Re: Muscle work

[Tucker Hiatt <hiattu00@USFCA.EDU>]

Thanks to Bill Beaty, Paul Johnson, and John Denker for responding to
my question.  However, I'm still not understanding why the pull-up
upstroke seems to require more muscle work than the downstroke.

At 2:04 PM, 7/21/01, Bill Beaty wrote:

> Maybe it's easier to do pull-ups if you tighten your muscles and let
> yourself "bounce" at the lower excursion, which would convert your
> downwards velocity into upwards velocity without your muscles needing to
> do as much work upon your body.

I believe it *is* easier to do such "bouncy" pull-ups.  In
particular, gymnasts on a regulation "horizontal bar" have the
benefit of a flexible bar that "gives" much more than the traditional
playground pull-up bar.  They can use a little muscle-bounce and a
lot of bar-bounce to fling themselves around with relative ease.
Even I can do several more pull-ups in the gym than I can on the
playground [... but only after correcting for the dreaded
"embarrassment factor" that's so debilitating on the public
playground].   ;-)


At 7:55 PM, 7/21/01, John Denker wrote:

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

Only "obvious"?!   Thanks for avoiding the #1 physics put-down: "trivial".

> The foregoing analysis is incomplete and misleading.

Well, perhaps.  But my spelling was dynamite.
O.K.  I'll stop joking around.  I really do want to understand.

>         work (upstroke) = negative work (downstroke)
> is not valid because it ignores dissipation.  Muscles are _highly_
> dissipative.

In the case of a round-trip, constant-speed pull-up, aren't muscles
*completely* dissipative?  What type of energy has the original
biochemical energy become but thermal energy?

> 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.

I have heard the following explanation for muscle fatigue during
isometric exercise:  Even though the muscle as a whole may not be
visibly moving, individual muscle fibers are moving over very small
distances.  Those fibers are contracting and relaxing microscopically
(and asynchronously).  So, those fibers are doing "work" that we just
can't visually detect.  However, as true isometric fatigue sets in,
the fibers may begin to contract in unison (why?), and the muscle
motion becomes macroscopic.  That concerted contraction and
relaxation is visible as trembling.  [I wonder if clams tremble
during prolonged attempts by predators to pry their shells apart.]

> 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.

As you might suspect, I pray to the god of conservation of energy.  I
believe in it.   I even have the temerity to think that I understand
energy conservation.  I was trying not to be hypnotized.  In fact,
the hypnosis I was avoiding was of the sort: "Energy obeys a local
conservation law.  Period.  That's all there is to it."

My problem is not with energy conservation, but with a particularly
irksome kind of energy (or "energy transfer") called work.  I teach
about "work" every fall.  And, every fall, I feel as though I dare
not talk at length about muscle work or the students will see my
nakedness.  I suspect I'm not the only classroom emperor who's
feeling a breeze on this topic.  I think it's hard to understand
muscle energetics -- and muscle work, in particular.

When I lower myself [note the wording -- gravity doesn't do the job
alone -- "I lower myself"] at constant speed, I SEEM to feel somewhat
less muscle fatigue than when I raise myself.  Maybe, after all, the
problem is in the seeming: What "seems" just may not be so.  But if
there is a difference, "obvious" or not, an explanation still eludes
me.

- Tucker