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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?

Respuesta :

skyluke89

Answer:

[tex]4.1\cdot 10^8 N[/tex]

Explanation:

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

[tex]p=p_0 + \rho g h[/tex]

where

[tex]p_0 =1.01\cdot 10^5 Pa[/tex] is the atmospheric pressure

[tex]\rho = 1000 kg/m^3[/tex] is the water density

[tex]g=9.8 m/s^2[/tex] is the gravitational acceleration

[tex]h=11,000 m[/tex] is the depth

Substituting,

[tex]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[/tex]

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

So the total area of the sphere is

[tex]A=4 \pi r^2 = 4 \pi (0.55 m)^2=3.8 m^2[/tex]

And so, the inward force exerted on it is

[tex]F=pA=(1.08\cdot 10^8 Pa)(3.8 m^2)=4.1\cdot 10^8 N[/tex]

johanrusli

The total inward force is about 4.1 × 10⁸ N

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Further explanation

Let's recall Hydrostatic Pressure formula as follows:

[tex]\boxed{ P = \rho g h}[/tex]

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!

[tex]\texttt{ }[/tex]

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:

[tex]F = P A[/tex]

[tex]F = ( P_o + \rho g h ) A[/tex]

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

[tex]F = ( 10^5 + 1000 \times 9.8 \times 11000 ) ( \pi \times 1.1^2 )[/tex]

[tex]F \approx 4.1 \times 10^8 \texttt{ Newton}[/tex]

[tex]\texttt{ }[/tex]

Conclusion:

The total inward force is about 4.1 × 10⁸ N

[tex]\texttt{ }[/tex]

Learn more

  • Buoyant Force : https://brainly.com/question/13922022
  • Kinetic Energy : https://brainly.com/question/692781
  • Volume of Gas : https://brainly.com/question/12893622
  • Impulse : https://brainly.com/question/12855855
  • Gravity : https://brainly.com/question/1724648

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure

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