The Bug and the Train

Now if the bug has the mass of a neutron star, well that's a different outcome altogether...

Mass times velocity = force...

How about this B.U.G.?(Big Ugly Guy)

Mass times velocity equals momentum here.

How about a VW bug?

SPLAT!

Of course it could be said that in an infinitely short duration moment no movement occurs anywhere, but the scenario I describe is not general, but specific. Since the BB reverses direction, we know that it will actually (not theoretically) come to a complete stop for a moment of infinitely short duration. If that moment of infinitely short duration, in which the BB is actually at a complete stop, could be captured on film, then we would observe that simultaneously at that infinitely short duration moment the train is also at a complete stop.

Are we to conclude that our camera, with its infinitely fast shutter speed has simultaneously recorded a truth (the stationary BB) and a falsehood (the stationary train), or are we to conclude that the train, like Schrodinger's cat, occupies two states simultaneously - moving and not moving. More analogously, it is as if we have two cats in a box - one that we know to be dead, and the other both dead and alive (ie: the unmoving BB, and the train both moving and not moving). If when we open the lid we observe that there are two dead cats, we know this to be true. If when we open the lid containing the BB and the train (ie: take a photo of the BB and the train), and we observe that they too are both dead, that is, not moving, should we not conclude that this is also true? If we accept that there are two dead cats at the instant of observation and measurement, then, to be logically consistent, we must accept that, at that instant of observation and measurement, both the BB and the train are not moving.

"Oh don't mind me. I'm just goofin' around!" - Babe Bennett (Cathy Jones)

The falsehood of your logic is a division by zero error. You are working with dV/dT, so when you look at the infinitesimally small dT you are introducing this error. Consider the extrapolation of your question. Decrease the size of the bug to the size of a molecule of air, which it hits very frequently. Now, does the train stop for an infinitesimally short period of time for each air molecule it encounters????

--JMM

Very good, JMM. I recall a "proof" that 2=1 that would fool a lot of people because the division by zero error was not apparent to them. However, the division by zero error does not apply to my syllogistic argument in Post #18:

"Object A is stationary relative to an on the ground observer. Object B is in contact with and is stationary relative to Object A. Therefore Object B is stationary relative to the on the ground observer."

It cannot be disputed that a BB (Object A) hitting the front of a train, will, for an instant become stationary relative to an on the ground observer. It cannot be disputed that at that instant the train (Object B) will be stationary relative to the BB (Object A). Therefore the stated conclusion follows: For that instant Object B (the train) will also be stationary relative to the on the ground observer.

It is too easy to respond, "But by Newtonian mechanics...etc." I submit that the internal logic of the syllogism is bulletproof (or should I say, BB proof?). There is no division by zero. We know the BB changes direction therefore we know that it must stop for a moment. There would only be division by zero if the duration of that moment were infinitely short - but if it were infinitely short the stop wouldn't be manifest - but the stop is manifest. It occurs not in theory, but in reality. Therefore the BB stop has duration (however small), and for that duration it is stationary relative to an on the ground observer. The train is in contact with the BB for that duration, and the train is stationary relative to the BB for that duration. Therefore, by unassailable logic, for that duration the train is also stationary relative to the on the ground observer.

A syllogism (Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

Based on your input I would disagree as as the deducted reasoning forgoes the fact that the train is built from hard iron and the BB would be of a softer alloy metal. The steel would absorb an impact and deflect where the BB would deflect even greater and absorb more impact and have greater deflection therefore the train could possibly be slowed sever so slightly not to be noticed by anyone.

Theoretically what you state is that smacking a tennis ball against a 10 tonne concrete block would and should move the block backwards, when in fact the tennis ball absorbs the impact, the air inside expands with the compression of the outer rubber layer and the ball explodes.

