Hi,
This is conceptual question;
Concept: This is based on Archimedes's Principle. According to this principle, when an object is partially or fully submersed in a given liquid then it displaces the equal amount of liquid that it has lost in its weight.
Consider hull of Titanic Ship has weight 'w' and area of base is 'A'. If ρ be the density of water. Let 'h' be the height of hull then the pressure exerted by hull at the surface of water 'P'.
The upthrust at the bottom of the ship is given as
F = Vρg
F=Ahρg
Hence the required weight of water should be more than the Ahρg.
Here, density of water(ρ) = 1000 kg /m^3, the value of g=9.8 m/s^2.
If A= 100 m^2 and h = 30 m then required mass of water
m = F/g
m=Ahρg /g
or, [tex] m=(100m^{2} )(30m)(1000kg/m^{3}) [/tex]
or, m = 3, 000,000 kg
or, m = 3,000 tons water is required.
The hull should displace sea water as much as : density of sea water x volume of immersed hull(ρf x Vh)
Archimedes states that the buoyant force acting on an object which is partially or completely immersed into a fluid is equal to the weight of the fluid displaced by the object
Buoyancy can be formulated
Fb = floating force
ρf = fluid density, kg / m3
Vf = volume of objects immersed in fluid
If the object is completely immersed, Vf = the volume of the object ,Vo
There are 3 conditions that occur in an object in a fluid that is floating, in the middle of the fluid and sink
Floating if the density of an object <the density of a liquid , ρo < ρf
in the middle of a fluid if the density of a liquid is the density of an object , ρf = ρo
sink if the density of an object> the density of a liquid , ρo > ρf
In the state of the hull of a ship is below the water, the ship's condition is in a floating condition.
In this situation, there is a balance between the buoyancy force and the weight of the object
ρs. Vs. g = ρf. Vh. g
rho s = density of ship
Vs = the volume of the ship
Vh = the volume of immersed hull
So the fluid mass, Mf (in this case sea water) that is moved (displaced) by the ship is:
[tex]\large{\boxed{\bold{{Mf=\rho_f\times Vh}}}[/tex]
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