Me: Suppose I tie an ice cube to a piece of string and dangle it from a tree branch. I set the string swinging like a pendulum while the ice slowly melts onto the warm sand below. What is the shape of the wet streak in the sand? Is it a circle, a square, a line, or a point?
Fun question. Various parameters are not given, and I could imagine some simplifying assumptions being intended, but… assuming the ice cube is fresh, I’d guess that very little of it would drip down before air resistance stops the swinging. If there is no wind, then at that point the remainder would drip down into a circle. If there is wind, then … well, the problem becomes rather underspecified at that point: you could get practically any wet shape with the right pattern of wind.
(Also, if there were no air resistance, and the string swung indefinitely… since water drips down in discrete drops, the places where it lands might not be contiguous. And I think the drops would be most likely to fall off at a certain point: the bottom of the swing, which is when velocity is highest (and I believe “a = v^2 / r” when following a circular path; plus gravity is opposite the centripetal force at that point). In that case, you’d get two puddles on either side—probably resembling circles.)
I expect that if you actually ran this experiment, the answer would be a point because the ice cube would stop swinging before all that much melting had occurred. Additionally, even in situations where the ice cube swings indefinitely along an unchanging trajectory, warm sand evaporates drops of water quite quickly, so a trajectory that isn’t a line would probably end up a fairly odd shape.
This is all because ice melting is by far the slowest of the things that are relevant for the problem.
Fun question. Various parameters are not given, and I could imagine some simplifying assumptions being intended, but… assuming the ice cube is fresh, I’d guess that very little of it would drip down before air resistance stops the swinging. If there is no wind, then at that point the remainder would drip down into a circle. If there is wind, then … well, the problem becomes rather underspecified at that point: you could get practically any wet shape with the right pattern of wind.
(Also, if there were no air resistance, and the string swung indefinitely… since water drips down in discrete drops, the places where it lands might not be contiguous. And I think the drops would be most likely to fall off at a certain point: the bottom of the swing, which is when velocity is highest (and I believe “a = v^2 / r” when following a circular path; plus gravity is opposite the centripetal force at that point). In that case, you’d get two puddles on either side—probably resembling circles.)
I expect that if you actually ran this experiment, the answer would be a point because the ice cube would stop swinging before all that much melting had occurred. Additionally, even in situations where the ice cube swings indefinitely along an unchanging trajectory, warm sand evaporates drops of water quite quickly, so a trajectory that isn’t a line would probably end up a fairly odd shape.
This is all because ice melting is by far the slowest of the things that are relevant for the problem.