A raft of density 600 ~g / m ^3 and mass 120 ~kg floats in water. How much weight can be put on the raft to make it just sink?

Step-by-step solution

The density of the raft is _ r = 600 kg/m ^3 . The mass of the raft is M = 120 kg . The volume of the raft is V = M _ r = 120 600 = 0.2 m ^3 . For the raft to just sink in water (density _ w = 1000 kg/m ^3 ), the total weight of the raft and the added mass m must be equal to the buoyant force acting on the raft when it is fully submerged. The buoyant force is F_ B = V _ w g = 0.2 1000 g = 200g . The total weight is (M + m)g = (120 + m)g . Equating the two, we have 120 + m = 200 . Therefore, m = 200 - 120 = 80 kg .