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Problem, where is the mistake ?

  1. Nov 9, 2007 #1
    Referring to the attached drawing:
    Two rods 3m long. Rod A is moving at 0,866 c from right to left.
    The pictures are taken from the point of view of rod B.

    ( 1 )In 1 a ray of ligth reaches the end of both rods. It happens that the reading of the clocks at rod A and rod B is 0.
    Because v = 0.866 *c -> l´= l * 0.5 , thats why the left end of rod A is at the middle point of rod B.

    ( 2 )In 2 after 10 ns ( at clocks on rod B ) the light reaches the left end of rod B, assuming c = 30 cm/ns.
    Rod A has moved 0.866 * c * 30 ns/cm = 260 cm.

    But, because t'= t *0.5, the reading on clocks at rod A is 5 ns. So the light has moved, in the frame of reference of A, 150 cm -> the light must be at the middle of rod A, and it isnt according to the explained in ( 2 ). Where is the mistake ?
     

    Attached Files:

    Last edited: Nov 9, 2007
  2. jcsd
  3. Nov 9, 2007 #2

    Dale

    Staff: Mentor

    You have the wrong formula for t'. The correct formula is:

    t' = γ(t-vx/c²)

    Your formula neglects the relativity of simultaneity.
     
  4. Nov 10, 2007 #3
    Thank you for the answer. I made a google search and I found your formula, but I dont know how to apply it ( what does x mean ? )

    Could you resolve the problem with numbers ?
    Is the drawing 1 correct ? ( the left end of rod A is at the middle of rod B ? )
    Where is the right end of rod A when the ligth reaches the left end or rod B ?
     
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