OK, check this out..you have two balls one is the size of a marble. one is the size of the moon. each ball is perfectly spherical and smooth. each ball is set upon a perfectly flat plane. quite naturally each sphere contacts the plane at one point, but is the surface area of contact greater on the larger sphere and less on the smaller sphere, or are they the same?
A circle has infinite sides, so I am supposing they are both resting on one of these sides (to stop movement). I mean, if the surface area was different, you're talking an astrologically small number I guess.
When I read the title the first thing that came to mind was this: https://www.youtube.com/watch?v=7sn1RUjbL1g"]YouTube- Dave Chappelle - Balls
A key concept is the center of gravity of a body at rest: it represents an imaginary point at which all the mass of a body resides. The position of the point relative to the foundations on which a body lies determines its stability towards small movements. If the center of gravity exists outside the foundations, then the body is unstable because there is a torque acting: any small disturbance will cause the body to fall or topple. If the center of gravity exists within the foundations, the body is stable since no net torque acts on the body. If the center of gravity coincides with the foundations, then the body is said to be metastable.
The moon would touch more of the plane. It's simple physics. The plane ceases to be "perfectly flat" as soon as any weight is applied. The larger mass will deform the shape of the plane more than the smaller mass, therefore allowing more surface area to come in contact. If you perform this in space, the mass of the moon will create enough gravity to deform the plane touching it. I recall my physics professor emphasizing that if a wire has a weight hanging from it, no amount of force can stretch the wire enough to make it flat.
I was under the assumption that two objects could never really come into contact because of the repulsion of electrons.
From a geometric point of view this is a simple case of tangency. The spheres rest on a plane just as a line is tangent to a circle. Thus no matter the diameter of the sphere the point of contact is the same.
That;s what i figured. they would warp however in a real life application. but theoretically you are correct sir.
I dunno man if we would ignore the force of gravity I think the size of the sphere will very much effects the surface area it will occupancy on the plane thingy. I mean take the needles sharp point and cut it off round it up and put it on a plane, count the atoms that touch the surface or give the charge and repel … Now take a sphere the size of earth and count the atoms that are in effect with the plane? U cant tell me that it will be the same number. We are living on a big ass marble and the corner of it that I occupancy is pretty much flat. FFs there was some misconception that the world is flat... take a bigger planet(sphere) and the effect is only magnified.
Id say the bigger one has a larger contact patch due to its size and its bigger so even though its a sphere its flatter than the marble
I think that if we are talking about tangent points it is either contacted completely flat, like the entire plane is touching, or there is an infinitesimal contact point which is completely immeasurably small. this value wouldnt change with the size of the sphere. does this make sense?
yes this is what makes the question interesting. it's a case of resolution. the larger circle appears to make more contact because it arcs closer to the line over a longer distance, but in fact it is still contacting the same amount as the smaller circle.
This is an interesting question. All material is somehow elastic, and there isn't any material that is completely smooth. Therefore, according to such phenomenon, the contact surface area of the larger ball is greater, since there is more mass to pull down. Everything is elastic. But, lets say we have an object that is not elastic. An ultimate, absolutely perfect sphere in any way. Does it have a contact surface at all? Where does the border go? My logic says it should be only one molecule, or even atom. But in metaphysical world of no-atoms, the area of contact should shrink infinitly. Therefore, does it even have an area of contact? Does it float?
