A supertanker filled with oil has a total mass of 1.09 109 kg. If the dimensions of the ship are those of a rectangular box 260 m long, 78 m wide, and 78 m high, determine how far the bottom of the ship is below sea level (ρsea = 1020 kg/m3).
the volume submerged is 260x78xh
That volume of water must weigh 1.07e9 kg to balance the weight.
1020 kg/m³ x 230x72xh m³ = 1.09e9 kg
solve for h
To determine how far the bottom of the ship is below sea level, we need to calculate the buoyant force acting on the ship. The buoyant force is the force exerted by a fluid (in this case, water) on an object immersed in it, and it's given by the formula:
Buoyant force = (density of fluid) * (volume of fluid displaced) * (acceleration due to gravity)
In this case, the fluid is water, with a density of ρsea = 1020 kg/m^3.
To calculate the volume of the fluid displaced by the ship, we need to find the volume of the rectangular box formed by the ship's dimensions. Therefore:
Volume of fluid displaced = length * width * height
Substituting the given values:
Volume of fluid displaced = 260 m * 78 m * 78 m
Next, we can plug all these values into the formula for the buoyant force:
Buoyant force = ρsea * (volume of fluid displaced) * (acceleration due to gravity)
Substituting the values:
Buoyant force = 1020 kg/m^3 * (260 m * 78 m * 78 m) * 9.8 m/s^2
Now, we need to equate the buoyant force to the weight of the ship to determine how far the bottom of the ship is below sea level. The weight of the ship is given as the total mass of the ship multiplied by the acceleration due to gravity:
Weight of ship = mass of ship * acceleration due to gravity
Substituting the given values:
Weight of ship = 1.09 * 10^9 kg * 9.8 m/s^2
Finally, we equate the buoyant force to the weight of the ship:
Buoyant force = Weight of ship
Solving this equation will give us the height that the bottom of the ship is below sea level.