What Happens When a Fly Hits a Train?

July 26, 2015 / Paradox / 0 Comments /

A common physics paradoxical puzzle is ‘what happens when a fly hits a train?’. According to the laws of physics, every force has an equal and opposite reaction. If this is true, then what a train hits a fly, the fly hits the train with exactly the same force – which you’d think should at least stop the train. Obviously, the train doesn’t stop, and in reality the fly will splat on the train – so what is going on? The laws of physics are laws, and can’t be broken, yet we know from experience and logic that the fly will just end up as a bug splat on the train. So lets have a look at at this problem in a bit more detail.


The fly will make a sound

When a train hits a fly, a faint ‘twang’ sound will be heard. Perhaps it will be hard to hear over the roar of the train, but it is made – I promise. This sound is a glimpse into what is going on over a very short period of time upon impact.

When the train hits the fly, the fly does indeed stop the part of the train which it hits. Say for arguments sake that the fly is 1cm2, a 1cm2 part of the train will be stopped and deflected back slightly by the fly, but only for a very very short period of time.  As the fly has a very small mass in relation to the force, the fly will accelerate very quickly up to the speed of the train. The acceleration of the fly is so great, that it manages to reach the same speed as the train over the distance of the indent.

Once the fly has reached the same speed as the train, which will happen incredibly quickly, the part of the train which indented will ping back to its original place, and overshoot. It will continue to vibrate in this manner until its original shape is restored, this is called elastic deformation.This vibration will release some energy as sound in the same way as hitting a metal sheet with a tennis ball does. I have tried my best to put this in three simple diagrams below so you can visualise what is going on (you can click to enlarge).

This is true for every such collision, and no matter how rigid a material is, there is always some amount of elasticity in it to allow this to happen. If you were to make an incredibly rigid material which had absolutely no elasticity, a fly would probably break a hole right through it, if it hit a fly at the same speed of a train.

A picture showing what happens when a train hits a fly


So the laws of physics are intact – every force does have an equal and opposite force. When the train hits the fly, the fly will indeed exert the same force back onto the train, but only on a small part of the train, which will cause it to deform elastically for a very short period of time before returning back to its original position. I did begin to do the calculations to illustrate how it all works, but there are a lot of unknown variable such as how far back the train dents when the fly hits (which is going to be a tiny number), which make it impossible.

So to answer the question – the fly will cause a very small part of the train for a very short period of time. This part of the train will vibrate under the impact until it reaches its original position.

Image courtesy of Don Harbor