Relativistic equations vs classical

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Homework Statement


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?


Homework Equations


G- x' = x - vt
L- x' = [tex]\gamma[/tex]x - vt


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?
 

Answers and Replies

  • #2
CompuChip
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The second one seems relevant. Can you explain why you wrote these down and what you think they mean?
 
  • #3
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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?
 
  • #4
HallsofIvy
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Homework Statement


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?


Homework Equations


G- x' = x - vt
L- x' = [tex]\gamma[/tex]x - vt


The Attempt at a Solution


I dont know what im trying to do exactly.
G-L = .01
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.
 
  • #5
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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.
 
  • #6
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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.

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:
  • #7
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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.
 

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