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Special Relativity

  1. Oct 10, 2008 #1
    1. The problem statement, all variables and given/known data
    A red light flashes at position xR = 3:00m and time tR = 1e-9s, and
    a blue light flashes at xB = 5:00m and tB = 9e-9 s, all measured in
    the S reference frame. Reference frame S` has its origin at the same point
    as S at t = t0 = 0; frame S' moves uniformly to the right. Both flashes
    are observed to occur at the same place in S'. (a) Find the relative speed
    between S and S`. (b) Find the location of the two flashes in frame S`.
    (c) At what time does the red flash occur in the S' frame?


    2. Relevant equations



    3. The attempt at a solution

    I am going crazy!!!!! This is my approach.

    taking the distance of S' from x_R to be L_p measured in S and distance of S' from x_B to be contracted length L_C as measured in S',

    [tex] L_p=L_c \times \gamma [/tex]
    [tex] x_A+2=x_A \times \gamma [/tex]

    at t_B distance travelled by S' frame is v X t'
    taking t' to be [tex]t_B \times gamma[/tex],
    [tex] x_A=3-vt' [/tex]

    But when i substituted [tex] x_A [/tex] back into the equation, i became stuck! so obviously something is wrong but i cannot figure out what is wrong.
     
  2. jcsd
  3. Oct 10, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I don't quite understand what you are doing. In any case, for a problem like this, why not use the Lorentz transformations directly. That's what they are for!
     
  4. Oct 13, 2008 #3
    Doc AI, thanks for helping me again. I have another question though that is slightly unrelated to this.

    Given that [tex] f=\frac{\bar u \bar v}{\bar u +\bar v}[/tex]

    show that

    [tex]e_f=f^2({\frac{e_u}{\bar u^2} + \frac{e_v}{\bar v^2}) [/tex]

    where [tex]e[/tex] refers to the error. ok so I added up the fractional uncertainties and I got this

    [tex]\frac{e_f}{f}=\frac{e_u}{u}+\frac{e_v}{v}+\frac{e_u+e_v}{u+v}[/tex]

    after some simplifying, I got to this,

    [tex]e_f=f^2(\frac{e_u(u+v)}{u^2v}+\frac{e_v(u+v)}{v^2u}+\frac{e_u+e_v}{uv})[/tex]

    and then I realized that I could never get the answer, however, if this term was negative,
    [tex]\frac{e_u+e_v}{uv}[/tex], i would get the answer perfectly, but how can it be negative??? Problem is even in division, shouldn't the fractional uncertianties add up??
     
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