Question

A 60.0-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 ✕ 0.0895 m. The bottom 0.021 m of the raft is submerged.

(a) Draw a force diagram of the system consisting of the survivor and raft. (Submit a file with a maximum size of 1 MB.)

(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. Solve for F_y, the y-component of the net force. Let upward be the positive y-direction.)
F_y =  

= 0

(c) Calculate the numeric value for the buoyancy, B. (Seawater has density 1025 kg/m³. Enter answer to at least the ones digit.)
N

(d) Using the value of B and the weight w of the survivor, calculate the weight w_r of the Styrofoam.
N

(e) What is the density of the Styrofoam?
kg/m³

(f) What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface?
N

(g) What total mass of survivors can the raft support?
kg

Answer 1