Consider U and T structures with rigid arms of proper length L, set up as shown
ID: 1711757 • Letter: C
Question
Consider U and T structures with rigid arms of proper length L, set up as shown below. If the disarming key (point A) does not touch the safety (point B) sufficiently early that a signal can travel from the safety to the detonator (point D) and deactivate it before the trigger (point C) touches the detonator, a huge explosion will occur. Suppose the T approaches the U with velocity v. If one only accounts for length contraction, there is an apparent paradox: a naive graphical analysis (compare the problem as seen in the respective rest frames of U and T) suggests the explosion would occur in T's rest frame but not U's. Does the explosion occur? Explain why or why not, and support your explanation with a that is valid in all reference frames.Explanation / Answer
Let use consider the event -
1) A touches B first - In this case three situations arises -
a) Both U & T moving with velocity v and A touches B first.This is possible when T's length is less than U.
b) When T is in rest and U moves and A touches B first.This is possbile when U's length is more than T.
c) When U is in rest and T moves and A touches B first.This is possible when T's length is shorter than U.
2) Second event - C touch D.In this case three situations arises -
a) Both U & T moving with velocity v and C touches D first.This is possible when U's length is less than T.
b) When T is in rest and U moves and C touches D first.This is possbile when U's length is less than T.
c) When U is in rest and T moves and C touches D first.This is possible when U's length is less than T.
As per the above analysis if U's length is less than T in any case explosion will occur whether T or U is moving.
So in all reference frame U's length should never be smaller than T to prevent explosion.
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