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 Step 2 (b) To make steel float on the water, we have to make the overall density of the steel smaller than the density of the water. This can be done by making the steel object such a way that the volume to mass ratio decreases. For example we can make a hollow sphere with making volume such that the density become less than water. Step 3 (c) Suppose the volume of the object is V , hence the mass of the object is M = V Now in order to float, the fluid displaced by the object will have same mass. So the mass of the displaced fluid is M . Now since the density of the fluid is , the volume of the displaced water is fluid M V fluid fluid Hence the ratio is V V fluid fluid V fluid M/ fluid M/V = V flui= ……………………………………………………………….(1) V fluid So the object must be submerged by fraction / . fluid