HW hints

For the first problem:

1. http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/polebarn.html
2. http://en.wikipedia.org/wiki/Ladder_paradox
3. http://www.xs4all.nl/~johanw/PhysFAQ/Relativity/SR/barn_pole.html

For the second problem, the length must be contracted according to the astronaut. The astronaut would report a velocity which is the contracted distance divided by the time he or she measured.

For the third problem, the proton sees a contracted length. It would observe a time consistent with this distance divided by the relative velocity, whereas in the laboratory we would observe a time which is the rest length of the tube divided by velocity.

For the last problem, the difference between dilated and proper time is 2s every 86400s. This must mean that the spaceship clock runs a factor (1+2/86400) slow.