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Limit speed of a whip in vacuum

Physics Asked by Nick The Dick on November 29, 2020

Inspired by this answer, I want to ask what is going to limit the speed of the tip of a whip in a vacuum?

From my understanding, on Earth the tip reaches speeds only several times bigger than the speed of sound in the air, because as the velocity increases, so does the resistance of the air, dissipating the energy inside the whip into the air.

But what happens in the vacuum? My intuition, probably wrong, is that after cracking the whip is going to start vibrating in a chaotic motion, but what’s of interest is the velocity the tip can reach before the limit motion of the whole whip takes over. Can it be kilometers per second or bigger? Why can’t it reach relativistic speeds?

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