Reprise of a "Dense and Tense Story"

Abstract

Consider the following problem. Two uniform cubes have sides of length L. Cube 1 has volume mass density p1, while cube 2 has density p2>p1 Their average density, p= (p1 +p2)/2, is equal to that of an incompressible fluid filling a beaker. The two cubes are glued together and fully immersed in the fluid with the lighter cube 1 positioned directly above cube 2, such that the interface between them is at depth H. Suppose that the glue has a density equal to that of the fluid, so that the combination of blocks and glue is overall neutrally buoyant in the fluid. Denote by F the maximum tensile force that the glue can withstand before tearing apart. Under what conditions will the cubes break apart (resulting in cube 1 rising to the surface and cube 2 sinking to the bottom)?

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2004
Accession Number
ADA574986

Entities

People

  • Carl E. Mungan

Organizations

  • United States Naval Academy

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  • Low Density
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  • United States Naval Academy

Readers

  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.
  • Surface Coatings Technology.