Re: irreversible lifting

[John Denker <jsd@MONMOUTH.COM>]

At 12:27 PM 11/1/99 -0500, Richard Tarara wrote:
> > What then is the minimum
> > percentage of work that must be done irreversibly?
> >
> > Can anybody come up with a nontrivial lower bound?
>
> Here's my attempt.  I'll use an Atwood's apparatus,
...
> about 3 parts in 10^7.  Is this what you had in mind?

Wow.  That's an interesting calculation.  But it's not quite what I had in
mind.

The nonlinearity of the gravitational field is, well, a nonlinearity.
Nonlinearity is not the same as dissipation.

Suppose I cancel the nonlinearity of the field by using a nonlinear spring
to help lift the weight.  (It is straightforward to engineer a suitably
nonlinear spring.) That would get rid of Richard's nonlinearity to leading
order.

By using a wheel with N spokes I can get rid of the nonlinearity to Nth
order in (distance moved) over (radius of earth).

==

Real dissipation involves things like friction.  Frictional dissipation
(per unit work) can be reduced (a) by using good bearings and (b) by doing
things slowly.  So minimum dissipation in favorable cases comes down to a
question of how slowly you can do things.

==

If you want to know what I *really* had in mind -- I'm not sure there is a
lower bound (greater than zero) for the dissipation of a simple process
like raising a weight.  If there is a lower bound it's reeeeally small.

Here's an upper bound on the lower bound:  The moon's orbit is slightly
elliptical.  The moon raises itself against gravity every month, with a
dissipation of less than one part in a billion.

==

A related puzzle for you:  Suppose you wanted to build a mechanical
oscillator with a Q of one million.  How would you do it?

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com