See the bullets on the video against a stationary steel plate and a golf ball against a steel plate

https://www.bing.com/videos/search?q=slow+motion+of+a+tbullet+impacting+steel&&view=detail&mid=C3B051F2DAB4CFCE2A46C3B051F2DAB4CFCE2A46&&FORM=VRDGAR&ru=%2Fvideos%2Fsearch%3Fq%3Dslow%2520motion%2520of%2520a%2520tbullet%2520impacting%2520steel%26qs%3Dn%26sp%3D-1%26pq%3Dslow%2520motion%2520of%2520a%2520tbullet%2520impacting%2520steel%26sc%3D0-40%26sk%3D%26cvid%3D60CE6549714A456EB4AD184CC150D397%26FORM%3DVDVVXX

https://www.bing.com/videos/search?q=slow+motion+of+a+tbullet+impacting+steel&&view=detail&mid=C3B051F2DAB4CFCE2A46C3B051F2DAB4CFCE2A46&&FORM=VRDGAR&ru=%2Fvideos%2Fsearch%3Fq%3Dslow%2520motion%2520of%2520a%2520tbullet%2520impacting%2520steel%26qs%3Dn%26sp%3D-1%26pq%3Dslow%2520motion%2520of%2520a%2520tbullet%2520impacting%2520steel%26sc%3D0-40%26sk%3D%26cvid%3D60CE6549714A456EB4AD184CC150D397%26FORM%3DVDVVXX

It would have to be said, that if the BB was huge and contained enough velocity and mass, and both metals were the same, it could possibly slow the train down a tad after the metals have absorbed all impact forces. But a BB would not do this and a ground observer could not possibly see and change in the train speed or direction of travel.

In my Post #7 I specified, for the sake of my argument, that both the BB and the train are comprised of perfectly incompressible material, and I stated that I knew that such a material does not exist. After some thought, I have concluded that this specification is unnecessary. What is important is that at some instant during the collision of the BB and the train, the BB is stationary relative to an on the ground observer; and that at that instant the train is stationary relative to the BB.

My syllogism:

Proposition #1: Object A (the BB) is stationary relative to an on the ground observer.

Proposition #2: Object B (the train) is in contact with and is stationary relative to Object A (the BB).

Conclusion: Therefore, Object B (the train) is also stationary relative to the on the ground observer.

Both the first and the second proposition are true at some moment during the interaction between the BB and the front of the train. Neither the relative masses nor the relative compressibilities of Object A and Object B will alter the truth of either proposition. Therefore the conclusion is valid.

I'm sorry to say that your log is flawed.

As others have already described mathematically, the conservation of momentum of the combined "system" is retained and thus the train does in fact continue, though slowed by that proportionate amount.

For your "incompressible" objects, then the mathematics/calculations would again need review. The incompressible item would actually "rebound" at its impact velocity relative to the train and thus the energy impacted to the train (and thus the slowing) would be double that of the bug of same mass that is essentially absorbed into the train over the impact duration. The slowing observed would thus be double.

If you follow your own logic, then if the bug "stops the train", the BB (of same mass as the bug) would provide some instantaneous reversal of the train.

You are saying that on the field of play of Newtonian mechanics I have broken the rules, and I don't dispute that. But I am not playing Newtonian football, I am playing on the field of syllogistic logic. Please see my reply (Post #27) to redfred. The questions I pose to him about the two propositions of my syllogism, I also pose to you. If you consider either proposition to be false, please explain why.

Fine, if you can dismiss my analysis of why Zeno just splats on the front of the train then I can dismiss your questions.

Good Day.

I'm not saying that you've broken the rules, simply that your assertions are flawed.

The conservation of momentum of the whole system (the train and the bug, or the BB) is retained through the whole sequence.

If let's say the ratio of BB to train is 1:1,000,000 for your assertion of totally inelastic impact and rebound.

Then before the collision we have 1,000,000 units of mass (UOM) travelling at 10 mph in one direction and one UOM travelling 25mph in opposite direction. Total momentum of the system is (1,000,000 minus 2.5) units. (999,997.5)

Following collision, we have 1 UOM now reversed in direction at (10 + 25) mph or 3.5 units. The remaining (999,997.5 minus 3.5) 999,994 units are associated to the train. Being 6/1,000,000ths of the initial 10 mph.

Thus while the train slows instantaneously, it doesn't stop.

We could then take this to the next level where coal trains design by my son weigh in with 120 wagons at 120 Tons each, plus three locomotives over 250 Tons each (15,150,000kg) and the BB weighs in at 0.0005kg. You can do the maths, but I think there are 11 zeros included in the delta speed factor. They don't worry about bugs. The grasshoppers are more of a problem.

