Paradox found in my first relativity sheet

[Toby_phys]

We have got some SR work to do, however we have only had 1 introductory lecture. I have a problem with one of the problems.

Question: A rod of 1m parrallel to the x-axis, travels at un-relativistic speeds at 45 degrees. It passes through a slit - also parallel to the x-axis - that is 1.1 meters wide.

Now assume the rod travels at 0.8c, does it fit through, look at it from both viewpoints, the rod and the slit?

In short, my answer was: I only need to look at the x velocity, y velocity will not cause the slit to shrink. X vlecocity = 0.8cos45 c

If you look at it from the slit's frame, the rod shrinks to about 0.8m and still fits. However if you look at it from the rod's frame, the slit shrinks to 0.9m, the rod doesn't fit.

How is this paradox resolved?

 

[mfb]

What happens to the "parallel to the x-axis" condition?
The y velocity is relevant.

 

[Ray Vickson]

We have got some SR work to do, however we have only had 1 introductory lecture. I have a problem with one of the problems.

Question: A rod of 1m parrallel to the x-axis, travels at un-relativistic speeds at 45 degrees. It passes through a slit - also parallel to the x-axis - that is 1.1 meters wide.

Now assume the rod travels at 0.8c, does it fit through, look at it from both viewpoints, the rod and the slit?

In short, my answer was: I only need to look at the x velocity, y velocity will not cause the slit to shrink. X vlecocity = 0.8cos45 c

If you look at it from the slit's frame, the rod shrinks to about 0.8m and still fits. However if you look at it from the rod's frame, the slit shrinks to 0.9m, the rod doesn't fit.

How is this paradox resolved?

No. in the rod's rest-frame the slit does NOT shrink; it is perpendicular to the direction of motion, so is not affected.

 

[Toby_phys]

Here is a diagram. How is the slit perpendicular to the motion

 

[Ray Vickson]

Here is a diagram. How is the slit perpendicular to the motion

Sorry; I mis-read the question.