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EAS208_Exam03_MakeUp_111210_FINAL_Solutions

EAS208_Exam03_MakeUp_111210_FINAL_Solutions - Name EAS208...

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EAS208 Fall 2010 – Exam 3 Make-up Exam SOLUTIONS Name: Person Number: Problem 1: Point is moving to the right with a constant velocity of C 20 in s . Also, from a previous calculation, the angular velocity of bar AB is 2.94 AB rad s ω = − and the angular velocity of bar BC is 1.18 BC rad s ω = . Determine: a) The acceleration of B b) The angular acceleration of bar and bar AB BC (30 points) Solution: The acceleration of point B relative to point is: A ( ) B A AB B AB AB B A A r r α ω ω = + × + × × a a r r r r r ( ) ( ) ( ) ( ) ( ) ( ) 0 4 4 4 B AB AB AB α ω ω = + × + + × × + a k i 4 j k k i j r ( ) ( ) 4 4 4 4 B AB AB AB AB A α α ω ω ω = − + + × − + a i B j k i j 2 2 4 4 4 4 B AB AB AB AB α α ω ω = − + a i j i j ( ) ( ) 2 4 4 4 4 B AB AB AB A α ω α ω = − + + a i 2 B j (1) The acceleration of point B relative to point C is: ( ) B C BC B BC BC B C C r r α ω ω = + × + × × a a r r r r r ( ) ( ) ( ) ( ) ( ) ( ) 0 10 7 10 B BC BC BC α ω ω = + × − + + × × − + a k i 7 j k k i j r ( ) ( ) 7 10 7 10 B BC BC BC BC B α α ω ω ω = − + × − a i j k i C j BC 2 2 7 10 10 7 B BC BC BC α α ω ω = − + a i j i j ( ) ( ) 2 2 10 7 7 10 B BC BC BC BC ω α ω α = + a i j (2)

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From Eq. (1) and Eq. (2): ( ) ( ) ( ) ( ) 2 2 2 2 4 4 4 4 10 7 7 10 B AB AB AB AB BC BC BC B α ω α ω ω α ω α = − + + = + a i C j i j The and i j components must be equal in the above equation, thus: ( ) ( ) ( ) ( ) 2 2 2 2 (1) (2) 2 2 2 2 4 4 10 7 4 4 10 7 4 4 7 10 4 4 7 10 AB AB BC BC AB AB BC BC AB AB BC BC AB AB BC BC α ω ω α α ω ω α α ω ω α α ω ω α + + = ⎧− =
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