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Forums
Physics
Special and General Relativity
Solve Relativistic "Bug on Band" Problem
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[QUOTE="Hiero, post: 6064939, member: 602040"] [USER=14402]@pervect[/USER] no question, I just wanted to share how the classical and relativistic answers compare. Everything you explained is precisely how I solved it. The last thing to mention is that if we work with the variable r = x/(L[SUB]0[/SUB] + vt) (the fraction the bug is along the band) instead of x, then both (relativistic and classical) equations become separable, and integration (from r=0 at t=0 up to r=1 at t=t[SUB]final[/SUB]) gives the results in my OP. I find it curious how the exponential approximates that complicated term. I also was interested in the time in the bug’s frame, but that integral was a bit more intimidating. If I’m not mistaken, we would just integrate ∫√(1-(w/c)^2)dt where w is the bugs speed as a function of time (as seen by the wall), which could be found explicitly from the original solution, but I think its messy. I haven’t tried it, so maybe this integral simplifies. I would be surprised though. [/QUOTE]
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Physics
Special and General Relativity
Solve Relativistic "Bug on Band" Problem
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