final_soln

final_soln - ME 274 Summer 2010 Final Exam PROBLEM NO 1...

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ME 274 – Summer 2010 SOLUTION Final Exam PROBLEM NO. 1 Given : System released at ! = 53.13 ° with the center of the disk moving downward with a speed of v B 1 . Consider the bar and the disk to be homogeneous. Find : Determine the angular velocity of disk B when = 0 . Use: m = 100 kg , L = 3 meters , v B 1 = 4 m / sec and R = 0.5 meters . Please clearly indicate the four steps in a neat and orderly presentation of your work. 1. FBDs : No nonconservative work done on the system. 2. Kinetics T 1 = 1 2 I D A 1 2 + 1 2 I C B 1 2 ; I C = I D = 3 2 mR 2 T 2 = 1 2 I D A 2 2 + 1 2 I C B 2 2 V 1 = mgLsin 1 V 2 = 0 ; @ datum Therefore, 1 2 I D A 1 2 + 1 2 I C B 1 2 + mgLsin " 1 = 1 2 I D A 2 2 + 1 2 I C B 2 2 # R 2 A 1 2 + B 1 2 ( ) + 4 gLsin 1 / 3 = R 2 A 2 2 + B 2 2 ( ) 3. Kinematics L 2 = s A 2 + s B 2 = constant ! 0 = 2 s A ! s A + 2 s B ! s B ! v A = " s B s A v B v B 1 A m L g massless rod no slip R R no slip B C D A m B A N B f B N A mg mg f A
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