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Find the centroid of the following cross-sections and planes. 6.1 HF. opiGIN

Find the centroid of the following cross-sections and planes. 6.1 HF. opiGIN

Elements Of Electromagnetics
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
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Find the centroid of the following cross-sections and planes for figures 6.1 and 6.2

### Finding the Centroid of Cross-Sections This section focuses on determining the centroid of given cross-sections and planes. Below are the details of the cross-sections for which the centroid needs to be determined. #### 6.1 **Diagram Explanation:** - The cross-section is a composite shape consisting of a rectangular block with a slot cut out. - The top part of the shape is a rectangle with: - Width: 10 inches - Height: 2 inches - Below the top rectangle, there's a slot with: - Width: 3 inches - Height: 6 inches - Positioned centrally within the width of the rectangle (2 inches from each side) - The overall height of the whole shape is 8 inches. **Key Dimensions:** - Total width: 10 inches - Total height: 8 inches - Slot width: 3 inches - Slot height: 6 inches - Distance from the edge to the slot: 2 inches (on each side) #### 6.2 **Diagram Explanation:** - The cross-section is a composite shape which consists of a trapezoid with a rectangular slot within it. - The top part of the trapezoid is: - Base: 4 inches (upper base) - Positioned 1 inch from the shorter side of the overall shape - The overall shape converges from a: - Width of 11 inches (bottom width) - Inclining sides to a width of 4 inches at the top - Both inclined sides converge at an angle, giving a slant height of 2 inches - Inside the trapezoid is a rectangular slot with dimensions: - Width: 1 inch - Height: 2 inches - Positioned centrally, 1 inch from the top edge. **Key Dimensions:** - Bottom width: 11 inches - Top width (trapezoid upper base): 4 inches - Trapezoid height: Not specified directly, bottom line height is 9 inches from ground level - Rectangular slot width: 1 inch - Rectangular slot height: 2 inches - Rectangular slot horizontal position: Central with 1 inch from the top Understanding how to calculate the centroid for these cross-sections requires breaking down the shapes into fundamental geometric sections (rectangles and slots), calculating individual centroids, and then using
Transcribed Image Text:### Finding the Centroid of Cross-Sections This section focuses on determining the centroid of given cross-sections and planes. Below are the details of the cross-sections for which the centroid needs to be determined. #### 6.1 **Diagram Explanation:** - The cross-section is a composite shape consisting of a rectangular block with a slot cut out. - The top part of the shape is a rectangle with: - Width: 10 inches - Height: 2 inches - Below the top rectangle, there's a slot with: - Width: 3 inches - Height: 6 inches - Positioned centrally within the width of the rectangle (2 inches from each side) - The overall height of the whole shape is 8 inches. **Key Dimensions:** - Total width: 10 inches - Total height: 8 inches - Slot width: 3 inches - Slot height: 6 inches - Distance from the edge to the slot: 2 inches (on each side) #### 6.2 **Diagram Explanation:** - The cross-section is a composite shape which consists of a trapezoid with a rectangular slot within it. - The top part of the trapezoid is: - Base: 4 inches (upper base) - Positioned 1 inch from the shorter side of the overall shape - The overall shape converges from a: - Width of 11 inches (bottom width) - Inclining sides to a width of 4 inches at the top - Both inclined sides converge at an angle, giving a slant height of 2 inches - Inside the trapezoid is a rectangular slot with dimensions: - Width: 1 inch - Height: 2 inches - Positioned centrally, 1 inch from the top edge. **Key Dimensions:** - Bottom width: 11 inches - Top width (trapezoid upper base): 4 inches - Trapezoid height: Not specified directly, bottom line height is 9 inches from ground level - Rectangular slot width: 1 inch - Rectangular slot height: 2 inches - Rectangular slot horizontal position: Central with 1 inch from the top Understanding how to calculate the centroid for these cross-sections requires breaking down the shapes into fundamental geometric sections (rectangles and slots), calculating individual centroids, and then using
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