Asking for help with a physical problem that uses a piston to push water

[vxiaoyu18]

@Baluncore is saying to consider the area S as made of two areas ...

Can you think of it this way, that if you don't change the height, no matter what S₂' prime does, it doesn't matter what S₁' prime does, and the value of F stays the same? Is F =-ρgHS1.

 

[vxiaoyu18]

I think I've figured out how to do it, and I can do it very quickly with PASCAL's law.
1. F=-ρgSH;
2. F=-（1/2）ρgSH;
3. F=-（1/2）ρgS（H₁+H₂）;
4. F =-ρgS(H₁+H₂).

Thanks for the answer, and I think I'm pretty sure now that the answer is correct, which is to use PASCAL's law.

 

[vxiaoyu18]

The sign of F will depend on convention. F = - ρ⋅g⋅H⋅S₁

Watch out for fires in your national forests. Be safe. Hope you get through this soon.