okay so
v = l/τgamma
= (l/τ)(1 - v^2/c^2)^1/2
so V^2 = (l/τ)^2 - (lv/τc)^2
so v^2 + (lv/τc)^2 = (l/τ)^2
so v^2(1 + (l/τc)^2) = (l/τ)^2
so v^2 = l^2/(τ^2(1 + (l/τc)^2)
Is that correct?
Yes that was a very silly mistake! Ah so I have! I always get them the wrong way round, something I need to get right for definite.
So now I have
v^2 = l^2/τ^2(1-(l/τc)^2)
Is that more like it? When I tried to do it a few other ways I see that my problem was always factorising the v...
oops that was a very silly mistake!
So instead I should have got
v = lgamma/τ
so v=l/τ(1 - v^2/c^2)^1/2
so v^2 = l^2/τ^2(1 - v^2/c^2)
but now I'm a little stuck. How do I factorise out v from this? Or have I used a wrong substitution?
so v=l/t
and t=gamma/τ
so v = lτ/gamma
and gamma=(1-v^2/c^2)^-1/2
so v=lτ(1-v^2/c^2)^1/2
v^2=(lτ)^2 (1-v^2/c^2)
I rearranged it to get
v^2(1 +(lτ)^2/c^2) = (lτ)^2
So
v^2= (lτ)^2 / (1 + (lτ)^2/c^2))
Is that correct?
so I tried gamma = (1- v^2/c^2)^-1/2) and rearranged to get
v = c(1- 1/gamma^2)^1/2
and tried subbing in either
gamma = τ/t
so v = c(1 - t^2/τ^2)^1/2
but I didn't really know where to go from there
Homework Statement
Λ particle has a proper life-time τ = 2×10−10 s. After being born in the cloud chamber (a
device to track energetic particles) of physics laboratory it left there a a 300cm long trail. Find
the speed of this particle in the laboratory frame.
Homework Equations...