Question

5. Consider the following method of tacking playing cards off a table: If you only have one card, place the card so it is halfway over the table. If you have two cards, place the top card so that half of it is hanging over the second card, and the second card such that 1 of it is hanging over the table. If you have three cards, place the top card so that half of it is hanging over the second card, the second of it is hanging over the third card, and the third card such that 1 of it is hanging over card such that the table. (Thus, continuing this pattern, we have a way to stack any number of cards) (a) Show that no matter how many cards you stack in this pattern, no cards will ever fall. Hint: Set your coordinate system so that 0 is the edge of any fixed card. The center of mass of the system of cards above the card you chose will be (t, y). The cards will topple over if is positive (V is irrelevant). Find i for stacks that are one card high, two cards high, three cards high, and then see if you can use these answers to help you derive the center of mass for a stack n cards high. You MUST justify your work! (b) Show that the top card can extend horizontally as far over the edge of the table as we want (provided we stack high enough!) Hint: Use a series to represent how long over the table the stack reaches. Show that this series diverges

Answer 1

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