# I Floating, hydrostatic forces, average density

1. Aug 21, 2016

### fog37

Hello Forum,
I am revisiting Archimedes principle and its important consequences.
I am aware that a cube (homogeneous) made of iron will always sink in water regardless of its mass. If we changed the iron cube into a different shape (cone, cylinder, prism, parallelepiped, etc.), the object would still sink. However, there are some possible transformations that can morph the iron cube into something that is able to float. This is often explained by saying that the "average' density of the object has become lower than the water density due to the inclusion of areas of emptiness in the calculation of the total volume. That is a good explanation but it hides a lot of interesting details. Essentially, I would like to gain a more detailed and qualitative understanding of why an iron cube sinks while a ship of the same mass floats. Archimedes force is the vertical upward directed component of net force which derives from the vectorial sum of the all the hydrostatic elementary normal forces acting on the surface of the immersed object. From the perspective of the hydrostatic normal force distribution that water exerts, what is different in the hydrostatic force distribution for the iron cube and for the iron boat? The mass, hence the weight is the same. The change in shape essentially leads to a redistribution of the mass. A computer calculation can provide the accurate answer but does anyone have some insight in what happens when we transform a homogenous sinking object into something (like a basin) that can float?

Thanks for any thoughts!

2. Aug 22, 2016

### Staff: Mentor

You just need its [under water] shape to be such that the body can displace more weight of water than its own weight, then it will float.

Last edited: Aug 22, 2016
3. Aug 22, 2016

### jbriggs444

One key difference between a boat and something that is almost a boat is that a boat does not leak.

4. Aug 22, 2016

### A.T.

Because the ship displaces more water.

5. Aug 22, 2016

### Staff: Mentor

Have you considered morphing a solid cube into a hollow cube enclosing much more volume with the same mass?

6. Aug 23, 2016

### fog37

Thanks everyone.

I see how one shape (the boat shape) must displace more water than the cube because that larger displaced mass of water corresponds to a larger buoyancy force. But I would like to understand, from a qualitative point of view, why that happens for the hull shape. The elementary forces add up to a larger vertical push (Archimedes force)...

7. Aug 24, 2016

### A.T.

https://arxiv.org/pdf/1110.5264.pdf