Archimedes principle says that the buoyant force exerted on an object that is (partially or totally) submerged

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Archimedes’ principle says that the buoyant force exerted on an object that is (partially or totally) submerged in water is equal to the weight of the water displaced by the object (see figure). Let ρw = 1 g/cm3 = 1000 kg/m3 be the density of water and let ρ be the density of an object in water. Let f = ρ/ρw. If 0 < f ≤ 1, then the object floats with a fraction f of its volume submerged; if f > 1, then the object sinks.

volume of displaced water buoyant force


Consider a cubical box with sides 2 m long floating in water with one-half of its volume submerged (ρ = ρw/2). Find the force required to fully submerge the box (so its top surface is at the water level). 

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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