IB Physics Relativistic train

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A tutorial sheet on special relativity, a topic that most HL students find difficult.

  1. A train (frame S') of proper length 3.2 km moves at 0.6c relative to a platform (frame S). At t = t'= 0, two light pulses are emitted in opposite directions from the centre of the train. At what times do the pulses reach the ends of the train in (a) frame S' (b) frame S? Benson, University Physics, Revised Edition, John Wiley and Sons, p 832, q32.
  2. When it is 10 8 m away in the Earth's frame (S), a rocket (frame S') travelling at 0.8c towards the Earth emits a flash. On receipt, it is immediately transmitted back to the rocket. How long does it take the flash return to the rocket according to the Earth frame? Benson, q 33.
  3. A detector (frame S') moves away from the origin of frame S at a speed V along the +x axis. Whhen it is at a distance x = L from the origin of S, a flash is emitted at the origin. How long does it take the flash to reach the detector according to observers (a) in S, (b) in S'? Benson q 37
  4. A train of rest length 800 m approaches a platform of length 1 km at 0.6c. The front reaches the left end of the platform at t = 0 in the platform frame. At what time does the rear of the train reach the right end of the platform in the platform frame? Benson, q 69.