# Modeling a plastic cup

## Main Question or Discussion Point

I've noticed that plastic cups exhibit some interesting physical behavior.
Some paper cups(maybe all actually, I'm not sure) have concave bottoms, and when the liquid in the cup gets high enough, the forces from simply raising the beverage from the table to my mouth create enough force to pop the concave region into a convex one, and then it pops back to the concave position when it's at rest. This is a lot like the popping tops of baby-food cans, where once you've opened them, you can press down on the center and it pops in and out.
Now, when the water is high enough, the resting position of the bottom is the convex position, and lowering the cup causes the popping behavior.
What I'm wondering about, is how to accurately describe this behavior physically. I understand that there's roughly an even pressure at every point on the bottom of the cup due assuming that the bottom of the cup doesn't pop up/down very far compared to the height of liquid, but I think the stress on the bottom caused by liquid above each point should be very different, since each point is at a different distance from the edge, and I think the force should be considered as acting on some sort of springy lever arm attaching each point being pressed on to a point on the rim.
I look forward to responses :)

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