An object of average density ?? floats at the surface of a fluid of density ???fluid. (a) How must the two densities be related? (b) In view of the answer to part (a), how can steel ships float in water? (c) In terms of ?? and ???fluid. What fraction of the object is submerged and what fraction is above the fluid? Check that your answers give the correct limiting behavior as ?? ? ???fluid and as ?? ? 0. (d) While on board your yacht, your cousin Throckmorton cuts a rectangular piece (dimensions 5.0 × 4.0 × 3.0 cm) out of a life preserver and throws it into the ocean. The piece has a mass of 42 g. As it floats in the ocean, what percentage of its volume is above the surface?

Solution 29E Step 1 (a) If the object is floating, the density of the object must be smaller than the density of the fluid. Hence the relation si < fluid