James Cameron piloted a submersible craft to the bottom of the Challenger Deep, the deepest point on the ocean's floor, 11,000 m

Answer:

Explanation:

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

where

denotes the atmospheric pressure

represents the density of the water

signifies the acceleration due to gravity

indicates the depth

By substituting these values,

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

Consequently, the inward force acting on the sphere equals

The inward force acting is approximately 4.1 × 10⁸ N

Further explanation

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

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!

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:

→ Area of Sphere = π d²

Conclusion:

The inward force totals around 4.1 × 10⁸ N

Learn more

• Buoyant Force:

• Kinetic Energy:

• Volume of Gas:

• Impulse:
• Gravity:

Answer details

Grade: High School

Subject: Physics

Chapter: Pressure