Final answer:
The minimum force to open the diving bell hatch is calculated by determining the pressure difference between the inside and the water pressure at the maximum depth, and then multiplying this difference by the area of the circular hatch.
Step-by-step explanation:
To calculate the minimum force necessary to lift open the hatch of the bell at the maximum depth, we need to consider the difference in pressure inside and outside the diving bell. The pressure outside at a depth of 25.0 meters in seawater is due to the weight of the water column above the hatch and the atmospheric pressure at the surface. With the air pressure inside the bell being equal to 1.00 atm, we calculate the outside pressure using the equation for pressure at depth (P = P0 + ρgh), where P0 is atmospheric pressure at the surface, ρ is the density of seawater (approximately 1025 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and h is the depth (25.0 m). The force required to open the hatch is then the product of this pressure difference and the area of the hatch.
The area of a circle is calculated using the formula A = πr², where r is the radius of the circle. For a hatch with a diameter of 0.450 m, the radius r is 0.225 m. Once we have the area, we multiply it by the pressure difference to get the force needed to open the hatch.