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Unformatted text preview: MEEN 221 —Fall 2006 Exam 1 October 12, 2006
Dr. McVay Section: Name: Student Number: "Aggies do not lie, cheat, or steal, nor do they tolerate those who do. " — Aggie Code of Honor By my signature below I pledge that my conduct on this exam is consistent in every way with the Aggie
Code of Honor: l
l Signature: 1. This exam consists of Five (5) problems that are egually weighted Some problems have multiple parts. Be sure to carefully read and properly analyze each question that is asked. Do not jump to unfounded conclusions, but also do not overlook or oversimplify problems eithﬁr. 4. Be sure to show all work, including sketches, Free Body Diagrams , and calc lations, and organize
your solution procedure as clearly and systematically as possible. 5. Work problems in the space provided on the exam' sheets. One extra space sheet is provided for
each problem. Clearly indicate continuation of the problem. Do not write on the back of any sheet. 9N 6. Work efficiently, neatly, and use pencil.
7. Clearly indicate final answers by enclosing in a "box" or place answer in Ex if box is provided.
Include any and all appropriate units.
8. No electronic device of any kind, except a hand calculator, is allowed.
9. Do not write your name on any other page of the exam.
Problem 1: I20
Problem 2: / 20
Problem 3: / 20
Problem 4: /20
Problem 5: / 20 TOTAL: mm:
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mm m Eon 2 8:0th 2 850 9: can < ESQ E :95 Em: m 9 8:0th m_ much 95 v6 95 $50 9:. .5505 E9w>m $65208
N>x m5 *0 E95 9: A 0 E63 Hm um: mwao. $95 9 8:936 39 m >5 8.533 m_ EQQS n. ooom < Amp—:2. ch N # Emioi Problem 3 (20 points) Consider the force and the couple shown in ﬁgure. Point B lies on line L that passes through point G and is parallel to the unit vector e = 2i +9 j —~3—k. All coordinates are 7 7 7
in meters. (a) Replace the force and the couple with an equivalent system at O. (b) What is the moment about the line OB? Draw a sketch to indicate the sense of this
moment. A (0, 4.5 ,0) " G(3,0,4) 5 kNm Problem 4 (20 points) Determine the reactions at support A and the tensibn in the cable
for the system shown below. Neglect the weight of the beam and assume the pulley at D
is frictionless. Include a free body diagram of the system. Sketch the resultant force at A. (5) 20 Pts. The ﬁgure (a) below shows a plate like structure suspended by 2 hinges and a
cable. The plate lies in the xy plane, i.e. z = 0, as shown in ﬁgure (b). The plate is bounded by the straight sides x=0 and yI = 3x and the curved side y2 = 4—x2. (i) 4 pts. Determine the area A of the plate. (ii) 4 pts. Determine the x coordinate xc of the centroid. (iii) 5 pts. Determine the y coordinate yc of the centroid. (iv) 1 Pts What is the x and y positions for the point of applicatiOn
of the weight vector W in the free body diagram for the plate? (v) 6 pts. Determine the x coordinate for the centroid of the composite area in
figure (c). TABLE 51 CENTROID LOCATIONS FOR A FEW COMMON LINE SEG ENTS AND AREAS Circular arc L=2ra
rsincr
IC?
0
Ic—O 2
2r
Y“="‘
’TT
21
yC‘W L=7rr
Ic=f
, _&
JL 7r Rectangular area A=l1l1
b
IC:?
II
Ilc=§ Tria nguJar area 17}:
“7
x .33
C‘ 3 _h
I/C"§ Triangular area bh
”“7
“a
Ac— 3 h
yc=§
212 v" ‘\ r/N
/ a CJ_I D Circular sector A=r2a t 21 sing
'C 3a
Ila=0 Quadrant of a circle 111'2
A=T
‘_4r
lC—3—7T
_4r
3/c3; Semicircular areh
‘D m
A _ 2
Kc = T
_ 1
VC 377
Quadrant of an ﬁllipse )‘
A : 711117, ‘I‘
4
4a AL I)
IC = — 32 _
371' T  ‘ I
_ 4b . H 1
yc — 377 ' a 
Parabolic spamdrel .” Quadrant of a parabola th
A=T'
_ _ 5!!
1.5?
_211
3/7—? ...
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 Spring '08
 McVay

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