Ant on a rubber band.

[frmky]

Originally Posted by charybdis

Consider the discrete version of the problem,

Creating discontinuities?! Ack!

[Uncwilly]

The ant will never get to the end. Since a rubber band is a loop, there is no end. Despite what the OP changed his post to say, rubber [B][U]bands[/U][/B] must be a band, that is a loop.

[retina]

Originally Posted by Uncwilly

The ant will never get to the end. Since a rubber band is a loop, there is no end. Despite what the OP changed his post to say, rubber [B][U]bands[/U][/B] must be a band, that is a loop.

Yeah it will.

When the rubber disintegrates due to age it will break apart and then it has ends.

[petrw1]

Originally Posted by Uncwilly

The ant will never get to the end. Since a rubber band is a loop, there is no end. Despite what the OP changed his post to say, rubber [B][U]bands[/U][/B] must be a band, that is a loop.

The op (aka me ) should have said a stretchy rope.

[kriesel]

Most definitions allow or require ends. https://www.merriam-webster.com/dictionary/band

[retina]

Originally Posted by chalsall

The ant will never reach the other end.

If the expansion was exponential (e.g. it expands by 10% each time preiod), and not linear as in the puzzle, then for some combinations of speed vs expansion rate then the ant can be prevented from ever reaching the end.

[Dr Sardonicus]

Originally Posted by Uncwilly

The ant will never get to the end. Since a rubber band is a loop, there is no end. Despite what the OP changed his post to say, rubber [B][U]bands[/U][/B] must be a band, that is a loop.

One can reasonably interpret "the end" to mean "the point at which force is being applied to stretch the band."

BTW, the [b]...[/b] and [u]...[/u] tags don't work inside [spoiler]...[/spoiler] tags.

Many years ago, the magazine Scientific American's "The Amateur Scientist" article (IIRC) was about making heat engines out of rubber bands. They exploit an unusual property of rubber - namely, it shrinks with increasing temperature.

[Uncwilly]

Originally Posted by kriesel

Most definitions allow or require ends. https://www.merriam-webster.com/dictionary/band

Why not look at the actual term rubber band in that same source?

[petrw1]

Is the problem/solution different if:

A. Ant moves 1 cm; band stretches 2 cm ... rinse and repeat as necessary
B. Ant moves at a constant rate of 1 cm/Sec while the band is being continuously stretched at 2 cm/Sec

[uau]

Originally Posted by petrw1

Is the problem/solution different if:

Doesn't make any real difference.


Variant question (still pretty easy):

The rubber band is stretched so that at time x its length is x². At what times can the ant start at one end and eventually reach the other end if it moves at speed 1?

[retina]

Originally Posted by uau

The rubber band is stretched so that at time x its length is x². At what times can the ant start at one end and eventually reach the other end if it moves at speed 1?

x = 0