- 2

- 0

**1. Homework Statement :**

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 vaulter

**inside**, then open them again,

**without**breaking 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. Homework 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 to

**5.000m(3d.p)**and the farmer will measure the pole to be length contracted to

**8.000m(3d.p)**.

Thus the farmer

**can**shut the vaulter in the barn for an instant in time,

**but**in the vaulter's reference frame the two events (the first and second doors opening) will

**not**be 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*
Last edited: