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Three Reference Frame Relativity Problem - Velocity Addition or Proper Lengths
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[QUOTE="Orodruin, post: 4868430, member: 510075"] If I understand your second approach correctly, this is what you tried: [LIST=1] [*]Compute the length of the rod in the spaceship frame by length contraction of the rest length in the pod frame. [*]Compute the length of the rod in the Earth frame by length contraction of the contracted length in the spaceship frame. [/LIST] This is generally not allowed because the length contraction formula is only valid when going from the rest frame of an object to a frame that is moving relative to it (i.e., only valid for step 1). This is based on the way that the length contraction formula is derived. Your first method is correct. Note: The ##\gamma## factor for the combined velocity of the pod in the Earth frame should be ##\gamma_1\gamma_2(1+v_1 v_2)##. Your second method (if it is what I described above) would give you ##\gamma_1 \gamma_2## so it would be off by a factor ##1+v_1 v_2 = 1+0.1\times 0.5 = 1.05##. In your answer that would make a difference of 0.04 which seems a bit bigger than what you are quoting... [/QUOTE]
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Three Reference Frame Relativity Problem - Velocity Addition or Proper Lengths
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