Re: There's work, and then there's work

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

Robert Cohen wrote:

> I may be totally misinterpreting DR's question but let me rephrase it=
>  in a way that I think my student's would ask it.  If we have two bal=
> ls connected by a spring and we compress the spring by holding one ba=
> ll stationary while moving the other ball toward it, haven't we done =
> work on*both* balls?
>
> After all, our muscles are working to keep the stationary ball steady=
> .  Where does that energy go if not into the stationary ball or at le=
> ast the two-ball configuration?

That's an excellent summary of many students' reaction to the question.
It's difficult to convince them that only the hand that is moving one of
the balls to compress the spring is actually doing what we define as work.
They do seem receptive, however, to the idea that the work results in an
energy increase of the entire system.

The problem is to carefully define the system and to carefully limit what
"work" affects the system. I suffer from a condition known as "essential
tremors". I know that if I hold a ball stationary in my hand - I'm
technically not doing work. But I also know that I can't hold the ball
steady for too long or it will go flying from my hand. My muscles are
constantly contracting and releasing due to the tremors during my attempt
to hold the ball steady. Even though the students may not see the ball
moving in my hand, my muscles are experiencing all kinds of internal
forces and displacements - and I'm expending a lot of energy to keep the
ball in place while I'm telling my students I'm not doing any work :-)

I think that in some sense the students are aware of a much milder version
of the same effect when they hold an object. They know their muscles are
getting somewhat tired, so they assume that they MUST be doing work on the
ball - after all they are applying a force. Part of the art of what we do
as teachers is to get the students to carefully define a physical
quantity, such as work or energy,  and then carefully stick with that
definition when subjected to conditions far different than those
originally considered. That's the only way we can share a set of terms
that allow us to rationally argue the physics of a situation.

The thread we've been following here is an excellent example of what
happens if you keep making ad hoc redefinitions of terms like work and
energy simply to justify a physical misconception. The discussion
disintegrates because we're never sure of what definition of a term is
being used at the moment.

Bob at PC