1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Relativistic equations vs classical

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    At what relative speed will the Galilean and the Lorentz expressions for position x differ by 1%? What fraction of the speed of light is this?


    2. Relevant equations
    G- x' = x - vt
    L- x' = [tex]\gamma[/tex]x - vt


    3. The attempt at a solution
    I dont know what im trying to do exactly.
    G-L = .01
    G = .99L
    G = L + .01L
    Do any of these seem relevant?
     
  2. jcsd
  3. Oct 17, 2008 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    The second one seems relevant. Can you explain why you wrote these down and what you think they mean?
     
  4. Oct 17, 2008 #3
    I was trying to figure out how to make them differ by 1%. would we say that at some speed they are equal and so when G = 1.01L then G is 1% less than L then solve for v or the v thats inside the gamma?
     
  5. Oct 17, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    This makes no sense! A % is always of a % of something!

    [/quote]G = .99L
    G = L + .01L
    Do any of these seem relevant?[/QUOTE]
    You want G and L to differ (G- L or L- G) by 1% of something. 1% of what? Possible choices are G-L= 0.01L so G= 1.01L, G- L= 0.01G so L= 0.99G, L- G= 0.01L so G= 0.99L, or L- G= 0.01G so L= 1.01G. Is [itex]\gamma[/itex] always larger than or always less than 1? That would affect which of these can be true.
     
  6. Oct 17, 2008 #5
    The two equations are different only because of the factor of [itex] \gamma [/itex] in the relativistic equation. So, you have to figure out for what speed [itex] \gamma=1.01 [/itex]. Note that [itex] \gamma [/itex] is never less than 1 [prove that yourself], and so there is no real ambiguity in the question here.
     
  7. Oct 19, 2008 #6
    Ok that makes sense, now what if we wanted the kinetic energies to differ by 1%? so
    1/2mv^2 and [tex]\gamma[/tex]mc^2 - mc^2 differ by one percent? do i plug in the velocity from part a into the gamma and solve for v in the classical equation?
     
    Last edited: Oct 19, 2008
  8. Oct 20, 2008 #7
    No, of course you don't use the same velocity as from part a, because the classical and relativistic kinetic energies do not simply differ by a factor of [itex] \gamma [/itex]. Since the relativistic kinetic energy is always larger than the classical one, there is again no ambiguity in how to make them differ by 1 percent.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?