184_Physics ProblemsTechnical Physics

184_Physics ProblemsTechnical Physics - 186 P6.68 Circular...

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186 Circular Motion and Other Applications of Newton’s Laws P6.68 (a) The bead moves in a circle with radius vR = sin θ at a speed of v r T R T == 22 ππθ sin The normal force has an inward radial component of n sin and an upward component of n cos Fm a n m g yy =− = :c o s 0 or n mg = cos FIG. P6.68(a) Then Fn m v r x sin 2 becomes mg m R R T cos sin sin sin πθ F H G I K J = F H G I K J 2 2 which reduces to g R T sin cos sin = 4 2 2 This has two solutions: sin θθ =⇒=° 00 (1) and cos π = gT R 2 2 4 (2) If R = 15 0 . cm and T = 0450 . s, the second solution yields cos .. . . 980 40 1 5 0 0335 2 2 ±ms ±s m 2 ej af and 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 .

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