Crew members attempt to escape from a damaged submarine 112 m below the surface. How much force must they apply to a pop-out hatch, which is 1.22 m by 0.590 m, to push it out?

To determine the force required to push open a hatch of a submarine located 112 meters underwater, we need to consider the pressure exerted by the water at that depth and the area of the hatch itself. The pressure increases with depth due to the weight of the water above, and we'll factor that in to find the force needed to open the hatch.

Calculating Water Pressure

The pressure exerted by a fluid in a gravitational field is given by the formula:

P = ρgh

• P is the pressure in pascals (Pa).
• ρ is the density of the fluid (for seawater, it's approximately 1025 kg/m³).
• g is the acceleration due to gravity (approximately 9.81 m/s²).
• h is the depth in meters (in this case, 112 m).

Plugging in the values, we calculate the pressure:

P = 1025 kg/m³ × 9.81 m/s² × 112 m

Calculating this gives:

P ≈ 112,000 Pa (pascals), or about 112 kPa.

Determining the Hatch Area

The area of the hatch can be calculated using the dimensions provided:

Area = length × width

For the hatch measuring 1.22 m by 0.590 m:

Area = 1.22 m × 0.590 m

Calculating this gives an area of:

Area ≈ 0.7198 m².

Calculating the Force Required

The force exerted by the water pressure on the hatch can be calculated using:

Force = Pressure × Area

Substituting the values we have:

Force = 112,000 Pa × 0.7198 m²

Calculating this results in:

Force ≈ 80,600 N (newtons).

Summary of Required Force

In summary, the crew members would need to apply a force of approximately 80,600 newtons to open the hatch against the pressure of the water at a depth of 112 meters. This force is significant and highlights the challenges faced in underwater escapes. Therefore, the design of submarine hatches must account for such high pressures to ensure they can be opened in emergencies.