Question

You inspect a submarine a submarine and the customer wants to know the maximun safe depth it can operate at. The biggest concern is a 17.2cm diameter window which is 8.6cm thick. The glass can withstand forces up to 1.1*10^6 N. What is the submarine's maximum safe depth? The pressure inside the sub is maintained at 1.0 atm.

What is the maximum depth the sub can go to without worrying about the window?

A: .0147 m

B: 4690.11 m

C: .0418 m

D: 34.688 m

E: 144397.12 m

F: none of the above

EQUATIONS WOULD BE APPRECIATED SO I CAN TRY AND UNDERSTAND IT.

Answer 1

Answer 2

area of window = pi * d^2 / 4 = pi *(0.172^2)/4 = 0.0232352192659501 m^2
Let us say the depth is h meters,
then the pressure at that point = ( density of water * g * h) + P0 atm
P0 = atmospheric pressure = 1 atm , g = acceleration due to gravity = 9.8 m/s^2
so, Pressure at the point = ( 1000 * 9.8 * h) + 1
Pressure inside =1 atm
so, force acting on glass = (Pressure at that point - Pressure inside) * area
force = 1.1 * 10^6 = (( 1000 * 9.8 * h) + 1-1) * 0.0232352192659501
By solving the above,
h = 4690.11 m is the answer.