9-39. Locate the center of gravity of the volume. The material is homogeneous. 2 m- 2 m y² = 2z ent is y
9-39. Locate the center of gravity of the volume. The material is homogeneous. 2 m- 2 m y² = 2z ent is y
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Title: Locating the Center of Gravity of a Homogeneous Volume
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**Problem Statement (9-39):**
Locate the center of gravity of the volume. The material is homogeneous.
**Diagram Explanation:**
The diagram depicts a 3D shape that appears to be a parabolic bowl. The bowl is oriented such that its open side faces upwards.
- The coordinate axes are marked as \(x\), \(y\), and \(z\).
- The parabola is defined by the equation \(y^2 = 2z\).
- Key dimensions:
- The maximum diameter of the parabola along the \(z\)-axis is 2 meters.
- The maximum depth from the vertex of the parabola to the rim along the \(z\)-axis is also 2 meters.
The objective is to find the center of gravity of this solid, assuming uniform material density throughout the volume.
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