The Train and the Fly

[THEROB]

Quick strange thingy -

If an object is thrown in the air and then comes down upon itself - at its peak it has stopped for a split second.

Well if a fly is flying along a train track in one direction and the train is coming in the opposite direction. When they meet the fly must go through zero in order to reverse its direction - if the train and fly are both together at that point then the train must be stopped at that moment in time (only for a split second) - how can a fly stop a train???

Rob

[Behemoth]

speed = distance/time

If the time is 0, this cannot be calculated. Any "instant in time snapshot" taken would render any "moving" objects stationary.

[Starman]

not sure about trains, but when a fly hits the windscreen of my car it tends to stop (in a very thin sort of way) rather than reverse it's direction. I suppose it could be said to have reversed it's direction as soon as the smear is travelling in the same direction as me but I think that bits of it reverse at a time rather than the whole fly at once, so there is no actual 'point' where the fly is stopped. The point where the fly is all travelling the other way is just after the bit it carries behind it has reached the screen. At times before this some of the fly is travelling in both directions, which probably accounts for it's discomfort. It's just a more extreme example of what happens when an Olympic swimmer turns at the end of the pool.

[bugzpodder]

what Starman was talking about is instantaneous velocity -- which differs from average velocity. and yes, at the time of impact, the instantaneous velocity of the fly at the time of impact would render 0 since a change of direction occurs (as in change of concavity in calculus) and in order for that to happen, an instantaneous velocity of 0 must occur at the precise moment of impact. the train however experienced very little change in speed. and since it is still going in the same direction, slowing down only a tiny bit, it did not experience a velocity of 0 at the time of impact.

[Starman]

was I ?, ah well there you are then.

What I was actually trying to point out was that the whole fly does not change direction at once, bits of it do, eyes, head, thorax, legs and the squishy stuff in the middle, but all at different times. There would be no 'point' at which the fly suddenly reversed.

[bugzpodder]

lol we consider the fly as one object. and so we consider the time when all parts of the fly changes direction the "point". now you are right in real life nothing goes smoothly. just like you can't really keep constant speed of exactly 60mph for any period of time, execept when we are talking about instantenous speed.

[Starman]

OK then we'll have a solid fly and give it a velocity of say 20mph.
If the train is moving in the opposite direction at 60mph then at the time of impact it is as though the fly hit a stationary train at 80 mph. There would surely be a small force which would cause the train to move backwards (in the direction of the fly). There would be an equivalent force on the train if both were moving in opposite directions, enough to slow the train (almost imperceptibly), but the train would not stop.

[snakeeyes1000]

actually, simple physics dictate that:

if the train is 80mph
and the fly is 20 mph

That the train's speed would be reduced by (flyweight/trainweight)*flyspeed. Thus, if the fly ways .001 pound, and the train ways 100000 punds, the train speed would be then

80-((.001/100000)*20). Therefore, the train would be traveling at 79.99999999mph, the fly at 0, and the train would instantly start to accelerate to 80, while the fly did not. If the train had no engine, and it continued travelling forever, then it would remain at 79.99999999mph forever(less friction, of course)

[Behemoth]

I'm not debating the speeds of the fly or the train, other than the following.

at the point of impact, there is no time. It is a single point. there can therefore be no speed or velocity. The question / problem is unfeasible. It does not exist.

[Destined Soul]

THEROB's conclusions are unfounded. What does happen is a sudden change in acceleration of the fly - in its reverse direction. Its velocity will decrease and eventually reverse direction. Energy/Momentum from the train is reduced, being passed into the fly giving it the impulse (or jerk) - change in acceleration. Instant change in direction would be an infinite acceleration.

On a second look, for the train to actually stop (even if for a very brief fraction of a second), how would it continue to move? (We know it does by conservation of momentum.)

I guess the confusion is that if you were to take a POINT in time (if possible), wouldn't it be like pausing a movie where the fly and the train are both "stopped" in place? In fact, they are not, because if we remove the fly from the scenario, just a train running down a track at a constant velocity. If we stop at a POINT in time, it too would appear "stopped," when we know full well that it is moving at a constant speed, by definition.

Hopefully I haven't confused you too much.

Destined

[bugzpodder]

now, we can graph displacement vs time, just like any other mathematical function -> let d=f(t), where d is the displacement and t is the time: and we are are doing is looking at the slope of the function. as you know, the slope of the function is the derivitive, also the slope of displacement is velocity. saying there is no time at a particular point is absurd -- any function is made from a [inifinite] series of points, this displacement function is no exception. if you understand the fundamental thoeries of derivitive:we are talking about the limit of the secant between two points on the curve as they get closer and closer. You are right, technically we are not looking at a single point, but the two point is inifinitely close that it can be considered the single point.

thus the first principles: f'(x)=lim (h->0) (f(x+h)-f(x))/h,

or in this case, f'(t)=lim (h->0) (f(t+h)-f(t))/h

and you must know that velocity is displacement over difference in time. same goes with instanteneous velocity, --- execept what we are calculating is when when difference time is approaching 0.

also, acceleration is velocity over time.


now lets look at earth, the acceleration due to gravity is:

let f(t) be displacement, f'(t) be velocity and f''(t) be acceleration

you can see this more clearly with the intergrals (I used "I" for the intergral sign):

f''(t)=9.8

f'(t)=I(f''(t))dt=9.8t+c

at time 0, f'(t)=c. in physics its also known as initial velocity, so we are going to use v₀

now to find f(t):
f(t)=I(f'(t))dt=4.9t²+v₀t+c

now c would be initial displacement so i'll replace it with d₀

so we end up with f(t)=4.9t²+v₀t+d₀ which is the model of the displacement of a freefall object with respect to time, on earth of course.

