Analytical Mech Homework Solutions 160

Analytical Mech Homework Solutions 160 - (b Atwoods machine...

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(b) Atwood’s machine … ( ) 1 2 V m gx m g l x = − 2 2 2 1 2 2 1 1 1 2 2 2 x T m x m x I a = + + ± ± ± [Includes the pulley] 1 2 2 T I p m m x x a = = + + ± , 1 2 2 p x I m m a = + + ± ( ) 2 1 2 2 1 2 2 2 p H T V m m gx m g I m m a = + = + + l 1 2 2 H p x I p m m a = = + + ± ( ) 1 2 H m m g x = − = − ± p , ( ) 1 2 p m m g = ± (c) Particle sliding down a smooth inclined plane … sin V mgx θ = − 2 1 2 T m = ± x T p mx x = = ± ± , p x m = ± 2 sin 2 p H T V mgx m θ = + = H p x p m = = ± sin H mg p x θ
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