Clearly you have not read my Post #34 reply to jmueller, nor my Post #36 reply to Truth is not a Compromise.

I find it astonishing that some here actually think that I was serious in my assertion that a BB can stop a train - and they twist themselves into Newtonian knots to convince me of my error. My syllogism is in the spirit of Zeno, the Greek philosopher famous for his reasoned paradoxes. He would present closely reasoned arguments as to why (for example) a fast runner can never overtake a slow runner. Everyone knows that a fast runner will overtake a slow runner (just as everyone knows that a BB will not stop a train), but knowing this does not identify the flaw in Zeno's (or my) reasoning.

In full earnest mode, you present a treatise on the conservation of momentum in an attempt to convince me that a BB fired at a train will not stop the train, but in all of your words you do not confront my syllogism head-on and identify the specific logical flaw in my reasoning. jmueller, in Post #31, addresses the syllogism on its own terms, and in one short paragraph, identifies the inherent logical flaw. In response I acknowledge the flaw, and graciously commend his insight.

Unfortunately incompressible is as impossible as infinite force.

The closer the objects get to incompressible closer the forces get to infinite, and, the closer the change in momentum gets to instantaneous.

I acknowledge in other posts that incompressible is an abstract concept. I also state in other posts that I know full well that that a BB shot from a BB gun cannot and will not stop a train. The syllogism I presented that purports to prove that a BB can do just that, was an intellectual exercise, analogous to a "proof" I know that 2=1. Everyone knows that 2 does not equal 1, but not everyone can identify the divide-by-zero error that is partially disguised in the algebra of that "proof".

To clarify, here is my syllogism again:

When the BB contacts the front of the train, it reverses direction. At the moment it reverses direction, the following two propositions are true:

Object A (the BB) is stationary relative to an on the ground observer.

Object B (the train) is stationary relative to Object A.

Therefore Object B (the train) is stationary relative to an on the ground observer.

Some posters have erroneously believed that to invoke Newtonian mechanics and conservation of momentum, and so on, thoroughly disproves the stated syllogistic conclusion, but those arguments do no such thing. They simply indicate that there must be a logical flaw somewhere in the syllogism, but do not identify that flaw.

In Post #31, jmueller identifies the flaw. Absent from his argument is the patronizing I'm-dealing-with-a-fool tone evident in posts of certain others. I sense that he (assuming he) recognized and accepted the syllogism as an intellectual exercise, and therefore confronted it on its own terms. Thankyou again jmueller.

Thank-you, CSW. I don't have sufficient mathematical skill to give a clear-cut statement of the mathematical error, but, as you agree, it is there.

--JMM

I agree, and, I have given JM a Good Answer.

It's just that my answer encapsulates why the objects cannot be incompressible (or if they are the other impossible conclusions).

As soon as you realise that the objects are compressible, it is obvious that the BB reverses direction before it starts moving at the same speed as the train.

In Post #35, Truth is not a Compromise wrote, "If the objects are incompressible, then the small object undergoes a step change in velocity that is at no time ever zero." - This is a difficult concept (to go from one velocity to another without passing through any intermediate velocities), but it is another abstract result that can be imagined as a consequence of the collision of abstract (incompressible) objects.

I understood the difficulty so I said, let the objects be compressible. You state that when the objects are compressible it is obvious that the BB reverses direction before it starts moving at the same speed as the train - that is, the BB becomes stationary relative to the ground before the train becomes stationary relative to the BB. Well, that obviousness eluded several posters here, who could only counter my syllogistic conclusion by producing conservation of momentum arguments. The contact of the BB with the train is so brief, and yet the two events described in my syllogism occur in that brief moment, so I'm not sure that the non-simultaneity of those two events is as obvious as you claim. I do agree, however, that it is obvious now that it has been pointed out.

Isn't it interesting though, that such a brief moment in time (less than the time the BB is in contact with the train) separates the instant when the BB is stationary relative to the ground, and the instant when the train is stationary relative to the BB? Those two events are infinitesimally close to being simultaneous. If they were simultaneous then my syllogistic conclusion (the train is also for that instant stationary relative to the ground) would have to be true, and the structure of Newtonian mechanics would collapse.

