Re: The worm problem

[ntganiel@weizmann.weizmann.ac.il (Uri Ganiel)]

Our main computer was down, and so I am only now looking at messages from
Friday.
Ludwik Kowalski says:
> I have no doubt that it was a challenging problem. The proof is that you,
> and several others, found is worth working on. But I was left outside of
> that "inner circle of smart guys". Let me exagerate and simulate a student
> who is disapponted by the received grade. I am penalized for not guessing
> what the professor had in mind. I am not stupid, I took him literally and
> he gave me an F. That is not fair. Physics stinks. Why should I assume,
> unless it is clearly stated, that the speed of the tractor is with respect
> to the road while the speed of the worm is with respect of a constantly
> expanding rope? Does the bug crowl as a worm (as a catapillar, as a flea)?
> This was irrelevant to me; the length of the bug was not specified and I
> assumed it was a point-like object. Therefore I did not try to deduce
> the acceleration of the bug (with respect to the road) from the "mechanism
> of walking". What was wrong with my reasonning? Why was I penalized? Who
> said I was not thinking? Who said my mathematical sophistication is not
> good? Who said ....?
>
> You see my point. Problems should be formulated clearly. This is trivial
> but here we are. Was I the only one who felt cheated?
>                                                        Ludwik Kowalski

Just two short remarks:
First: while I agree that exam problems must be carefully stated, problems
like this may be a little fuzzily(sp?) stated, as part of the challenge.
Second: if you look at the problem as Leigh posted it, you will see that he
was very careful to make it very explicit:
"...At time t=0 a worm
starts to crawl from one end of the rope to the other at a speed of one
centimeter per second. The rope itself is attached to a tractor which
is stretching the rope at a rate of one kilometer per second. The problem
as it was originally stated specifies that the rope lengthens by one
kilometer at the end of each second, and it is this discrete version of
the problem I will continue with here. At the end of one second the worm
has marched one centimeter toward the other end of the rope. At that
instant he is instantaneously transported to the 2 centimeter mark on a
rope which is now two kilometers in length. By calculation you will see
that at the end of the second second he will be three centimeters along
his way on the two kilometer rope, which will then lengthen to three
kilometers, taking the worm to the 4.5 cm point, etc."

By specifically giving the position at the end of 1 and 2 seconds, you
easily understand the "rules of the game".

Uri

Prof. Uri Ganiel
Head, Department of Science Teaching
The Weizmann Institute of Science
Rehovot 76100, ISRAEL

Phone: 972-8-9343894
FAX:    972-8-9344115

E-mail:  NTGANIEL@weizmann.weizmann.ac.il