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Analytical Mech Homework Solutions 37

Analytical Mech Homework Solutions 37 - h= re 1 2 2re v 2z...

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2 2 2 1 2 2 e e e r r h r g = D z v ( ) , e h z r ± 2 2 1 2 2 e e z e r r v gr = D h From Appendix D, ( ) 2 1 2 1 1 2 8 x x x + = + + 2 4 2 2 2 4 e e z z e r r v v h g gr = + + + D D 2 2 1 2 2 z z e v v h g gr + D D From Example 2.3.2, 2 2 g D v h = 1 2 1 2 e v gr D And with ( ) 1 1 1 x x + , 2 2 1 2 2 e v v h g gr + D D 4.7 For a point on the rim measured from the center of the wheel: ˆ ˆ cos sin r ib jb θ θ = K v t t b θ ω = = D , so r i ˆ ˆ sin cos v jv θ θ = − D D K ² Relative to the ground, ( ) ˆ ˆ 1 sin cos v jv v i θ θ = D D K For a particle of mud leaving the rim: sin y b θ = − D and v v cos y θ = − D D So v v cos y y gt v gt θ = = − D D and 2
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