186 Circular Motion and Other Applications of Newton’s LawsP6.68(a)The bead moves in a circle with radius vR=sinθat a speedofvrTRT==22ππθsinThe normal force hasan inward radial component of nsinand an upward component of ncosFma nmgyy∑=−=:cos0ornmg=cosFIG. P6.68(a)Then Fnmvrx∑sin2becomesmgmRRTcossinsinsinπθFHGIKJ=FHGIKJ22which reduces to gRTsincossin=422This has two solutions:sinθθ=⇒=°00(1)and cosπ=gTR224(2)If R=15 0. cm and T=0450.s, the second solution yieldscos....98040150033522±ms±sm2ejafand =°70 4.Thus, in this case, the bead can ride at two positions
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .