Question

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

Answer 1

Answer:

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