An express train weighing hundreds of tons hurtles down a track at 100mph. Minding it's own business and travelling in the opposite direction is a fly. The fly weighs less than 1 gram and is travelling at less than 1mph. The fly hits the front of the train, and instantaneous goes from travelling at 1mph on one direction to travelling at 100mph in the opposite direction. Since the fly's direction of travel has been reversed 180 degrees there must have been a point, no matter how short, when the fly was stationary. At that point the fly was in contact with the front of the train, so the train must also have been stationary.
Has the fly really stopped the train?
**************
To make the situation more scientific (and to avoid answers involving the squashing of the fly or the denting of the front of the train) keep the relative weights and speeds the same but imagine both fly and train were made of an infinitely hard material that cannot be deformed. And to avoid the fly being deflected by the train's slipstream, imagine the whole event take place in a vacuum, or alternatively that the fly is fired from a gun so it definitely hits the train.
So, does the train stop?
Jeremy
No the train does not stop, not even for an instant, no matter how miniscule.
And in addition, the fly did not stop completely all at once, either. In fact, his body stopped in stages, starting with his head, then his shoulders, then is abdomen, etc.
And of course you know the last thing to go through that fly's mind when he hit that train? His @$#.
Quote from: gumpy on January 22, 2007, 03:40:55 PM
And in addition, the fly did not stop completely all at once, either. In fact, his body stopped in stages, starting with his head, then his shoulders, then is abdomen, etc.
That is one of the three answers I usually get. I've asked a lot of people this question, including physics professors, and everyone agrees that the train doesn't stop, but no one yet has been able to explain it after I've added in the bit about the theoretically undeformable train and fly.
I also wonder if even with a normal train and fly whether the situation is actually any different - if you only consider the very first quark of the very first proton of the very first atom of the fly - that quark still has to change direction 180 degrees whilst it's touching the first quark of the train, so the train must be stationary.
Jeremy
PS. I also have another question which I have been annoying people with for years about a satellite attached to the earth by a cable. But after Captain Ron's post I daren't post it here now.
I am with Gumpy on this one. The train does not stop, even for a pico second, because its direction is not changing. Superfly however is experiencing an instantaneous velocity and direction change without ever experiencing zero velocity due to the assumptions given. And in those last two words is the bug in the equation (pardon the intentional pun). The assumptions break the laws of physics making it impossible to explain through physics. Unobtanium can't exist, compression of the fly would be a factor in understanding the vector velocities.
Jeremy,
Nothing on this earth stands still at 17,000 mph...... ;D That is only relitive to the sun though. :o
?? I'm without an answer for sure.
Nick-
Every action has an equal but opposite reaction.
A given weight of fly impact depend on whatever type of surface material & thickness & location of reinforcement bracket or mounting will....I mean it will flex somewhat while vehicle moving at any speed or flying object moving:
1) to toward non moving vehicle (stand still)
2) moving same direction but faster than leader
3) heading toward each other
The bottom line is that all vehicle tail end is still moving somewhat while still absorbing the impact of front or leading end. Nothing stops until all reaction is stop.
So in this case of locomotive or train would never stop at any time but in the area of impact may have stop nanosecond & being absorb by heaver motion to keep going.
Newton's Cradle is consisting of several steel balls on triangle string to keep in straight path.
A special high speed movie camera aim close up of the impact of 2 steel balls that will show change (very little) of shape like an egg for microsecond before normal shape.
FWIW
Sojourn for Christ. Jerry
All I now is that when your cruising along at 100mph on a Harley,and a decent sized fly hits you in the neck it stings pretty good.I'm guessing that the last thing that went through the fly's mind was its @$#!! ;D ;)
Quote from: HighTechRedneck on January 22, 2007, 06:34:52 PM
Superfly however is experiencing an instantaneous velocity and direction change without ever experiencing zero velocity due to the assumptions given. And in those last two words is the bug in the equation (pardon the intentional pun). The assumptions break the laws of physics making it impossible to explain through physics.
This is the conclusion I have also come to after thinking about it for years; it's problamatic though as I thought from my studies of differentiation & integration at college that there was no such thing as 'instantaneous'. There certainly
are plenty of things in existance that break the laws of physics though (as Steven Hawking will tell you).
