Is there a vibratory rate at which my hand would just pass right through the object and it could not be perceived by touch anymore?
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4$\begingroup$ No. You must have a completely wrong idea of what a vibrating solid is. $\endgroup$– anna vCommented May 6, 2014 at 15:37
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$\begingroup$ Well, I did say any rate of vibration. It's theoretical of course, but if it was vibrating at 100,000 times a second, or 10 million, there's probably a point where the solid cannot be perceived by touch anymore... correct? $\endgroup$– AndyCommented May 6, 2014 at 16:07
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$\begingroup$ No. Your finger is prevented from passing through the iron sphere by the exchange force, and vibrating the sphere does not affect this force. $\endgroup$– John RennieCommented May 6, 2014 at 16:48
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$\begingroup$ If it was vibrating between your fingers that fast, you'd probably feel that it was touching both your fingers at once. It'd be moving so fast that your sense of touch wouldn't be able to catch up. $\endgroup$– mikhailcaziCommented May 6, 2014 at 16:53
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$\begingroup$ Vibrations are energy, after a certain frequency the ball would melt and your fingers too. $\endgroup$– anna vCommented May 6, 2014 at 18:30
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I could be wrong here, and if I am, please do correct me. As far as I know the exchange force mentioned above by John Rennie is one and the same as the electromagnetic force, which propagates at the speed of light. Vibrating the sphere at any velocity lower than that of light would not make any difference in being able to detect that it is still a physical object through the exchange force.
On the other hand, if you could (and you can't) somehow increase the velocity of the sphere to any velocity above that of light, you would have used an infinite amount of energy to accelerate the sphere to this velocity.