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Unformatted text preview: 2. Hydraulic Oscillator Mata!” t,
A solid wooden disc with radius gharid mass density—pmd ﬂoats in a deep cylindrical
container of radius R partially ﬁlled with fluid with mass density pnuid. The disc is pushed down almost to submersion and released, whereupon it bobs up and down (always remaining upright) without damping. Determine the angular frequency w of the vertical
oscillations of the disc. Do not assume a<<R. f‘ﬁ. Qcc c MEN : 54'qu 3 (“”7) WG1 TL =7',’ 12'" 1..
”anti 3 “CL —§—Hum 3C4+7)H_41 M : 3W t {TOLL 12>
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Shank 1"“ t '2 I 3. Cantilever Bridge Consider a "bridge" construction technique wherebya closed book of length L is cantilevered (extended) over the edge of a desk. No glue is used to hold the book down,
" But Conventional static friction is present. Obviously, the maximum distance the book can be extended before becoming unstable ile/Z. Now consider a similar situation with stacked and displaced identical books (see example
drawing). Determine if it is possible for the topmost book in the stack to extend fully
beyond the edge of the desk (i.e. can the far end of the book be at horizontal position
x>L, where x=0 is the edge of the desk?) It is not necessary that successive books have
equal relative cantilever distances (i.e. in the drawing the dn's are not necessarily equal).
If such stacking is not possible, prove it. If such stacking is possible, find a) the minimum number of books needed, and b) the maximum distance the top—most book can extend beyond the desk edge, given
an whim number of books. m
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 Fall '08
 Lanzara
 Physics

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