U-shaped tube, pressure problem, what am i doing wrong?

[jenzao]

Homework Statement

What am I doing wrong in this pressure problem?
a U-shaped tube is filled with water.
left side area of opening is .05m^2
right side is .08m^2
the right side water level is .43m HIGHER than the left side, because two pistons push down on either side with different force on each side.
the force pushing down on right side is 138N

Q: What is the force pushing down on left side?

Homework Equations

I know that P=F/A and also P= Pnaught + rho*g*h

The Attempt at a Solution

so i rearrange to get F=PA
and P=rho*g*h (because i can factor out air pressure (Pnaught) because of the pistons,
so i now have F= rho*g*h*A
This is wrong though, and i can't figure out why, please help! thanks

 

[mgb_phys]

You are looking for the extra pressure needed to make the side 0.43m higher
So you need the pressure to lift 0.43m of water, this is just the static pressure at the bottom of that extra water column.

The extra pressure on the input piston is the same as this - then to get the force just use the area - be carefu about which area you are using.

 

[nlightner]

It seems like you have the right equations and approach to solving this problem. However, it's important to note that the pressure on each side of the U-shaped tube is equal, despite the different forces pushing down on each side. This is due to the fact that the water is at the same height on both sides of the tube, creating an equilibrium of pressure. So, the equation you should be using is P = F/A, where P is the pressure on both sides of the tube. To solve for the force on the left side, you can rearrange the equation to F = P*A. You can then plug in the known values of P (which is the same on both sides) and A (from the given area of the opening) to solve for the force on the left side. I hope this helps!