A cubical block of ice floating in water must support a metal piece weighing 0.5 kg . Determine the minimum edge length of the block such that it does not sink in water. The specific gravity of ice is 0.9 .

Step-by-step solution

Let the edge length of the cubical block of ice be L . Volume of the ice block, V = L^3 Density of water, _ w = 1000 kg/m ^3 Density of ice, _ ice = 0.9 1000 = 900 kg/m ^3 Mass of the ice block, m_ ice = V _ ice = 900 L^3 Mass of the metal piece, m_ metal = 0.5 kg For the ice block to just float without sinking, it must be completely submerged. The buoyant force provided by the displaced water must balance the total weight of the ice block and the metal piece. Equating the buoyant force to the total weight: V _ w g