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

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