Equilibrium of a Floating Vessel

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When a boat of weight floats in water, a fraction of its volume is submerged and displaces an equivalent volume of water. According to Archimedes' principle, the boat experiences a buoyancy force equivalent to the weight of the water displaced; is greater than the weight of the boat, making it float. To stabilize the boat, its center of gravity must be as low as possible. When the boat tilts to one side, the center of buoyancy (the center of mass of the displaced water) shifts. The "metacenter" (in yellow) is the intersection of the vertical line through and the axis of symmetry of the boat. If the tilt is not too great, the net force tends to right the boat. If is below , or the deck sinks below water level, the boat is likely to capsize.

Contributed by: Enrique Zeleny (January 2011)
Open content licensed under CC BY-NC-SA


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