A Couple of Physics Musings.
I’m no physicist, but I do idly think about physics sometimes.
How Flat are Frozen Lakes?
It occurs to me that as the ice freezes on a lake or pond, it’s pretty flat. I don’t live in such a region to wait for winter and walk out with a level or other tool to try to measure it, but I wonder how flat the ice actually is. That’s setting aside any kind of ice shove or otherwise disrupted ice (including from things like precipitation or sublimation).
My thought is that it doesn’t all freeze at once, and minor timing changes put some amount of height difference into the surface as it freezes, and on some sort of random-walk basis, it varies. But how much? The smaller the area, the less variation, obviously. Over a mile-wide lake, the low-point might be at least centimeters lower than the high point. But is it really that much? That’s what I want to know! No idea.
There’s surely some limit of how much it can differ before it would force disruptions at whatever thin point exists between two heights, as ice gets heavy. Some of the trapped air under the ice may also impact the height of its development or how it settles as it freezes over.
Ball Over a Curb.
I was curious how much the size of a wheel and height of a curb affects how much disruption the curb causes to a moving ball. I looked around a bit, and I think most physics models that as a wheel rather than a ball. Intuitively, a really huge wheel or a really small curb sees almost zero disruption, but what is the cutoff?
I think it probably comes down to how much of the ball or wheel is over the curb at the time or point of contact. The more that’s over it, the less disruption, and therefore the less speed the ball needs to move over the curb (to overcome its resistance). Obviously a wheel whose side-midpoint is lower or at the height of the curb will deflect. At some intermediate point, it will tend to ramp up but still pass (given enough speed). I guess that is the half-way point between the bottom of the ball and the side, but that’s ultimately what I’d like to know.
You could also take curb-angle into account. I assumed a straight curb (90° from the ground), and I think anything over straight would tend to act about like a straight curb, but shallower angles are easier to surmount.
I like these little questions. Frozen lakes seem flat, so it would be cool to know how flat they really are. Rolling a tennis ball over the carpet can make you wonder how it would act different if it were bigger or smaller but with the same mass.