peterv@runx.OZ (Peter Vels) (10/12/85)
In previous articles I have noted that flies "turn around in zero time". Following on from that idea, can anyone explain the following story in mathematical terms to me? A fly is heading south above some train tracks. Unluckily for him, a train is heading in the opposite direction. They collide. Assume that before the moment of impact the fly and the train were moving at the same speed (ie. the train's velocity = -(fly's velocity). After impact, the fly (now dead) is stuck to the front of the train. In order to "turn around" (change from a positive velocity to a negative one) the fly must have had a zero velocity at some point in time (my assumption). Having a velocity of zero, the fly must have been stopped. At that time, the fly would have been in contact with the front of the train. As the two bodies were not rotating, would not the train have been stopped as well? If not, then why not? Peter Vels.
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (10/13/85)
> In order to "turn around" (change from a positive velocity to a negative one) > the fly must have had a zero velocity at some point in time (my assumption). > Having a velocity of zero, the fly must have been stopped. > At that time, the fly would have been in contact with the front of the train. > As the two bodies were not rotating, would not the train have been stopped as > well? If not, then why not? This is just another variant on Zeno's paradoxes. You ask "would not the train have been stopped?" on the basis of undemonstrated assumptions. If you assume an incompressible point fly, then obviously in your scenario it underwent an infinite force at the precise moment of impact, a force applied by the train. In such a case, its velocity undergoes discontinuous change and is never zero. In a more realistic model of the interaction, the momentum of the train changed by a minute amount, the momentum of the fly by the same amount in the opposite direction, and the fly absorbed a certain amount of energy. Indeed, if the fly sticks to the train, it must absorb some energy. In all such problems, beware of taking extreme limits as actualities; consider systems that are not quite so ideal and you will find that the analysis is much easier.
hes@ecsvax.UUCP (Henry Schaffer) (10/14/85)
<my article quoter is broken - I wish the same on many others> The original article asked the question about a fly hitting a train which was going at the same speed (velocity of fly = -v of train.) It asked why when the fly's speed went to zero, doesn't the train's speed go to zero, as well. doug gwynn answered in terms of discontinuities. Not contradicting him, I think that the original question may have contained a different problem. The velocity constraint given in the original article is an initial condition, not a constraint on continuing events. Therefore, regardless of what happens to the fly's speed, you don't know what the train's speed is. (Physics says that the train's speed after the collision depends on the relative masses of the fly and train, ..., which weren't given.) --henry schaffer
bhuber@sjuvax.UUCP (B. Huber) (10/14/85)
> > In order to "turn around" (change from a positive velocity to a negative one) > > the fly must have had a zero velocity at some point in time (my assumption). > > Having a velocity of zero, the fly must have been stopped. > > **** At that time, the fly would have been in contact with the front of the train. > > As the two bodies were not rotating, would not the train have been stopped as > > well? If not, then why not? > > In all such problems, beware of taking extreme > limits as actualities; consider systems that are > not quite so ideal and you will find that the > analysis is much easier. Discontinuous momentum is an example of such an extreme limit. Actually, if the fly decelerated to zero speed, stopping sufficiently far from the train, then the train would just catch up with it as it began its acceleration backwards. At the time the two met, they would have identical velocities; no momentum transfer need occur. From that moment on, the fly would be moving faster, not slower, than the train, and so would speed on ahead.
oleg@birtch.UUCP (Oleg Kiselev x268) (10/19/85)
> The original article asked the question about a fly hitting a train > which was going at the same speed (velocity of fly = -v of train.) > It asked why when the fly's speed went to zero, doesn't the train's speed > go to zero, as well. Why not assume that the RELATIVE of the fly, the train speed was 0, and the fly did 2X clip. Then it is possible to say that the fly stops at the collision and its speed does go to 0, that is the train's speed ( minus the conservation of momentum in the system) if the collision was INELASTIC. Assuming a perfectly elastic collision the fly will get to speed of 0 (stop relative to the train) and then bounce off. Other than concervation of momentum, nothing should effect the train -- DISCLAMER: The above are the opinions of a type V demon who took posession of me as a result of a failed AD&D summoning spell. Send flames to /dev/Gehenna. ----------------------------------+ With deep indifference, "I disbelieve an army of invisible| Oleg Kiselev. mind-flayers!" |...!trwrb!felix!birtch!oleg "OK. They are *still* not there." |...!{ihnp4|randvax}!ucla-cs!uclapic!oac6!oleg