How Do Piston Forces Compare in Balancing Different Masses?

[Garrant3]

Homework Statement

Rank in order, from largest to smallest, the magnitudes of the forces F1, F2, and F3 required for balancing the masses shown in the figure.
There are three pictures of different kinds of pistons. In the first picture, there are four pistons: three with 500 kg masses on top, and one where F1 is pushing down. In the second, there are three pistons: two with 600 kg masses on top, and one where F2 is pushing down. In the third, there are only two pistons: one with a 600 kg mass and another with F3 pushing down.

Homework Equations

I know that Pascal's Principle is important, that when a force is applied the pressure is distributed equally throughout the fluid. The area of the pistons are all equal, or so I think I can assume because the values aren't given.

The Attempt at a Solution

I thought that for the first picture with the 500 kg masses, F1 would just have to equal 500(9.81), right? And then that force would push up equally on the three other pistons and balance them. And then for the second two pictures it would just be 600(9.81). So F2 and F3 would both have to be the largest. I tried that though and got it wrong. Any suggestions?

 

[cupid.callin]

I all the surface areas (including where masses are kept) then i guess that each force must be equal to the mass he has to support!

Edit: force must be equal to the weight he has to support!

 

[SammyS]

The Attempt at a Solution

I thought that for the first picture with the 500 kg masses, F1 would just have to equal 500(9.81), right? And then that force would push up equally on the three other pistons and balance them. And then for the second two pictures it would just be 600(9.81). So F2 and F3 would both have to be the largest. I tried that though and got it wrong. Any suggestions?

Hi Garrant.

I agree with your analysis.

Are you sure that the areas of the pistons are the same, within anyone picture, and that the elevations of the pistons are all the same?

 

[Garrant3]

Thanks for the responses!
I'll try to recreate the picture to see if it helps at all. @Sammy the only values given are the masses, so it's tough to tell for sure.

Picture 1: _ __ __ __

Picture 2: _ __ __

Picture 3: _ __

The forces are being exerted on the smaller surfaces, and the masses are on the longer ones, but I don't think that would make much of a difference in my answer, would it?

 

[cupid.callin]

Ummm ... No