A wooden block of density 600 kg m⁻³ floats in water of density 1000 kg m⁻³. If 40% of its volume is pushed additionally below the original waterline and released, the restoring force is kx for small vertical displacement x. If k=ρ_water g A/n, where A is horizontal area, find n.
Physics · Fluid Mechanics · pascal law and buoyant force
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Question

A wooden block of density 600 kg m⁻³ floats in water of density 1000 kg m⁻³. If 40% of its volume is pushed additionally below the original waterline and released, the restoring force is kx for small vertical displacement x. If k=ρ_water g A/n, where A is horizontal area, find n.

Physics · Fluid Mechanics · pascal law and buoyant force

G1 Physics · Accepted Answer

For a vertical displacement x, additional displaced volume is Ax, so additional buoyancy and restoring force is ρ_water gAx. Hence k=ρ_water gA and n=1. The given 40% preload does not change the small-displacement stiffness while the block remains partially submerged.