You are correct. Same thing happens when you jump up. When your velocity is zero, so is your weight

A syllogism will make the point clearer. Here is the general syllogism:

Object A is stationary relative to an observer. Object B is in contact with and is stationary relative to Object A. Therefore Object B is stationary relative to the observer.

Now, let us identify Object A and Object B in the syllogism:

An incompressible BB (Object A) is stationary relative to an observer. An incompressible train (Object B) is in contact with and stationary relative to the incompressible BB (Object A). Therefore the incompressible train (Object B) is stationary relative to the observer.

The train doesn't change direction, so why should it stop?

Momentum, which equals mass x velocity, is conserved. So if m is the mass of the bug, M is the mass of the train, and dV is the change in speed of the train with the bug:

Momentum of train + momentum of bug = momentum of (train + bug)

25*M - 10*m = (25+dV)*(M+m)

25*M - 10*m = 25*M+25*m+dV(M+m)

-10*m=25*m+dV(M+m)

dV=-35*m/(M+m)

The train would slow down by 35*m/(M+m) miles per hour and would be a few microseconds late for the next stop.

I presume the bug is named Zeno.

All I know is if the bug had the guts, would he do it again?

The last thing going through the bugs mind is not if he stopped the train. Its his backside.

Gee guys! I almost hate I mentioned it now!

If you feel the train stops momentarily, what force do you propose brings the (perfectly incompressable) train back up to speed?

I think the problem lies in perfect incompressibility. it means the bug will not actually be a rest at any moment. There will be a step change in velocity from initial to final.

This is from my Post #22 (note that I have changed the OP's bug to a BB shot from a BB gun):

"In my Post #7 I specified, for the sake of my argument, that both the BB and the train are comprised of perfectly incompressible material, and I stated that I knew that such a material does not exist. After some thought, I have concluded that this specification is unnecessary. What is important is that at some instant during the collision of the BB and the train, the BB is stationary relative to an on the ground observer; and that at that instant the train is stationary relative to the BB."

Whether compressible or incompressible, it is indisputable that since the BB changes direction upon striking the train, it will be for a moment stationary relative to an on the ground observer. That moment cannot be of an infinitely short duration, because then the moment would not exist, and the BB would never be at rest. But since the BB changes direction, it must come to rest - not in theory but in actuality. In that finite moment in which the BB is stationary relative to an on the ground observer, the train will be in contact with the BB and therefore stationary relative to the BB. If the train is stationary relative to the BB, and the BB is stationary relative to the on the ground observer, then, by unassailable logic, the train is also for that finite moment, stationary relative to the on the ground observer.

Refer also to Post #22 for a concise statement of my syllogism.

No. Once you change the laws of Physics you can no longer rely on what those changed laws will produce. There are no incompressible objects. Time does not stand still for anyone. Saying something is not moving when time never changes is a contradiction.

Maybe you will see the folly of this with a review of L'hopital's rule.

When I presented my syllogism in Post #18 I did stipulate (non-existent) incompressible materials for the BB and the train, but I have since stated that, after some thought, I do not consider this necessary - that my syllogism holds true without the introduction of the concept of incompressibility.

With respect to my syllogism, kindly answer the following two questions:

Object A (the BB) will at some moment during its interaction with the train, be stationary relative to an on the ground observer. This is the first proposition of my syllogism. Do you agree or disagree, and why?

Object B (the train) will at some moment during its interaction with Object A (the BB), be stationary relative to the BB. This is the second proposition of my syllogism. Do you agree or disagree, and why?

When time stands still, no motion can occur. In other words, at all moments of time (Δt=0) no motion occurs for anything.

I take that as an agreement that both of my propositions are true, but only for Delta T =0, therefore no real world conclusion can be drawn. But there indisputably exists a real world moment in which the BB is stationary relative to an on the ground observer. It changes direction, so at the moment of directional change, it is stationary. The critical question therefore is: Does that moment of stasis have duration?

