Collision of a Bee and Train: Reversing Direction without Zero Velocity

[Driftwood1]

A head-on collision occurs between a flying bee and a moving train.

The bee smashes and sticks onto the front of the train and both continue in the direction of the train.

For the bee to completely reverse its direction, does the bee's velocity need to equal zero at any point during this event?

If so, does the train have a zero velocity as awell?

How does an object reverse its direction without at some point having a zero velocity?

 

[cosmicraj]

See,the velocity of bee will become zero and reverse its direction ,but train is going in the same directon.it can not change because momentum of bee is nothing compared to the momentum of of train

 

[Driftwood1]

See,the velocity of bee will become zero and reverse its direction ,but train is going in the same directon.it can not change because momentum of bee is nothing compared to the momentum of of train

true - there is big difference in momentum between the two objects

I am just posing the question - And as you say the bee must attain a zero velocityt before it can reverse directions and travel in the same direction as the train.

Doesnt this zero velocity occur when the bee collides with the train and is therefore in contact with the train?

Does the train stop at that point?

 

[Driftwood1]

How does the bee go from having a velocity V1 to a velocity V2 (train and bee) where V2 is in the opposite direction, without having a zero velocity somewhere in between?

 

[rcgldr]

when the bee collides with the train ... Does the train stop at that point?

A very tiny spot on the surface of the train at the point of collision deforms and stops (relative to an outside observer) for a tiny moment then springs back (assuming no dent occurs) and continues forward again. The rest of the train is essentially unaffected.

 

[Danger]

Good answer, Rcgldr. (Could you not think of a username that was harder to spell from memory?)
The deformation of a steel plate will be essentially unnoticeable, but it can be extrapolated downward. If you are on a motorcycle without a face shield and encounter that same bee (excluding possible sting effects), you will evidence bruising after the fact. You won't slow down to any appreciable extent, but you'll sure as hell feel it.

 

[Dale]

A very tiny spot on the surface of the train at the point of collision deforms and stops (relative to an outside observer) for a tiny moment then springs back (assuming no dent occurs) and continues forward again. The rest of the train is essentially unaffected.

A train is pretty rigid. I would think that almost all of the deformation would be in the bee.

 

[Danger]

I would think that almost all of the deformation would be in the bee.

I'm not sure why (perhaps due to its subtle understatement), but I find that phraseology hilarious.

 

[arildno]

To be or not to be bee, that IS the question...

 

[HallsofIvy]

Setting aside the hilarity for the moment, Driftwood1, this does not happen instantaneously. There will be a period of a moment when the head of the bee has 0 velocity but his backside is still moving forward immediately afterward, some other part of the bee will be stopped but his head will be moving with the train. Eventually (in a very small fraction of a second) all of the bee will be moving at the speed of the train.

Now, back to the hilarity: one of my fiancee's favorite jokes: What was the last thing on the bee's mind? His ***!

 

[Danger]

one of my fiancee's favorite jokes: What was the last thing on the bee's mind? His ***!

I'm so happy that my mind is capable of seeing through software censors.

Fiancee? I thought that you were long-married. Congrats.

 

[arildno]

Now, back to the hilarity: one of my fiancee's favorite jokes: What was the last thing on the bee's mind? His ***!

It does have a certain..sting to it..

 

[Danger]

It does have a certain..sting to it..

Dammit, Greg! Once again I ask where the hell that "groan" smiley is, which you've been promising us for 5 years.

 

[Driftwood1]

A very tiny spot on the surface of the train at the point of collision deforms and stops (relative to an outside observer) for a tiny moment then springs back (assuming no dent occurs) and continues forward again. The rest of the train is essentially unaffected.

interesting...

and this MUST occur for the bee to be able to reverse directions?

Why should only one small region of contact between bee and train at the moment of impact be affected and the rest of the train unaffected?

Why does the dent need to spring back?

What does "essentially unaffected" mean?

 

[Driftwood1]

It does have a certain..sting to it..

I have been strictly informed by the powers that be in here, that any attempt at humour or wit will be met with infractionised point allocation punishment

 

[rcgldr]

A very tiny spot on the surface of the train at the point of collision deforms and stops (relative to an outside observer) for a tiny moment then springs back (assuming no dent occurs) and continues forward again. The rest of the train is essentially unaffected.

and this MUST occur for the bee to be able to reverse directions?

Yes, once contact between bee and train occur, the surfaces of both bee and train at the point of contact move at the same speed.

Why should only one small region of contact between bee and train at the moment of impact be affected and the rest of the train unaffected?

Because the size and mass of the bee is small compared to the train. Only a very tiny area just outside the point of contact will be significantly affected at all.

Why does the dent need to spring back?

It doesn't, but I assume that the amount of deformation on the surface of the train at the point of contact is small enough to be almost completely elastic (meaning it springs back).

