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Archimedes® Principle A spherical buoy has a radius of I m and a density one-fourth that of seawater. By Archimedes Principle, the weight of the displaced water will equal the weight of the buoy. • Let x = the depth to which the buoy sinks. • Let d = the density of seawater. • Let r= the radius of the circle formed where buoy, air, and water meet. See the figure below. Notice in the figure that r² = 1 – (1 – x)² = 2x – x², and recall from geometry that the volume of submerged spherical TX cap is V = 6. * (3r² + x²). (d)Approximate the depth to which the buoy will sink.

Archimedes® Principle A spherical buoy has a radius of I m and a density one-fourth that of seawater. By Archimedes Principle, the weight of the displaced water will equal the weight of the buoy. • Let x = the depth to which the buoy sinks. • Let d = the density of seawater. • Let r= the radius of the circle formed where buoy, air, and water meet. See the figure below. Notice in the figure that r² = 1 – (1 – x)² = 2x – x², and recall from geometry that the volume of submerged spherical TX cap is V = 6. * (3r² + x²). (d)Approximate the depth to which the buoy will sink.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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Archimedes® Principle A spherical buoy has a radius of I m and a density one-fourth that of seawater. By Archimedes Principle, the weight of the displaced water will equal the weight of the buoy. • Let x = the depth to which the buoy sinks. • Let d = the density of seawater. • Let r= the radius of the circle formed where buoy, air, and water meet. See the figure below. Notice in the figure that r² = 1 – (1 – x)² = 2x – x², and recall from geometry that the volume of submerged spherical TX cap is V = 6. * (3r² + x²). (d)Approximate the depth to which the buoy will sink.
Transcribed Image Text:Archimedes® Principle A spherical buoy has a radius of I m and a density one-fourth that of seawater. By Archimedes Principle, the weight of the displaced water will equal the weight of the buoy. • Let x = the depth to which the buoy sinks. • Let d = the density of seawater. • Let r= the radius of the circle formed where buoy, air, and water meet. See the figure below. Notice in the figure that r² = 1 – (1 – x)² = 2x – x², and recall from geometry that the volume of submerged spherical TX cap is V = 6. * (3r² + x²). (d)Approximate the depth to which the buoy will sink.
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