I argue that it does. If it didn't have duration, it wouldn't be a moment. It wouldn't in any real sense exist. It would just be a concept, like a dimensionless point. But the BB changes direction, and on the very razor edge of that directional change, it stops. It stops not in theory, not as an abstract concept. It actually stops. It stops in real time, so Delta T has to be greater than zero. Infinitesimally greater than zero, but that is all that is required to establish the truth of my two propositions.

Thankyou. I was waiting for that. You are correct that if those two moments are not simultaneous my conclusion does not hold. You have maybe found the Achilles heel of my syllogism.

When the BB strikes the front of the train, it will begin to slow as it compresses and also as the point of impact on the train compresses. At the moment of maximum compression, the train will be stationary relative to the BB. But is that moment of maximum compression also the moment when the BB is stationary relative to the ground? In the absence of experimental data, I have to admit, not necessarily. If the BB is stationary relative to the ground at some moment during the compression rather than at the end of the compression then the described moments in my two propositions are not simultaneous, and the conclusion does not follow. To preserve the logic and proof of my syllogism I would have to once again stipulate incompressible materials, and then we are into the abstract rather than the real.

In any case, I think I did Zeno proud, and as I stated in an earlier post, "Oh, don't mind me. I'm just goofin' around!"

1. object A (when compressible) will deform upon impact, while it is deforming different portions of object A will be att different speeds relative to a ground observer.
2. object B (when compressible) will also deform upon impact. in the immediate area of the impact there may (under the right conditions) be miniscule portions of object B that momentarily pass through zero speed with respect to an observer on the ground.

If the objects are incompressible, then the small object undergoes a step change in velocity that is at no time ever zero.

In the compressible scenario the bb on average accelerates through zero velocity with respect to an observer on the ground, but the train velocity does not have to match the bb velocity because the connection is not rigid.

In Post #31 jmueller pointed out the probable non-simultaneity of the two events, and I agreed in Post #34 that this was a valid refutation of my syllogism, as is yours, which provides even better detail.

PS: Did anyone here really think that I was serious in my assertion that a BB can stop a train? It was my attempt to formulate a paradox in the tradition of Zeno, the Greek philosopher.

I have to agree that there is a flaw in your theory. The front, (impact point), of BB would be traveling forward until impact, where upon, on impact with the train, the point of the BB would be stationary for a miniscule period of time, then immediately reverse while the back of the BB would still be traveling forwards to meet the BB point. Basically turning itself inside out. The momentum of the small surface area of the BB point impacting then reversing, would not be sufficient to create any stoppage of the train, as not all of the BB would impact at the same time, or with the same force to cause any observable stoppage of the train. And the trailing force of the BB would be significantly reduced by the point impacting.

I also have to concede, that there would be a specific point where the BB or bug does actually stop on impact, and then immediately reverse. This time point would be so minuscule that at no point would it be noticed by any observer relative to anything.

As I comment in Post #52, however minuscule the moment when the BB is stationary relative to the ground, and however minuscule the moment when the train is stationary relative to the BB, if those two events were simultaneous, then the logical conclusion that the train is also stationary relative to the ground at that moment could not be ignored. I am convinced that this does not occur, but if it did, man oh man! That minuscule moment of simultaneity would be a very large wrench thrown into works of Newtonian mechanics.

One can not exactly define position and momentum simultaneously.(The uncertainty principle).

The more precisely one is described,the more uncertain is the other.

Maybe, it would be better to start by asking: If a train is coasting at some specific velocity, under totally frictionless conditions, in contact with with totally frictionless railroad tracks, all in a complete vacuum, and was struck by a single column of a zillion bugs, all flying, one eactly after the other, all at the exact same velocity, but in exactly the opposite direction, such that the collision of the last bug totally stopped the train, which has a mass exactly equal to that of the entire zillion bugs, then, would not the train have suffered a zillon collisions, having been been slowed one zillionth of the original velocity for each bug-train-collision, but not actually stopped until the very last collision ?

(for ease of computation, a ''zillion'' = 10^z ), and a ''zillionth'' = 10^-z ) ...

I'm not going to clean up that mess.

FYI, with 10+ minutes still showing, my edit was disallowed...

I think redfred was referring to the mess caused by a zillion dead bugs by the tracks.

