Final Exam 102 2009 with Answers

# Final Exam 102 2009 with Answers - MAE 102 FINAL EXAM FALL...

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MAE 102 FINAL EXAM FALL 2009 1. The disc of mass m and radius r is connected to the wall by the spring of stiffness k = mg/r , and the disc rolls without slipping on the horizontal floor. The block of mass m slides on the floor, and there is no friction between the block and floor or between the block and the disc. The block is not attached to the disc. Therefore, the disc can push on the block but not pull on it. The system is released from rest with the block touching the disc and the spring compressed by the amount r . Find (a) the maximum velocity of the center of the disc, v = p 2 gr/ 5 (b) the final velocity of the block, v = p 2 gr/ 5 (c) the maximum stretch in the spring (it is not r ). δ = p 3 / 5 r k m, r m

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2. A disc of mass m and radius r is released from rest on the fixed incline. The coefficients of static and kinetic friction between the disc and the incline are the same and are denoted by μ . (a) Let μ 0 = the minimum value of μ for which the disc rolls without slipping, and find μ 0 as a function of β . μ 0 = tan β/ 3
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