A floating research platform is built from a rectangular array of buoyant, foam-filled planks. The deck area available for scientists to stand on measures 2.5m×2.0m. Structural analysis of the deck material shows that it can safely withstand a maximum normal stress (pressure) of 2.2×104Pa before permanent deformation begins. Each scientist who boards the platform, along with personal equipment, contributes an average additional mass of 82kg. The mass of the empty platform itself is negligible compared with the load.
(a) Derive an expression for the total pressure exerted on the deck as a function of the number N of scientists on board. Clearly identify all variables and constants used.
(b) Using your expression, calculate the greatest integer value of N that keeps the deck pressure below the deformation limit.
(c) After deployment, three sealed instrument crates, each of mass 15kg, are added to the deck. Reevaluate the maximum allowable number of scientists when the crates are present.
(d) Discuss two design modifications—other than simply enlarging the deck area—that could allow the platform to accommodate additional scientists without exceeding the pressure limit. Justify each suggestion using principles of pressure and force distribution.