Archimedes’ Principle states that the buoyant force on an object partially or fully submerged in a fluid is equal to the weight of the fluid that the object displaces. Thus, for an object of density ρ0ρ0 floating partly submerged in a fluid of density ρfρf, the buoyant force is given by
where g is the acceleration due to gravity and A(y) is the area of a typical cross-section of the object (see the figure). The weight of the object is given by
(a) Show that the percentage of the volume of the object above the surface of the liquid is .
(b) The density of ice is and the density of seawater is . What percentage of the volume of an iceberg is above water?
(c) An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts?
(d) A sphere of radius and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the water is .
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