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Old 2022-02-01, 03:22   #12
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Quote:
Originally Posted by charybdis View Post
Consider the discrete version of the problem,
Creating discontinuities?! Ack!
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Old 2022-02-01, 03:28   #13
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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.
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Old 2022-02-01, 03:57   #14
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Quote:
Originally Posted by Uncwilly View Post
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.
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Old 2022-02-01, 04:48   #15
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Quote:
Originally Posted by Uncwilly View Post
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.
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Old 2022-02-01, 07:21   #16
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Most definitions allow or require ends. https://www.merriam-webster.com/dictionary/band
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Old 2022-02-01, 07:47   #17
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Quote:
Originally Posted by chalsall View Post
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.

Last fiddled with by retina on 2022-02-01 at 07:47
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Old 2022-02-01, 13:42   #18
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Quote:
Originally Posted by Uncwilly View Post
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.
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Old 2022-02-01, 14:48   #19
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Quote:
Originally Posted by kriesel View Post
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?
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Old 2022-02-01, 14:51   #20
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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
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Old 2022-02-01, 15:54   #21
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Quote:
Originally Posted by petrw1 View Post
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?

Last fiddled with by uau on 2022-02-01 at 15:54
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Old 2022-02-01, 15:58   #22
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Quote:
Originally Posted by uau View Post
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
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