SAMPLE PROBLEM 5/6 12" Locate the centroid of the shaded area. 4" Solution. The composite area is divided into the four elementary shapes shown in the lower figure. The centroid locations of all these shapes may be ob- tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) are taken as negative in the following table: 4" 3" 12" 5" 2" yA in 3 xA PART in.? in. in. in.3 ont 1 120 6. 720 600 100 -18 30 14 10/3 420 -14.14 1.273 -84.8 4 -8 12 4 -96 -32 ТОТTALS 127.9 959 650 The area counterparts to Eqs. 5/7 are now applied and yield 3 EAx X = 959 = 7.50 in. 127.9 X = blov Ans. ΣΑ ΣΑ 650 Y = ΣΑ Y = 127.9 = 5.08 in. Ans. SAMPLE PROBLEM 5/7 Anprovimato the r cOordinate of the volume centroid of a body whogo longth
SAMPLE PROBLEM 5/6 12" Locate the centroid of the shaded area. 4" Solution. The composite area is divided into the four elementary shapes shown in the lower figure. The centroid locations of all these shapes may be ob- tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) are taken as negative in the following table: 4" 3" 12" 5" 2" yA in 3 xA PART in.? in. in. in.3 ont 1 120 6. 720 600 100 -18 30 14 10/3 420 -14.14 1.273 -84.8 4 -8 12 4 -96 -32 ТОТTALS 127.9 959 650 The area counterparts to Eqs. 5/7 are now applied and yield 3 EAx X = 959 = 7.50 in. 127.9 X = blov Ans. ΣΑ ΣΑ 650 Y = ΣΑ Y = 127.9 = 5.08 in. Ans. SAMPLE PROBLEM 5/7 Anprovimato the r cOordinate of the volume centroid of a body whogo longth
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
100%
a)
Remove the semi-circular void from the composite area.
The x-coordinate of the centroid of the composite area is _____ in.
b)
Remove the semi-circular void from the composite area.
The y-coordinate of the centroid of the composite area is _____ in.
c)
Remove the semi-circular void and the rectangular void from the composite area.
The x-coordinate of the centroid of the composite area is _____ in.
d)
Remove the semi-circular void and the rectangular void from the composite area.
The y-coordinate of the centroid of the composite area is _____ in.
![function of y and z does not affect X.
256 Chapter 5 Distributed Forces
SAMPLE PROBLEM 5/6
Locate the centroid of the shaded area.
12"
4"
Solution. The composite area is divided into the four elementary shapes
shown in the lower figure. The centroid locations of all these shapes may be ob-
tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) are
taken as negative in the following table:
4"
3"
2"
Solution
taken as a
y that th
The n
3
5"-
ements sh
A
2" 2"
yA
in 3
xA
PART
in.2
in.
in.
in.3
1
120
720
600
30
planation.
14
10/3
420
100
3
-14.14
1
1.273
-84.8
-18
4
-8
12
4
-96
-32
2
ТОTALS
127.9
959
650
For Part
mass is or
The area counterparts to Eqs. 5/7 are now applied and yield
3
[x-]
ΣΑΤ
ATes beco
X= 959
127.9
ΣΑ
= 7.50 in.
Ans.
EAy
Y =
ΣΑ
650
Y =
127.9
= 5.08 in.
They- ane
iant by i
the form
Ans.
SAMPLE PROBLEM 5/7
PART
Approximate the x-coordinate of the volume centroid of a body whose length
is 1 m and whose cross-sectional area varies with x as shown in the figure.
6.
4
Solution. The body is divided into five sections. For each section, the average
area, volume, and centroid location are determined and entered in the following
table:
1
TOTALS
0.
0.2
0.4
1.0
Aav
0.6
x, m
Volume V
0.8
INTERVAL
m
m3
Vx
0-0.2
3
0.2-0.4
0.6
0.1
4.5
0.90
0.060
0.4-0.6
5.2
0.3
1.04
0.270
0.6-0.8
5.2
0.5
0.8-1.0
1.04
0.520
4.5
0.7
0.90
0.728
0.9
ТОТALS
0.810
4.48
2.388
X =
EVI
X =
4.48
Helpful Hint
2.388
EV
= 0.533 m
%3D
Ans.
1 Note that the shape of the body as a
the borninor
2611.
A, m2
18 E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fa7ac50-e43d-4267-956c-145cd19bd43c%2Fa4a9f0e0-a3a0-478e-b01f-ba058316a604%2Fi0poa6k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:function of y and z does not affect X.
256 Chapter 5 Distributed Forces
SAMPLE PROBLEM 5/6
Locate the centroid of the shaded area.
12"
4"
Solution. The composite area is divided into the four elementary shapes
shown in the lower figure. The centroid locations of all these shapes may be ob-
tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) are
taken as negative in the following table:
4"
3"
2"
Solution
taken as a
y that th
The n
3
5"-
ements sh
A
2" 2"
yA
in 3
xA
PART
in.2
in.
in.
in.3
1
120
720
600
30
planation.
14
10/3
420
100
3
-14.14
1
1.273
-84.8
-18
4
-8
12
4
-96
-32
2
ТОTALS
127.9
959
650
For Part
mass is or
The area counterparts to Eqs. 5/7 are now applied and yield
3
[x-]
ΣΑΤ
ATes beco
X= 959
127.9
ΣΑ
= 7.50 in.
Ans.
EAy
Y =
ΣΑ
650
Y =
127.9
= 5.08 in.
They- ane
iant by i
the form
Ans.
SAMPLE PROBLEM 5/7
PART
Approximate the x-coordinate of the volume centroid of a body whose length
is 1 m and whose cross-sectional area varies with x as shown in the figure.
6.
4
Solution. The body is divided into five sections. For each section, the average
area, volume, and centroid location are determined and entered in the following
table:
1
TOTALS
0.
0.2
0.4
1.0
Aav
0.6
x, m
Volume V
0.8
INTERVAL
m
m3
Vx
0-0.2
3
0.2-0.4
0.6
0.1
4.5
0.90
0.060
0.4-0.6
5.2
0.3
1.04
0.270
0.6-0.8
5.2
0.5
0.8-1.0
1.04
0.520
4.5
0.7
0.90
0.728
0.9
ТОТALS
0.810
4.48
2.388
X =
EVI
X =
4.48
Helpful Hint
2.388
EV
= 0.533 m
%3D
Ans.
1 Note that the shape of the body as a
the borninor
2611.
A, m2
18 E
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