Final answer:
To find the force needed to open a submarine hatch underwater, calculate the water pressure using the formula P = ρgh and then calculate the force on the hatch by multiplying this pressure by the hatch's area. Subtract the force due to internal air pressure to get the total force needed.
Step-by-step explanation:
To calculate the force needed to open a submarine hatch underwater, we need to decide the water pressure at the depth where the submarine is located. According to the information given, the submarine hatch is situated 25.0 m below the surface. The water pressure can be found using the formula P = ρgh, where ρ is the density of the water, g is the acceleration due to gravity, and h is the depth.
The density of seawater is approximately 1025 kg/m³, and the standard acceleration due to gravity is 9.81 m/s³. Therefore, the water pressure at the depth of 25.0 m is P = 1025 kg/m³ × 9.81 m/s³ × 25.0 m.
Once we have the water pressure, we can determine the force exerted on the hatch using this pressure and the area of the hatch. The hatch is circular with a diameter of 0.450 m, so its area, A, can be found using the formula for the area of a circle, A = πr², where r is the radius of the hatch.
Since the atmospheric pressure is also acting on the other side of the hatch from inside the submarine, the total force needed to open the hatch is the difference between the force due to external water pressure and the force due to internal air pressure.
This requires us to calculate the force due to air pressure (1.00 atm) and subtract it from the force due to the water pressure calculated earlier. However, it's necessary to ensure both pressures are in the same units before performing the subtraction.