Collision between a steel plate and meterstick in frame S?

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SUMMARY

The discussion centers on the collision dynamics between a moving steel plate with a circular hole and a meterstick in a relativistic framework. The steel plate, moving in the +y direction at speed v, does not experience a relativistic change in the diameter of its hole. In contrast, the meterstick, moving in the x direction at speed v/c, undergoes length contraction. The conclusion is that there will be no collision between the two objects as they reach the same point simultaneously, despite the relativistic effects on the meterstick.

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A very thin steel plate with a circular hole one meter in diameter centered on the y-axis lies parallel to the xz plane in frame S and moves in the +y direction at constant speed v, a mterstick lying on the x-axis moves in the x directoin with v/c.The steel plate arrives at the y=0 plane at the same instant the center of the meterstick reaches the origin of S. Will there be a collision?
 
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Not all that paradoxical. The steel plate (more specifically, the hole) moves in the y-direction so there is no relativistic change in the diameter of the hole. The meter stick is moving in the x direction so there is contraction. By the way, (although it doesn't affect the answer) are you sure about that "with v/c"? Was that "with speed v/c"? In that case, what are the units?
 
yeah, but if you see it in the meter stick' coordinate, then the steel plate does have a relativisic change: it moves in the x direction
 

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