10_InstSolManual_PDF_Part34 - 10-34 Chapter 10 10.84 Set Up...

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10.84. Set Up: When the marble rolls without slipping it has both rotational and translational kinetic energy and Let be upward. Take at the bottom of the hill so and The initial speed is Solve: (a) (i) no slipping: At the maximum height, so so This gives so and (ii) no friction: Gravity does work and converts to gravitational potential energy. But there is no torque for an axis through the center of mass and and remain constant. Only is converted to and (b) The ball goes higher with friction. The friction force, that reduces
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Unformatted text preview: is directed up the hill. v , h 5 v 2 2 g . 1 2 m v 2 5 mgh U grav . K tran K rot v K tran h 5 7 v 2 10 g 7 10 m v cm 2 5 mgh 1 2 I cm v 2 5 1 2 A 2 5 mR 2 B1 v cm / R 2 2 5 1 5 m v cm 2 1 2 m v cm 2 1 1 2 I cm v 2 5 mgh . K i 5 U f . K f 5 U i 5 0, v 5 0. v cm 5 v cm 5 R v . U i 1 K i 5 U f 1 K f . v cm 5 v . y f 5 h . y i 5 y 5 1 y I cm 5 2 5 mR 2 . v cm 5 R v . 10-34 Chapter 10...
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