Fluid mechanics sinking barrel

[xxxzyon]

Homework Statement

Suppose a cylindrical barrel falls off a ship and sinks to the bottom of the sea at a depth of 1.61 km. Assume that the seawater is incompressible, so that its density at the bottom of the sea is the same at the surface :1020 kg/m^3

If the pressure inside the barrel is 1.00 atm (it was sealed at sea level) and the total surface area of the barrel is 3.50 m^2 , find the NET INWARD FORCE acting on the surface of the barrel when it reaches the bottom of the ocean.

Homework Equations

P tot = Psurface + water x g x h
P= F/A

The Attempt at a Solution

For my attempt, I used the formula Ptot = P surface + ρ density of water x g x h.
The total pressure I got was 116 atm, then I plugged this pressure into P = F/A and got a force of 4. 67 x 10^6 N...

I am not sure what I am supposed to be doing first actually, any guidance would be helpful!

 

[paisiello2]

Can you show explicitly how you came up with the 116 atm?

 

[haruspex]

Sea surface pressure will balance the pressure inside the barrel, so you can ignore this for the 'net force'.
That in turn means there's no point in converting to atms. Do it all in MKS units. (I think you'll find you've made an arithmetic error.)

That said, I really don't like this question. Force is a vector; a net force involves performing a vector sum; the net force acting on the outside of the barrel is zero. Yes, you can take the pressure and multiply by the magnitude of the surface area, but the number that results has no physical meaning. Again, area is technically a vector here, so that multiplication should be done as a vector integral ∫P.dA = P∫dA = 0.
It is just possible that this is a trick question and the required answer is zero.