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The Answer Is Forty-Two — Many Mechanics Problems, Only One Answer
1.Paul Hewitt, Phys. Teach. 40 (8), 456 & 501 (Nov. 2002).
2.In the original Figuring Physics question, it was stated that the block might be released with some initial speed (but less than the escape velocity). If the initial velocity were not precisely toward or away from the point of tangency, then the block would go into orbit on the plate (for small displacements an ellipse with center at the point of tangency) rather than “oscillating to and fro” in a degenerate ellipse. Throughout this paper, I will assume that the object is simply released at rest, thus giving one-dimensional (“to and fro”) oscillatory motion.
3.For those who find that choice obscure, I quote brief excerpts from The Hitchhiker's Guide (pp. 178–180): “Seventy-five thousand generations ago, our ancestors set this program in motion, and in all that time we will be the first to hear the computer speak.” “An awesome prospect, Phouchg,” agreed the first man …. “We are the ones who will hear,” said Phouchg, “the answer to the great question of Life …!” “The Universe …!” said Lonquawl. “And Everything…!” … “Tell us!” “All right,” said Deep Thought. “The Answer to the Great Question …” “Yes…!” “Of Life, the Universe and Everything…” said Deep Thought. “Yes…!” “Is…” said Deep Thought, and paused. “Yes…!” “Is…” “Yes…!!!…?” “Forty-two,” said Deep Thought, with infinite majesty and calm.
4.This may be referred to in Argentina or Chile as the “Hole to China Problem,” but in the United States it should properly be called the “Hole to the Indian Ocean Problem.” In China, it is presumably referred to as the “Hole to Argentina Problem.”
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