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)

[MarkRae]

The fly doesn't stop the train, not even for a nanosecond. It reduces the train's speed by a minute amount for a minute period of time.

[factor-fiction]

"At that instant it was in contact with the train so the train's velocity must also have been zero"
The flaw in the logic is that the statement is wrong: why must the train's velocity have been zero at the point of impact?

[Barnacle_Bill]

Facto,
You're probably on to something, but if two bodies are in contact, don't they have to have the same velocity?

[MarkRae]

I'm not sure how you arrive at that conclusion. Go and punch the wall - did the wall have the same velocity as your fist when they came in contact...? Of course not!

[poodicat]

Thought it might of gone in the train drivers eye and blinded him thats my theory lol

[MarkRae]

<sigh>

[Barnacle_Bill]

So Mark,
To get back to the fly, what you're saying is that, although the fly has now become part of the train for all practical purposes, it can be going at 0mph while the train is going at 40 mph, even if only momentarily. Can that be right?

[MarkRae]

No.

If both the train and the fly are travelling at 40mph, at the moment of collision the fly's speed is reduced to zero in an infinitesimally small amount of time. The train's speed is also reduced by an infinitesimally small amount, but the huge difference in relative mass means that the train recovers its speed in an infinitesimally small amount of time. At no point does the train's speed reduce to zero. If this were the case, it would never get moving in the first place, since it's constantly colliding with air particles.

[Barnacle_Bill]

Gen,
I'm using velocity because it comprises a direction as well as a speed - and the fly certainly changes direction!

[Barnacle_Bill]

Mark,
I'm not really suggesting the train is stopped or even impeded. I just want to identify the flaw in the reasoning - because there obviously is one!
If you say the train stops for an infinitesimal time, what would happen with a bumble-bee or a sparrow - you can't have a slightly greater infinitesimal time

[Barnacle_Bill]

Mark,
Sorry, that should have said,
"If you say the" FLIES "velocity is zero for an infinitesimal amount of time...."

[Barnacle_Bill]

Mark,
or even FLY'S

[jno]

NoKnow, while you're here, I have just given you a Nostradamus award on the Bully thread for this

http://news.bbc.co.uk..._politics/8531377.stm

[Clanad]

A collision between two objects results in a force being applied to both objects, obviously.

According to Newton's Third Law, both objects experience forces which are equal in magnitude but opposite in direction. But... the collison causes one object to speed up and the other to slow down (changes in momentum). However, according to Newton, the magnitude remains the same for both. But the Law says while the forces are equal in magnitude, the "acceleration" is not necessarily equal in magnitude... the acceleration being dependent on the mass of either object. Since, in your case, the masses are dramatically different, the acceleration of each will be unequal . F=m*a proves the object with the lesser mass will receive the greatest momentum. Since the bug has lesser mass it receives the greater acceleration which it structurally can't withstand. The splattering also conserves energy since the momentum vector is changed (and some energy is converted to heat)...

[Clanad]

The corollary states that the faster an object moves the more energy it contains. So, it's possible that, if you accelerate the bug to a massive speed (which it probably could not withstand) it's energy . You know... E=mc^2. The ratio of the momentum of an object to its velocity produces relatavistic mass (sometimes mislabeled weight). Relatavistic mass can become infinite at speeds near that of light (c). However, one need not accelrate to that unattainable speed to greatly increase the kinetic energy of a small mass. Think of a 1/2 inch diameter bullet bringing down a Cape Buffalo in full, head-on charge or a very fine piece of space dust punching a hole though a space ship... same thing could be applied to your hapless bug... Just speed it up enough...

[mibn2cweus]

This ain't rocket science. Ker-splatt, end of . . . well maybe a president . . .

http://www.youtube.co...M1I&NR=1&feature=fvwp