Explanation Given: The centroid of the differential element along the z- axis is z ˜ . The volume of each segment is represented by V . The height of the top cone ( h ) is 1.2 ft. The height of the bottom part of the cone is 4 ft. Explanation: The homogeneous cones are divided into two segments as shown in Figure (1). Determine the location of the centre of gravity of the volume along the z -axis ( z ¯ ) using the relation. z ¯ = ∑ z ˜ V ∑ V (I) Here, the total volume is ∑ V . Write the formula for the volume of a cone. V = 1 3 π r 2 h (II) Here, the radius of the cone is r and the height of the cone is h . Conclusion: Substitute 1.2 ft for h and 1.5 ft for r in Equation (II) for segment 1. V 1 = 1 3 π ( 1.5 ft ) 2 ( 1.2 ft ) (III) Substitute 4 ft for h and 1.5 ft for r in Equation (II) for segment 2. V 2 = 1 3 π ( 1.5 ft ) 2 ( 4 ft ) (IV) Apply Equations (III), (IV), and use the spreadsheet to calculate the value of z ˜ V for the two segments as shown in Table (1)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 9.2, Problem 84P

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The distance (z¯) to the buoy’s center of gravity G.

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Chapter 9.2, Problem 83P

Chapter 9.2, Problem 85P

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The distance ( z ¯ ) to the buoy’s center of gravity G .

Solution Summary: The homogeneous cones are divided into two segments as shown in Figure (1). Determine the centre of gravity of the volume along the z-axis using the relation.

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The distance (z¯) to the buoy’s center of gravity G.

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