Re: Muscle work

["John S. Denker" <jsd@MONMOUTH.COM>]

At 11:05 AM 7/21/01 -0700, Tucker Hiatt wrote:
> When I (barely) do a pull-up, my arm and shoulder muscles do plenty
> of work.  I'd like to understand why the constant-speed "upstroke"
> seems harder to perform than the constant-speed "downstroke".

I think it's rather obvious why the upstroke is harder than the downstroke.

> The only forces at work on my body are gravity and a complex,
> collective force that I hope I can characterize as "muscle force".
> The TOTAL work done by BOTH forces acting on my body during one
> complete cycle must be zero since my change in KE is zero.  Since
> gravity is a conservative force, the total back-and-forth work that
> it does must be zero.  That means that my muscles must, collectively,
> also do work that totals to zero.

The foregoing analysis is incomplete and misleading.  Here's is a more
complete analysis.

Let's talk about energy rather than force.  There are three main energy
reservoirs here:
 -- chemical energy
 -- gravitational potential energy
 -- thermal energy

During the pull-up, certain muscles contract.  Some chemical energy is
converted to GPE.  Additional chemical energy is converted to thermal energy.

During the let-down, the muscles extend.  It requires _additional_ chemical
energy to make this happen.  There is no fundamental physical reason why
this chemical energy is required, but it is required by the biochemical
physics of the muscle.  (If you don't believe me, please explain rigor
mortis.)  This chemical energy is converted to thermal energy.  Also the
GPE is converted to thermal energy.

For more details, try something like:
  http://www.google.com/search?q=sarcomere+ATP

> .... don't my muscles do precisely the same (magnitude of) work
> during the upstroke as during the downstroke?

No, they don't.  The alleged equation
        work (upstroke) = negative work (downstroke)
is not valid because it ignores dissipation.  Muscles are _highly_ dissipative.

And the alleged equation
        work (upstroke) = work (downstroke)
has no basis whatsoever.  It might be approximately valid if we ignored the
external work that the muscle is doing against gravity, but we can't do
that in this case.

> When I try to pay close attention to the agony level during both
> motions, I am surprised how similar they are when I truly manage to
> descend at constant speed.  But still there is a difference.  Why?

1) My perceptions of this situation do not agree.

2) Even if we agreed, I would not consider "agony level" to be a
sufficiently quantitative measure of energy.

Much of the perception of "burn" during a highly anerobic exercise such as
this is due to lactic acid buildup.  The lactic acid level will be higher
on the downstroke simply because it comes after the upstroke.

Analogy:  why is the hottest day of the year not the longest day of the year?

====================

Here is an additional way of seeing that it is not appropriate to analyze
this situation in terms of "upstroke work" and "downstroke work".  Do a
pull up, and just _hold_ yourself in the up position.  It's obvious that
you don't do any "work" while hanging there, but you will get real tired
real fast.  Chemical energy is being converted to thermal energy at a
goodly rate.  Maybe if you were a clam you could exert a big steady force
without dissipating a lot of power, but human muscles don't work that way.

=====================

This question serves as yet another illustration of a misconception that we
have seen again and again.  Except in the simplest situations, it is bad
luck to focus on the _form_ of energy _transfer_.  When energy is
transferred from system A to system B, it might leave system A in one form
(e.g. work) and show up in system B in another form (e.g. thermal
energy).  Energy is conserved, but work is not.

As a corollary:  This is why I shudder when I see people state the first
law of thermodynamics in terms of so-called work and so-called heat (by
which they mean thermal energy transfer).  It's not (mainly) the choice of
words that's troublesome -- it's the whole formulation, the whole way of
looking at the physics.

To say it again in more positive terms:  To me, the first law of
thermodynamics is:
        Energy obeys a local conservation law.
Period.  That's all there is to it.

That's true.  That's reliable.  Make sure you count all forms of energy.

If you let yourself get hypnotized by one sub-type of energy (such as
muscle "work" and gravitational "work") you're going to have trouble.