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Problem 5.155
y
2 in
3 in
2 in
1 in
r = 1.25 in
x
z
0.75 in
2 in
2 in
r = 1.25 in
For the machine element
shown, locate the z coordinate
of the center of gravity.
Problem 5.155
y
2 in
2 in
1 in
3 in
Solving Problems on Your Own
r = 1.25 in
x
z
For the machine element
shown, locate the z coordinate
of the center of gravity.
Determine the center of
gravity of composite body.
2 in
r = 1.25 in
2 in
For a homogeneous body
the center of gravity coincides
with the centroid of its volume. For this case the center of gravity
can be determined by
0.75 in
XSV = SxV
YSV = SyV
ZSV = SzV
where X, Y, Z and x, y, z are the coordinates of the centroid of the
body and the components, respectively.
Problem 5.155 Solution
y
2 in
2 in
1 in
3 in
Determine the center of gravity
of composite body.
r = 1.25 in
First assume that the machine
element is homogeneous so
that its center of gravity will
coincide with the centroid of
the corresponding volume.
x
z
0.75 in
2 in
2 in
r = 1.25 in
y
V
Divide the body into
five common shapes.
III
II
z
IV
I
x
y
y
V
2 in
IV
I
III
2 in 1 in
3 in
r = 1.25 in
x
II
x
z
z
0.75 in
2 in
2 in
I
II
III
IV
V
S
V, in3
(4)(0.75)(7) = 21
(p/2)(2)2 (0.75) = 4.71
-p(1.25)2 (0.75)= -3.68
(1)(2)(4) = 8
-(p/2)(1.25)2 (1) = -2.45
r = 1.25 in
z, in.
3.5
7+ [(4)(2)/(3p)] = 7.85
7
2
2
27.6
Z S V = S z V : Z (27.6 in3 ) = 95.8 in4
z V, in4
73.5
37.0
-25.8
16
-4.9
95.8
Z = 3.5 in