A large ocean liner floating in the sea has a volume of 375 000 meter square
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.
First, let's correct the units as the volume should be in cubic meters (m³) rather than square meters (m²). So, the ocean liner has a volume of 375,000 m³, and it displaces 50,000 m³ of sea water.
To determine the density of the ship, we will need to find its mass first. We can use the principle of buoyancy and Archimedes' principle. When the ship is floating, the buoyancy force (FB) equals the weight of the displaced water (WD), which is also equal to the weight of the ship itself (WS).
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. We know that the ship displaces 50,000 m³ of sea water.
Density of sea water (DSW) is approximately 1,025 kg/m³. To find the mass of the displaced water, we can use the formula:
Mass of Displaced Water (MDW) = Volume of Displaced Water (VDW) × Density of sea water (DSW)
MDW = 50,000 m³ × 1,025 kg/m³
MDW = 51,250,000 kg
Since the weight of the ship is equal to the weight of the displaced water, the mass of the ship (MS) will also be 51,250,000 kg.
Now that we have the mass of the ship, we can determine its density. Density (ρ) is mass (m) divided by volume (v):
Density (ρ) = Mass of Ship (MS) / Volume of Ship (VS)
ρ = 51,250,000 kg / 375,000 m³
ρ ≈ 136.67 kg/m³
The density of the ship is 136.67 kg/m³, and its mass is 51,250,000 kg.
The ship is able to float, despite being made of metal, because of its shape and design that allows it to displace enough water to generate the necessary buoyancy force to keep it afloat. The ship's volume is filled with air and other lightweight materials, which decrease its overall density, and so its density becomes lower than the density of the sea water. When the density of an object is lower than the density of the fluid it's in, the object will float. In this case, the ship's density is lower than the density of the sea water, thus allowing it to float.