A large ocean liner floating in the sea has a volume of 375 000 meter the power of two and displaces 50 000 meter the power of two of sea water. Determine the density and mass of the ship. explain why, despite being made of metal, the ship is able to float.

Answer 1

To determine the density and mass of the ship, we can use the following equation:

density = mass / volume

First, let's find the mass of the ship. We know that the ship displaces 50,000 m² of sea water, and the density of sea water is approximately 1,025 kg/m². To find the mass of the ship, we can use the mass of the displaced water using Archimedes' principle:

mass of ship = mass of displaced water = density of water * displaced water volume
mass of ship = 1,025 kg/m² * 50,000 m²
mass of ship = 51,250,000 kg

Now we can calculate the density of the ship using:

density of ship = mass of ship / volume of ship
density of ship = 51,250,000 kg / 375,000 m²
density of ship = 136.67 kg/m²

The density of the ship is 136.67 kg/m² and the mass of the ship is 51,250,000 kg.

The ship is able to float despite being made of metal because its overall density is less than the density of the water it displaces. This is due to the air-filled space inside the ship that helps lower its overall density. According to Archimedes' principle, an object will float if the upward buoyant force exerted by the fluid (in this case, water) equals or exceeds the downward gravitational force exerted by the object's mass. In this case, since the density of the ship is less than that of the water, the buoyant force is strong enough to keep the ship afloat.