Final answer:
The maximum depth the submarine can go without damaging the window is approximately 5.59 meters.
Step-by-step explanation:
To determine the maximum depth the submarine can go without damaging the window, we need to consider the pressure exerted by the water at that depth. The pressure at a certain depth in a fluid can be calculated using the formula:
Pressure = density × gravity × height
Given that the diameter of the window is 30 cm, we can calculate its radius (r) as 15 cm or 0.15 m. The area of the window (A) can be calculated using the formula for the area of a circle (A = πr^2). Since the force the window can withstand is mentioned, we can assume that the maximum pressure it can withstand is reached at its weakest point, which is at the center. Using the equation for pressure, we can solve for the maximum depth (h) as follows:
Pressure = Force / Area
Force = 5.20 × 105 N
Area = π × (0.15 m)^2
Pressure = 5.20 × 105 N / (π × 0.15 m^2)
Solving for the maximum depth:
Pressure = density × gravity × height
5.20 × 105 N / (π × 0.15 m^2) = 1000 kg/m^3 × 9.8 m/s^2 × height
height = (5.20 × 105 N / (π × 0.15 m^2)) / (1000 kg/m^3 × 9.8 m/s^2)
height ≈ 5.59 m