Final answer:
The density of the 10cm x 10cm x 10cm wood block floating in water can be calculated using Archimedes' Principle and the concept of buoyancy, factoring in that only 10% of the block is submerged. When a 0.5 kg mass is added to the polystyrene, the amount of block submerged increases, meaning less of it remains above water.
Step-by-step explanation:
To address the student's question regarding the 10cm x 10cm x 10cm wood block floating in water and its density and behavior when additional mass is added, we need to apply the principles behind Archimedes' Principle and buoyancy.
(a) Given that 90% of the polystyrene block floats above the water surface, only 10% is submerged. We can use the formula for density (ρ = mass/volume) and knowing the density of water is 1000 kg/m³, we can find the density of the polystyrene. Since the block is floating, the weight of the displaced water equals the weight of the block. If V is the volume of the block, then 0.1V is the volume of the water displaced. The weight of the displaced water (mass of water x g, where g is gravity) equals the mass of the polystyrene block x g. Thus, ρ₀ of water x 0.1V x g = ρ of polystyrene x V x g. Canceling out g and V from both sides and taking ρ₀ as 1000 kg/m³, we find ρ of polystyrene to be 100 kg/m³.
(b) When a 0.5 kg mass is placed on the block of polystyrene, the block will sink further into the water until the weight of the block plus the additional mass equals the weight of the water displaced. The new volume of water displaced is now equal to the volume of the polystyrene block x its submerged fraction plus 0.5 kg of water. The calculation will show a larger fraction submerged and thus a smaller percentage of the block remains above water, which can be found through similar steps as those in part (a).