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Homework Help: Special relativity question

  1. May 20, 2010 #1
    1. The problem statement, all variables and given/known data

    I have correctly figured out part a but am stuck on part b. Thanks for your help in advance.

    An unstable particle called the pion has a mean lifetime of 25 ns in its own rest frame. A beam of pions travels through the laboratory at a speed of 0.587c.
    (a) What is the mean lifetime of the pions as measured in the laboratory frame?
    30.75 ns

    (b) How far does a pion travel (as measured by laboratory observers) during this time?
    m


    2. Relevant equations

    [ Delta t x c (speed of light) ] / 2

    3. The attempt at a solution

    using the answer from part a and converting to meters:

    [(3.075E-8)(3E8)] / 2 = 4.6125 I've checked for errors and always come up with this number--which according to the web program is incorrect.

    What am I not doing/understanding?
     
  2. jcsd
  3. May 20, 2010 #2

    Doc Al

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    Staff: Mentor

    :confused: Where in the world did you get this formula?

    Hint: How fast is it moving? How long is it moving for? How do you calculate distance traveled?
     
  4. May 20, 2010 #3
    I got the formula from my professor.
    As far as I can tell it is moving at 0.587c = 176100000 m/s for 25 ns.

    Distance = rate x time.

    So then I suppose I would do the following:

    176100000 m/s x (2.5 x 10^-10) = 0.044025 meters?
     
  5. May 20, 2010 #4

    Doc Al

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    Staff: Mentor

    It must be meant for some specific application--but not this one.
    Why 25 ns? Stick to the lab frame.

    That's all you need.
     
  6. May 20, 2010 #5
    o.k. then,

    176100000m/s x (3.075 x 10^-10) = 0.05415075 ~ 0.0542 and convert to meters = 5.4 m
     
    Last edited: May 20, 2010
  7. May 20, 2010 #6

    Doc Al

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    Staff: Mentor

    Two things, the first being the most important:
    - check your exponents
    - use a more accurate value for the time in part a (redo it); only round off at the end.
     
  8. May 20, 2010 #7
    thank you I should have typed:

    176100000m/s x (3x 10^8)x 30.75 (the answer from part a) = 5415075000

    then convert from nano to meters (9 decimal spaces to the left) = 5.41 meters

    which is the correct answer. Thank you for your guidance. K
     
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