Re: irreversible lifting

[Richard Tarara <rtarara@SAINTMARYS.EDU>]

----- Original Message -----
From: John Denker <jsd@MONMOUTH.COM>
> Now, would anybody care to try for a non-comical estimate?
> In particular, suppose that rather than lifting the weight by muscle-power
> alone, suppose we lift it using various arrangements of counterweighted
> levers, pulleys, springs, and gas-pistons.  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, frictionless pulley,
massless rope, and two equal masses starting at the same height.  I need add
only a minute amount of energy (essentially zero) to one side (say the right
side) and then the right-hand mass will fall lifting the left-hand mass.
'Gravity' has done the work.  But this is not reversible because now the
gravitational force on the right-hand mass is greater than that of the
left-hand mass and to get the machine to reverse, I must now add a
measurable amount of energy to the left-side.  The ratio should look like
r^2/(r+h)^2 where r is the radius of the earth (assumed spherical and
ignoring rotational effects).  For h = 1 meter this is about 3 parts in
10^7.  Is this what you had in mind?

Rick