A large ocean liner floating in the sea has a volume of 375000 square meter and displaces 50000 square meter 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. The density of sea water is approximately 1025 kg/m³. The amount of water displaced by the ship, which is equal to the weight of the ship according to Archimedes' principle, is:
Weight_ship = Displaced_water_volume * Density_water
Weight_ship = 50000 m³ * 1025 kg/m³
Weight_ship = 51,250,000 kg
Now, we can determine the density of the ship. Density is calculated using the formula:
Density = Mass / Volume
Density_ship = Weight_ship / Volume_ship
Density_ship = 51,250,000 kg / 375,000 m³
Density_ship ≈ 136.67 kg/m³
Therefore, the density of the ship is roughly 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 its average density is lower than the density of seawater. According to Archimedes' principle, any floating object displaces its own weight of the fluid in which it floats. So, as long as the ship's average density is less than the density of the seawater, it will float.