2020HW5soln
pdf
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School
North Carolina State University *
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Course
208
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
6
Uploaded by Amonanny
MAE 208 Engineering Dynamics
Dr. Saul
March 16 2020
Total Possible Points: 30
Check your work using the informationprovided. Boxyour answer to the underlined question.
1.
The rod assembly is supported by ball-and-socket joints at A and B. At the instant shown, it is rotating
about the y axis with an angular velocity
ω
=5 rad/s and has an angular acceleration of
α
=8 rad/s
2
.
Determine the magnitudes of the velocity and a
c
c
e
l
e
r
a
t
i
o
n
of point C at this instant. Use the coordinate
system shown.
CHECK: v
c
= 2.5 m/s
SOLUTION: a
c
=13.1 m/s
2
- 2 -
K. Saul MAE 208
2.
If the slider block C is moving at v
c
=3 m/s, determine the angular velocity of BC and the
c
r
a
n
k
A
B
at
the instant shown.
CHECK:
ω
BC
=2.69 rad/s (this is a magnitude, be sure to specify the direction in your answers)
SOLUTION:
ω
AB
=4.39 rad/s
- 3 -
K. Saul MAE 208
3.
The angular velocity oflink AB is
ω
AB
= 4 rad/s. Determine the velocity of the collar at C and the
a
n
g
u
l
a
r
v
e
l
o
c
i
t
y
o
f
t
h
e
l
i
n
k
C
B
at the instant
θ
= 60
o
and
ϕ
= 45
o
. Link CB is horizontal at this instant.
CHECK: v
c
= 2.45 m/s
SOLUTION: w
CB
= 7.81 rad/s
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- 4 -
K. Saul MAE 208
4.
The anemometer measures the speed of the wind due to the rotation of the three cups. If during a 3-s
time period a wind gust causes the cups to have an angular velocity of
ω
= (2t
2
+ 3) rad/s where t is in
seconds, determine the speed of the cups when t = 2 s. W
h
a
t
i
s
t
h
e
t
o
t
a
l
d
i
s
t
a
n
c
e
t
r
a
v
e
l
e
d
b
y
e
a
c
h
c
u
p
d
u
r
i
n
g
t
h
e
3
-
s
t
i
m
e
p
e
r
i
o
d
,
a
n
d
t
h
e
a
n
g
u
l
a
r
a
c
c
e
l
e
r
a
t
i
o
n
o
f
t
h
e
c
u
p
s
w
h
e
n
t
=
2
s
?
Neglect the size of
the cups for the calculation.
CHECK: v = 16.5 ft/s
SOLUTION: s = 40.5 ft,
α
= 8 rad/s
2
- 5 -
K. Saul MAE 208
5.
Determine the angular accelerations oflink AB a
n
d
l
i
n
k
B
C
at the instant
θ
= 90
o
if the collar C has a
velocity of v
c
= 5 ft/s and deceleration of a
c
= 2 ft/s
2
.
CHECK:
α
AB
= -52.8 rad/s
2
SOLUTION:
α
BC
= 47.2 rad/s
2
- 6 -
K. Saul MAE 208
6.
While the swing bridge is closing with a constant rotation of 0.5 rad/s, a man runs along the roadway at
a constant speed of 4 ft/s
relative to the roadway
. Determine his velocity and a
c
c
e
l
e
r
a
t
i
o
n
at the
instant d = 10 ft.
CHECK: v
m
= 5
i
-4
j
ft/s
SOLUTION: a
m
= 4
i
+2.5
j
ft/s
2
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