Something about a fly and a train though experiment

[Pengwuino]

I've remembered in bits and pieces a thought experiment that I can't get a grasp on what was suppose to be explained and I was wondering if anyone happens to know what this is. Supposedly this was a famous thought experiment or osmething and I must have been told of it years ago, possibly even in high school but all I can remember is bits and pieces and I certainly don't remember what the goal of the experiment was.

The experiment went something like this. A fly is traveling down a set of train tracks headlong into a speeding train. The thought experiment centers on what happens to the momentum of the train upon impact. I don't think it mattered whether the fly bounced off or was more realistically, "splatted" onto the train. One thing I remember was the false argument that the train would have to come to an instantaneous velocity of 0 in order for that fly to ever have 0 instantaneous velocity (since going from the positive velocity the fly original has to the negative velocity it has upon bounce or splat). Does anyone remember the entirety of this thought experiment? I'm thinking it might have had something to do with the idea of there being no such thing as a perfectly incompressible material.

 

[rcgldr]

On a very small component of the surface of the train would initially decelerate and travel backwards, then stop, and then travel forwards, the result of a small amount of deformation (compression) at that small component of surface.

 

[DaveC426913]

The flaw in the thought experiment is that it assumes that both the train and the fly are perfectly rigid objects. If they were, there would be a problem as to how the train could stop and reverse the fly's motion.

Fortunately, there is no such thing as a perfectly rigid object, so no paradox. Both train and fly deform - the train momentarily, the fly for the rest of its life.

 

[Pengwuino]

Yes that is what I'm thinking. Was it postulated in Newtonian mechanics that perfectly rigid bodies were allowable?

 

[Vanadium 50]

Was it postulated in Newtonian mechanics that perfectly rigid bodies were allowable?

Even if it were, it is clear even to Newtonians that flies and trains are not perfectly rigid.

 

[rcgldr]

If you have perfectly rigid objects, then you have infinite forces and accelerations and velocity changes are instantaneous. Note that incompressable (and frictionless) fluids are used to approximate real world situations via Bernoulli equations, when the compressability factor is less than about 5%. This can lead to paradoxes like zero or negative pressures, or the idea that a solid moving through such a fluid has zero drag:

http://en.wikipedia.org/wiki/D'Alembert's_paradox