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me270 e1 fa2013 ans.pdfME 270 – Fall 2013 Exam
me270_e1_fa2013_ans.pdfME 270 – Fall 2013 Exam
me270 e1 fa2013 ans.pdfME 270 – Fa...
me270_e1_fa2013_ans.pdfME 270 – Fall 2013 Exam
Page 4
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
1 (d)
Suppose that an area is defined as shown in the following diagram between
x
= 0 and
x
= 2 ft.
(i) Find the area of under the curve, A.
(ii) Determine the centroid of the area in the
x
direction,
X
.
A
= ________________________
(2 points)
X
=
________________________
(3 points)
Page 5
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
PROBLEM 2. (20 points)
GIVEN:
A hot air balloon is suspended 3 feet above the ground,
and is held in place by three cables, attached at ring A.
The balloon exerts an upward force on ring A.
Cable AD
runs parallel to the xaxis, and has a tension of 84.0 lbs.
FIND:
a)
On the axes provided, draw a free body diagram of ring A.
(4 pts)
b)
Write vector expressions for the forces in cables AB and AC
in terms of their unknown magnitudes and their known unit
vectors.
(6 pts)
c)
Using your equations of static equilibrium, determine the magnitude of the forces in cables AB and
AC, and the magnitude of the upward force from the balloon.
(10 pts)
Page 6
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
Page 7
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
PROBLEM 3.
(20 points)
GIVEN:
Bar ABC is loaded with four forces as shown and
is held in static equilibrium by a fixed support at A
(Note
–
This is not a pin joint at support A.).
FIND:
a)
On the artwork provided, complete the free body diagram. (4 pts)
b)
The two 200N forces shown form a forcecouple.
Determine the magnitude and direction of the
forcecouple in vector form.
A
B
C
b)
C
M
=
3 pts
A
B
C
1 m
Page 8
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
c)
Use your equations of static equilibrium to determine the magnitudes of the reactions at the fixed
support at A.
d)
If the length of bar segment BC has shortened, what effect would this have on the reactions at the
fixed support at A?
(Increase, Decrease or Remain the Same)
Circle One
(2 pts)
c)
x
y
A
(3 pts)
(3 pts)
A
=
A
=
M=
(5 pts)
Page 9
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
ME 270 Exam 1 Equations
Distributed Loads
L
eq
0
F
=
w
x
dx
L
eq
0
xF
=
x w
x dx
Centroids
c
x dA
x =
dA
c
dA
y =
dA
y
ci
i
i
i
i
xA
x =
A
ci
i
i
i
i
yA
y =
A
In 3D,
ci
i
i
i
i
xV
x =
V
Centers of Mass
cm
x
ρdA
x =
ρdA
cm
y
ρdA
y =
ρdA
cmi
i
i
i
i
i
i
x
ρA
x =
ρA
cmi
i
i
i
i
i
i
y
ρA
y =
ρA
Page 10
ME 270
–
Fall 2013 Exam 1
NAME (Last, First): ________________________________
Solutions for Exam 1
1A.
F =
200 i + 346.4j
N
OA
r
=
4 i + 5j + 3k
ft
O
M
=
360 i  300j + 20k
ftlb
1B.
AB
u
= 0.635 i + 0.762j + 0.127k
AB
F
= 7.803 kN
1C.
F = 4400N
X = 3.45 m
1D.
2
8
A =
ft
3
5
X =
ft
4
2A.
AB
AB
4
3
ˆ
ˆ
T
= T

j 
k
5
5
AC
AC
2
2
1
ˆ
ˆ
ˆ
T
= T
i +
j 
k
3
3
3
2B.
AC
T
= 126 lb
AB
T
= 105 lb
2C.
B
F
= 105 lb
3A. FBD
3B.
C
M
= 200k Nm
3C.
X
A
= 300 N
y
A
= 350 N
A
M
= 37.5 Nm
3D. Remain the same
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