A U-shaped structure made of the strongest steel contains a detonator switch con
ID: 1843091 • Letter: A
Question
A U-shaped structure made of the strongest steel contains a detonator switch connected by wire to one metric ton (1000 kg) of the explosive TNT, as shown in the figure below. A T-shaped structure made of the same strong steel fits inside the U, with the long arm of the T not quite long enough to reach the detonator switch when both structures are at rest in the laboratory. Now the T structure is removed far 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. Therefore there will be no explosion. However, look at the same situation in the rest frame of the T structure. In this frame the arm of the 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 and there will be a terrible explosion. Is there an explosion or isn't there? Explain clearly your reasoning. The wire from the detonator switch to the TNT is restrung through point B on the U structure when both structures are at rest, and a laser is installed at point A on the T structure. Later, when the two structures collide at A, the laser files a pulse at B that cuts the detonator wire. Does this new apparatus change your prediction about detonation of the TNT?Explanation / Answer
a) The explosion does happen. It cannot 'not happen' in one frame of reference and happen in another. If it causes detonation in one frame, it has to do the same in all frames of reference. The T, when hits the U in the moving T frame of reference, upon collision with the U at such a high speed, will basically make the T a non rigid body with the T- Cap moving at one velocity and the T-arm moving at the initial velocity inciting an expansion in length of the foreshortened arm ultimating touching the switch of detonator. Hence an explosion is inevitable.
b) With the laser, there maybe a defuse instead of a detonation since the foreshorten expansion would not be matching the speed of light/laser whihc would be faster at reaching the wire than the T-arm reaching the switch
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