Special relativity assignment - pole moving in two dimensions

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SUMMARY

The discussion centers on a special relativity assignment involving a pole moving in two dimensions, specifically in a frame S with speed v, where \(\gamma(v) = 3\), and speed w in the negative y-direction. The pole, appearing 6 ft long in frame S, must pass through a 3-ft hole in frame S', which is moving with velocity v relative to S. The challenge lies in reconciling the apparent width of the pole, which becomes 18 ft in S', with the reduced size of the hole due to length contraction. The key insight is that the pole's skewing in frame S' due to relativistic effects must be considered to explain how it fits through the hole.

PREREQUISITES
  • Understanding of special relativity concepts, particularly Lorentz transformations.
  • Familiarity with the concept of length contraction and its implications in different reference frames.
  • Knowledge of the Lorentz factor, \(\gamma\), and its calculation.
  • Basic grasp of two-dimensional motion and how it interacts with relativistic effects.
NEXT STEPS
  • Study the derivation and application of Lorentz transformations in special relativity.
  • Explore detailed examples of length contraction in multiple dimensions.
  • Investigate the implications of relativistic velocities on object dimensions and shapes.
  • Learn about the concept of simultaneity in different reference frames and its effects on observations.
USEFUL FOR

Students of physics, particularly those studying special relativity, educators teaching advanced relativity concepts, and anyone interested in the practical applications of relativistic physics in two-dimensional motion scenarios.

luisf
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Hi!
I'm a bit stuck with this special relativity assignment, here's is the problem:
In a frame S a pole moves in the x-direction at speed v such that \gamma(v)=3 and in the negative y-direction at speed w, while remaining parallel to the x-axis and being of apparent length 6 ft. The centre of the pole passes the centre of a 9-ft hole in a plate that coincides with the plane y=0. Explain, from the point of view of the usual second frame S' moving with velocity v relative to S, how the pole gets trough the now 3-ft hole.

So the problem here is that not only does the hole shrink in S', as stated in the problem description, the pole should also be wider by a factor of 3 in this frame. So we have an 18 ft wide pole that has to move through a 3 ft wide hole. Since it will obviously fit through the hole in S, there must be an explanation for how it would fit in S' and usually there's some quirk of some physical law that will just take care of things. I can't really think of any law that would aid me in this situation however, the only explanation I can think of is that the pole is perhaps skewed in S' because of length contraction in both x- and y-direction. I'm not at all sure how that would work though, hopefully I could get some guidance from you guys.

Thanks.
 
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See if the ends of the pole will pass through the opening.
 

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