(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data:

We have a pole vaulter, and farmer, and a barn. The vaulter is traveling at 0.866c (as measured by the farmer), and carrying a pole that,in his reference frame, is 10 meters long. The barn has an open door at either side, and is 10 meters wide,in the farmer's reference frame. The farmer believes he can shut both doors simultaneously for an instant in time, with the vaulterinside, then open them again,withoutbreaking the vaulter's pole. The vaulter believes that farmer cannot do this. Prove, that when properly analysed, the farmer and the vaulter agree on the outcome, and include both quantitative calculations and a written explanation. We are told to assume the walls (and doors) are paper thick, that the pole would break without slowing down, and that it is possible for the farmer to shut both doors simultaneously (in his reference frame) for the purposes of this question.

2. Relevant equations:

Obviously the one for length contraction:

L = Lp/[tex]\gamma[/tex]

where Lp is the proper length and gamma is:

[tex]\gamma[/tex] = 1/[tex]\sqrt{1-(v^2/c^2)}[/tex]

And then, part of why I am struggling with this: one to prove a breakdown in simultaneity.

Possibly also time dilation: [tex]\Delta[/tex]t = [tex]\gamma[/tex][tex]\Delta[/tex]t'

3. The attempt at a solution

So far, I have, using the length contraction formula above, shown that the vaulter will measure the barn as length contracted to5.000m(3d.p)and the farmer will measure the pole to be length contracted to8.000m(3d.p).

Thus the farmercanshut the vaulter in the barn for an instant in time,butin the vaulter's reference frame the two events (the first and second doors opening) willnotbe simultaneous.

(the explanation is fine AFAIK, in terms of special relativity theory), and I don't know how to do this. Also, does time dilation affect the result? Obviously it takes place, but does it actually affect the result here?However, I need to mathematically prove the breakdown in simultaneity

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# Homework Help: Relativity: Breakdown in Simultaneity Question

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