ME 270 – Spring 2021 Exam 1 PM
NAME (Last, First): _____________________________
(Please PRINT)
PUID #: _________________
PROBLEM 1 (20 points)
1A. Three forces act on a L-beam as shown in the following
diagram (it is not an equilibrium problem). Replace these
three forces
by an equivalent force-couple
system acting at
O where F is the equivalent force and M is the equivalent
moment written in vector notation. (5 pts)
F = ______________________________N (3 pts)
M = _________________________ N-m (2 pts)
1B. As shown in the following diagram, 4 forces are
concurrent at point O. For the equilibrium of the truss,
determine the magnitudes of T and F. (5 pts)
T = ______________________________kN (3 pts)
ME 270 Exam 1 PM – Spring 2021
F = _____________________________ kN (2 pts)
Page 2
ME 270 – Spring 2021 Exam 1 PM
NAME (Last, First): _____________________________
(Please PRINT)
PUID #: _________________
1C. Using the composite method, find the area (A) and the ycentroid of (yc) of the shaded trapezoidal area. (5 pts)
A = ________________________units2 (2 pts)
(yc)
= _____________________________ units (3 pts)
1D. Using the method of integration, find the area (A) and the xcentroid (xc) of the shaded area. (5 pts)
A = ________________________units2 (2 pts)
ME 270 Exam 1 PM – Spring 2021
(xc)
Page 3
= ___________________________units (3 pts)
ME 270 – Spring 2021 Exam 1 PM
NAME (Last, First): _____________________________
(Please PRINT)
PUID #: _________________
PROBLEM 3. (20 points)
GIVEN: A pole of negligible mass is held in
static equilibrium by two cables (AB and AC)
that are attached to the wall at B and C, and a
ball-and-socket support at point D. A 400N
load is applied to the pole as shown.
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a) Complete the free body diagram of the pole using the artwork below. (2 pts)
6
6
789
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=
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B
CD
E
ME 270 Exam 1 PM – Spring 2021
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Page 8
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ME 270 – Spring 2021 Exam 1 PM
NAME (Last, First): _____________________________
(Please PRINT)
PUID #: _________________
b) Write expressions for tension vectors AB and AC acting on the pole using their unknown
magnitudes and known unit vectors. (5 pts)
787
R8I
7:F
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H IJJ !
:
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H4#14))Q%)QM0
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4
MN$
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4
4
$N$
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4
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I 0 7:-
K
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OP
1S+
,
#QS1
4
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)3QM 0
78>
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789
3MQ$ 0
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1 T
,
1)7
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1)
6]
$+, = .(
0⃗+, . ∗ [( __________)
$N
3M
T
,̂ + (____________)
4. + (___________)0
(2 pts)
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MN
)3
:0 ]
$78 = .(
0⃗+9 . * [( __________)
O
T
,̂+ (____________)
4. + (___________)
(2 pts)
O
13
IF
Applied Load= 400 N * [( _______)
,̂+ (________
)4. + (_________)
06 ]
(1 pt)
4
4
:
:
:
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3**+
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4
2
c) Determine the magnitude of the tension in each of the cables AB and AC. (8 pts)
,.(
#M
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4
4
> R': W 7I! 0
,
MN1
7:- >4
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H #1 0
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W
,
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H #7 0
%
H
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4
H
QEM3+ 0 7:4
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3
4
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E
$N$
3EN$
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4
I
789
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4
4
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QES1
4
4
3**+
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> R.':
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,
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7:-
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> 1#S 0
4
1#S
[F]
(4 pts)
0⃗78 . =
.C
##S
[F]
(4 pts)
Page 9
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4##SV^
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U
0⃗7I . =
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ME 270 Exam 1 PM – Spring 2021
Z
ME 270 – Spring 2021 Exam 1 PM
NAME (Last, First): _____________________________
(Please PRINT)
PUID #: _________________
d) At point D, determine the reactions at D and express as a vector. (4 points)
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4
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,
4
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:
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.
Page 10
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O
O
0D
0⃗ = [( __________)
,̂ + (____________.̂
+ (___________)
ME 270 Exam 1 PM – Spring 2021
MN
(6 pts)
0
