Fluid Mechanics · Flow kinematics and material derivatives
A composite body consists of a foam cylinder (diameter 0.20 m, length 0.35 m, specific…
Problem
A composite body consists of a foam cylinder (diameter 0.20 m, length 0.35 m, specific gravity 0.12) glued end-to-end to a steel cylinder of the same diameter, length 0.040 m, and specific gravity 7.85. The body is fully submerged in freshwater with the steel end down and is attached to a vertical linear spring of stiffness 850 N/m whose other end is fixed to the floor. When the spring is unstretched the top of the foam is 0.50 m below the free surface. Find the equilibrium extension of the spring.
Hint
Surplus buoyancy \(F_B-W\) is balanced by spring tension \(k\delta\); the unstretched position is already fully submerged and remains so after a millimetre-scale rise.
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