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Re: [Phys-l] definitions ... purely operational, or not



How is the strain gauge set up? If it's all within the shadow of the cube it probably won't register anything either way.

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Chuck Britton
Sent: Monday, November 08, 2010 9:04 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] definitions ... purely operational, or not

So the strain gauge measurement does or does NOT differ with water
under the block or not under the block?


At 1:51 PM -0700 11/7/10, John Denker wrote:
On 11/07/2010 07:35 AM, Chuck Britton wrote:

I have tried to avoid such definitional difficulties by specifying
at
strain-gauge style force measurement on the bottom of the aquarium.

Works for me.

Does the flexing of the bottom depend on whether a layer of water
exists between the lead cube and the bottom of the aquarium?

Just to be clear (since a number of variants have been mentioned)
we are comparing two cases:
a) The block has some narrow feet, such that there is water
*almost everywhere* between the block and the thing it is
resting on. The feet occupy a negligible percentage of the
area, but are needed to support the net weight of the block.
Here "net weight" means the total dry weight minus the buoyancy.
b) The block has no feet, and conforms to the bottom of the
aquarium, so that there is water *almost nowhere* between
the block and the thing it is resting on.

I think
not, but others seem to differ in there opinions? or not.

There is no difference in the total force between case (a) and
case (b). There are profound force-balance arguments and
conservation of momentum arguments that require it.

There may be subtle differences in how the force is distributed,
but these can be minimized by artful engineering. Fluids
automatically
distribute the force evenly, whereas solid/solid contacts might not.

I'm also trying to avoid the need for 'suction-cup effects' in
this analysis.

You can't avoid it. Not in case (b) anyway.

Think about it in terms of the principle of virtual work. If
the notion of "force" is to mean anything at all, we need to
consider what happens if we raise the block an infinitesimal
amount. Thereupon either an infinitesimal amount of water
rushes into the gap underneath the block ... or it doesn't.
The force that you get is wildly sensitive to this.

I've said it about five times now: This issue is absolutely
central to the entire discussion. You can get any answer you
want, positive or negative, depending on whether you assume
the water can weasel in or not. People will continue talking
past each other and going around in circles until they deal
with this issue.

As I said in my very first note on the topic, the case of a
block "just barely" conforming to the shape of the bottom is
a pathological case. More formally, it is a singular limit.
The water pressure is present for all h>0 and absent for all
h<0. And vice-versa for the solid/solid contact force. The
sum of the two is constant, but if you insist on asking about
the two forces separately, there is going to be a discontinuity.

Some clever person (CB) suggested using a trampoline to soften
the discontinuity, but that doesn't entirely solve the problem.
At some point it becomes a dynamics problem: How fast can the
water enter/exit the gap?

If you insist on a simple model of contact versus non-contact,
and simplify the analysis by not paying attention to the
discontinuities and/or the dynamics ... then by this point the
bathwater and the baby are long gone. The water that rushes
into that tiny gap (or not) is central to any semblance of
understanding of this system.
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Forum for Physics Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l