Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: yourlifeteam on 24/09/2015 16:46:32
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A train is heading west and a fly is buzzing along the tracks heading east. The train collides with the fly. The fly at some point must go from heading east to heading west, so at some point its speed must be 0mph. As the fly is in contact with the train, the train must also be going 0mph at this time. Has the fly just stopped a train?
Two sisters debate this question here:
What do you think?
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A train is heading west and a fly is buzzing along the tracks heading east. The train collides with the fly. The fly at some point must go from heading east to heading west, so at some point its speed must be 0mph.
Correct, if with "the fly" you mean "its centre of mass". Incorrect if you pretend to describe the fly as a point mass, because in this last case its velocity is not a continuos function of time, it has a jump discontinuity from a positive to a negative value so it's impossible to say that "at some point it must be 0mph".As the fly is in contact with the train, the train must also be going 0mph at this time.
Incorrect. When the fly "is in contact with the train", its speed is not 0mph any longer because it has already accelerated towards west.
If you want to describe the fly's motion in terms of continuous functions (of time, for example) you can't use the point mass description, you have to describe the fly as a system of points or as a continuous system; then the first points/parts of the fly which comes in contact with the train immediately acquire its velocity -Vt (minus sign because this velocity is in opposite direction of that of the fly, which I choose as positive), while the last parts still have the initial velocity of the fly Vf.
During this process, the fly's centre of mass velocity decreases continuously from Vf to 0 to -Vt. All the parts/points of the fly are "in contact" of the train (not moving with respect to the train) only at the end of this process.
Everything would appear more simple in the train's reference frame: the fly's initial velocity is Vf + Vt and its centre of mass' velocity decreases continuously from that value to 0.
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Is there another perspective?
When the fly and train collide, the fly is distorted, but so, to a much lesser extent, is a very small portion of the front of the train. Thus, a minute part of the train stops for a very small instant of time.
Is this any less likely than maintaining that if I drop a stone, the stone moves towards the Earth, and the Earth also moves towards the stone?
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This rather nullifies the argument about different mass cannon balls dropped from the leaning tower of Pisa taking the same time to fall, due to the mutual attraction between the Earth and the cannon balls the heavier one will take less time to reach the ground than the lighter one assuming they are dropped at separate times.
The difference is very small and would be difficult to measure but easy to calculate.
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the fly is distorted, but so, to a much lesser extent, is a very small portion of the front of the train
It is true that the impact of a fly would distort the steel by a microscopic amount (OK, maybe an electron microscope...). This causes a sound wave to travel backwards through the train at around 6km/second (http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html), which is much faster than the train is moving forward.
However, the train's engine and the wheel noise is much louder than the impact of a fly, and propagates through the steel in all directions (including forwards). This sound moves forwards much faster than the train is moving forwards.
So, overall, the impact of the fly is lost in the general random vibration of the atoms in the train, and does not change the average velocity of these atoms by a measurable amount.