Analytical Mech Homework Solutions 114

Analytical Mech Homework Solutions 114 - 12 Energy is...

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12 8.15 Energy is conserved: a x m 2 m 1 2 22 12 2 1 111 222 2 x mx I mgx mgx E  + ++   ± ±± = 21 2 0 I m xx m xx xx m gx m gx a + ++−= ±±± ± ± ( ) 2 mmg x I mm a = 8.16 While the cylinders are in contact: 2 cos cm r mv f mg R r θ = =− R G mg G b a rab = + , so 2 cos cm mg R ab mv = + v cm From conservation of energy: () 11 cos cm a b mv I mg a b mg ω += + + + From table 8.3.1, 2 1 2 I ma = cm v a = ( 2 2 1 1c o s 2 cm cm v mv ma mg a b a ) + 2 4 o s 3 cm mv mg + When the rolling cylinder leaves,
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