What Is the Maximum Safe Depth for the Submarine with a 40cm Window?

[KINkid92]

Homework Statement

A research submarine has a 40.0cm -diameter window 8.70cm thick. The manufacturer says the window can withstand forces up to 1.20×10^6N . What is the submarine's maximum safe depth?

Homework Equations

P= atmosheric pressure + ρg(depth)
Pressure = Force/crossectional area

The Attempt at a Solution

1.2*10^6N/∏(.4/2)^2= Safe pressure
9.55*10^6N/m^2=Psafe

Psafe= 1atm+ρgd=101300N+1025kg/m^3*9.8m^2
9.55*10^6kg/m^3/m^2=101300kg*m/s^2+ 1025kg/m^3*9.8m^2


I really just don't even know how to proceed figuring out this moshpit of units or even if I'm doing this right in the first place?

 

[voko]

What's the pressure inside the submarine and what is the difference with the total water pressure?

 

[KINkid92]

Inside the sub is 1 atm. And what do you mean? Difference between which values?

 

[voko]

If the pressure inside is equal to the pressure outside - will there be any force on the window?

 

[Nickie]

Don't worry, it's common to feel overwhelmed when dealing with multiple units in a problem. Let's break it down step by step.

First, let's convert the diameter of the window from centimeters to meters. We can do this by dividing 40.0cm by 100cm/1m. This gives us a diameter of 0.4m.

Next, let's use the formula for pressure: P= F/A. We know the force is 1.2×10^6N and the area is the cross-sectional area of the window, which is πr^2, where r is the radius. We already have the diameter, so we can divide it by 2 to get the radius. So the area is π(0.4/2)^2 = 0.0503m^2.

Now we can plug these values into the formula and solve for the safe pressure: P = 1.2×10^6N/0.0503m^2 = 2.39×10^7N/m^2.

Next, we need to calculate the pressure at the maximum safe depth of the submarine. We can use the formula P= ρgd, where ρ is the density of water, g is the acceleration due to gravity, and d is the depth. We can rearrange this formula to solve for d: d = P/ρg. Plugging in the values, we get d = 2.39×10^7N/m^2 / (1025kg/m^3 * 9.8m/s^2) = 244.9m.

Therefore, the maximum safe depth for the submarine is approximately 244.9 meters. It's important to always double check your units and make sure they cancel out correctly in the final answer. You did well in your attempt, just remember to pay attention to the units and convert them when necessary. Keep up the good work!