A supertanker filled with oil has a total mass of 14.1·10^8 kg. If the dimensions of the ship are those of a rectangular box 271 m long, 93.1 m wide, and 93.1 m high, determine how far the bottom of the ship is below sea level (ρsea = 1020 kg/m^3).
To determine how far the bottom of the ship is below sea level, we need to calculate the buoyant force acting on the ship and then use it to find the displacement of the ship in the water.
First, let's calculate the volume of the ship:
Volume = length x width x height
Volume = 271 m x 93.1 m x 93.1 m
Next, let's calculate the mass of the water displaced by the ship, which is equal to the mass of the ship:
Mass of water displaced = mass of ship = 14.1 x 10^8 kg
Now, we can calculate the density of the water displaced:
Density = Mass / Volume
Since the volume is the same for both the ship and the water displaced, we can write:
Density of water displaced = Mass of ship / Volume
Next, we compare the density of the water displaced with the density of the sea water (ρsea). If the density of the water displaced is less than ρsea, the ship will float. If it's equal, the ship will be neutrally buoyant. If it's more, the ship will sink.
So, we set up the following equation:
Density of water displaced = ρsea
Now, solve for the density:
Mass of ship / Volume = ρsea
Substituting the given values into the equation, we get:
14.1 x 10^8 kg / (271 m x 93.1 m x 93.1 m) = 1020 kg/m^3
Now we can solve for the volume of water displaced by the ship.
Volume of water displaced = Mass of ship / ρsea
Substituting the given values into the equation, we get:
Volume of water displaced = 14.1 x 10^8 kg / 1020 kg/m^3
Now we can use the volume of water displaced to calculate the vertical distance the bottom of the ship is below sea level.
Height = Volume of water displaced / (length x width)
Substituting the given values into the equation, we get:
Height = (14.1 x 10^8 kg / 1020 kg/m^3) / (271 m x 93.1 m)
Calculating this expression will give you the distance the bottom of the ship is below sea level.