Question

A submarine is stranded on the bottom of the ocean with its hatch 21.0 m below the surface. calculate the force (in n) needed to open the hatch from the inside, given it is circular and 0.420 m in diameter. air pressure inside the submarine is 1.00 atm.

Answer 1

28,400 N

Step-by-step explanation:

Let's start by calculating the pressure that acts on the upper surface of the hatch. It is given by the sum of the atmospheric pressure and the pressure due to the columb of water, which is given by Stevin's law:

`p_(top) = p_(atm) + \rho g h=1.013\cdot 10^5 Pa + (1000 kg/m^3)(9.8 m/s^2)(21.0 m)=3.071 \cdot 10^5 Pa`

On the lower part of the hatch, there is a pressure equal to

`p_(bot)=p_(atm)=1.013\cdot 10^5 Pa`

So, the net pressure acting on the hatch is

`p=p_(top)-p_(bot)=3.071 \cdot 10^5 Pa - 1.013\cdot 10^5 Pa=2.058 \cdot 10^5 Pa`

which acts from above.

The area of the hatch is given by:

`A=\pi r^2 = \pi ((0.420 m)/(2))^2=0.138 m^2`

So, the force needed to open the hatch from the inside is equal to the pressure multiplied by the area of the hatch:

`F=pA=(2.058\cdot 10^5 Pa)(0.138 m^2)=28,400 N`