A supertanker can carry 2.2x10 m of oil with a density of 0.88g/cm. 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 m high. Given that the density of seawater is 1.03 g/cm , how deeply is the hull submerged in the water?
density of seawater is about 1.03*10^3 kg/m^2
bulk modulus of tanker hull is about 0.9
call draft = h
so mass of water displaced = 1.03 *10^3 * 0.9 * 400 * 60 * d
that must equal the mass of the fully loaded tanker
2.3 * 10^8 = 2.22*10*7 h
h = 10.4 meters
Math people are likely to not know about bulk modulus (ratio of underwater volume to rectangular box) so if this is a math subject and not a ship design subject divide answer by 0.9
Typo corrections:
density of seawater is about 1.03*10^3 kg/m^2
bulk modulus of tanker hull is about 0.9
call draft = d
so mass of water displaced = 1.03 *10^3 * 0.9 * 400 * 60 * d
that must equal the mass of the fully loaded tanker
2.3 * 10^8 = 2.22*10*7 d
d = 10.4 meters
Math people are likely to not know about bulk modulus (ratio of underwater volume to rectangular box) so if this is a math subject and not a ship design subject multiply d by 0.9
By the way, it is unlikely that the question is worded correctly. The ship would float lower in the water if fully loaded. However that is what it says and we do not know the cargo volume anyway.
To determine how deeply the hull of the supertanker is submerged in water, we need to compare the weight of the supertanker to the buoyant force acting on it.
1. Calculate the volume of the supertanker:
Volume = length × width × height
= 400 m × 60 m × 38 m
2. Convert the volume to cubic centimeters:
Volume = Volume × (100 cm/m)^3
3. Calculate the mass of the oil carried by the supertanker:
Mass of oil = Density of oil × Volume of oil
4. Calculate the total mass of the fully loaded supertanker:
Total mass = Mass of oil + Mass of supertanker
5. Calculate the weight of the supertanker:
Weight = Total mass × Acceleration due to gravity
6. Calculate the buoyant force acting on the supertanker:
Buoyant force = Density of seawater × Volume of the submerged hull × Acceleration due to gravity
7. Set the weight of the supertanker equal to the buoyant force and solve for the volume of the submerged hull:
Weight = Buoyant force
8. Divide the volume of the submerged hull by the length and width of the hull to get the depth of the hull submerged.
Let's calculate step by step:
Step 1:
Volume = 400 m × 60m × 38 m
Step 2:
Volume = Volume × (100 cm/m)^3
Step 3:
Mass of oil = Density of oil × Volume of oil
Step 4:
Total mass = Mass of oil + Mass of supertanker
Step 5:
Weight = Total mass × Acceleration due to gravity
Step 6:
Buoyant force = Density of seawater × Volume of the submerged hull × Acceleration due to gravity
Step 7:
Weight = Buoyant force
Step 8:
Submerged depth = Volume of submerged hull / (length × width)