A large ocean linear 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.
To determine the density and mass of the ship, we should first find the mass of the ship. We know that the ship displaces 50,000 square meters of sea water, and the density of sea water is approximately 1025 kg/m^3. We can use the formula:
mass = volume x density
mass of displaced water = 50000 x 1025 (since the ship displaces 50,000 m^3 of sea water)
mass of displaced water = 51,250,000 kg
By Archimedes' principle, the mass of the ship is equal to the mass of the displaced water. Therefore, the mass of the ship is 51,250,000 kg.
Next, we'll find the density of the ship. The formula for density is:
density = mass / volume
density of ship = 51,250,000 kg / 375,000 m^3 (since the ship has a volume of 375,000 m^3)
density of ship = 136.6667 kg/m^3
So, the density of the ship is 136.67 kg/m^3, and the mass of the ship is 51,250,000 kg.
Despite being made of metal, the ship is able to float because its overall density is less than the density of the sea water it displaces. By Archimedes' principle, an object will float in a fluid if its density is less than the density of the fluid. In this case, the density of the ship (136.67 kg/m^3) is less than the density of sea water (1025 kg/m^3), which allows the ship to float.