3. In phyeiee work is the integral of foree over dietanee. We want to compute the work to lift a stone sphere out of water. Initially, the pllt-'J'E is totally submerged in water with the north pole touching the water surface. At the end, the sphere ir- iu the air with the eouth pole touching the water. In between, the gravitational force is I" '' 9'",an + yvusiprl _ law) where g gravitationaj realism-tuts Va volume of the part of the sphere in the air, V", volume of the part of the sphere in the waterT .9, density of mane for the sphere, p", density of mass [or water. The rst term reprments the gravitational force of the sphere above water and the second term the force of the part below water. In the latter the diepleoed water is euhtraeuei. Expreae the tome as a function of zpneition of the north pole1 where z ' 0 is the water line. Find tr'l and V5 as functions of 2. Then compute the work an an integral over the zvariable