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Question 3.2: A loaded pontoon has a mass of 200000 kg. Its length is 20 m......

A loaded pontoon has a mass of 200000 kg. Its length is 20 m and its width 9 m, and its overall centre of gravity is 5.6 m above the base of the pontoon. The pontoon floats in salt water with a density (\rho _{S}) of 1025 kg/m³. Is it stable?

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Since it is floating, mass of pontoon, M = mass of sea water displaced = 200000 kg. Volume of sea water displaced, V = {M}/{\rho _{S}} = 200000 / 1025 = 195.12 m³ Depth of immersion, h = V/lb = 195.12/(20 × 9) = 1.08 m Therefore height of centre of buoyancy B above base = h/2 = 1.08/2 = 0.54 m

BM = {I_{WS}}/{V}  where  I_{WS} = {lb^{3}}/{12}

BM = (20 × 93)/(12 × 195.12) = 6.23 m
Height of M above the base of the pontoon = 6.23 + 0.54 = 6.77 m

M is above G (6.77 m > 5.6 m) so the pontoon is stable, and GM = 6.77 – 5.6 = 1.17 m

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