How Much Does a Fly Hitting a Train Slow It Down?

fly hitting a train
The Scenario: a fly hitting a train.
Say you have a train, a locomotive traveling along a straight railroad track. The atmosphere is absolutely free of every conceivable impediment except for one lone housefly. Unfortunately (for the fly), it and the train collide head-on. You have a fly hitting a train. Clearly, the fly will turn into a smear.

How much does that fly slow the train down that it has hit? The train will suffer no apparent change in speed, yet it does slow down, even if there is no obvious change. How much does it slow down?

Fly Hitting a Train: Specific Numbers

We will attempt to use realistic numbers. We choose the following:

Locomotive: 4,000 tons [a light train]
Fly: 14 milligrams
Locomotive Speed: Exactly 30 mph
Fly Speed: 5 mph

Although the numbers vary, the above choice of values will give us a good idea of what occurs when a fly hits a train head-on.

Momentum First

It is not merely the speed of the fly and the speed of the train that determines how much the train slows. It is the momentum. One equation for momentum (p) is:

P = M•V

This equation tells us momentum equals mass times velocity. Now momentum is a directional property. The train is traveling in one direction, the fly in the opposite direction. So if we take the momentum of the train, and call it positive, the momentum of the fly is negative.

Mtrain – Mfly = Mremaining

(8,000,000 lbs) • (30 mph) – (3.1×10–5 lbs) • (5 mph) =

240,000,000 lbs-mph – 0.00016 lbs-mph = 239,999,999.99984 lbs-mph

Speed Second

Let’s convert the momentum of the train into its reduced speed.

239,999,999.99984 lbs-mph / 8,000,000 lbs = 29.99999999998 mph

The fly slowed the train by 0.00000000002 mph. That is, 2 one-hundred-billionths of a mile per hour. Not significant, perhaps, but real? Yes.

Note: You might also enjoy Spacecraft Invisibility – Is Cloaking Possible?

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