A meter stick lies along the x axis of the lab frame and approaches the origin w

Question

A meter stick lies along the x axis of the lab frame and approaches the origin with velocity ß. A thin plate parallel to the xz laboratory plane moves upward in the y direction with speed ßy. The plate has a circular hole with a diameter of one meter centered on the y axis. The center of the meter stick arrives at the lab frame origin at the same time in the lab frame as the rising plate arrives in the y=0 plane. Since the meter stick is Lorentz contracted in the lab frame it will easily pass through the hole in the rising plate. Therefore there will be no collision between the meter stick as each continues its motion. However, someone who objects to this conclusion can make the following argument: In the rocket frame in which the meter stick is at rest, the meter stick is not contracted, while in this frame the hole in the plate IS contracted. Therefore, there must be a collision between the meter stick and the plate.

Resolve this paradox.

Answer unequivocally the question: will there be a collision between the meter stick and the plate?

Explanation / Answer

In the laboratory the front of the meter stick and the back of the meter stick arrive "simultaneously" at the circumference of the hole. Events that are simultaneous in one frame are not simultaneous in a frame moving with respect to a frame at rest. An observer in the moving frame will see the front of the meter stick arriving at the front edge of the hole before the back of the meter stick arrives at the back edge of the hole - when the back of the meter stick arrives at a later time it can pass thru the hole.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.