Final answer:
To open a submerged hatch, the crew must overcome the external water pressure at 25 meters depth, minus the internal atmospheric pressure, while also accounting for the weight of the hatch. The calculation involves converting pressures to force by multiplying with the hatch area and then comparing the two to find the force needed to push upwards.
Step-by-step explanation:
The subject question pertains to the force required to open a hatch on a submerged vehicle, taking into account the external water pressure at a depth and the atmospheric pressure inside the vehicle. To calculate the total force needed to push the hatch open, we must consider both the water pressure acting on the hatch from outside and the opposing force provided by the internal pressure.
Water pressure increases with depth due to the weight of the water above. At a depth of 25 meters, the water pressure can be calculated using the formula P_water = ρgh, where ρ is the density of the water, g is the acceleration due to gravity, and h is the depth. The atmospheric pressure inside the vehicle is given as 1.0 atm. The total force exerted by the water pressure on the hatch is the product of the pressure and the area of the hatch (P_water × Area).
To find the total force needed to push the hatch open, we subtract the force due to the internal pressure from the force due to the external water pressure. The force due to internal pressure is simply the atmospheric pressure converted into Newtons (since 1 atm = 101,325 Pa) multiplied by the area of the hatch (1.0 atm × Area).
The difference between the external force due to water pressure and the internal atmospheric force, plus the weight of the hatch, gives us the total force that the crew must exert to push the hatch open.