98_Problem CHAPTER 10

98_Problem CHAPTER 10 - PROBLEM 10.86 Collar A can slide...

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Unformatted text preview: PROBLEM 10.86 Collar A can slide freely on the semicircular rod shown. Knowing that the constant of the spring is k and that the unstretched length of the spring is equal to the radius r, determine the value of corresponding to equilibrium when m = 20 kg, r = 180 mm, and k = 3 N/mm. SOLUTION Stretch of spring s = AB - r = 2 ( r cos ) - r s = r ( 2 cos - 1) V = = 1 2 ks - Wr cos 2 2 1 2 2 kr ( 2cos - 1) - Wr cos 2 2 dV = -kr 2 ( 2cos - 1) 2sin + 2Wr sin 2 d Equilibrium dV = 0: - kr 2 ( 2cos - 1) sin + Wr sin 2 = 0 d -kr 2 ( 2cos - 1) sin + Wr ( 2sin cos ) = 0 or ( 2cos - 1) sin W = 2cos kr Now ( 20 kg ) 9.81 m/s2 W = = 0.36333 kr ( 3000 N/m )( 0.180 m ) 2 cos - 1 = 0.36333 2cos ( ) Then Solving = 38.2482 = 38.2 ...
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