Redditor splongo asks two questions:
I'm at a loss for a completely coherent answer. I don't think that, as a physical reality, there can be a perfectly spherical or flat object. But as a theoretical model (e.g. the formula for a sphere), there can be such objects, and therefore intersection between them. Would the surface area of the intersection point be non-dimensional, or just incalculably small?
How would you answer splongo's questions?
Link -via The Agitator | Photo: katerha
If a perfectly spherical ball is sitting on a perfectly flat surface, what is the size of the contact area? Would it not be infinitely small?
I'm at a loss for a completely coherent answer. I don't think that, as a physical reality, there can be a perfectly spherical or flat object. But as a theoretical model (e.g. the formula for a sphere), there can be such objects, and therefore intersection between them. Would the surface area of the intersection point be non-dimensional, or just incalculably small?
How would you answer splongo's questions?
Link -via The Agitator | Photo: katerha
But in physics, the contact area is as "small as it is possible to be", i.e. one squared Planck length (equal to 1.6162×10?35 metres)
http://en.wikipedia.org/wiki/Planck_length
Both are impossible in reality, but mathematicians will come up with a different answer from physicists.
But of course this is a non-physical world. If you worked out the force on that point it would be infinite, so something would need to give. The ball would become non-spherical, or the surface non-flat (and more likely, both), until the force in the contact patch - that's the area where the two surfaces touch - is no longer strong enough to continue to deform the objects. Either that, or one of them breaks.