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1 month ago

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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?

2 answers:

serg [3.5K]1 month ago

8 0

Answer:

$4.1\cdot 10^8 N$

Explanation:

To begin with, we must determine the pressure acting on the sphere, which is calculated using:

$p=p_0 + \rho g h$

where

$p_0 =1.01\cdot 10^5 Pa$ denotes the atmospheric pressure

$\rho = 1000 kg/m^3$ represents the density of the water

$g=9.8 m/s^2$ signifies the acceleration due to gravity

$h=11,000 m$ indicates the depth

By substituting these values,

$p=1.01\cdot 10^5 Pa + (1000 kg/m^3)(9.8 m/s^2)(11,000 m)=1.08\cdot 10^8 Pa$

The sphere's radius is calculated as r = d/2 = 1.1 m/2 = 0.55 m

Thus, the sphere's total surface area can be expressed as

$A=4 \pi r^2 = 4 \pi (0.55 m)^2=3.8 m^2$

Consequently, the inward force acting on the sphere equals

$F=pA=(1.08\cdot 10^8 Pa)(3.8 m^2)=4.1\cdot 10^8 N$

Ostrovityanka [3.2K]1 month ago

4 0

The inward force acting is approximately 4.1 × 10⁸ N

$\texttt{ }$

Further explanation

Let’s revisit the Hydrostatic Pressure equation, expressed as follows:

$\boxed{ P = \rho g h}$

where:

P = hydrostatic pressure ( Pa )

ρ = fluid density ( kg/m³ )

g = acceleration due to gravity ( m/s² )

h = height of the liquid column ( m )

Now, let’s solve the problem!

$\texttt{ }$

Given:

depth of the ocean floor = h = 11 000 m

diameter of pilot sphere = d = 1.1 m

atmospheric pressure = Po = 10⁵ Pa

Required:

total inward force = F =?

Solution:

$F = P A$

$F = ( P_o + \rho g h ) A$

$F = ( P_o + \rho g h ) ( \pi d^2 )$ → Area of Sphere = π d²

$F = ( 10^5 + 1000 \times 9.8 \times 11000 ) ( \pi \times 1.1^2 )$

$F \approx 4.1 \times 10^8 \texttt{ Newton}$

$\texttt{ }$

Conclusion:

The inward force totals around 4.1 × 10⁸ N

$\texttt{ }$

Learn more

Buoyant Force:

Kinetic Energy:

Volume of Gas:

Impulse:
Gravity:

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Pressure

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