A sealed cylindrical research buoy has mass 42.0 kg, external cross-sectional area 0.180 m² and total height 0.500 m. It floats upright in seawater of density 1025 kg m⁻³. Calculate its submerged depth and freeboard. A 12.0 kg instrument is added centrally; calculate the new freeboard and decide whether the buoy remains safe if 0.080 m freeboard is required. Discuss stability information missing from this one-dimensional model.

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Initial submerged depth = 0.228 m and freeboard = 0.272 m. With the instrument, submerged depth = 0.293 m and freeboard = 0.207 m, so it meets the 0.080 m requirement. Floating equilibrium requires buoyant force equal weight: ρgAh = mg. Gravity cancels, so h = m/(ρA). Initially h = 42.0/[1025(0.180)] = 0.228 m. Freeboard is 0.500−0.228 = 0.272 m. With the instrument, total mass is 54.0 kg. Then h = 54.0/[1025(0.180)] = 0.293 m and freeboard is 0.207 m. Because 0.207 m exceeds the required 0.080 m, the buoy passes the stated vertical-displacement criterion with 0.127 m margin. This model says nothing about tipping. Safety also depends on centre of mass, centre of buoyancy, metacentric height, wave loading and whether the instrument shifts. A tall central mass can reduce rotational stability even while freeboard remains adequate.

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