Date: Sun Sep 9 04:34:14 2001
Posted by No name entered.
City: No city entered. State/Province: No state entered. Country: No country entered.
Area of science: Physics
ID: 1000024454.Ph
Message:
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I take it from Edwin F. Taylor's Spacetime Physics, P.185, problem 6-5.
A U-shaped structure contains a detonator switch connected by wire to one ton
of the TNT. A T-shaped structure fits inside the U, with the arm of the T not
quite long enough to reach the detonator switch when both structures are at
rest.
Now the T is removed to the left and accelerated to high speed. It is Lorentz-
contracted along its direction of motion. As a result, its long arm is not long
enough to reach the detonator switch when the two collide.
However, look at the same situation in the rest frame of the T structure. In
this frame the arm of T has its rest length, while the two arms of the U
structure are Lorentz-contracted. Therefore the arm of the T will certainly
strike the detonator switch. The question is whether there will be an explosion.

Figure:
|       =======+
|======       S|~~~~TNT (S denotes the switch)
|       =======+
<--x-> <--y-->

The answer is there will be an explosion. Someone said that due to there is no
absolutely rigid body so the arm of T will continue its motion for some time
even the cap of T strike the arms of U. But can we prove the two frames agree
quantitatively?

In the rest frame of T, the sufficient condition for the explosion is x>=y*Sqrt
[1-v^2], but in the rest frame of U, the condition depends on when the arm stop
and I can't make it agree with the condition in the rest frame of T exactly.
How do you resolve it?

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