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conantee
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« on: January 06, 2010, 12:23:48 PM »

Question 69-71
A car of rest length 5 meters passes through a garage of rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage's rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.

71. Which of the following statements is the best response to the question:
"Was the car ever inside a closed garage?"
(A) No, because the car is longer than the garage in all reference frames.
(B) No, because the Lorentz contraction is not a "real" effect.
(C) Yes, because the car is shorter than the garage in alll reference frames.
(D) Yes, because the answer to the question in the garage's rest frame must apply in all reference frames.
(E) There is no unique answer to the question, as the order of door openings and closing depends on the reference frame.
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conantee
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« Reply #1 on: January 06, 2010, 12:30:47 PM »

This is a little bit tricky question. If you notice that, in some reference frame, the garage is never closed, i.e., the front and back door are not closed simultaneously, then you can go to the answer, which is (E).

However, if you don't know the trick, check each choice. You will see that (B) is certainly wrong (We believe in relativity!). (A) and (C) are too strong arguments. There are some frames that one sees both car and garage moves with same speeds. Then, the length contraction should be the same. (D) is wrong since "answer" or more specifically, numbers in each frame may be different, for example, each frame see the length of garage differently. However, all perspectives should present same physical quality, for example, there is no physical damage due to crash between car and garage in all frames.

The correct answer is (E). 65 of 100 people got the correct one.
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