Can a fly stop a train?

[Barnacle_Bill]

Probably an old chestnut, but it's been worrying me since schooldays - and that's a long time.

A train is heading down the track and a fly is travelling up it. The two collide. The fly's velocity has changed from positive to negative (or vice versa!) so at some instant in time it must have been zero. At that instant it was in contact with the train so the train's velocity must also have been zero. So for that instant the fly stopped the train. I don't think so, but where's the flaw in the logic?

The only thing I can think of is that the fly's velocity has INSTANTLY changed without going through zero, but that doesn't sound very satisfactory. Can anyone finally put me out of my misery? (I hope calculus is not involved)

[vascop]

We've gone through all this before on AB. Try and find it.
In the meantime, the flaw in your initial statement is that you say that when the fly's velocity is zero, that the trains must be zero as well. This is not true, Think of a billiard ball travelling towards a stationary billiard ball. At the instant of impact the moving billiard ball has a NON-ZERO speed and the stationary billiard ball is still stationary.
So when the fly's speed is instantaneously zero, the train's speed is still 50 mph or whatever.

[sara3]

from a non-scientific point of view.. how very ridiculous, lol!

[waterboatman]

The fly's body absorbs the impact as it squashes. so it does not stop the train.

[society]

"but if two bodies are in contact, don't they have to have the same velocity? "

O no, I lay still at times.

[jake-the-peg]

The real question here is does the impact with the fly slow the train by a tiny tiny amount?

This, and other questions like it come up a lot and often the given answer is yes but it's so small you can't measure it.

I think of this as the theoreticians fallicy ( but then I come from the experimentalist tradition so I would say that wouldn't I? )

The thing is you see theoreticians deal with idealised objects a "perfect" gas, a frictionless surface, bodies that operate at 100% efficiency.

This allows them to reach conclusions without having to worry about all the horrible nasty details that mess things up in real life.

Now that's fine and dandy as long as you estimate what these variables are and determine that they are small enough that you can reasonably ignore them because what you are measuring is much larger than that.

However people then come along who are less rigorous or who ae deliberately michievous and ask questions like the fly and the train.

Now the force acting on the train is so small that effects like variation of friction on the track, the efficiency of the engine under different conditions, even gusts of wind are suddenly way way larger that the effect that we want to consider.

Now no longer is it a case that we can neglect these other issues but they become so large that we are forced to neglect the very thing we are interested in (the braking effect if the fly)

So no the fly does not brake the train at all because other variations drown out the effect

[vascop]

If two bodies are in contact they DO NOT have to have the same velocity at the instant they make contact, that is the point. Obviously if they then remain in contact they will have to have the same velocity.

[vascop]

Jake says:the real question here is does the impact with the fly slow the train by a tiny tiny amount?
No it isn't - read the original question again.

[daftgrandad]

If it was on the line it would.
Everything on lines stops them,snow,leaves etc.

[mibn2cweus]

However, in zhe case where the fly bounces off zhe train then the train would indeed be moving backwardz for a period of time . . . relative to zhe rest frame of zhe fly.

[Panic Button]

... and what is the last thing to go through the fly's mind at the moment of impact?

[Panic Button]

His @rse

[jake-the-peg]

No vascop that's not what I mean

I think that ones been answered - but the slow the train question is more representative of the type of similar question question that gets asked a lot - see the one about the charged battery being more massive for a recent example.

This one is just a variation of Zeno's arrow paradox

http://en.wikipedia.o...xes#The_arrow_paradox

[sara3]

now I'm worried that flies might be bashing into planes :o/

[Barnacle_Bill]

As Vascop says, the nub of the question is :- if 2 objects are in contact can they have different velocities? It would seem that the answer is, for a very short period of time, yes - otherwise the fly can be said to have momentarily stopped the train. Hard to imagine though. Different parts of the fly will have different velocities but the parts actually making contact - eyeball(s), antennae etc. - are hard to visualise. You could imagine down to molecular level I suppose - that's where I was afraid calculus might come in!

[MarkRae]

> so if there was a constant line of flies on a train journey from London to Edinburgh
> the train would stop eventually?

No, because each individual impact would not be sufficient to exert any measurable force on the train due to the radically different mass of the two bodies.

However, if the train hit a trillion flies at exactly the same instant, that might certainly be sufficient to stop it or, at the very least, slow it down a bit...

[bibblebub]

Back to the OP: Can a fly stop a train? No. End of story.

[Tim123]

Here is what would actually happen in an idealised situation. The fly is hit by the train and decelerates to zero then accelerates to the velocity of the train very quickly indeed. The portion of the train in contact with the fly deforms minutely, and for an instant that tiny tiny portion of the train stops moving relative to a stationary observer. The deformation lasts for a small but finite period, after which elasticity returns the train to its origial form. The important point is that the train is made up of atoms and, therefore, not totally rigid.