Explanation Given: The centroid of the differential element along x axis is x ˜ . The area of each segment is represented by A . Explanation: Show the shaded area is divided into two segments as in Figure 1. Determine the location of the centroid C of the shaded area along x axis ( x ¯ ) using the relation. x ¯ = ∑ x ˜ A ∑ A (I) Conclusion: Refer to Figure (1) and use the spreadsheet to calculate the value of x ˜ A for three segments as shown in Table 1. Segment A ( in . 2 ) x ˜ ( in . ) x ˜ A ( in . 3 ) 1 1 2 r 2 α 2 r 3 α sin α ( 2 r 3 α sin α ) ( 1 2 r 2 α ) = 1 3 r 3 sin α 2 − 1 2 ( r sin α ) ( r cos α ) 2 3 r cos α ( 2 3 r cos α ) [ − 1 2 ( r sin α ) ( r cos α ) ] = − 1 3 r 3 sin α cos 2 α ∑ 1 2 r 2 α + − 1 2 ( r sin

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

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Chapter 9.2, Problem 69P

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The location (x¯) of centroid C of the shaded area.

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Chapter 9.2, Problem 68P

Chapter 9.2, Problem 70P

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The location ( x ¯ ) of centroid C of the shaded area.

Solution Summary: The author explains how to determine the location of centroid C of the shaded area along x axis.

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The location (x¯) of centroid C of the shaded area.

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Chapter 9 Solutions