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Atom clock problem

  1. May 29, 2015 #1
    1. The problem statement, all variables and given/known data
    An atomic clock moves at 1,000 km/h for 1.00 h as measured by an identical clock on the Earth. At the end of the 1.00 h interval, how many nanseconds slow will the moving clock be compared with the Earth clock?

    2. Relevant equations
    (1/ sqr rt 1 - v^2/c^2)

    3. The attempt at a solution
    1,000 km/h = 278 m/s
    Convert the 1,000 km/h to met/sec. first
    (1/ sqr rt 1 - v^2/c^2)

    = (1/ sqr rt 1 - 278^2/3.00 X 10^8 m/s)
     
  2. jcsd
  3. May 29, 2015 #2
    I am not sure how to convert from 1,000 km/h to m/s, I think I divide it by 3600 seconds which would equal 0.277 m/s, so how do I change that to 278 m/s?
     
  4. May 30, 2015 #3

    ehild

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    Convert also km-s to meters.
     
  5. Jun 6, 2015 #4
    1,000 km/hr to met./sec. = 1,000km X 1,000met. = 1,000,000 met./ hr
    1,000,000 met. divided by 3600 seconds = 277.7met./sec. = 278 met./sec.

    Equation used: 1/ (squr rt 1 - v^2) = 1/ (squrrt 1 - 278^2/3.00 X 10^8 met./sec. = 1/ 1 - 77284/3.0 E8 = 1/-77283/3.0 E8 = 1/-2.5761e12 The Answer is supposed to be 1.54 Nanoseconds, what am I doing wrong?
     
  6. Jun 7, 2015 #5

    ehild

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    You
    You did not write any equation. As I see, you intended to calculate the factor ##\sqrt{1-\frac{v^2}{c^2}}##, but you forgot to square c, did not apply parentheses and made some more errors.
    Look after Lorentz transformation in your Lecture Notes.
     
  7. Jun 8, 2015 #6

    andrevdh

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    Multiply with conversion factors do get the values in the correct units eg. 1km = 1000 m
    So you can multiply with the conversion factor 1 km / 1000 m and the value will not be
    altered since you are multiplying by one . So 35.7 km = 35.7 km x 1000 m / 1 km = 35 700 m
    The km units cancel each other out so only the meter units are leftover, which is the units
    of the answer.
     
  8. Jun 8, 2015 #7
    I figured out the problem but thanks.
     
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