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Imagine a tank that accelerates towards a relativistic speed. As the caterpillars are at rest with respect to the ground, the caterpillars will show no length contraction there. But the tank body above it will.

The upper part of the caterpillars, on the other hand, will show more contraction than the tank body does.

What will happen? Will the lower parts of the caterpillars slide along the tank body to "deliver" an extra piece of caterpillar for the upper part which contracts more than the tank body? Will the caterpillars snap? I'm not sure.

Il Guercio
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    There are practical problems with getting tank tracks to operate at high speeds, well before relavistic effects become significant, since mechanical stresses propagate at the speed of sound through the material, and light speed is roughly a million times sound speed. I have some info on this in relation to spinning bodies in this answer: https://physics.stackexchange.com/a/686011/123208 – PM 2Ring Aug 29 '23 at 06:17

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The tank frame measures a track length less than the frame perimeter, so unless the frame perimeter is allowed to compress, or the tracks are allowed to stretch, something breaks.

For the breakage of the tracks in the track frame, you can get the general idea from Bell's Spaceship Paradox if you ignore the vertical movement of the treads and treat the treads as just accelerating in the horizontal direction one way from the farthest back point on the tread and the other way from the farthest forward point on the tread as they round the ends.

For the resolution of amount of track under or over the frame varying depending on which frame you're in, you want the Barn Ladder Paradox.

g s
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"Imagine a tank that accelerates towards a relativistic speed." There is not enough information here to answer your questions. The tank shrinks, expands, or maintains its length depending on exactly when and where you apply the forces that cause it to accelerate. Once you carefully specify all those forces (including forces coming from friction with the ground, etc), all that remains is a straightforward calculation. Until you specify the forces, anything can happen.

WillO
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  • Just imagine that seen by an observer at rest, all accelerations of the tank occur simultaneously (which means inside the tankframe all accelerations occur at different times, and maybe we even have to apply the Rindler metric because it's an accelerated frame). An observer at rest sees the tank shrink while the caterpillars on the ground stay the same length. – Il Guercio Aug 29 '23 at 07:23
  • In a frame where the accelerations are simultaneous. the length of the tank can't change. – WillO Aug 29 '23 at 14:40