Re: [Phys-l] fun ill-posed questions

["Krishna Chowdary" <professor.head@gmail.com>]

On 10/10/06, John Denker <jsd@av8n.com> wrote:
> *) A Yo-Yo rolls without slipping on the floor.  When I pull the string,
> does it roll toward me or away from me?
>   http://www.av8n.com/physics/ill-posed.htm#sec-yo-yo

This is one of my favorite introductory mechanics questions.  At your
web-site, you offer the Huge hint: Principle of Virtual Work.  I don't teach
this (nor in fact did I learn this) in introductory mechanics; I'm not sure
if my experience is typical or not (i.e. if PVW is a tool that most physics
students get in their first course).  As far as I can see by my quick survey
of the indices of intro calculus based physics texbooks in my office, none
of them talk about virtual work.  It is in Goldstein, which must have been
the first place I saw it (so grad school).  Do engineers see it sooner than
physicists?

The hint that I give my students is to choose the point of contact (of the
yo-yo on the surface) as the reference point (and determine the torques
about that point).   It is still a difficult problem for most of my
students.


How about this as another example of an ill-posed problem?

You blow up two balloons such that balloon A is larger than balloon B.  You
twist the balloons closed rather than tying them in a knot, and connect them
via a straw.  Use string or tape to make sure that no air will leak out, and
then untwist the balloons so that air can transfer between the balloons.
What will happen to the sizes of the balloons?

Another balloon one:  How much work does it take to blow up a balloon?

--
regards
-Krishna

Krishna Chowdary
Department of Physics & Astronomy
Bucknell University