a large ocean liner floating in the sea has a volume of 375000 square meters and displaces 50000 square meters of sea water. determine the density and mass of the ship. explain why, despite being made of metal, the ship is able to float.
First, we need to find the mass of the ship. We know the volume of the ship (375,000 m³) and the volume of the water it displaces (50,000 m³).
According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid that is displaced by the object. So, the weight of the displaced water is equal to the weight of the ship.
The density of sea water is approximately 1025 kg/m³.
Now, we can find the mass of the displaced water:
Mass of water = Volume of water × Density of water
Mass of water = 50,000 m³ × 1025 kg/m³
Mass of water = 51,250,000 kg
Since the weight of the displaced water is equal to the weight of the ship, the mass of the ship is also 51,250,000 kg.
Now we can calculate the density of the ship:
Density of ship = Mass of ship / Volume of ship
Density of ship = 51,250,000 kg / 375,000 m³
Density of ship ≈ 136.67 kg/m³
Now we know the density of the ship is approximately 136.67 kg/m³, and the mass of the ship is 51,250,000 kg.
The ship is able to float, despite being made of metal, because the overall density of the ship is less than the density of the sea water it displaces. This is because the ship has a large volume filled with air and other materials with densities lower than water, which lowers its overall density. The buoyant force created by the displacement of water counteracts the weight of the ship, allowing it to float.