FYKOS Year 38 Series 2 Problem 3 — floating pyramid · FYKOS 38 #38.2.3

Physics · mechanics

Problem

Consider a homogeneous pyramid with density

\rho_{\mathrm{j}}=250\,\mathrm{kg\cdot m^{-3}}

floating on water with density

\rho=1~000\,\mathrm{kg\cdot m^{-3}}

. While floating, its axis is vertical. Is the position more stable when the apex of the pyramid is pointing up or down? The height of the pyramid is

h=20\,\mathrm{cm}

and the surface area of its base is

S=49\,\mathrm{cm^2}