Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Andrew Price on 05/11/2010 11:30:06
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Andrew Price asked the Naked Scientists:
An old but an interesting one
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A train weighing say 1000 tons is trundling along a track at say 20 m.p.h. and a (titanium) ball bearing is thrown at  say 20 m.p.h. towards the front of the train (Which interestingly has a solid plate of titanium welded to its nose). The result surely is that the ball bearing hits the target of the train at a contact speed of 40 mph, bounces off the front of the train thereby changing direction by approximately 180 degrees. Now, at some point in the trajectory of the ball bearing it must, by changing its direction of travel into the opposite direction, have been absolutely stationary relative to the ground - just for an instant. The train of course does not hesitate, it just keeps trundling at 20 mph...   how can this be?
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The answer would seem to be compression of the ball bearing and/or the front of the train to make this possible or is this too obvious for although the suggestion here is titanium, there must be un compressible materials.
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In front of me, as I send this email,  I place my forefinger of my right hand extended onto my desk top and I slide this (the train) slowly and constantly to my left and at the same time, I roll my pen (the ball bearing) towards my approaching finger. On contact with my finger  the pen has been sent to roll in the opposite direction thereby being motionless relative to my desk top for a moment  but my right finger continues unabated on its course - perhaps I should get out more ...?.
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Love the programme (http://www.thenakedscientists.com/HTML/podcasts/)
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Andrew Price
Spain
What do you think?
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Just speculating
Naturally the titanium ball has a small mass compared to the train.
The compression of this ball (titanium) is so small, I think it can be neglected.
Since the surface and the ball are made of the same material, is there any thermal conductivity on impact and can there be a small exchange of the thermal energy exist at the time of impact?
Ever so slight, that this energy transfer is the lost of kinetic energy, which prevents an instantanious redirection or a short pause before exiting the surface contact?
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I think that the ball will compress and deform - a shock wave pass through it at the speed of sound, when that wave reaches the impact sight after having rebounded off the back of the ball the ball will bounce off and continue distorting as it moves away from train.
The ball on average will be stationary with respect to the front of the train whilst in contact, (obviously that's bound up with the definition of in contact). With respect to the ground, at some very brief point whilst the ball is slowing and deforming the ball will be stationary, but not sure if this is at a defined point.
The collision will not be completely elastic - the ball and the train plate will warm up, there will be a noise. I see no reason it shouldn't behave in roughly the same way (with the distortions at a much lower level) as the classic slow motion golf ball hit - video here (http://www.youtube.com/watch?v=AkB81u5IM3I&feature=related)
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Distortion seems to be the answer, as it is with the more common example of a fly hitting a train. However, we should perhaps bear in mind that if we drop that ball to the ground, not only does the ball move towards the Earth, the Earth also moves towards the ball. If we believe that, could we not believe that the train stopped for period that was so brief it could not be measured?
A physics student once explained to me that the train stopped "for a period of no time". I was unable,then, to see how that differed from not stopping. Now, 55 years later, I still can't make that distinction. Have I made no progress? [:(]
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The train of course does not hesitate, it just keeps trundling at 20 mph... how can this be?
I don't know what the problem is here - what would you expect to happen? Why do you consider it interesting?
The train slows down by a tiny amount because of conservation of momentum, but it doesn't stop. The ball distorts in the same way that a tennis ball would, but by a smaller amount.