An electrical short cuts off all power to a submersible...

An electrical short cuts off all power to a submersible diving vehicle when it is 30 m below the surface of the ocean. The crew must push out a hatch of area 0.75 $\mathrm{m}^{2}$ and weight 300 $\mathrm{N}$ on the bottom to escape. If the pressure inside is 1.0 atm, what downward force must the crew exert on the hatch to open it?

Key Concepts

Pressure Unit Conversion

Unit conversion, especially between atmospheres and pascals, is a key concept in solving fluid mechanics problems. Atmospheric pressure is often given in atm, where 1 atm is equivalent to 101325 Pa. Converting between these units allows for the proper application of formulas and ensures consistency in calculations across different measurement systems.

Hydrostatic Pressure

This concept refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. The pressure increases with depth in a fluid and is calculated using the formula P = P? + ?gh, where P? is the pressure at the surface, ? is the fluid density, g is the acceleration due to gravity, and h is the depth. Understanding hydrostatic pressure is crucial when analyzing how pressure differences occur in submerged environments.

Pressure Difference

Pressure difference is a critical concept in fluid mechanics that examines how variations in pressure across a boundary can generate net forces. In closed systems, such as a hatch, the difference between the internal pressure and the external pressure must be overcome to initiate movement or opening. This concept is fundamental when considering the effects of environmental pressures acting on submerged structures.

Force and Pressure Relationship

This principle explains that force is the product of pressure and the area over which it acts, as given by the formula F = ?P × A. In the context of the problem, the crew must counteract the net force created by the pressure difference acting on the hatch’s surface area. Recognizing this relationship is essential for solving problems that involve pressure-induced forces.

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