Homework Help: A simple contraction question.

1. May 22, 2007

MathematicalPhysicist

A rod. having slope m relative to the x axis of S, moves in the x direction at speed u. what is the rod's slope in the usual second frame S'? (S is at rest realtive to S' which moves along the x direction with velocity v).
well obviously the horizontal length of the rod is contracted or lengthened, depends on your frame:
i think that if L is the length of the rod, and $$u'=\frac{u-v}{1-\frac{uv}{c^2}}$$ then we have: L'_x=Lcos(theta)/gamma(u')
and the slope in S' is: m'=m*gamma(u') cause the vertical portion of the rod doesnt get change.

the problem is that in the answer key we have:
m'=m*gamma(v)*(1-uv/c^2)
but i dont get this, even with some algebraic manipulations, so i guess im wrong here, can someone help here?

2. May 22, 2007

neutrino

3. May 22, 2007

MathematicalPhysicist

S is at rest relative to S', where S' moves with horizontal velcoity compared to S, what's not understood here?

4. May 22, 2007

Staff: Mentor

(1) S is at rest relative to S'
(2) S' moves with a horizontal velocity compared to S

Sounds contradictory to me! You might want to reword your problem statement.

5. May 22, 2007

MathematicalPhysicist

what's wrong here?
one frame is stationary the other one moves with constant speed, what's wrong with this?

6. May 22, 2007

neutrino

In SR, you cannot say that something is at rest in an absolute sense. It has to at rest with respect to/relative to something. So if S' is at rest with respect to S, then the relative velocity between the two is 0. If, on the other hand, S' has a velocity of v as measured by S, then S' measures the velocity of S to be -v(assuming standard configuration).

7. May 22, 2007

MathematicalPhysicist

yes i see your point, i meant that S' has velocity v as measured by S.

8. May 22, 2007

neutrino

Now that we have taken care of that, back to the problem...

I don't really see how to manipulate your answer, which is correct, to the form given in the book, and I also don't see how it is simpler than just having gamma(u').