A submarine rests on the ocean floor at a depth of 800 m. Calculate A) the pressure at this depth and B) the force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere.

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**Problem Statement:**

A submarine rests on the ocean floor at a depth of 800 meters. Calculate:

A) The pressure at this depth.

B) The force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere.

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**Detailed Explanation:**

To solve this problem, we need to consider the concepts of pressure in fluids and forces exerted on surfaces due to pressure differences.

**Part A: Calculating Pressure at Depth**

The pressure at a certain depth in a fluid is given by the formula:

\[ P = P_0 + \rho g h \]

Where:
- \( P \) is the pressure at depth.
- \( P_0 \) is the atmospheric pressure at the surface (1 atmosphere = 101,325 Pa).
- \( \rho \) is the density of seawater (approx. 1025 kg/m³).
- \( g \) is the acceleration due to gravity (9.81 m/s²).
- \( h \) is the depth (800 m).

Substitute these values to find the pressure at 800 meters.

**Part B: Calculating the Force on the Hatch**

Once the pressure at 800 meters is found, the force on the hatch can be determined using:

\[ F = (P - P_{\text{inside}}) \cdot A \]

Where:
- \( F \) is the force acting on the hatch.
- \( P_{\text{inside}} \) is the pressure inside the hatch (1 atmosphere = 101,325 Pa).
- \( A \) is the area of the hatch (0.6 m²).

Calculate the difference in pressure between the outside and the inside of the hatch, and then multiply by the area to get the force.
Transcribed Image Text:**Problem Statement:** A submarine rests on the ocean floor at a depth of 800 meters. Calculate: A) The pressure at this depth. B) The force acting on a 0.6 m² hatch on the conning tower of the submarine, assuming that the pressure inside the hatch is 1 atmosphere. --- **Detailed Explanation:** To solve this problem, we need to consider the concepts of pressure in fluids and forces exerted on surfaces due to pressure differences. **Part A: Calculating Pressure at Depth** The pressure at a certain depth in a fluid is given by the formula: \[ P = P_0 + \rho g h \] Where: - \( P \) is the pressure at depth. - \( P_0 \) is the atmospheric pressure at the surface (1 atmosphere = 101,325 Pa). - \( \rho \) is the density of seawater (approx. 1025 kg/m³). - \( g \) is the acceleration due to gravity (9.81 m/s²). - \( h \) is the depth (800 m). Substitute these values to find the pressure at 800 meters. **Part B: Calculating the Force on the Hatch** Once the pressure at 800 meters is found, the force on the hatch can be determined using: \[ F = (P - P_{\text{inside}}) \cdot A \] Where: - \( F \) is the force acting on the hatch. - \( P_{\text{inside}} \) is the pressure inside the hatch (1 atmosphere = 101,325 Pa). - \( A \) is the area of the hatch (0.6 m²). Calculate the difference in pressure between the outside and the inside of the hatch, and then multiply by the area to get the force.
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