The Buttered Toast Problem
At what minimum height h above the edge of a height-H table should you hold a square (side 2R) piece of toast butter side up, so that if its edge clips the table edge when you drop it the toast will land butter side down?
. . .
If the toast is height h above the table, the speed when it hits will be v = Sqrt[2gh]. But how might we model the table’s impact? Suppose after collision that the toast center has a downward speed v’ and angular velocity of ω=v’/R where R is the edge distance. Then collision impulse FΔt=m(v-v’) and angular impulse RFΔt=Iω are linked. Solving for v’ gives v’=v/(1+I/mR2). Time to the floor and the amount of rotation can now both be calculated as a function of h, and then h adjusted so that the butter side lands down.
Will that work?
Short answer, I have no effin’ idea. 🙂
I don’t get half of what Unitsphere is saying because my brain doesn’t comprehend mathematical delta-ω stuff. But I think I get the gist of the buttered toast problem: variables come into play. They must be considered and factored into the equation. Manipulate those variables, manipulate the end result. Theoretically.
Which brings me to my little novel.
Right now, my manuscript has been read by two betas, partially read by a third, and is being read by a fourth. Reactions thus far have been mixed but I do know this: ALBERT needs work. My problem is, how do I make EFFIN’ ALBERT a better novel; a richer, deeper novel? A more suspenseful novel? How do I ensure that my novel lands sunny-side up for the majority of my readers?
Not an easy task, considering the variables: each reader brings to the table a unique set of experiences and expectations. Each filters what (s)he reads through a unique lens. Each has a specific skill-set. Mind-set. These are truths, out of my control and non-negotiable.
But there are aspects of my novel I can manipulate, variables relative to plot and characterization. Word choice. Story structure. Foreshadowing. Should betas reach a consensus relative to any of those things, either for or against; if they reach similar conclusions, offer similar suggestions, it would behoove me to go back in there and consider what they are telling me, give it serious thought, perhaps factor in what they say, wholly or in part, accordingly. Will that work?
I guess we’ll see.