PROBLEM 5.2
Locate the centroid of the plane area shown.
SOLUTION
For the area as a whole, it can be concluded by observation that
Y =
2
(72 mm)
3
or Y = 48.0 mm
Dimensions in mm
A, mm 2
x , mm
x A, mm3
1
1
× 30 × 72 = 1080
2
20
21,600
2
1
× 48 × 72 = 1728
2
46
79,488
Σ
Then X A = Σ x A
2808
101,088
X (2808) = 101, 088
or X = 36.0 mm
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
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554
PROBLEM 5.6
Locate the centroid of the plane area shown.
SOLUTION
Then
A, in 2
x , in.
y , in.
x A, in 3
y A, in 3
1
14 × 20 = 280
7
10
1960
2800
2
−π (4) 2 = −16π
6
12
–301.59
–603.19
Σ
229.73
1658.41
2196.8
X=
Σ xA 1658.41
=
ΣA
229.73
X = 7.22 in.
Y =
Σ y A 2196.8
=
Σ A 229.73
Y = 9.56 in.
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
558
PROBLEM 5.26
A thin, homogeneous wire is bent to form the perimeter of the figure
indicated. Locate the center of gravity of the wire figure thus formed.
SOLUTION
Then
y , in.
xL, in 2
yL, in 2
3
80.498
40.249
7.5
36
22.5
9
9
54
54.0
3
6
7.5
18
22.5
5
6
3
6
18
36.0
6
6
0
3
0
18.0
Σ
37.416
206.50
193.249
L, in.
x , in.
1
122 + 62 = 13.4164
6
2
3
12
3
6
4
X ΣL = Σx L
Y ΣL =Σ y L
X (37.416) = 206.50
Y (37.416) = 193.249
X = 5.52 in.
Y = 5.16 in.
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
579