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Homework Help: Time dilation of cells

  1. Aug 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Two cells that divide on earth each 10s start a travel to the Sun at v = 0.85c (Distance earth-sun: 1.5·10^11 m). How many cells should exist when the rocket they travel in carshes with the Sun?

    2. Relevant equations

    Time dilation: t=t0/sqrt[1-v2]

    being t0 the time from a 'rest' sytem.

    3. The attempt at a solution

    My results are:

    10 seconds on earth mean 18.9 seconds on the rocket, due to time dilation, thus it will be less divisions by the time a person on earth watches the rocket crashes with the Sun. So:

    259 cells (From system Earth) = 5,77·1017 cells
    232 cells (From system Rocket) = 4 294 967 296 cells

    Is this correct? Thank you.
     
    Last edited: Aug 27, 2010
  2. jcsd
  3. Aug 27, 2010 #2

    Doc Al

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    Staff: Mentor

    No, not correct. First things first: How long does the trip take according to Earth observers?
     
  4. Aug 27, 2010 #3

    Andrew Mason

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    Homework Helper

    It appears you are using 590 seconds for t0. How do you determine that?

    What is your answer? You have given two different ones.

    AM
     
  5. Aug 27, 2010 #4
    Yes, I used 590 seconds, obtained: t = [distance earth-sun)/(speed of light), that is the time that the rocket takes to reach the sun for an oberver on earth.

    Because of time for each observer is not the same, a person on earth will measure 258 divisions and another one on the rocket (in which the cells are) will measure 232 divisions - I forgot to say that in the beginning there was 2 cells. ten seconds later, will be 22, at 20 seconds will be 23... and son on.

    Thanks
     
  6. Aug 27, 2010 #5
    According to earth observers: 588,24 s. In this time will be more divsions from earth than from rocket, due to the time for a single division in rocket is not 10 secds like on earth, but 18,9 seconds.

    I'm a little confused


    Thanks
     
  7. Aug 27, 2010 #6

    Doc Al

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    Staff: Mentor

    OK, I see what you're saying and I understand your answers now. (You had labeled both answers as "From system Earth", which threw me off.)

    The way I'd state it would be that the travel time according to earth observers is 588 s. Thus, due to time dilation, the travel time according to the rocket clocks would be 588/1.9 s.

    Good!
     
  8. Aug 27, 2010 #7
    Ok! I already fixed that! Thanks, I've understood the problem!
     
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