Exploring the Bridge Fall Paradox: A Look at Stress and Damage in Materials

[sweet springs]

Bridge fall paradox

Another thread urges me to think of stress in materials in TOR and let me make a "paradox" to think of it as follows.
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A train is running on a bridge over a wide river. Evil terrorists switch on the bombs set on legs of the bridge to crash whole the bridge into dust in a moment. Train falls on the river and gets damaged. Fortunately all the passengers and the crews have already jumped out before the train comes to the bridge with no injury at all. Before inspection of the damaged train, two inspecters say,

A: Train is damaged homogeneously. Terrorists set the bombs to explode simultaneously, so the train fell keeping horizontal position. Every bottom of the train hit the water surface similarly.

B: The front part of the train is the most damaged. In train system bombs explode not simultaneously. The header, the earlier. The train did not keep horizontal position. Its front is downer. The front is the first part to hit water surface, so it is most heavily damaged.

Which is right?
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The answer is homogeneous damage. The train behaves like spaghetti, even if how rigid it is, in the train system.

I am glad if you would have some fun.

 

[Nugatory]

Which is right?

You have to specify whether the supports are removed simultaneously in the frame in which the bridge is at rest or the frame in which the train is at rest. The result will be different.

 

[sweet springs]

Thanks for your interest. Simultaneous explosion in the frame of the bridge (A says so), accordingly not simultaneous in the frame of the running train (B says so explicitly).

 

[Ibix]

If the bridge rests on two supports then the points of support will start to drop first, and the rest of the bridge later (cf slinky drop). So the idea of the bridge and train falling at once seems to me to be problematic if the train is moving at anything comparable to the speed of sound in the material of the bridge.

Also the front of the train will take the brunt of the damage from sliding to a stop even if it does fall horizontally.

 

[Nugatory]

So the idea of the bridge and train falling at once seems to me to be problematic if the train is moving at anything comparable to the speed of sound in the material of the bridge.

Yes, the train/bridge paradox (and its stick/grate relative) require many additional idealizations to make them "right":
- The train must have negligible vertical height before its downward acceleration at a point along its length is defined.
- The water underneath the bridge must be moving at the same speed as the train if there is to be any possibility of a flat landing (accelerometers on the train read straight up at impact).
- The bridge cannot be modeled as a rigid object supported at both ends (no rigid objects allowed!). Instead we have to imagine an arbitrarily large number of supports for arbitrarily small lengths of bridge, all independently removed.

I find that there is some pedagogical value in mentioning all of these after the basic resolution has been provided.

 

[sweet springs]

Thanks for your interest. I would like to concentrate on TOR effect by setting ideal conditions e.g.
- Small many bombs for local disappearance of bridge parts are placed almost continuously with precise setting of clocks synchronized in the bridge IFR
- Train falls on river water, hard rock base or any flat floor without touching the riverside ahead.

Sound speed has nothing to do with this, I think.

After I wrote above I noticed #5. Thanks. I admit many idealization are necessary but believe the essence works.