Keep working on the liquid pressure problem

[vxiaoyu18]

Homework Statement

Deep understanding of liquid pressure formula.

Relevant Equations

F=ρgSH

Without calculating the friction, if the force of gravity on the piston, the initial force F on the piston S is what?
1. F=-ρgSH;
2. F=-（1/2）ρgSH;
3. F=0;
4. Other.
I'm not sure which is the correct result, can someone help me analyze it again?

 

[Chestermiller]

The force on the left side of the blue piston is $-\rho g H S_1$. This must also be the force on the right side of the blue piston. So, the pressure inside the compartment must be $-\rho g H/2$ (since the area on the right side of the blue piston is twice the area on the left side of the blue piston). Since S = S1, that means that the force on the left and right sides of the red piston must be $-\rho gH S/2$.

 

[vxiaoyu18]

Thank you for your patience. I finally understand. The calculation process of this method is very clear. Is F=-（1/2）ρgSH.

 

[Chestermiller]

Thank you for your patience. I finally understand. The calculation process of this method is very clear. Is F=-（1/2）ρgSH.

That's what I said.