Question

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?

Answer 1

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.