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12_P70InstructorSolution

12_P70InstructorSolution - 12.70 Model The pulley is a...

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12.70. Model: The pulley is a rigid rotating body. We also assume that the pulley has the mass distribution of a disk and that the string does not slip. Visualize: Because the pulley is not massless and frictionless, tension in the rope on both sides of the pulley is not the same. Solve: Applying Newton’s second law to 1 , m 2 , m and the pulley yields the three equations: ( ) ( ) 1 G 1 1 G 2 2 2 2 1 1 2 0.50 N m T F m a F T m a T R T R I α = + = = Noting that 2 1 , a a a = = 2 1 p 2 , I m R = and / , a R α = the above equations simplify to 2 1 1 1 2 2 2 2 1 p p 1 1 0.50 N m 1 0.50 N m 2 2 0.060 m a T m g m a m g T m a T T m R m a R R R ⎞⎛ = = = + = + ⎟⎜ ⎠⎝
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