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15 May, 19:33

An undersea research chamber is spherical with an external diameter of 4.70 m. The mass of the chamber, when occupied, is 54300 kg. It is anchored to the sea bottom by a cable. The density of seawater is 1025 kg/m3. Part A

What is the buoyant force on the chamber?

Part B

What is the tension in the cable?

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  1. 15 May, 23:10
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    Answer: a) 557.3kN b) 543kN

    Explanation:

    Buoyant force = weight of water displaced.

    Formula for buoyant force = mg * (density of fluid/density of object)

    Density of fluid = density of sea water = 1025kg/m³

    Mass of the chamber (m) = 54300kg

    g = acceleration due to gravity = 10m/s²

    Density of chamber = mass/volume

    Where volume of sphere = 4/3Πr³

    radius = 4.70/2 = 2.35m

    Volume = 4/3*Π (2.35) ³

    Volume = 54.37m³

    Density of chamber = 54300/54.37

    = 998.7kg/m³

    Substituting the values into the formula for buoyant force

    Buoyant force = 54300*10*{1025/998.7}

    = 557299N

    = 557.3kN

    b) Tension in the cable = mass of cable * acceleration due to gravity

    = 54300*10 = 543000N or 543kN.
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