Relativity: Formulating dT, v, l Expression

[shyguy79]

Homework Statement

Formulate an expression linking the change in time (dT) and the particle's velocity (v) with it's length (l) occurring at relativistic speeds

Homework Equations

γ = 1/√1-(v^2/c^2)
T = γT
l = γl

The Attempt at a Solution

Not really sure what it's after...

 

[HallsofIvy]

You have "dT" but no other "d". You must have either "dl" or "dv". Which is it?

 

[shyguy79]

I think it implies dL

 

[shyguy79]

Just been looking at this question again and knowing that provided that v is a constant in the Lorentz Length Contraction:

$L_{0}=L\sqrt{1-\frac{v^{2}}{c^{2}}}$

Then shouldn't we be able to rearrange this for $\sqrt{1-\frac{v^{2}}{c^{2}}}$ to make

$\sqrt{1-\frac{v^{2}}{c^{2}}}=\frac{L_{0}}{L}$

and then feed this into the equation for Δt perhaps? So that

$\delta T=\frac{\delta T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

becomes

$\delta T=\frac{\delta T_{0}L}{L_{0}}$

It's just an idea...

 

[shyguy79]

Does anyone have any pointers? Perhaps try this under a different sub-forum maybe?