Consider the following problem.1 Two uniform cubes have sides of length L. Cube 1 has volume mass density ρ1, while cube 2 has density ρ2 > ρ1. Their average density, ρ = (ρ1 + ρ2)/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)?

1.
Adapted from “Physics Challenges for Teachers and Students: Dense and tense story,” Phys. Teach. 40, 48 (Jan. 2002).
2.
“Physics Challenges for Teachers and Students: Dense and tense story,” Phys. Teach. 40, 253 (April 2002). I thank B. Korsunsky for discussions of this analysis.
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© 2004 American Association of Physics Teachers.
2004
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