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3 years 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:

Over [174]3 years ago

8 0

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

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

riadik2000 [5.3K]3 years ago

4 0

The total inward force is about 4.1 × 10⁸ N

$\texttt{ }$

<h3>Further explanation</h3>

Let's recall Hydrostatic Pressure formula as follows:

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

<em>where:</em>

<em>P = hydrosatic pressure ( Pa )</em>

<em>ρ = density of fluid ( kg/m³ )</em>

<em>g = gravitational acceleration ( m/s² )</em>

<em>h = height of a column of liquid ( m )</em>

Let us now tackle the problem!

$\texttt{ }$

<u>Given:</u>

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

diameter pilot sphere = d = 1.1 m

atmospheric pressure = Po = 10⁵ Pa

<u>Asked:</u>

total inward force = F = ?

<u>Solution:</u>

$F = P A$

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

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

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

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

$\texttt{ }$

<h3>Conclusion:</h3>

The total inward force is about 4.1 × 10⁸ N

$\texttt{ }$

<h3>Learn more</h3>

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

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Pressure

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