09_InstSolManual_PDF_Part16

09_InstSolManual_PDF_Part16 - v 1 R 2 v 2 R 2 1 2 I v 2 5 1...

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(c) (d) 9.73. Set Up: Use projectile motion to find the speed the marble needs at the edge of the pit to make it to the level ground on the other side. The marble must travel 36 m horizontally while falling vertically 20 m. Let be downward. Then use conservation of energy to relate the initial height to the speed at the edge of the pit. so conservation of energy gives Let so and Rolling without slipping means Solve: (a) Projectile motion: gives Then gives Motion down the hill: (b) independent of R . I is proportional to but is proportional to for a given translational speed Reflect: The answer to part (a) also does not depend on the mass of the marble. But, it does depend on how the mass is distributed within the object. The answer would be different if the object were a hollow spherical shell.
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Unformatted text preview: v . 1 / R 2 v 2 R 2 1 2 I v 2 5 1 5 m v 2 , h 5 7 v 2 10 g 5 7 1 17.8 m / s 2 2 10 1 9.80 m / s 2 2 5 22.6 m. mgh 5 7 10 m v 2 . U i 5 K f . v 5 v x 5 x 2 x t 5 36 m 2.02 s 5 17.8 m / s. x 2 x 5 v x t t 5 Å 2 1 y 2 y 2 a y 5 2.02 s. y 2 y 5 v y t 1 1 2 a y t 2 y 2 y 5 20 m. a y 5 9.80 m / s 2 . v y 5 0. K 5 1 2 I cm v 2 1 1 2 m v 2 5 1 2 A 2 5 mR 2 B v 2 1 1 2 m v 2 5 7 10 m v 2 . v 5 R v . K i 5 0. y i 5 h . U f 5 y f 5 K i 1 U i 5 K f 1 U f . W other 5 v 1 y v K rot K tot 5 20 J 436 J 5 4.6% K 5 436 J K tran 5 1 2 m v 2 5 1 2 1 75 kg 21 3.33 m / s 2 2 5 416 J; 9-16 Chapter 9...
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