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?

Answer 1

Answer:

$4.1\cdot 10^8 N$

Explanation:

First of all, we need to find the pressure exerted on the sphere, which is given by:

$p=p_0 + \rho g h$

where

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

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

$g=9.8 m/s^2$ is the gravitational acceleration

$h=11,000 m$ is the depth

Substituting,

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

The radius of the sphere is r = d/2= 1.1 m/2= 0.55 m

So the total area of the sphere is

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

And so, the inward force exerted on it is

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

Answer 2

The total inward force is about 4.1 × 10⁸ N

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Further explanation

Let's recall Hydrostatic Pressure formula as follows:

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

where:

P = hydrosatic pressure ( Pa )

ρ = density of  fluid ( kg/m³ )

g = gravitational acceleration ( m/s² )

h = height of a column of liquid ( m )

Let us now tackle the problem!

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Given:

depth of the ocean's floor = h = 11 000 m

diameter pilot sphere = d = 1.1 m

atmospheric pressure = Po = 10⁵ Pa

Asked:

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

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

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

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Conclusion:

The total inward force is about 4.1 × 10⁸ N

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Learn more

• Buoyant Force : brainly.com/question/13922022

• Kinetic Energy : brainly.com/question/692781

• Volume of Gas : brainly.com/question/12893622

• Impulse : brainly.com/question/12855855
• Gravity : brainly.com/question/1724648

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure