# Fly and a Train?

## Main Question or Discussion Point

Me and some friends where down the pub and an interesting idea came up.

say a fly is flying and collides with an on comming train then the train and the fly at an instant must stop?

how can this be? im trying to think of a way of analysing this. this is my guess. according to newtons third law (object A exerts an equal and opposite force on object B) (i am sure you are aware =] ) then the fly when it collides with the train exerts an equal and opposite force and at that instant stops it?

is this true can someone shed some light and help explain this to me =] .

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russ_watters
Mentor
I'm not quite following this - if a fly collides with a train, the fly will rapidly be accelerated to the speed of the train while the train will see no noticeable effect of the collision. Obviously, flies/bugs hit trains (not to mention my car) all the time and don't cause them to derail.

sorry i dont think i worded the question very well i believe what u where saying that when the fly collides with the oncoming train then the fly will rapidly accelerate in the other direction.

However they believe that the overpowering mass of the train will force the fly to travel in the opposite direction. To do this the fly must first stop. So, in that millisecond when the fly stops to change direction it is in contact with the train, therefore the train must be stopped too?

to me that doesnt really make much sense and goes against my intuition completely..

have i worded that better?

mgb_phys
Homework Helper
Yes the fly must momentarily stop - and so must 'the part of the train' in contact with the fly. It doesn't say the whole train stops.

It might help to imagine the front window of the train as made of rubber - at small scales all materials are rubbery

ye im trying to convince him using some sort of analogy. so far iv said that its similar to throwing a ball up in the air at its maximum height the ball will have a velocity of zero even though it will continue to accelerate downwards and therefore have a force in this case weight

is that a fair enough explaination =]

mgb_phys
Homework Helper
It's not an analogy, the fly and the point on the train that it hits do stop.
The 'trick' to the paradox is that the point on the windscreen bends backwards (relative to the rest of the train) as the fly hits, momentarily stops and then springs forward - the main part of the train keeps going forward

vanesch
Staff Emeritus
Gold Member
I don't think that even one single atom of the train window actually stops (in the ground reference frame - given my experience in that DWFTTW thread, better be careful :-).
True, part of the windshield will slow down a little bit, but it doesn't need to come to a full stop at all. After all, that would even be contradictory, because imagine the train drives at 100 mph, and the fly comes in at 30 mph. In this ground reference frame, it means that there must be a point on the windshield that momentaneously has 0 mph velocity wrt ground, and hence - 100 mph wrt the train.
But now consider that the fly comes in at 100 mph and the train does only 30 mph. That's the same impact, no ? (schroder, keep out of this).
But now the window should only do momentaneously -30 mph wrt the train and hence undergo a much smaller deformation ?

No, there's no reason to have 0 mph for a point on the window. What happens is that at the point of impact, at the moment of impact, given the relative rigidities of the two objects, you can consider the fly's body as a liquid. The first few atoms of the fly will undergo a large acceleration in the forward direction, need to undergo a force for that, and that force will come from a small deformation of the windshield (the deformation is a function of the force needed and the rigidity of the windshield).
After that, you get a compression of the body-fluid of the fly and as the shockwave propagates through the fluid, more and more body material gets accelerated forward. This modifies the force on the windshield which will bend accordingly.

Every atom of the fly's body will eventually come to a stop and then go forward, but that doesn't mean that the point on the windshield has to. The distance between these atoms and the windshield can change when the fly's atoms come to a stop. They don't have to be rigidly constant (or 0, when "touching"). There is a finite interatomic distance, and the force starts acting when this distance is not 0 and not yet at its minimum.

rcgldr
Homework Helper
A good analogy would be a small spring impacting on a large spring. From the perspective of each spring, the highest velocity of the leading surface occurs just after initial contact, then decreases due to the opposing force related to compression. The opposing force also increases with respect to compression unless it's inelastic.

Getting back to the OP, the leading surface molecules of the train collide with the leading surface molecules of the fly, with the leading surface molecules on both object initially moving backwards, until those molecules collide with molecules deeper in the surface and compression occurs. A very thin leading surface of the train ends up at 0 mph (relative to the ground) for an instaneous moment during the initial compression stage of the collision. The same thing happens with the leading surface of the fly.

Like Jeff seems to say, the resonances from the collision travel back and forth along the train (+fly), while damping - due to thermal interaction - dissipates the momentum of the fly. The impact increases the probability that a given atom of the train-fly distribution will stop relative to the ground.

Is this a rephrasing of Zeno's paradox?

mgb_phys
Homework Helper
No not really - that's more to do with not understanding infinitesimals

vanesch
Staff Emeritus
Gold Member
A very thin leading surface of the train ends up at 0 mph (relative to the ground) for an instaneous moment during the initial compression stage of the collision. The same thing happens with the leading surface of the fly.
As I said, that 0 mph is a frame-dependent quantity, so cannot be a physical thing. In the frame of the train, 0 mph means that the window doesn't move. At most one could require that both parts (atoms of fly and atoms of window) have a point of velocity 0 in their center of mass system (and then it depends on what masses play in this).

This would be the case if there were "contact forces": that is, no interaction beyond a certain distance, and a rigid binding at the "contact distance". But this is not how interatomic forces work: there is a smooth interaction potential. So the "spring" you allude to is not a material spring, but rather a description of the interaction potential between atoms.

rcgldr
Homework Helper
Is this a rephrasing of Zeno's paradox?
No, because the collision only affect a tiny amount of the surface of the train. Depending on the relative mass and speed of the molecules of the fly and train, the initial molecular collisions could result in a net "backwards" movement of both. If there was a large enough difference in the molecular mass, then as vanesch pointed out, the fly's much lower mass molecules would bounce off the trains molecules without slowing the trains molecules to 0 mph or below.

To eliminate the mass per molecule issue, replace the fly with a very small marble made of the same material as the train.

vanesch
Staff Emeritus
Gold Member
If there was a large enough difference in the molecular mass, then as vanesch pointed out, the fly's much lower mass molecules would bounce off the trains molecules without slowing the trains molecules to 0 mph or below.
That is correct if you consider the molecules as almost not bound together (if the fly and the train both were made of jelly or something). I was considering that the molecules are much more strongly bound in the train window than in the fly's body.
Otherwise, indeed, they both will come to a momentary standstill, but not in the ground frame, but in the center of mass frame of the colliding parts (which, for a fast train, and a slow fly, is moving forward).

rcgldr
Homework Helper
It would seem that the surfaces remain in contact while the fly accelerates in the direction of the train, transitioning from velocity opposing the train to velocity in the direction of the train. Somewhere during this transition the fly's surface is instaneously moving at 0 mph relative to the ground and since the surface between fly and train remain in contact the same thing happens to the trains surface.

It's a case of how thin a surface you're willing to consider. I don't know what the limit is at the molecular level, but it would seem you'd still have a compression related reaction due to the forces involved with the collision at the collision involved surfaces.

vanesch
Staff Emeritus