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What kind of a bomb? answer:the exploding kind. 
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#1
Sep2407, 10:05 AM

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i have this question from wheeler and taylor book, the answer is that bomb does get explode but i dont know how to explain it obviously T is acclerating so it's not an inertail frame, but still i don't see how will an observer in U see an explosion take place, anyone care to explain, has it got to do with simulatenity?
thnkasin advance. the pic is in the attachment. 


#2
Sep2407, 10:18 AM

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Realize that an observer in U will see the top of the T smack into the U, while the long arm of the T keeps going. (Since signals cannot travel faster than c, the T cannot be considered a rigid body that stops as a whole when one end is stopped.)



#3
Sep2407, 10:54 AM

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so the answer is there are no rigid bodies, and when the first time the top T smack the U, the T keeps moving with the U so the arms of the U get eventaully shoretend and kaboom, is this correct or am i way off?
thanks in advance. 


#4
Sep2407, 11:59 AM

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What kind of a bomb? answer:the exploding kind.
The structural strength of any possible steel should be totally negligible in this problem.
The arms of a bar made out of the strongest steel are not going to be anywhere near strong enough to stop the remainder of the bar. It's doubtful that the U tube will fare very well either. "Deform" is too mild a word to describe what's going to happen to them both when the collision occurs. The energy contained in the moving bar is probably going to be much greater than the energy in the TNT, as well, considering that 1 ton of TNT has an energy of 4*10^9 joules, while 1 gm of the material in the T has an energy of approx (gamma1)*10^14 joules, (i.e. (gamma1)*m*c^2), where 1/gamma is the length contraction factor. We don't have the dimensions, but it's likely that the T is going to weigh a lot more than 1 gm, and in order to get any appreciable length contraction gamma is going to have to be "large", say at least 1.1. So the energy released by the TNT will probably also be negligible, the real fireworks are going to be in the relativistic collision. It's not clear how to model this, and it's probably not the point of the problem. I would guess offhand that you have more than enough energy in the relativistic collision to vaporize the entire assembly. The TNT will probably contribute it's small amount of energy to this process, eventually. However, the detonation speed of the TNT is going to be much slower than the relativistic speeds involved in the collision. Basically, the relativistic collision will probably result in something that looks a lot like a nuclear fireball. It could easily be a larger energy release than anything in our current nuclear arsenal if the steel 't' bar is not very, very tiny. 


#5
Sep2407, 12:10 PM

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it's only a textbook question, you got way off with it pervect.



#6
Sep2407, 12:20 PM

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Maybe. I don't really think it is a very good textbook question, though, because if you take it very literally and seriously "as written", you almost have to answer it as I did.
I think that The barn in the pole problem (click on the link for details) is a much better problem along the same lines, that doesn't take you off into tangents if you try to figure out what would actually, physically, happen. 


#7
Sep2407, 01:02 PM

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#8
Sep2407, 01:19 PM

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#9
Sep2407, 03:40 PM

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But if we imagine a Tshaped structure that's actually "made of the strongest steel", it will deform significantly even at .0001c, which is 30 km/sec. Think of trying to build a steel tshaped spring which is strong enough to launch itself into orbit at 30 km/sec. I think I can say without doing a full mechanical analysis that that is not possible even "for the strongest steel". It just can't store enough mechanical energy to achive that sort of speed. Offhand, I'd say that you'd be lucky to get some fraction of the speed of sound in steel as an absolute upper limit. At least at .0001c, the structure will only deform and break, rather than explode in a nuclear fireball :). While perhaps I am being a bit silly, it comes from just being very literal, and reading the problem exactly as it was written. 


#10
Sep2507, 12:04 PM

P: 3,220

so the long arm of T keeps moving while the shockwave from the back gets to the front up to that event the arm keeps moving and it gets to the TNT, but then it means that the back is deformed while T keeps moving, so the first picture is wrong cause T's shape doesnt stay the same as pervect argued there.
I agree with pervect not intuititve problem. I have another puzzler which seems quite simple: a runner has a mirror in his arm, the runner runs near the speed of light will he be able to see himself in the mirror? my answer is yes, cause in any inertial frame the laws of physics are the same, so if were at rest he would see himself in the mirror i.e the law of reflection still applies also in the inertial frame when he moves compared to the lab for example. 


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