The detonator problem. Please show all work. Thanks. 2. The Detonator Problem: C
ID: 3307853 • Letter: T
Question
The detonator problem. Please show all work. Thanks.
2. The Detonator Problem: 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. loth at rest Does the explosion occur? Explain why or why not, and support your explanation with a proof that is valid in all reference frames. (Hints: (i) Use LT's with event 1: A touches B, event 2: C touches D. (i) There is a "special" reference frame in which this problem becomes simple.) Runblomt The most distaut star we can see with the naked eve is V762Cas, which isExplanation / 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.