It's OK. Admittedly, I certainly could, and should, have composed my response more succinctly.

The over-riding point was that it would be better to start by totally idealizing the situation being examined, and then, further analysing from there.

It might be more easy to choose-to-view that situation, first, as one VERRRRY dense cue ball (i.e.: the train) on tracks only wide enough for the train-cue-ball's diameter, to be colliding with a convoy of a zillion mutualy-de-tatched, VERRRRRRRRRRRRRRY light-weight object balls (each one having their diameter equal to that of the train-cue-ball, but with the mass of each of the zillion convoy-object-balls equal to only one-zillioth of the mass of the train-cue-ball) such that the ''train'' and the ''convoy'' were both frictionlessly traveling in equal, but opposing, directions, in a vacuum ?

A cue ball of collapsed matter makes this much more complicated to say who stopped what because spacetime distorts.

I'm still not going to clean anything up.

... and you haven't ...

... and, just how much ''spacetime distortion'' do you personally calculate takes place when two objects collide with a relative velocity of such a (whopping ? ) difference of 35 mph? ...

With a cue ball of collapsed matter for one object, the relative velocity difference won't stay at 35 mph for very long.

Is that your idea of a (calculation) of (space-time-distortion) ? ...

I'm not quite sure what you're getting at, but it seems to be something like this:-

The train is travelling at the same speed as the bugs but in the opposite direction.

The bugs have the same density and diameter as the train, but, if there are n bugs then their length is 1/n times the length of the train.

I've drawn four bugs above.

Non elastic collisions.

If there was only one bug then when they splat both train and bug come to a standstill.

If there are two bugs then after the first collision the train and first bug are moving at 1/3rd the original speed of the train; after the second splat whole mess comes to a standstill.

.............................

I don't see how an analysis of a zillion bugs would be any different.

Randall, I appreciate that you took the time and effort to draw what you have presented. Thank you!

Your multi-sided-cylinders would work equally well to my solid-pool-balls analogy.

At equal densities, and equal diameters, the length of the train-cylinder would exactly equal the total length of all zillion of the individual bug-cylinder lengths.

My admittedly implied, but un-written, assumption was that all collisions would start out as perfectly elastic, at equal but opposing velocities, and analysis would proceed from there.

For perfectly elastic collisions you have to do all the simultaneous equations using conservation of momentum and kinetic energy. It's easy but very time consuming.

I got as far as discovering that with two bugs (each weighing half the train) after the first collision the train is moving backwards at one third it's original speed and the first bug is travelling towards the second at 1 and two thirds it's original speed. Then I decided to do it the easy way. I haven't used Algodoo for years, so, I was pleased to see that it's still available and free.

I also had to find a video capture program. I used EZvid. But couldn't figure out how to stop it concatenating all the screen captures. So the following video has the train and two bugs twice followed by the train and four bugs, and finally the train and "many bugs". (And you can see me trying to figure out how to use the tools in the first sections.) To make the many bugs like a "zillion" I made the train very dense and the bugs very light. But I only used 14 bugs, so the last half of the simulation is not accurate.

https://youtu.be/DaPYxhtogZ4

Hello,

No tension or frustration from this side. Understand that it was always ever a "hypothetical" discussion. Seems I missed the specificity of your question.

Don't worry, be happy.

Disclaimer....

No bugs were harmed in the making of this thread....PETA certified

The thread has also been approved by adherents to the precepts of Jainism:

"In its strictest form, Jainism is practiced by ascetic monks and nuns in India, some of whom renounce all worldly possessions (including clothing in one tradition), cover their mouths with a white cloth to avoid causing unnecessary harm with their breath and saliva, and carry a soft brush or feather duster while walking to gently sweep away any tiny souls (in insects) in their path."

Having good experience of living in India, I'm not sure where you got that information from as it a a tad misguided. Yes, they do indeed walk down the street naked and they have protectors walking with them. As for the gentle sweepings and covering their mouths, this I have never seen, not even at the places where they congregate in mass. Maybe they have forgotten to update their web page. And what is interesting, no one takes notice of a naked man walking down the busy roads and it is only the men who wander about naked.

Ha!

A Jain Train would have rendered the whole thread null and void:-