t2_2007_summer_answers

t2_2007_summer_answers - Key Name MIME 2300 Test 2 In all...

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MIME 2300 Test 2 Name _______________________ July 16, 2007 In all the problems show all equations used with variables and then with values substituted so partial credit can be given wherever possible. Give units on all answers and write only in the space provided. On problems where appropriate, draw coordinate systems, datums, FBDs, K.Ds or velocity diagrams. Do not use F=ma as the primary method to solve any problems on this test ! 1. The disk with center at C rolls on the ground without slipping with the motion shown. The pin P is imbedded in the disk and slides freely in the slot in link AB. Link AB is free to rotate about point A which is fixed to the ground. A velocity analysis has been done with the results that link AB is rotating clockwise with an angular velocity of 2.16 rad/s clockwise and the length from A to P is increasing at a rate of 14.4 in/s. Find the angular acceleration of link AB at this instant. (38 points) Solution: ( 29 CD 2 CD D C r r a a ϖ - × α + = ( 29 ( 29 j 2 6 j 2 k 8 j a i a 2 D C - × - + = i 16 a C = j 72 a D = ( 29 PC 2 PC C P r r a a ϖ - × α + = ( 29 j 6 j 1 k 8 i 16 a 2 P - × - + = j 36 i 24 a P - = ( 29 ( 29 PA PA PA PA PA 2 PA PA PA A P u r r 2 r r a a + × ϖ + ϖ - × α + = j 36 i 24 a P - = 0 a A = ( 29 i 3 j 4 j 3 i 4 k r PA PA PA PA PA α - α = + × α = × α ( 29 ( 29 j 14 i 7 . 18 j 3

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t2_2007_summer_answers - Key Name MIME 2300 Test 2 In all...

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