Use single integration (use a thin, long vertical sliceas your integration element) to determine the x and y coordinates of thecentroid of the plane region shown.y (mm)xy = 3175x (mm)102 mm25 mm127 mm

Answered: Use single integration (use a thin,…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

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 = $\int d A$

$= \int_{25}^{120} \frac{3175}{X} d x$

$= 3175 [\ln (120) - \ln (25)]$

Area $= 4980.355 m m^{2}$

Step 2 Y coordinate of the centroid.

The centroid coordinates are given by,

$\bar{y} = \frac{\int Y d A}{A} \bar{x} = \frac{\int X d A}{A}$

For y coordinate,

$\bar{y} = \frac{\int Y d A}{A}$

$\bar{y} = \frac{\int_{25}^{120} \frac{3175}{2 X} [\frac{3175}{X} d x]}{A}$

$= \frac{\frac{{(3175)}^{2}}{2} {[\frac{1}{X}]}_{25}^{120}}{A}$

$= \frac{- 5040312.5 [\frac{1}{120} - \frac{1}{25}]}{A} = \frac{159609.8958}{4980.335}$

$\bar{y} = 32.04 m m$

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19:49 wamap.org Compute the coordinates of the centroid (x, y) of the area shown. Also compute the area moment of intertia about the x' and y' axes with origin at the centroid. ул C 2013 Michael Swanbom cc 130 f a Variable Value 38 cm 18 cm 74 cm a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. a b C The x coordinate of the centroid is x cm. The y coordinate of the centroid is y The moment of inertia about the x' axis going through the centroid is I' cm4. cm. The moment of inertia about the y' axis going through the centroid is I' cm4.
Find Ix and Iy for the L-shaped cross-section shown.

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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