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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.math
Subject: Re: Fly and train
Message-ID: <2092@brl-tgr.ARPA>
Date: Sat, 12-Oct-85 23:31:52 EDT
Article-I.D.: brl-tgr.2092
Posted: Sat Oct 12 23:31:52 1985
Date-Received: Tue, 15-Oct-85 05:34:52 EDT
References: <508@runx.OZ>
Organization: Ballistic Research Lab
Lines: 28

> In order to "turn around" (change from a positive velocity to a negative one)
> the fly must have had a zero velocity at some point in time (my assumption).
> Having a velocity of zero, the fly must have been stopped.
> At that time, the fly would have been in contact with the front of the train.
> As the two bodies were not rotating, would not the train have been stopped as 
> well?  If not, then why not?

This is just another variant on Zeno's paradoxes.
You ask "would not the train have been stopped?"
on the basis of undemonstrated assumptions.

If you assume an incompressible point fly, then
obviously in your scenario it underwent an infinite
force at the precise moment of impact, a force
applied by the train.  In such a case, its velocity
undergoes discontinuous change and is never zero.

In a more realistic model of the interaction,
the momentum of the train changed by a minute
amount, the momentum of the fly by the same amount
in the opposite direction, and the fly absorbed
a certain amount of energy.  Indeed, if the fly
sticks to the train, it must absorb some energy.

In all such problems, beware of taking extreme
limits as actualities; consider systems that are
not quite so ideal and you will find that the
analysis is much easier.