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The train and the fly

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I think this is an old one but I've never seen a satisfactory solution.

A train is travelling eastwards along a track at 60 mph

A fly is flying westwards towards the train at 10 mph.

The train hits the fly which is squashed onto the front of the train.

Question: Did the train stop when it hit the fly?

At first it seems obvious that the train didn't stop. However, think about it.

When the train hit the fly the fly was travelling west at 10 mph. Suddenly it had reversed direction and was now travelling east at 60 mph. The fly's speed therefore changed from, say plus 10 mph to minus 60 mph. To do this its speed must have passed through zero i.e. it had stopped when it reversed direction. When it was at zero mph it was in contact with the train. Therefore the train must also have stopped!!

JoWo

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Posted · Report post

I think there is a little confusion / misdirection (pardon the pun). The fly will have had a point at 0 mph when it went from +10 to -60, but the train continued in the -60 direction relative to the fly.

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Posted · Report post

Welcome to the boards, jowo!

Question: Did the train stop when it hit the fly?

No.

To do this its speed must have passed through zero i.e. it had stopped when it reversed direction. When it was at zero mph it was in contact with the train. Therefore the train must also have stopped!!

JoWo

It is not necessary for the train to come to a stop just because the fly did. The collision did cause the train to slow down (ever so slightly), however, it never comes to a complete stop. The train chugs along while the fly stops and reverses direction.

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Posted · Report post

It is not necessary for the train to come to a stop just because the fly did. The collision did cause the train to slow down (ever so slightly), however, it never comes to a complete stop. The train chugs along while the fly stops and reverses direction.
Right.

When two elastic bodies collide, both energy and momentum are conserved.

The fly was anything but elastic, becoming and remaining a simple

grease spot, so in this case only momentum is conserved.

Simply put,

[Mass of fly] x [velocity change of fly] = [mass of train] x [velocity change of train]

Let's say for argument's sake the train is ten times more massive than the fly.

[That would be one big, m......f........ fly, by the way...]

That gives you ... canceling mass of fly from both sides ...

velocity change of fly = 10 x velocity change of train.

the fly's velocity changed from +10 to -60 = 70 mph

that means the train's velocity changed by 70/10 = 7 mph.

The train continues moving forward, slowing from 60 mph to 53 mph.

Even a fly weighing 1/10 the weight of the train won't stop it.

Here's an interesting point.

A detailed analysis of what happened to the fly reveals that it never

actually came to rest! The first miniscule portion of the fly to contact the

train instantaneously assumed the train's speed, producing a progressive

collapse and deformation of the fly into a grease spot. The rear portions

of the fly were still moving forward while its forward parts were traveling

backwards. As a whole, the fly never had zero velocity, and thus technically

never stopped.

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What was the last thing that went through the flies mind when he hit the train?

His backside! Ha Ha

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