Final answer:
To determine the maximum safe depth for the submarine's window, calculate the pressure it can withstand, convert it to depth using the relationship between pressure and depth in a fluid, and add the atmospheric pressure inside the submarine.
Step-by-step explanation:
To find the maximum safe depth the submarine can reach without the window breaking, we need to calculate the difference between the external pressure exerted by the seawater at a certain depth and the internal pressure, which is 1 atm (maintained inside the submarine). Since the force the window can withstand is given as 1.1×106 N, and pressure is force per unit area, we will first find the area of the 40-cm-diameter window using the formula for the area of a circle (πr2). The radius r is half of the diameter, so r = 20 cm = 0.2 m. The area A = π(0.2 m)2 = 0.1256 m2. Now, we convert the maximum force into pressure by dividing by the area, P = F/A = 1.1×106 N / 0.1256 m2 = 8.75×106 Pa.
The external pressure at a certain depth d in seawater can be found using the formula P = ρgd, where ρ is the density of seawater (approximately 1025 kg/m3), g is the acceleration due to gravity (9.81 m/s2), and d is the depth in meters. The internal pressure (1 atm) is equivalent to 101,325 Pa. Therefore, the maximum external pressure the window can withstand is Pmax = 8.75×106 Pa + 101,325 Pa.
Solving for d gives d = (Pmax - Patm) / (ρg). Substituting the values, d = (8.75×106 Pa + 101,325 Pa) / (1025 kg/m3 × 9.81 m/s2) yields the depth that corresponds to the maximum safe limit for the submarine's window.