Question

A modern high-speed train is on its way through a 100.0 m long tunnel underneath a mountain. A hermit lives on the mountain and wants to play a trick on the train by closing a door on the far end of the tunnel and not opening it back up until the back end of the train is just inside the tunnel, at which point the far door opens simultaneously with the front door closing behind the train. However, the train is 160.0 m long, so the hermit sends a signal to the train to speed up to 0.866c. The hermit knows that at this speed, the train’s length will be only 80.0 m and will fit nicely inside the 100.0 m long tunnel. However, the train’s engineer sees the hermit scampering off to close the front door and realizes that if the hermit doesn’t open the far door until the train is clear of the front door, the train will smash the far door since the tunnel is only 50.0 m long to the engineer!

Does the train make it through safely? Show that, when properly analyzed, both the engineer and the hermit agree on the outcome. Your analysis should contain both written qualitative explanation and quantitative calculations. It’s obvious that the train cannot stop quickly, so let’s assume the doors are paper thin and that the train would break through them without slowing down. (The hermit studied relativity but not materials.)

Answer 1