a community that values intellectual effort, curiosity
and discovery. I understand that in order to truly claim my educational and academic
achievements, I am obligated to act with academic integrity. Therefore, I affirm that I carried out
the work on this exam with full academic honesty, and I rely on my fellow students to do the
same.
For this exam I understand that:
1. I must work alone in writing out the answers to this exam.
2. I cannot copy solutions to these problems from any person or resource.
3. I cannot use any electronic resources to assist me in the solution to the questions on this
exam except for a calculator.
4. I cannot discuss any part of this exam or discuss what was covered on this exam with
anyone else, post it in any electronic form, or communicate in any way that would
provide assistance to anyone as to what is being covered on the exam.
Signature:
Print Name:
Exam Date:
1
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
Problem 1 (20pts): Identify the zero force members in each of the structures shown. For each
zero force member explain why they are zero force members.
1a.
1b.
2
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
PROBLEM 2 (40pts): Three couples are formed by the three pairs of equal and opposite forces.
2a. Determine the resultant of the three couples.
3
MER212: Rigid Body Mechanics
Spring 2014
Exam II
4
Union College
Department of Mechanical Engineering
MER212: Rigid Body Mechanics
Spring 2014
Exam II
2b. Determine the component of the resultant along the fold.
5
Union College
Department of Mechanical Engineering
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
2c. Determine the component of the resultant perpendicular to the fold along the horizontal
surface.
6
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
2d. Determine the component of the resultant perpendicular to the fold along the diagonal
surface.
7
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
PROBLEM 3 (40pts): The upper jaw D of the toggle press
slides with negligible friction resistance along the fixed vertical
column when a force F is applied as shown. This produces a
compressive force R exerted on the cylinder E.
3a. Using the diagram below, draw the free body diagram.
8
MER212: Rigid Body Mechanics
Spring 2014
Exam II
Union College
Department of Mechanical Engineering
3b. Calculate the compressive force R exerted on the cylinder E and the force supported by the
pin at A if a force F=200N is applied to the handle at an angle of θ=75°.
9
MER212: Rigid Body Mechanics
Spring 2014
Exam II
10
Union College
Department of Mechanical Engineering

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