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Can a fly stop a train?
105 Answers
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)
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)
Answers
vascop, sorry, you are wrong. A tiny part of the train deforms, and in so doing the point of contact really does stop moving relative to a stationary observer. I'm not suggesting that the whole train stops, only the point of contact with the fly. The amount of the deformation and its duration may well be too small to measure, but it does happen. That's how the...
12:30 Thu 25th Feb 2010
The crux of the misunderstanding here seems to be that a lot of contributors have convinced themselves that if 2 bodies are in contact at some instant, and one is stationary at that same instant, then the other must be stationary as well at that instant.
This is clearly not correct.
You might just as well say:
If a body is going at 5 kmph and another is going at 100 kmph then when they make contact they are both going at 5 kmph. Why choose 5? Why not say they must both be going at 100? They can't be doing both speeds.
The truth is they are both going at their respective speeds at the instant of impact.
If one of these speeds just happens to be 0 (stationary), then how can you argue that both must be stationary? Why not both going at the other, non-zero velocity?
There's nothing special about speed zero.
In one of Tim's posts he talks about a balloon moving with respect to an observer, and a marble moving towards the balloon (see post above for details) and says that when the marble hits the balloon and eventually stops stretching the balloon and is stationary, with respect to the balloon, then the balloon is also stationary with repect to the observer. If that WERE the case, then why aren't the velocities the same BEFORE the marble stops stretching the balloon? It's still in contact with the balloon! It doesn't make sense to give zero speed a special significance.
This is clearly not correct.
You might just as well say:
If a body is going at 5 kmph and another is going at 100 kmph then when they make contact they are both going at 5 kmph. Why choose 5? Why not say they must both be going at 100? They can't be doing both speeds.
The truth is they are both going at their respective speeds at the instant of impact.
If one of these speeds just happens to be 0 (stationary), then how can you argue that both must be stationary? Why not both going at the other, non-zero velocity?
There's nothing special about speed zero.
In one of Tim's posts he talks about a balloon moving with respect to an observer, and a marble moving towards the balloon (see post above for details) and says that when the marble hits the balloon and eventually stops stretching the balloon and is stationary, with respect to the balloon, then the balloon is also stationary with repect to the observer. If that WERE the case, then why aren't the velocities the same BEFORE the marble stops stretching the balloon? It's still in contact with the balloon! It doesn't make sense to give zero speed a special significance.
Vascop,
Tim didn't say that. He said that the part of the ballon in contact with the marble would be stationary. He didn't say the whole balloon.
And what I'm saying (and Tim if I'm not being presumptious to Tim) is that WHEN 2 particles are in contact (not before) and you know the velocity of one, then the other's velocity is the same. Nothing special about zero, except that at some point in time the flies velocity IS zero and thus for that tiny time and for that tiny point of contact, the velocity of the material of the train will also be zero (even if it is hard).
Tim didn't say that. He said that the part of the ballon in contact with the marble would be stationary. He didn't say the whole balloon.
And what I'm saying (and Tim if I'm not being presumptious to Tim) is that WHEN 2 particles are in contact (not before) and you know the velocity of one, then the other's velocity is the same. Nothing special about zero, except that at some point in time the flies velocity IS zero and thus for that tiny time and for that tiny point of contact, the velocity of the material of the train will also be zero (even if it is hard).
The answer to this question depends on a number of factors unspecified in the question and therefore can not be resolved directly. For instance, the ultimate fate of the fly depends on the unspecified initial velocities as well as the properties and orientation of the surfaces making initial contact and the relationship of these surfaces to what lies behind them. Even the properties of the air between them just prior to contact or impact can have a significant bearing on the outcome.
One thing that can be reckoned in a fairly straightforward manner is that for any realistic velocity (direction and/or speed) of a living fully functional flesh fly, the trains overall velocity is not going to be significantly altered at any point in the encounter.
If one wants to make a case for what happens on the scale of individual molecules, atoms or subatomic particles then these scenerios need to be specified and clearly laid out before any possible outcome can be logically resolved, but in any such case, we would no longer be talking about a train or a fly.
One thing that can be reckoned in a fairly straightforward manner is that for any realistic velocity (direction and/or speed) of a living fully functional flesh fly, the trains overall velocity is not going to be significantly altered at any point in the encounter.
If one wants to make a case for what happens on the scale of individual molecules, atoms or subatomic particles then these scenerios need to be specified and clearly laid out before any possible outcome can be logically resolved, but in any such case, we would no longer be talking about a train or a fly.
-- answer removed --
The idea that the point of contact stops because the fly stops seems compelling but it is wrong.
The point of contact on the train is being considered differently from the point of contact on the fly. The conjecture considers the whole fly as rigid while treating the train as flexible as in the marble and ballon example.
The centre of mass of the fly can stop as observed. This does not mean that that the fly's point of contact with the train stops even instantaneously. On contact it immediately gives way, accelerating to the speed of the train.
Take it down to the atomic level. Ultimately the point of "contact" is the repulsion between the atomic nuclei. The atoms never really touch. The big heavy iron atoms exert an enormous repulsive force on the small atoms in the fly pushing them out of the way as they approach.
The point of contact on the train is being considered differently from the point of contact on the fly. The conjecture considers the whole fly as rigid while treating the train as flexible as in the marble and ballon example.
The centre of mass of the fly can stop as observed. This does not mean that that the fly's point of contact with the train stops even instantaneously. On contact it immediately gives way, accelerating to the speed of the train.
Take it down to the atomic level. Ultimately the point of "contact" is the repulsion between the atomic nuclei. The atoms never really touch. The big heavy iron atoms exert an enormous repulsive force on the small atoms in the fly pushing them out of the way as they approach.
In fact mibn2cweus is on the money with the mention of the air. The fly is initially deformd by the pressure in the air between it and the train.