Jeremy
Quote from: Jeremy on January 23, 2007, 02:10:54 AM
Quote from: HighTechRedneck on January 22, 2007, 06:34:52 PM
Superfly however is experiencing an instantaneous velocity and direction change without ever experiencing zero velocity due to the assumptions given. And in those last two words is the bug in the equation (pardon the intentional pun). The assumptions break the laws of physics making it impossible to explain through physics.
This is the conclusion I have also come to after thinking about it for years; it's problamatic though as I thought from my studies of differentiation & integration at college that there was no such thing as 'instantaneous'. There certainly are plenty of things in existance that break the laws of physics though (as Steven Hawking will tell you).
Jeremy
Certainly, mathmatically there is no such thing as instantaneous. But those laws of mathmatics rely on the laws of physics as assumptions in the proof. When the physics are broken, the math no longer holds. Indeed, with all that humanity has discovered of the laws of the universe, there is much that we still don't know.
"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
Shakespeare, Hamlet, Act 1, Scene V
I'm way too lazy to look it up in the dusty text books I kept from college, but I do remember something from one of those classes applying differential equations to camshaft lobe design.
Integral (?) of displacement = velocity
Integral (?) of velocity = acceleration
Integral (?) of acceleration = jerk
If jerk = 0, all was good, if not, then you could get valve float, spring breakage, etc. So I'm guessing there are some incredibly high acceleration & jerk forces involved as the two meet.
Also since EVERYTHING flexes in the real world, by the time the fly hits the train, it has already changed direction.
Now in the theoretical fantasy world of the perfectly rigid bodies colliding, - you can make up any answer you like because there is no reality there anyway.
neat question for mental masturbation tho.
It is the whole "infinitely hard material that cannot be deformed" business that takes this question outside the realm of traditional physics. Since the stuff with these properties isn't known to exist, virtually any answer can be given and not disputed.
Traditional physics holds that Force = (mass of an object) x (acceleration). With normal materials, the impact involves deformation (either temporary or permanent) of the one or both of the objects. This spreads the velocity change over some finite period of time, yielding an acceleration value we can talk about. If there is no deformation the velocity change would be instantaneous. An instantaneous velocity change would be "infinite acceleration". From F=ma above, unless the mass of the body changes, that would create an infinite force.
So when we start working with materials that do not deform, we are free to write our own new laws of Physics. .. and who's to say who is wrong?
My answer is that the train keeps moving forward, but everybody's wrist watch on the train gains .000000000000001 seconds. The fly, on the other hand, is immediately transported to Brooklyn in the early 1960's.
Prove me wrong.
WEC4104
Quote from: WEC4104 on January 23, 2007, 05:53:07 AM
It is the whole "infinitely hard material that cannot be deformed" business that takes this question outside the realm of traditional physics. Since the stuff with these properties isn't known to exist, virtually any answer can be given and not disputed.
Traditional physics holds that Force = (mass of an object) x (acceleration). With normal materials, the impact involves deformation (either temporary or permanent) of the one or both of the objects. This spreads the velocity change over some finite period of time, yielding an acceleration value we can talk about. If there is no deformation the velocity change would be instantaneous. An instantaneous velocity change would be "infinite acceleration". From F=ma above, unless the mass of the body changes, that would create an infinite force.
So when we start working with materials that do not deform, we are free to write our own new laws of Physics. .. and who's to say who is wrong?
My answer is that the train keeps moving forward, but everybody's wrist watch on the train gains .000000000000001 seconds. The fly, on the other hand, is immediately transported to Brooklyn in the early 1960's.
Prove me wrong.
WEC4104
Hi Wayne,
Great explanation..... I for one, think that the fly is just as you say. FUBAR!
Nick-
Everything here makes my eyes cross, but I like this:
Quote from: WEC4104 on January 23, 2007, 05:53:07 AM
My answer is that the train keeps moving forward, but everybody's wrist watch on the train gains .000000000000001 seconds. The fly, on the other hand, is immediately transported to Brooklyn in the early 1960's.
LOVE it! :D
Brian B.