exam03_soln

exam03_soln - ME 274 Spring 2010 Examination No 3 PROBLEM...

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SOLUTION Examination No. 3 PROBLEM NO. 1 Given : A homogeneous disk A of mass m A is attached to a block B of mass m B using the cable and pulley system shown. The disk rolls without slipping . The system is released from rest. The masses of the pulleys are to be considered to be negligible. Find : For this problem, determine: a) the acceleration a B of block B after release. b) the tension T in the cable anchored to point G. Use the following parameters in your analysis: m A = 20 kg, m B = 10 kg. 1. FBDs 2. Newton/Euler Disk : M C ! = " TR = I C !! # $ T = " 1 R 3 2 m A R 2 % ' ( ) * !! = " 3 2 m A R !! Block : F y ! = " 2 T + m B g = m B !! y Combining above gives: 3 m A R !! ! + m B g = m B !! y 3. Kinematics x + 2 y = constant ! !! x = " 2 !! y Since C = IC of disk: ! x = R ! " !! = !! x / R = # 2 !! y / R 4. Solve 3 m A R ! 2 !! y / R ( ) + m B g = m B !! y " !! y = m B g 6 m A + m B " a B = ! !! y j g N f C
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exam03_soln - ME 274 Spring 2010 Examination No 3 PROBLEM...

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