It was found recently that the thin layer of air under a drop of water colliding with a solid surface is expelled at supersonic speed. This is an extraordinaty acceleration and accompanying pressure. That air pressure will produce a similar acceleration of the fly's point of contact with the train.
It was found recently that the thin layer of air under a drop of water colliding with a solid surface is expelled at supersonic speed. This is an extraordinaty acceleration and accompanying pressure. That air pressure will produce a similar acceleration of the fly's point of contact with the train.
Beso,
"The big heavy iron atoms exert an enormous repulsive force on the small atoms in the fly pushing them out of the way as they approach. "
OK, if you must, replace the fly with an iron ball-bearing fired from a catapult. You have exactly the same paradox. The materials involved are irrelevant. Are you persuaded now that there's a deformation on the train's surface? If not, how about a cannonball? By your reasoning at what magic values of size or density or hardness do the deformation effects start to happen?
"The centre of mass of the fly can stop as observed. This does not mean that that the fly's point of contact with the train stops even instantaneously. On contact it immediately gives way, accelerating to the speed of the train. "
Every part of the fly at some point in time has a velocity of zero. Draw a graph of velocity against time, time on the x-axis. When the fly-part changes direction, the line on the graph has to cross the x-axis which denotes a velocity of zero.
"The big heavy iron atoms exert an enormous repulsive force on the small atoms in the fly pushing them out of the way as they approach. "
OK, if you must, replace the fly with an iron ball-bearing fired from a catapult. You have exactly the same paradox. The materials involved are irrelevant. Are you persuaded now that there's a deformation on the train's surface? If not, how about a cannonball? By your reasoning at what magic values of size or density or hardness do the deformation effects start to happen?
"The centre of mass of the fly can stop as observed. This does not mean that that the fly's point of contact with the train stops even instantaneously. On contact it immediately gives way, accelerating to the speed of the train. "
Every part of the fly at some point in time has a velocity of zero. Draw a graph of velocity against time, time on the x-axis. When the fly-part changes direction, the line on the graph has to cross the x-axis which denotes a velocity of zero.
While I do not recall where a however slight deformation has been disputed . . . I would dispute the assertion that the deformation effects of a fly upon impact with an approaching train would at any point reduce its instantaneous velocity to zero. Upon impact, neither iron, steel nor windscreen are going to deform to the degree or at the rate of a fly.
Precluding a paint blister or fly with cannonball in tow, this should be enough to put even the most stubborn fly (as fond as we've all grown of it . . . and this thread) out of its misery.
Precluding a paint blister or fly with cannonball in tow, this should be enough to put even the most stubborn fly (as fond as we've all grown of it . . . and this thread) out of its misery.
The mistaken assumption here is that two objects in contact must have the same instantaneous velocity. Furthermore the "stop the train" proponents continue to treat the deformation of fly and the train in different ways,
I am happy to move to the ballbaring. We accept that as the iron atoms in each object approach each other, the electrostatic field between the nuclei deform producing an immense repulsive force. The repulsive force is experienced equally by both atoms regardless of their speed due to the Newton's Law of Equal and Opposite Force.
This will also stress the crystalline structure of the iron, deforming both objects. We can accept this deformation is equal at the microscopic level of interaction between atoms even though the macroscopic outcome reflects the larger geometric properties of the objects.
The motion of the atoms under the influence of the repulsive force is governed by the conservation of momentum. The ball bearing atom's momentum (considering fly velocities) is perhaps one tenth of the train's atom. The force acting against the lower momentum on the ball causes it to change momentum (and hence velocity) ten times as much as the atom on the train.
Lets assume a brave soul fires the ball head on into the train at 10 kph while the train travels at 100kph. The train atom will slow from 100kph to 90kph while the ballbearing atom will accelerate from 10kph to -90kph.
At no time does the atom on the train stop.
I am happy to move to the ballbaring. We accept that as the iron atoms in each object approach each other, the electrostatic field between the nuclei deform producing an immense repulsive force. The repulsive force is experienced equally by both atoms regardless of their speed due to the Newton's Law of Equal and Opposite Force.
This will also stress the crystalline structure of the iron, deforming both objects. We can accept this deformation is equal at the microscopic level of interaction between atoms even though the macroscopic outcome reflects the larger geometric properties of the objects.
The motion of the atoms under the influence of the repulsive force is governed by the conservation of momentum. The ball bearing atom's momentum (considering fly velocities) is perhaps one tenth of the train's atom. The force acting against the lower momentum on the ball causes it to change momentum (and hence velocity) ten times as much as the atom on the train.
Lets assume a brave soul fires the ball head on into the train at 10 kph while the train travels at 100kph. The train atom will slow from 100kph to 90kph while the ballbearing atom will accelerate from 10kph to -90kph.
At no time does the atom on the train stop.
Ditto with the cannonball (presuming it does not destroy the train).
However if ball is travelling at the same speed as the train then the atoms in the train will indeed stop momentarily. Likewise if the speed of the ball is higher than that of the train, the atoms in the ball will not be stopped by the train and the atoms in the train will momentarily reverse until they are reaccelerated by the forces exerted by parts of the iron that are continuing forwards.
Of course, following the initial impact, other factors governed by the geometry of the objects rapidly take over as the primary influence on the respective speeds of the atoms.
However if ball is travelling at the same speed as the train then the atoms in the train will indeed stop momentarily. Likewise if the speed of the ball is higher than that of the train, the atoms in the ball will not be stopped by the train and the atoms in the train will momentarily reverse until they are reaccelerated by the forces exerted by parts of the iron that are continuing forwards.
Of course, following the initial impact, other factors governed by the geometry of the objects rapidly take over as the primary influence on the respective speeds of the atoms.
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