Re: [Phys-l] Definition of upthrust or buoyancy

[John Denker <jsd@av8n.com>]

On 10/21/2010 01:32 PM, LaMontagne, Bob wrote:
> If you will put up with me talking to myself here, let me extend your
> example to clarify something for myself. If I slightly revise your
> example to, say, two cups put together rim to rim with an O-ring
> between the rims and plunge them under water, they will stay together
> because of the net compression pushing the two halves together. But
> if I glue a string to the bottom of one of the cups, the pair will
> float upward because they are less dense overall than water, but the
> string stopping them from rising will be under tension - even though
> the O-ring is in compression.
>
> If the bottom of one of the cups is glued to the botton of the pond
> with no water between the cup and the pond, the cups are still under
> net compression along the O-ring. If I am following the arguments
> being made correctly, the claim would be that the glue is actually
> under compression as well.
>
> I guess the question I am wrestling with is how small can I make the
> glob of glue so it no longer covers the bottom of the cup completely
> and now starts acting like a string and becomes under tension. What
> is the essence of that transition from compression to tension?

Interesting question.  I didn't see that one coming.

Dimensional analysis suffices:   A = F / P
  where A = area of glue
        F = net buoyant force of object
        P = pressure

If you want more detail, consider an object tied by a string to
a piston, and ask for the relationship between pressure, piston
area, and tension in the string.