Surface areas of touching snooker balls

[Mac attack]

If you have two snooker balls which are placed side by side and are touching, how much of the surface area of each is touching the other one?
How can you measure it?

[fo3nix]

technical answer: it depends how close you are to the surface. look from far away, you probably wont know that they're touching. look closer, and you can see that they are touching. look closer, to atomic levels, and you'll see that a good propertion of what you thought was touching actually isn't.

short answer: perhaps put some felt tip pen ink on one of the balls, then put it next to the other, so that it touches, and you can remove them and see how much ink has passed.

[x.lisa.x]

its kind of complicated but work out the suface area of the snooker balls. then like fo3nix said put a felt tip mark around the circle that is touching the other ball. Then work out the area of that circle by doing pie x diameter then take that away from the area of the ball i guess :S xx

[fo3nix]

to expand on lisa's idea:

area of a sphere (approximate the snooker balls to a sphere - hey i'm a physicist!) is:

A(sphere) = 4 pi r^2

so measure the width of your snooker ball, that'll be its diameter. divide by two to get its radius (r in the above equation). this will let you calculate the entire area.

assume that the area of the dot made by the ink is small enough (compared with area of entire sphere) to be treated as a circle, and find its area by

A(circle) = pi r^2

where this r is the radius of the circle made by the ink.

area touched as a percentage = A(circle) / A(sphere)

[bernardo]

That method would depend on the thickness of the ink. If the snooker balls are perfect spheres, the touching area would theoretically be zero. Therefore the true answer depends on the irregularities of the surfaces, and/or the definition of "touching" at the atomic / molecular level.

[matt_london]

<PRE>Why would it be zero? Surely they're either touching, or they're not?</PRE>

[Loosehead]

As Bernardo says if the spheres are perfect then they would not actually touch. The 2 atoms that are closest to each other being 99.9% empty space would simply give the impression of touching using the Nuclear force.

However they spheres are not perfect so the ink transference method seems good to me!

[matt_london]

<PRE>But wouldn't that reasoning apply to cubes too? They don't really touch, just appear to. If they are perfect spheres, would it not be fair to say that just one atom from each is 'touching' the other.</PRE>

[Loosehead]

At an atomic level things don't youch in the conventional sense. Take the simplest atom, hydrogen now if the nucleus was the size of the head of a pin then on that scale the electron would be orbiting 1km away. so if two of them where next to each other the nuclear forces would preven overlap. So the only way they could be deemed to be touching is if the electrons from each atom where to collide.

I think that's what Bernardo is getting at anyway!

[bernardo]

Yes, that is what I was getting at.
No, the same reasoning would not apply to cubes. If two cubes were touching, and were perfect cubes, then it would be poissible for the whole face of one cube to be touching the face of the other cube. When two spheres are touching, only a singular point is touching and therefore has no area.