1. Problem 5.155 y For the machine element shown, locate the z coordinatex
0.75 in z
1 in
2 in
3 in
r = 1.25 in
For the machine element
shown, locate the z coordinate
of the center of gravity.

2. X S V = S x V Y S V = S y V Z S V = S z V
0.75 in z
1 in
2 in
3 in
r = 1.25 in
Problem
Solving Problems on Your Own
For the machine element
shown, locate the z coordinate
of the center of gravity.
Determine the center of gravity of composite body. 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
X S V = S x V Y S V = S y V Z S V = S z V
where X, Y, Z and x, y, z are the coordinates of the centroid of the body and the components, respectively.

3. Determine the center of gravity of composite body.x
0.75 in z
1 in
2 in
3 in
r = 1.25 in
Problem Solution
Determine the center of gravity
of composite body.
First assume that the machine
element is homogeneous so
that its center of gravity will
coincide with the centroid of
the corresponding volume. y x z I II
III IV V
Divide the body into five common shapes.

4. II (p/2)(2)2 (0.75) = 4.71 7+ [(4)(2)/(3p)] = 7.85 37.0 y x z I II
III IV V y x
0.75 in z
1 in
2 in
3 in
r = 1.25 in
V, in3 z, in z V, in4
I (4)(0.75)(7) =
II (p/2)(2)2 (0.75) = [(4)(2)/(3p)] =
III p(1.25)2 (0.75)=
IV (1)(2)(4) =
V (p/2)(1.25)2 (1) = S
Z S V = S z V : Z (27.6 in3 ) = 95.8 in Z = 3.5 in