The mosquito

[John in AR]

An old one…


A mosquito is flying east at 30 mph, and hits head-on into a freight train heading west at 30 mph. The now-dead mosquito, stuck to the front of the train, is now traveling back west at 30 mph, along with the train.

The mosquito has completely reversed direction and speed, going from 30 east to 30 west; or as a number line would illustrate, from "+30" to "-30".

Since you can’t go from +30 to -30 on a number line without crossing zero along the way, at some instant, for some micro-unit of time, the mosquito was at zero miles per hour on the number line.

Since it unquestionably crossed zero, and it was physically stuck to the train, how do we avoid the conclusion that the train also had to be doing zero for whatever time interval the mosquito was?

If we can’t find a way around that, it means we acknowledge that a mosquito can stop a freight train…

[Aslan]

actually, there is a point at which the mosquito has zero velocity relaitve to the train, but non-zero velocity relative to the ground.

If you measure the distance the train moves at sub nano-second intervals, you will find that the train is practically motionless. Since the actual impact of the mosquito and the train probably took less than a nano-second, the mosquito hit a stopped train, with 30mph of momentum, like wise, the train struck a motionless mostiquito.

what's really freaky is when the motionless train managed to collide with the motionless mosquito....

my brain exploded....


:devil:

[John in AR]

actually, there is a point at which the mosquito has zero velocity relaitve to the train, but non-zero velocity relative to the ground.

If you measure the distance the train moves at sub nano-second intervals, you will find that the train is practically motionless. Since the actual impact of the mosquito and the train probably took less than a nano-second, the mosquito hit a stopped train, with 30mph of momentum, like wise, the train struck a motionless mostiquito.

what's really freaky is when the motionless train managed to collide with the motionless mosquito....

my brain exploded....


:devil:

See, this is the problem with being a big, dumb redneck.

I can't tell if you're actually that much smarter than me, or if you just make crap up...

[Chippathingy]

And here I thought that it would actually reduce the trains speed by and infinitesimally small amount of newtons...

Newtonian physics is just plain weird.

[Magnum88C]

The mosquito both goes to a zero velocity in reagrds to the ground. It goes through that zero point as it's body is being crushed absorbing the impact. However, what you have to understand, is that the point in time at which the mosquito goes to zero velocity is just that -- a point in time. Through derivative calculus you could plot the point at which the instantaneous velocity of the mosquito is zero.
The train, however, never does reach a zero velocity. It's instantaneous velocity is always above zero. The mosquito's impact would have an infinitesimal effect on the train's speed, but would be unmeasurable.

[Rich Z]

No man. The train only reached zero velocity in relation to the mosquito. It NEVER reached zero velocity in relation to anything else. The mosquito, on the other hand reached zero velocity in relation to the train and the ground at the instant of impact, then CONTINUED at zero velocity in relation to that train from that moment on TO THE TRAIN ONLY, but not to the ground.

It's ALL relative to a point of reference. You just have to pick the point.

[Aslan]

well, that's what I was getting at (in the most convoluted manner I could), that there are multiple Newtonian frames of reference to which the velocities of the various actors (train, mosquito, ground) could be looked at from.

:devil:

[John in AR]

...The train only reached zero velocity in relation to the mosquito. It NEVER reached zero velocity in relation to anything else. The mosquito, on the other hand reached zero velocity in relation to the train and the ground at the instant of impact, then CONTINUED at zero velocity in relation to that train from that moment on TO THE TRAIN ONLY, but not to the ground...

Not being intentionally dense or obstinate, but as you say, the mosquito is at "zero velocity" in relation to the ground, (which we agree on), and it's physically stuck to the train.

We agree that:

- the mosquito is "at zero" in relation to the ground
- the mosquito is physically stuck to (basically "one with" the train)

How can a train with a mosquito stuck to it, be travelling at a different velocity "in relation to the ground" than the mosquito itself?

(No, I don't really believe a train comes to a complete stop every time a mosquito hits it head-on. I'm just trying to get a fixed, objective explanation, reconciling the apparent paradox.)

[Aslan]

There's really no paradox, as you really don't have a zero point of speed, except for a tiny instant, (less than a nano second)

If you look at the velocities as vectors, meaning they have both magnitude and directions components to them, it's just a simple vector addition problem with a result.

Since the momentum of the train is infinite compared to the mosquito, the train never really stops. The velocity of the train is totally unaffected. It is the velocity of the mosquito that instantaneously changes. (simple sign reversal)

:devil:

[krept]

The velocity of the train is totally unaffected.

well, TECHNICALLY speaking...

just kidding, great stuff. thumbs up

[Aslan]

Given the variations in roughness of the track, friction on wheels, slight imperfections in the wheels, vibrations caused by the engine, aerodynamic forces, etc ad nauseum, it would be impossible to detect the effects of the mosquito.

Think about all the things that would cause slight variations in the measured forward velocity of the train.

A bit of dirt on the track, a gust of wind, etc.

Yes, there is a theoretical effect, but it would be impossible to isolate and measure.

:devil:

[krept]

:devil: LOL

i was JUST KIDDING