[Kalkewl8ter]

And the great bugzpodder is, once again, I believe, correct!

[snakeeyes1000]

good job bugz, i could not have said it better myself.

[THEROB]

I'm not sure if I understand - the fly must stop in order to change its direction - then if the train and fly are both in contact at that time then the train must be stopped also

I know this can't be true - but I would like to find a proper explaination.

[bugzpodder]

the fly must stop in order to change its direction

true

- then if the train and fly are both in contact at that time then the train must be stopped also

why do you say that?the train however did not change direction or even slow down even a bit. so it didn't stop.

[THEROB]

If the fly is stopped - and at that time the train and the fly are together then the train must be stopped aswell!

[bugzpodder]

I don't follow your logic. just because two objects are together and one is in still motion doesn't mean the other one is too!

[THEROB]

If we consider the 2 objects - the train and the fly - as one object because they are together - then if one is stopped - the other must be.

[bugzpodder]

lol who's rule is that? we can't consider them as one object just because they have physical contact!

[A$$Bandit]

It's an elastic collision. If both the train and the fly were 0% elastic then yes the train would in fact stop for the infinitely small point in time where the fly's velocity is zero, killing everyone on the train due to the infinite deceleration. However, neither are perfectly inelastic, so when they hit, the train slows a tiny bit to cushion the fly, and the fly splats to cushion the train. That doesn't explain whether or not the fly stops, just that they shouldn't be counted as one body when the fly hits.

[yrwyddfa]

Hmmm . . .

Pure solutions demand that the algebraic abstractions modelled here are continuous.

The fly is made up (like the rest of the natural/unnatural world) of small chunks of energy called quanta which are essentially discrete (well, we measure them that way)

When the fly hits the train, the motion is a statistical function of expected observation.

We could expect unusual consequences (read Heisenberg) because we would change what is predicted by the pure abstract model simpy by observation.

It is entirely feasible that the fly and the train could be travelling at a velocity of zero at the time of impact - well at least one strain of a statistical analysis would show this to be true . . .

(Incidentally, the concept of zero is a convenient abstraction to help with calculus/algebra/geometry etc. I cannot think of one thing in the universe that would ever have a 'state' of zero - which is why you cannot divide by zero)

[NotLKH]

Thru the laws of thermodynamics, and conservation of momentum and energy, considering the fly and the train as a closed system,

then it is impossible for the total momentum of the system to become zero at the time of impact.

And so, the total velocity is also never zero.

Or, something like that....

[A$$Bandit]

Well, my mechanics teacher writes most of the A-Level papers (public exams u take in the UK at 18) for maths so he'd probably know... I'll ask him.

[snakeeyes1000]

there's some physisc law about combined velocities... I think I explained it. Neither are ever going 0, the train slows down and the fly speed up. Even if they both had the same elasticty, the train would continue due to it's momentum/intertia. Millions of particles of dust fall on your shoulders every day; how many times have you been beaten down by dust...

[Behemoth]

nobody has responded to my point...

They cannot be stopped for an infinitely small instant in time. Speed (velocity if you prefer) needs a time as well as a distance. The time is non existant, so the speed cannot be calculated.

[snakeeyes1000]

you're right behemoth. There are multiple laws and mathematical example proving that this entire thread is ludicrous(no offense to THEROB).

[beachbum]

I feel obligated to construct a real world experiment involving me, my car and that damn jogger that passes by each morning... I will let you know the results

[Destined Soul]

Both snakeeyes and NotLKH are correct in that having both velocities at 0 would violate the conservation of momentum.

momentum (p) = mass times velocity.

In a closed system, momentum is conserved.

p_total = m₁v₁ + m₂v₂

If the fly and train were one mass (ie: same object) and they were both stopped, then

p_total = m_train+flyv_train+fly = 0 which implies

m₁v₁ = -m₂v₂

Just plugging some numbers into these shows that the fly (I'm assuming it's not some mutant superfly ) has to be moving a LOT faster (by a factor of the difference in their masses) to stop the train.

HOWEVER:

Even if this was possible, it would be impossible for the train to start moving again, since p_train+fly = 0 at one point in time - if the train is to continue moving (with fly "attached" ), then the mass would have to be 0 if the velocity was non-zero if momentum was to be conserved.

Oh well. I'm sure there's other proofs out there as well, but I felt like I should do this one since I didn't have anything better to do.

Destined

[Behemoth]

Hey there Mr. Bum...Can you arrange for him to wear a fly suit and hit him with a train? otherwise the results may be biased and unusable...

thanks

[beachbum]

I was hoping to extrapolate but I will see his wife tonite and see what we can come up with