Question

Question:

James Cameron piloted a submersible craft to the bottom of the Challenger Deep, the deepest point on the ocean's floor, 11,000 m below the surface. What was the total inward force on the 1.1-m-diameter pilot sphere in which Cameron sat?

Hydrostatic pressure:
The pressure exerted by a liquid at a depth inside it is called hydrostatic pressure.

This pressure is given as rho g h

where h is the depth from the free surface,

g is the acceleration due to gravity,

rho is the density of the fluid.

This pressure is proportional to the depth.

The pressure is the same at all points at the same depth.

The pressure is due to the weight of the liquid.pressure

Answer 1

410585609.949 N

Step-by-step explanation:

`P_0` = Atmospheric pressure = 101325 Pa

`\rho` = Density of water = 1000 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

h = Depth = 11000 m

d = Diameter = 1.1 m

r = Radius =
`(d)/(2)=(1.1)/(2)=0.55\ m`

Pressure on the sphere is given by

`P=P_0+\rho gh\\\Rightarrow P=101325+1000* 9.81* 11000\\\Rightarrow P=108011325\ Pa`

Area of sphere is given by

`A=4\pi r^2\\\Rightarrow A=4\pi 0.55^2\\\Rightarrow A=3.80132\ m^2`

Force is given by

`F=PA\\\Rightarrow F=108011325* 3.80132\\\Rightarrow F=410585609.949\ N`

The inward force on the sphere is 410585609.949 N