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*From*: sample@lyon.edu (John D. Sample)*Date*: Wed, 26 Feb 1997 18:01:28 -0600

At 6:07 AM on 2/25/97, <phys-l@mailer.uwf.edu> wrote:

And now for something completely different!

I call this (inappropriately) "The Rubber Worm Problem": You are providedGood problem. I started my computer calculating the position of the worm

with an elastic rope exactly one kilometer in length. 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.

First question: Has our worm embarked on a Sisyphusian journey; will he

ever reach the end of his rope? If not, prove that.

as a function of step number. (Thank goodness for those multi-tasking

Macs). It seems I will have to train the worm to make each step in say a

tenth the time it took to take the previous step, but I can't program the

Mac to do this! (Is that a Windows feature?) And of course the end of the

string will have to be moving well over the speed limit in short order.

What is the life span of this worm anyway?

I estimate he's within 10^4466 steps of getting there.

Leigh

Chip

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