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

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

What a cool problem.  To cast it a little bit differently:

A flat-bottomed object of density rho_o and volume V_o is in a
flat-bottomed vessel filled to a depth h (with the object in it) with
fluid of density rho_f < rho_o.  Find the area of the spot of glue (that
cannot be penetrated by the fluid) needed to glue the object to the
bottom of the vessel such that the average normal stress in a horizontal
cross-section of the glue is zero.  Find the diameter of a thin circular
disk of such glue for the case of a wooden cube of edge length 50 cm and
density half that of fresh water, in fresh water of depth 1 meter.

I posted a solution at:

< http://www.anselm.edu/internet/physics/phys-l/glueProb.pdf> 

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of LaMontagne, Bob
> Sent: Thursday, October 21, 2010 1:32 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Definition of upthrust or buoyancy
>
> 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?
>
> Bob at PC