What does "essentially unaffected" mean?

The total momentum of the bee and train is conserved, but since the bee's mass is tiny compared to the train, the train only slows down by a very tiny amount.

 

[Driftwood1]

Setting aside the hilarity for the moment, Driftwood1, this does not happen instantaneously. There will be a period of a moment when the head of the bee has 0 velocity but his backside is still moving forward immediately afterward, some other part of the bee will be stopped but his head will be moving with the train. Eventually (in a very small fraction of a second) all of the bee will be moving at the speed of the train.

Now, back to the hilarity: one of my fiancee's favorite jokes: What was the last thing on the bee's mind? His ***!

"in a small fraction of a second|?

so what are you saying? That the bee does not have a zero velocity at any stage? That is goes from V1 to -V2 instantaneously?

Show me a graphical representation of the Bee's velocity with respect to time before, during and after the collision with the train

 

[Stonebridge]

Yes the bee, or at least the various parts of it, all have a zero velocity relative to the ground at some point. The bee isn't perfectly rigid, it squashes, so the question about the speed of the "bee" is oversimplifying the case.
What is being missed here is the meaning of "in contact with". Let's just consider the first atom of the bee that meets the first atom at the front of the train.
It doesn't "touch" that atom, it gets nearer and nearer until the mutual repulsion of its outer electrons (with those of the train) causes it to stop and reverse. At the point where it stops, the first atom of the train is still moving forwards. Two atoms at this microscopic level cannot "touch" so they do not need to both be at rest at the same time.
This effect is then transmitted through the bee as it crushes.
In this diagram, you can see the effect I'm trying to describe.

The atoms of the bee, as it strikes the train and squashes, are one by one stopped and reversed. But at no time does the train stop. The atoms never touch. The interatomic forces see to this. The first bee atom has stopped at the position of the vertical yellow line. (His rear end is still moving forwards, though.)
The train at this point is still moving forwards.

 

[NobodySpecial]

But at no time does the train stop. The atoms never touch. The interatomic forces see to this...The train at this point is still moving forwards.

But Newton's laws still apply - the atoms don't touch but the atom of the train is pushed back by the same force that the atom of the bee feels.

There is no problem with the front of the train moving back - trains aren't infinitely rigid.

 

[Stonebridge]

But Newton's laws still apply - the atoms don't touch but the atom of the train is pushed back by the same force that the atom of the bee feels.

There is no problem with the front of the train moving back - trains aren't infinitely rigid.

The first, and subsequent, atoms of the train do indeed experience a backwards force, and Newtons Laws will tell you that it has little effect on them, certainly not the effect it has on the bee. It's irrelevant to the question, though. The "train" doesn't stop. It doesn't need to.
It's all about the interatomic repulsion and the space between the atoms.

 

[rcgldr]

The first, and subsequent, atoms of the train do indeed experience a backwards force, and Newtons Laws will tell you that it has little effect on them, certainly not the effect it has on the bee. It's irrelevant to the question, though. The "train" doesn't stop.

Not the entire train, but the outer atoms on the surface of the train at the point of contact will momentarily be moved backwards, as the surface compress a tiny amount. As mentioned above, the train is not infinite rigid, and a tiny portion of the surface at the point of contact deforms for a very brief period of time.

 

[Mattenerinfo]

The bee's backside actually stops, at one given point, while the front is pushed by the train, and in said simultaneous moment when the bee cannot instantly go from V1 to V2 and the front is having force exerted on by the train, the structure breaks down, causing the squish.

 

[Stonebridge]

Not the entire train, but the outer atoms on the surface of the train at the point of contact will momentarily be moved backwards...

Not necessarily. If the atoms in the train surface are held by very strong bonds, they will only be slowed down very slightly, momentarily. There are an awful lot of tightly held atoms behind them with an awful lot of momentum. All that will happen is a compression/shock wave that travels backwards along the train. What determines the precise motion of the train's atoms will be their momentum at impact (compared with the bee's) and the strength of the interatomic bonds. It is perfectly possible, and more than likely in this case, that the train's atoms will be slowed, causing the pressure wave, but not stopped relative to the ground.
In my diagram, the 5th train atom down on the left will be slightly nearer its neighbour at the point where the bee's 1st atom has come to rest. However, its motion is still always forwards. There is no need for it to reverse its direction. The "slack" is taken up by the interatomic spacing. There is no actual "contact" with the bee atom, and therefore no requirement to stop.

Anyway, the question was about the train stopping. We are agreed it doesn't, I think.

Interesting discussion, by the way. :)

 

[Dale]

Stonebridge has a good point. Newton's laws require:
1) that the force the train exerts on the bee is equal and opposite to the force the bee exerts on the train
2) that the force is proportional to the acceleration

They do not require:
3) that the velocity of the surface of the bee match the velocity of the surface of the train