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smithg86
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Homework Statement
A rod of length L_0 moves with a speed v along the horizontal direction. The rod makes an angle of [tex]\vartheta[/tex]_0 with respect to the x'-axis.
(a) Show that the length of the rod as measured by a stationary observer is given by
L = L_0 [1-(v/c)[tex]^{2}[/tex] cos [tex]^{2} ( [/tex] [tex]\vartheta[/tex]_0 ) ] [tex]^{1/2}[/tex]
(b) Show that the angle that the rod makes with the x-axis is given by the expression
tan [tex]\vartheta[/tex] = [tex]\gamma[/tex] tan [tex]\vartheta[/tex]_0.
These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)
Homework Equations
[tex]\gamma[/tex] = [1- (v/c)^2]^(-1/2)
(Length contraction formula) L_0 = L / [tex]\gamma[/tex]
The Attempt at a Solution
The horizontal component of the rod in the x'-axis is:
x_0 = L_0 cos ( [tex]\vartheta[/tex]_0 )
Applying the length contraction formula, I was able to show (which differs from what I was supposed to show):
L = L_0 cos [tex]\vartheta[/tex]_0 / [1- (v/c)^2]^(1/2)
I do not understand why this is not the correct answer. I did not attempt the second part of the question.