Chapter 9, Problem 32P

A 62.0-kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m × 2.00 m × 0.090 0 m. The bottom 0.024 m of the raft is submerged. (a) Draw a force diagram of the system consisting of the survivor and raft. (b) Write Newton’s second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and w_r for the weight of the raft. (Set a = 0.) (c) Calculate the numeric value for the buoyancy, B. (Seawater has density 1 025 kg/m³.) (d) Using the value of B and the weight w of the survivor, calculate the weight w, of the Styrofoam. (e) What is the density of the Styrofoam? (f) What is the maximum buoyant, force, corresponding to the raft being submerged up to its top surface? (g) What total mass of survivors can the raft support?