A conveyor belt that can rotate at infinite speed and accelerate arbitrarily quickly i.e. can match the speed of the wheels as stated.
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Replying to @cybergibbons @whitequark
The wheels would just stop. They aren't under power.
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Replying to @gsuberland @whitequark
Rotational speed would tend to infinity.
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Wheels are spinning at 10rpm. Conveyor is matching this speed. Thrust of plane moves plane forwards infinitesimally. RPMs increase, conveyor matches speed. Repeat.
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Replying to @cybergibbons @whitequark
Nope. As stated in the problem, the wheel speed is matched by the conveyor, which results in the belt position tracking the plane's position (you can prove this via derivation of basic motion laws). The only way the wheels ever rotate is if the belt's acceleration is limited.
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Replying to @cybergibbons @whitequark
The belt counters the wheel rotation. Not the plane's motion.
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Replying to @gsuberland @whitequark
Then you just have a plane being pushed forwards by a conveyor.
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Replying to @cybergibbons @whitequark
If the belt attempts to stop the wheels (i.e. wheel RPM = 0), which is the interpretation I took from it, the belt position would just track the plane position.
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"All in all, it’s a lovely recipe for an internet argument, and it’s been had too many times. So let’s see if we can avoid that." https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ …
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