Relativistic equations vs classical

[phyguy321]

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' = \gammax - vt

The Attempt at a Solution

I don't know what I am trying to do exactly.
G-L = .01
G = .99L
G = L + .01L
Do any of these seem relevant?

 

[CompuChip]

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

 

[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 that's inside the gamma?

 

[HallsofIvy]

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' = \gammax - vt

The Attempt at a Solution

I don't know what I am 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 \gamma always larger than or always less than 1? That would affect which of these can be true.

 

[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.

 

[phyguy321]

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.

Ok that makes sense, now what if we wanted the kinetic energies to differ by 1%? so
1/2mv^2 and \gammamc^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?

 

[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.