[Phys-L] PVW (was: fluid)

[John Denker <jsd@AV8N.COM>]

In the context of:

> > Putting your finger at the top of a straw immersed in a glass of water allows you to lift
> > the straw. I understand that the difference in pressure between the water near the top of the
> > straw and that at its bottom causes the water to rise, but what forces lift the straw?

Kilmer, Skip wrote in part:

> Thanks

:-)

> ... experiment, as usual, triumphs.

Yes, but theory also is a winner.  (It's not a zero-sum game.)

If you think about this problem the right way, you can see the
answer in less time than it takes to state the question.  All
you need is PVW : the principle of virtual work.

PVW is easy to learn, easy to apply, and very powerful.

Reference: Feynman volume I chapter 4.

Feynman sometimes used the Epitaph of Stevinus (figure 4-4)
as "the" icon of PVW, but my favorite PVW icon is the bridge
shown in this figure:
   http://www.av8n.com/physics/img48/bridge.png

The load W is the dominant load on the bridge;  the weight
of the bridge structure can be neglected.  The question is,
which segments of the truss can be made of flexible cable
(because they are under tension) and which must be made of
rigid girders (because they are not under tension).

Hint/example:  The AB segment must be a rigid girder.

Reference: This is an exercise from Leighton-Vogt.

There are two ways to solve this problem:
  a) some people work out the force vectors using trigonometry,
   which takes hours and hours;  meanwhile
  b) some people solve it using PVW in a trice ... maybe half
   a trice.

The contrast is striking:  group (a) takes the bridge exercise
as evidence that doing physics is ugly and laborious, while group
(b) takes the same exercise as evidence that knowing some physics
is nifty and makes things easy.

Suggestion:  When you see a problem of this sort, try attacking
it with PVW.  That is, see if energy considerations suffice to
solve the problem.  Sometimes that won't suffice, and you will
have to work out the forces in detail ... but you should try the
energy approach first, because if it succeeds it will usually
be much easier than the force approach.  Scalars are usually
easier than vectors.

My motto is, if you see a fish in a barrel, you might as well shoot
it.  (Not all fishes are in barrels, but some of them are.)
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