Mythbust pt 2: The fly and the train

Eliot Rosewater

A train is traveling at 100km/hr. A fly is coming towards it at, say, 10km/hr. One moment the fly is traveling in one direction at 10km/hr; after hitting the train it is traveling in the other direction at 100km/hr.

Its presumed there must have been a moment when the fly was stationary (between going one way and the other).

The argument is that because of this, the train must also have been stationary for a tiny period of time.

What is the solution to this?! Is it based on a misunderstanding of discrete time vs continuous time?

Pherekydes

One word: momentum.

Momentum is a vector quantity. It has direction. The fly changes direction and must therefore stop; the train does not change direction.

I realised this while driving in France over several summers. (It dawned on me only gradually). When we reached our destination and found the car covered in flies the kids remarked that the journey wasn't as jerky as it may have appeared to a stationary observer. That got me thinking, and many years later, I realis...

Wait, what was the question?

Mellor

Eliot Rosewater wrote: »

A train is traveling at 100km/hr. A fly is coming towards it at, say, 10km/hr. One moment the fly is traveling in one direction at 10km/hr; after hitting the train it is traveling in the other direction at 100km/hr.

Its presumed there must have been a moment when the fly was stationary (between going one way and the other).

The argument is that because of this, the train must also have been stationary for a tiny period of time.

What is the solution to this?! Is it based on a misunderstanding of discrete time vs continuous time?

What a ridiculous assumption.

Obviously the train was never stationary. The mass of the fly is so small that it has no effect (of an unmeasurable effect) on the train.


In fact the fly was never stationary either, his face was moving back through his hole before his arse hit the train

bnt

A useful concept here is Impulse, the change in momentum, which can also be described as the integral of Force w.r.t. Time. (If the Force is constant, you just multiply it by the Time.) The fly had a certain momentum before the collision, a certain momentum after the collision, and the difference is the Impulse. Assuming there were no losses, the train also experienced the same Impulse.

Force and Time come in to it if you imagine that the front of the train was very softly padded: the fly would experience less force and might survive the collision; and that lower force would be applied for longer as it bounces, rather than a quick fatal Splat. Integrate the Force w.r.t. Time, you get the same Impulse in either case.

PS: if you can take an infinitesimally-small moment in time (0 seconds), everything is stationary. :pac:

Fremen

I guess the real problem (for the fly) is that different bits of it change direction at different times.

Richard Cranium

According to "Does Anything Eat Wasps" or one of those popular science books, the fly is stationary for a split second, and the tiny part of the front of the train is also stationary for a split second, then it kind of pops back into place, and oscillates a little bit until it's back moving with the rest of the train. This vibration is what makes the "splat" sound when the fly hits the train.




Simple English ftw!

MathsManiac

Just to correct the reference: that article is in "Why don't penguins' feet freeze?", which is the follow-up book to "Does anything eat wasps?"

FoxT

Before I get into an answer - Mellor that was a brilliant answer!

"The argument is that because of this, the train must also have been stationary for a tiny period of time.

In practice, this does not happen. When the fly strikes the train, the piece of the train that hits the fly will slow down as it applies a force F=ma to the fly. This force will cause the fly to slow down and change direction. It will also deform the piece of the train. At some point, the fly and the piece of the train in contact with it will in theory have a velocity of 0. The entire train will lose speed but will not halt.

As the fly is accelerated by the train, the bit of the train in contact with the fly will return to its original shape ( we can safely assume that the forces involved would be insufficient to exceed the elastic limit of the piece of the train struck by the fly.

Capt'n Midnight

the point of impact of both the train and fly deform , the fly more so than the steel of the locomotive

if you add the distance both deform then it's the distance over which the fly changes it's velocity by 110Km/hr you could then work out the acceleration.

if you say the velocity changes instantly then the fly would undergo infinite acceleration, which in means it would go splat


lets suppose you are running inside the train and a fly bumps into you , which frame of reference would you use to determine who was stationary