Explanation Given: The centroid of the differential element along the z- axis ( z ˜ ) is 0.5 ft. The volume of each segment is represented by V . The radius of a cone ( r ) is 1.5 ft. The height of a bottom part of a cone is 4 ft. Show the homogeneous cones are divided into two segments as in Figure (1). Using Figure (1), Determine the location of the centre of gravity of 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) Conclusion: Substitute 1.5 ft for r in Equation (II) for segment 1. V 1 = 1 3 π ( 1.5 ft ) 2 ( h ) (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 spreadsheet to calculate the value of z ˜ V for two segments as shown in Table (1). Segments V ( ft 3 ) z ˜ ( ft ) z ˜ V ( ft 4 ) 1 1 3 π ( 1.5 ) 2 ( h ) ( − h 4 ) 1 12 π ( 1.5 ) 2 ( h 2 ) 2 1 3 π ( 1.5 ) 2 ( 4 ) 4 4 9

15th Edition

ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

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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, Problem 80P

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The height (h) of the top cone.

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Chapter 9, Problem 79P

Chapter 9, Problem 81P

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The height ( h ) of the top cone.

Solution Summary: The author shows the homogeneous cones are divided into two segments as in Figure (1).

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