- #1
Kaguro
- 221
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Rod R1 has a rest length `1m and rod R2 has rest length 2m. R1 is moving towards right with velocity v and R2 is moving towards left with velocity v with respect to lab frame. If R2 has length 1m in rest frame of R1, then v/c is what?
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I let vel of R1 be u, of R2 be w w.r.t lab and velocity of R2 w.r.t. R1 be w'.
Then u = v, and w = -v.
Then by relativistic velocity addition formula:
w' = (w - u)/(1- (u*w)/c^2)
=> w' = -2v/(1+v^2/c^2) -----------(1)
Now, according to Lorentz contraction:
L/L0 = √(1 - (w'/c)^2 )
But L/L0 = 1/2
Solving, I find w'/c = (√3)/2 ------------(2)
From simplifying (1) and (2):
v^2 + (4/√3) vc + c^2 = 0
So, v = -c/√3 or v = -√3 *c.
But... why is answer negative?
Even if I reject the 2nd one and accept the magnitude of first, I get v = 0.577c...
But the exact answer given is v = 0.6c.
Where did I go wrong?Also, the solution given says:
Where did this one come from??
Any help will be appreciated.
[Moderator's note: Moved from a technical forum and thus no template.]
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I let vel of R1 be u, of R2 be w w.r.t lab and velocity of R2 w.r.t. R1 be w'.
Then u = v, and w = -v.
Then by relativistic velocity addition formula:
w' = (w - u)/(1- (u*w)/c^2)
=> w' = -2v/(1+v^2/c^2) -----------(1)
Now, according to Lorentz contraction:
L/L0 = √(1 - (w'/c)^2 )
But L/L0 = 1/2
Solving, I find w'/c = (√3)/2 ------------(2)
From simplifying (1) and (2):
v^2 + (4/√3) vc + c^2 = 0
So, v = -c/√3 or v = -√3 *c.
But... why is answer negative?
Even if I reject the 2nd one and accept the magnitude of first, I get v = 0.577c...
But the exact answer given is v = 0.6c.
Where did I go wrong?Also, the solution given says:
Where did this one come from??
Any help will be appreciated.
[Moderator's note: Moved from a technical forum and thus no template.]
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