# cw16 - center is 2 5 M R 2 Correct answer 6 58787 m s...

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patel (kp9583) – CW16 – Mackie – (20211) 1 This print-out should have 2 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 oF 2) 10.0 points A solid sphere oF radius 20 cm is positioned at the top oF an incline that makes 27 angle with the horizontal. This initial position oF the sphere is a vertical distance 3 . 1 m above its position when at the bottom oF the incline. The sphere is released and moves down the incline. 20 cm M μ 27 3 . 1 m Calculate the speed oF the sphere when it reaches the bottom oF the incline iF it rolls without slipping. The acceleration oF gravity is 9 . 8 m / s 2 . The moment oF inertia oF a sphere with respect to an axis through its
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Unformatted text preview: center is 2 5 M R 2 . Correct answer: 6 . 58787 m / s. Explanation: ±rom conservation oF energy we have U i = K trans,f + K rot,f M g h = 1 2 M v 2 + 1 2 I ω 2 = 1 2 M v 2 + 1 2 p 2 5 M R 2 P p v 2 R 2 P = 7 10 M v 2 v 1 = r 10 7 g h = r 10 7 (9 . 8 m / s 2 ) (3 . 1 m) = 6 . 58787 m / s . 002 (part 2 oF 2) 10.0 points Calculate the speed oF the sphere iF it reaches the bottom oF the incline by slipping Friction-lessly without rolling. Correct answer: 7 . 79487 m / s. Explanation: ±rom conservation oF energy we have U i = K trans,f M g h = 1 2 M v 2 v 2 = R 2 g h = ± 2 (9 . 8 m / s 2 ) (3 . 1 m) = 7 . 79487 m / s . keywords:...
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