Use single integration (use a thin, long vertical slice as your integration element) to determine the x and y coordinates of the centroid of the plane region shown. y (mm) xy = 3175 x (mm) 102 mm 25 mm 127 mm

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Use single integration (use a thin, long vertical slice
as your integration element) to determine the x and y coordinates of the
centroid of the plane region shown.
y (mm)
xy = 3175
x (mm)
102 mm
25 mm
127 mm
Transcribed Image Text:Use single integration (use a thin, long vertical slice as your integration element) to determine the x and y coordinates of the centroid of the plane region shown. y (mm) xy = 3175 x (mm) 102 mm 25 mm 127 mm
Expert Solution
Step 1 Area of the whole region.

XY = 3175

Y = 3175 / X

Taking a vertical strip of area dA,

dA = Y . dx

dA = [ 3175 / X ] dx

Area = dA

= 25120 3175X dx

= 3175 [ ln (120) - ln (25) ]

Area= 4980.355 mm2

Step 2 Y coordinate of the centroid.

The centroid coordinates are given by,

y¯ =  Y dAAx¯ =  X dAA

For y coordinate,

y¯ = Y dAA

y¯ = 2512031752X3175XdxA

= (3175)221X25120A

= - 5040312.5  1120 - 125A= 159609.89584980.335

y¯ = 32.04 mm

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