A large ocean liner floating in the sea has a volume of 375 000 square meter and displaces 50 000 meter square 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 calculate the density, we need to divide the mass of the ship by its volume. We are not given the mass of the ship, but we can find it using the displacement of the water. The displaced water volume is equal to the weight of the ship. We can find the mass of the ship, m_ship, using the following relation:
m_ship = (density of sea water) * (displacement of sea water) / g,
where g is the acceleration due to gravity (9.81 m/s²).
The density of sea water is approximately 1025 kg/m³. With the given displacement of 50,000 m³, we can find the mass of the ship:
m_ship = (1025 kg/m³) * (50,000 m³) / 9.81 m/s²
m_ship = 5,231,905 kg
Now, we can find the density of the ship:
density_ship = mass_ship / volume_ship
density_ship = 5,231,905 kg / 375,000 m³
density_ship = 13.95 kg/m³
Now that we have the density and mass of the ship, we can explain why the ship is able to float.
The key to understanding why the ship floats is the concept of buoyancy, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by that object. If the buoyant force is greater than or equal to the weight of the object, the object will float.
Since the density of the ship (13.95 kg/m³) is less than the density of sea water (1025 kg/m³), the overall ship has a lower "average" density which allows it to float on water. This happens because of the air trapped inside the ship's hull. The ship's structure and architecture help to spread out the weight of the heavy metal over a large area, which in turns decreases the average density of the ship.
Essentially, the ship is mixing the air and metal to create a structure with an average density that is lower than water, allowing it to float. This is the reason why the ship, despite being made of metal, is able to float on water.