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A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its center of mass. Often the centroid of a complex composite body is found by, first, cutting the body into regular shaped segments, and then by calculating the weighted average of the segments' centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a = 1.50 ft, where a is the diameter of the semi-circle,b = 3.74 ft, and c = 2.45 ft. A hole with diameter d = 0.700 ft is centered at (1.17, 0.750). Figure b X 1 of 2 >

A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its center of mass. Often the centroid of a complex composite body is found by, first, cutting the body into regular shaped segments, and then by calculating the weighted average of the segments' centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a = 1.50 ft, where a is the diameter of the semi-circle,b = 3.74 ft, and c = 2.45 ft. A hole with diameter d = 0.700 ft is centered at (1.17, 0.750). Figure b X 1 of 2 >

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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**Understanding Centroids in Composite Bodies** A centroid represents the geometric center of an object. In uniformly composed objects, the centroid also functions as the center of mass. To determine the centroid of a complex composite body, one typically cuts the body into regularly shaped segments, and then calculates the weighted average of these segments' centroids. In this example, we examine an object made from a uniform piece of sheet metal. The dimensions are as follows: - \( a = 1.50 \, \text{ft} \): the diameter of the semi-circle. - \( b = 3.74 \, \text{ft} \) - \( c = 2.45 \, \text{ft} \) Additionally, there is a hole with a diameter of \( d = 0.700 \, \text{ft} \) centered at coordinates \( (1.17, 0.750) \). **Diagram Explanation** The accompanying figure illustrates the structure: - The \( x \)- and \( y \)-axes are labeled, establishing a coordinate system. - The semi-circle on the left has a diameter \( a \), and is part of the composite shape. - The rectangle lies along the \( x \)-axis with a length of \( b \). - A triangle with hypotenuse \( c \) forms the right side. - A circular hole with diameter \( d \) is included, positioned according to its given center coordinates. This configuration aids in understanding how to calculate the centroid of the overall shape by considering the individual elements and their respective centroids.
Transcribed Image Text:**Understanding Centroids in Composite Bodies** A centroid represents the geometric center of an object. In uniformly composed objects, the centroid also functions as the center of mass. To determine the centroid of a complex composite body, one typically cuts the body into regularly shaped segments, and then calculates the weighted average of these segments' centroids. In this example, we examine an object made from a uniform piece of sheet metal. The dimensions are as follows: - \( a = 1.50 \, \text{ft} \): the diameter of the semi-circle. - \( b = 3.74 \, \text{ft} \) - \( c = 2.45 \, \text{ft} \) Additionally, there is a hole with a diameter of \( d = 0.700 \, \text{ft} \) centered at coordinates \( (1.17, 0.750) \). **Diagram Explanation** The accompanying figure illustrates the structure: - The \( x \)- and \( y \)-axes are labeled, establishing a coordinate system. - The semi-circle on the left has a diameter \( a \), and is part of the composite shape. - The rectangle lies along the \( x \)-axis with a length of \( b \). - A triangle with hypotenuse \( c \) forms the right side. - A circular hole with diameter \( d \) is included, positioned according to its given center coordinates. This configuration aids in understanding how to calculate the centroid of the overall shape by considering the individual elements and their respective centroids.
**Part B** Find \( \bar{x} \), the \( x \)-coordinate of the body's centroid. ([Figure 1](#)) Express your answer numerically in feet to three significant figures. - **View Available Hint(s)** \[ \bar{x} = \] [Submit] [Previous Answers] **Incorrect; Try Again** --- **Part C** Find \( \bar{y} \), the \( y \)-coordinate of the body's centroid. ([Figure 1](#)) Express your answer numerically in feet to three significant figures. - **View Available Hint(s)** \[ \bar{y} = \] --- Note that the interface includes options for mathematical formatting and vectors. The user is prompted to enter their answers and has options to submit or review previous attempts. In Part B, the initial attempt is marked incorrect.
Transcribed Image Text:**Part B** Find \( \bar{x} \), the \( x \)-coordinate of the body's centroid. ([Figure 1](#)) Express your answer numerically in feet to three significant figures. - **View Available Hint(s)** \[ \bar{x} = \] [Submit] [Previous Answers] **Incorrect; Try Again** --- **Part C** Find \( \bar{y} \), the \( y \)-coordinate of the body's centroid. ([Figure 1](#)) Express your answer numerically in feet to three significant figures. - **View Available Hint(s)** \[ \bar{y} = \] --- Note that the interface includes options for mathematical formatting and vectors. The user is prompted to enter their answers and has options to submit or review previous attempts. In Part B, the initial attempt is marked incorrect.
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