# Relativistic equations vs classical

1. Oct 16, 2008

### phyguy321

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' = $$\gamma$$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. Oct 17, 2008

### CompuChip

The second one seems relevant. Can you explain why you wrote these down and what you think they mean?

3. Oct 17, 2008

### phyguy321

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. Oct 17, 2008

### HallsofIvy

Staff Emeritus
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 $\gamma$ always larger than or always less than 1? That would affect which of these can be true.

5. Oct 17, 2008

### borgwal

The two equations are different only because of the factor of $\gamma$ in the relativistic equation. So, you have to figure out for what speed $\gamma=1.01$. Note that $\gamma$ is never less than 1 [prove that yourself], and so there is no real ambiguity in the question here.

6. Oct 19, 2008

### phyguy321

Ok that makes sense, now what if we wanted the kinetic energies to differ by 1%? so
1/2mv^2 and $$\gamma$$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
7. Oct 20, 2008

### borgwal

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 $\gamma$. 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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