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22 April, 04:31

The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of 880 kg/m3 to make it buoyant. If it is totally submerged in seawater with a density of 1025 kg/m3 and neither rising nor sinking, what is the weight of the Trieste craft? A) 127 kN

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  1. 22 April, 05:51
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    so weight of the Trieste craft is 227 kN

    Explanation:

    given data

    length = 15.2 m

    diameter = 3.66 m

    density = 880 kg/m³

    seawater density = 1025 kg/m³

    to find out

    what is the weight of the Trieste craft

    solution

    we know here neither rising nor sinking meaning that

    sum of force is zero

    so we can say

    ∑F = 0 ... 1

    so

    Fb - Fg = 0

    Fb = Fg

    here Fb is bouyant force

    and Fg is gravitational force

    and

    we know Bouyant foce Fb = ρ (w) Vg

    and Fb = mg = (mt + mh) g = mt g + mh g

    here mt is mass of trieste and mh is mass of hull

    we need only weight of trieste so take mt g

    so

    mt g = Fb - mh g = [ ρ (w) - ρ (gas) ] Vg

    mt g = (1025 - 880) * πr²l * g

    mt g = 145 * π*1.83²*15.2 * 9.8

    mt g = 227242.58 N

    so weight of the Trieste craft is 227 kN
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