A supertanker can carry 2.2 x 105m3 of oil with a density
of 0.88 g/cm3. When fully loaded its mass is 2.3 x 108 kg, and the dimensions of its hull are approximately 400 m long, 60 m wide, and 38 meters high. Given that the density of seawater is 1.03 g/cm3, how deeply is the hull submerged in the water?
the volume of the ship is 912000 m^3
so its density is
(2.3*10^8 kg)/(9.12*10^5 m^3) = 233 kg/m^3 = 0.233 g/cm^3
hmmm. doesn't look right. Did I miss something?
To find out how deeply the hull of the supertanker is submerged in water, we need to compare the weight of the tanker to the buoyant force exerted on it by the seawater.
First, let's calculate the weight of the loaded tanker:
Mass of the tanker = 2.3 x 10^8 kg
Next, we need to calculate the volume of the tanker:
Volume of the tanker = Length x Width x Height
Volume of the tanker = 400 m x 60 m x 38 m
Now, let's calculate the weight of the oil:
Density of the oil = 0.88 g/cm^3
Volume of the oil = 2.2 x 10^5 m^3
Mass of the oil = Density of the oil x Volume of the oil
Total mass of the loaded tanker = Mass of the tanker + Mass of the oil
To find out how deeply the hull of the tanker is submerged, we need to compare the weight of the loaded tanker (including oil) with the buoyant force:
Buoyant force = Weight of the seawater displaced by the submerged part of the tanker
Weight of the seawater = Density of seawater x Volume of the submerged part of the tanker
If the tanker is fully submerged, its weight will equal the buoyant force. Therefore, we can set up the equation:
Weight of the loaded tanker = Buoyant force
Now, let's calculate the submerged volume of the tanker:
Submerged volume of the tanker = Total volume of the tanker - Volume of the air
Volume of the air = Length x Width x (Height - Depth of the hull submerged in water)
Depth of the hull submerged in water = (Height - Volume of the submerged part of the tanker) / [Length x Width]
Finally, we can substitute the values into the equation and solve for the depth of the hull submerged in water.
To determine how deeply the hull of the supertanker is submerged in water, we need to calculate the volume of the hull that is underwater.
First, we need to find the total volume of the supertanker. The volume of a rectangular prism (which represents the hull) is calculated by multiplying its length, width, and height.
Volume of the supertanker = Length x Width x Height
Volume of the supertanker = 400 m x 60 m x 38 m
Next, we need to determine the volume of the hull that is above the water. To do this, we need to subtract the volume of water displaced by the submerged part of the hull from the total volume of the supertanker.
The volume of displaced water can be calculated using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. The weight of the displaced water is equal to the weight of the supertanker when submerged.
Weight of the supertanker = mass x acceleration due to gravity
Weight of the supertanker = 2.3 x 10^8 kg x 9.8 m/s^2
Now, let's calculate the volume of the displaced water using the density of seawater:
Volume of displaced water = Weight of the supertanker / Density of seawater
Volume of displaced water = (2.3 x 10^8 kg x 9.8 m/s^2) / (1.03 g/cm^3)
Since the density of water is given in grams per cubic centimeter (g/cm^3), we need to convert the mass of the supertanker into grams:
2.3 x 10^8 kg = 2.3 x 10^11 g
Now, let's substitute the values into the equation:
Volume of displaced water = (2.3 x 10^11 g x 9.8 m/s^2) / (1.03 g/cm^3)
Finally, to find the depth to which the hull is submerged, we divide the volume of displaced water by the area of the hull (Length x Width):
Depth of hull submerged = Volume of displaced water / (Length x Width)
Substitute the calculated volume and hull dimensions into the equation to find the depth of the hull submerged.