1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

    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

    User Avatar

    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

    User Avatar

    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

    User Avatar

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook