My brother’s favorite joke:
What’s the last thing to go through a fly’s mind as it hits a windshield?
A: His asshole! :o
Why did you put “were” in quotation marks?
-FrL-
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In the same sense, if the fly lands on the rail does the rail bend?
Answer: Yes
I’ll leave it to you to go out with your tape measure and a fly (it doesn’t have to be alive) to validate the answer.
This is, in a way, where Heisenberg Uncertainty Principle shows up in plain view. If the very definition of a quantity relies on a rate of change of another over time, then it’s kind of obvious that you can’t have both.
Boy, that’s a long time to wait. :dubious:
What if there were a stream of flies one after the other willing to die for the cause? If they kept hitting the windshield before it had time to reform would the train stop or would they bore a hole in the glass?
Suppose a train weighs 1,000 tons, and is travelling at 50 mph. If you piled up 1,000 tons of dead flies on the tracks in front of the train, then (ignoring friction, and the effects of the engine powering the train) the speed of the train should be reduced to 25 mph, and 1,000 tons of dead flies will be travelling along the track at 25 mph ahead of the train. A frightening concept.
What if the fly is the size of Jupiter, and made from Tungsten, and the train is a model made out of meringue and marshmallows? What then? Huh?
There are two distinct facets to this question. One is the issue of instantaneous change in direction of the fly, and the other is the suggestion that the collision with the fly somehow causes the velocity of the train to be zero at some point in time.
The issue of the train reaching zero velocity is a kind of a false paradox, very similar to Zeno’s Paradox to which Thudlow Boink alluded. At no time does the windshield’s velocity drop to zero with respect to the ground. This is slight of hand caused by talking about the state of the system at a point in time. A point in time is a point, not an interval. You could make the same (false) claim without introducing the fly. The fly is a red herring thrown in to confuse the issue.
A train is going 100 MPH. So in half an hour it goes 50 MPH; in 15 minutes it goes 25 MPH; in 1 second it goes 1/36 of a mile; in 1 nanosecond it goes 2.78 x 10[sup]-11[/sup]. As the time interval approaches zero, the distance traveled approaches zero, so if we look at a small enough time interval, the train must be standing still. The flaw in this reasoning is that no matter how small the time frame we examine, the train’s velocity is still 100 MPH. Velocity becomes meaningless at a point in time because there is no duration and therefore calculating velocity gives you a divide-by-zero error.
There is indeed the problem of the fly’s instantaneous reversal in direction. Given infinitely rigid participants, as the OP states, “there will be a point in time that the fly decelerates from 10mph to 0mph and then is accelerated up to the train’s 100mph speed.”
He goes on to say, “I think the laws of physics dictate that there is no way the fly can instantly change from 10mph in one direction to 100mph in the other.” You are sort of correct on this. I do not know for sure if the laws of physics prohibit it but the amount of force needed for a true infinite acceleration in the collision of infinitely rigid bodies would, I think, be a kind of singularity at a point in time, and there is no practical way to generate infinite force. But what happens in reality, as discussed exhuastively above, is that the fly and the windshield deform slightly (the former more than the latter) to cause a very high, but less than infinite, acceleration of what is left of the fly.
Sir, I would like to finance this experiment. Meet me in the shadow of the Eiffel tower in June. Bring a pencil and a notepad. Actually, better make that two pencils.
I will be recogisiible as the one holding another spare pencil, just in case. Don’t dress too warmly for we will be in Egypt before the day is through.
It was in refernce to a line in post #2.
“The train and the windshield are not a perfectly rigid body, nor the fly.”
I was asking “but what if the were?”
If the fly and the train were perfectly rigid (and indestructible) bodies, then I think there would have to be a very brief moment at which the train stopped while the fly reversed direction - the problem with this is that something would have to happen to all the kinetic energy at that moment - I’m guessing it would be converted mostly to heat - and there would be no reason for the train to start moving again afterwards (except the action of any motors).
A perfectly rigid, free-rolling train colliding head-on with a perfectly rigid fly would just stop.
Fearless Fly could, but he’s not around anymore:
This would violate the laws of physics, conservation of momentum.
Let’s approximate here. Assume the train weighs a gigagram (about 1,000 tons), and the fly weighs a gram – which would be a very large fly. Assume the train travels at 100 kilometres per hour, and the fly is stationary (just hovering in the air.
By my calcxulations, if both a perfectlly elastic, the train would reduce its speed by about 10^(-9) of its present speed, i.e., it would be travelling about 0.1 micrometer per hour slower, while the fly wound be travelling at 100 kimometres per hour in the same direction as the train, i.e., floating away from the front of the train at 0.1 micrometer per hour, until gravity and wind resistance changed things. So, as far as the driver of the train could see, it would slide down the front of the train, with the main component of its acceleration being that caused by gravity. (Wind resistance would almost immediately push the fly back against the front of the train). And the reduction of the speed in the train would be undetectable by the driver, especially compared with larger effects, such as changes in the movement of the train caused by irregularities in the track.
How strong would you need to be to kill a “perfectly rigid” fly? Could you use an ordinary swatter?
In real life, the only perfectly rigid flies are dead ones, so youn would not need to kill; it,
Even if the train were to be considered motionless for some non-zero length of time, whence would come the force that would restore its velocity? The whole supposition doesn’t work.
If you’ve ever played pool, you know this isn’t true. Give the cue ball a good hard smack. If the cue ball strikes another ball head on, the cue ball stops and the other ball moves off at the cue ball’s former velocity.
Treat the 1,000 tons of dead flies as a single sphere. The train has a flat front. The fly-ball strikes the train smack dab in the middle at the height of its center of gravity.
In the idealized case (typical in freshman physics classes) is to consider the objects to be infinitely elastic, that is, no kinetic energy is lost in the collision.
First, by conservation of momentum,
mv[sub]t0[/sub] = mv[sub]t1[/sub] + mv[sub]f1[/sub] [1]
Second, by conservation of energy,
0.5(mv[sub]t0[/sub][sup]2[/sup]) = 0.5(mv[sub]t1[/sub][sup]2[/sup] + mv[sub]f1[/sub][sup]2[/sup]) [2]
Substitute v[sub]t0[/sub] from [1] in [2] gives
0 = v[sub]t1[/sub]v[sub]f1[/sub]
So one of these velocities is zero. We know that the speed of the train is decreased because the force on it is opposite to its direction of motion, so
0 = v[sub]f1[/sub]
and
v[sub]t0[/sub] = v[sub]f1[/sub]
So after the collision, the train is stationary and the fly-ball is moving 50 mph.