# Buoyancy Problem - Cubes in water

I have a tank with water (10 m high) , with an ideal seal at the bottom (water can't fall down, but can enter bodies).

I have a system of 6 cubes ( of polystyrene density= 20 Kg/m^3) with dimension 1x1x1 m. These cubes are connected with a rope (volume negligible). They are in vertical column, and are all submerged except one, that is out in the bottom part.

So there is a buoyancy force (the 5 cubes) that will pull up, the weight forces of the cubes (rope volume and weight negligible) that go downwards, and the opposing force at the bottom, in the seal for the cube that is out. This force is caused for the column of water.

The result of all this forces doesn't allow the bottom cube to penetrate completely (case impossible). Is the buoyancy force sufficient to lift the bottom cube into the water, given that the column of water is pressing down on the seal? If the cube does get pulled up, then how far?

-
Thank you EnergyNumbers, very kind. Here's the link: IMAGE 1 i39.tinypic.com/30ic4s6.jpg IMAGE 2 i43.tinypic.com/mwuopj.jpg and a video too youtube.com/watch?v=JrhurV3pp1I – Kamira Jun 8 '13 at 10:28
Ok Energy. Thanks for pacience and explaining how it goes in this forum. I will add, my road, but i think i will be wrong. – Kamira Jun 8 '13 at 11:27
That's ok: we're here to explain the concepts to each other: so if you set out your calculations, we can see where, if anywhere, you're going wrong, and set out the right concepts for you then to get the calculation right. – EnergyNumbers Jun 8 '13 at 11:51
Here Energy, thank you!: oi39.tinypic.com/2vd0ht4.jpg – Kamira Jun 8 '13 at 13:03
I have 3 more images.A real case, do thes computation convince you ? IMAGE1 oi43.tinypic.com/2yukin5.jpg IMAGE2 oi40.tinypic.com/2vdi7ub.jpg IMAGE3 oi40.tinypic.com/nf5u13.jpg – Kamira Jun 12 '13 at 9:31

No, the buoyancy of the upper cubes can never be enough to even begin to pull the bottom cube into the water.

Note that only the pressures on the top and bottom surfaces of the cubes are relevant. For each cube in the water, the difference in this pressure is related to the height of the cube, since each cube has the same horizontal crossection. The total buoyancy force from the string of cubes is therefore proportional to the total height of all the floating cubes. However, the downward pressure on the top face of the cube trying to enter at the bottom is the full water column height. This is clearly more than the total height of all the cubes, and can never be less than the height of all the floating cubes.

This is one of the "free energy" concepts that pop up regularly. Usually they have it "almost working", just need funding to perfect the bottom seal. It seems there will always be a supply of people that didn't pay attention in physics class.

-
Here my calculation. The cube will never penetrate totally. But Will it penetrate a little? Who cans...can you put this image in the post ? i39.tinypic.com/2vd0ht4.jpg – Kamira Jun 8 '13 at 12:51
Olin. Thanks. I am not interested in free energy. Neither in perpetual motion. I just want to understand this problem. It's not necessary to be offensive using frase as "t seems there will always be a supply of people that didn't pay attention in physics class." I just want to understand, and i ask for help. – Kamira Jun 8 '13 at 12:57
@Kamira: No need to be defensive. I didn't say you were trying to make a free energy machine, just pointing out that this concept comes up regularly in that context. No, the bottom cube won't penetrate at all. The force pulling it up by the rope will never exceed the force of the full water column pressing on its top surface. If these weren't cubes but tapered instead, then the bottom object would penetrate the seal partly until its cross sectional area times the water column pressure ballanced the upward pull on the rope. – Olin Lathrop Jun 8 '13 at 13:17
Thank you Olin :) . So Where is my mistake in my calculation? And from the unstable situation...the cubes will move up...and stops exactly when the bottom cube will touch the seal and the water? Is it correct? And the calculation and steps for demostrate it? – Kamira Jun 8 '13 at 13:27
We can says that due the inertia gained from the initial postition the cube penetrate a little but then the force due the column of water push the bottom cube completely out, until the stable final position. (Cube out) Isn't it? – Kamira Jun 9 '13 at 13:37