Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2019-resit/7/solution

Let be the train's proper length, the tunnel's length in the track reference frame, and . The Lorentz factor is . At one track-frame time, length contraction makes the train
Yes, the whole train fits inside at a single track-frame time. Set when the rear enters the near portal. Until the front reaches the far portal, the rear and front are at and , respectively. Complete containment lasts
a track-frame interval of approximately , counting boundary contact.
In the train's reference frame, its length is , while the moving tunnel has simultaneous length . No single train-frame time has the whole train between the portals. The two answers refer to different simultaneity slices.
For an explicit check, denote the rear-entry event by and the front-exit event by . In track coordinates,
The Lorentz transformation gives
Thus the front leaves before the rear enters in train coordinates. These spatially separated events have a frame-dependent order, as allowed by relativity of simultaneity; neither answer asserts a different local event at a portal. No collision with closed doors has been stipulated.

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