# hw27 - This print-out should have 12 questions....

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Unformatted text preview: This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A solid sphere of radius 25 cm is positioned at the top of an incline that makes 23 ◦ angle with the horizontal. This initial position of the sphere is a vertical distance 2 . 9 m above its position when at the bottom of the incline. The sphere is released and moves down the incline. 25 cm M μ ℓ 23 ◦ 2 . 9m 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 center is 2 5 M R 2 . Correct answer: 6 . 37181 m / s. Explanation: From 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 parenleftbigg 2 5 M R 2 parenrightbigg parenleftbigg v 2 R 2 parenrightbigg = 7 10 M v 2 v 1 = radicalbigg 10 7 g h = radicalbigg 10 7 (9 . 8 m / s 2 ) (2 . 9 m) = 6 . 37181 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 . 53923 m / s. Explanation: From conservation of energy we have U i = K trans,f M g h = 1 2 M v 2 v 2 = radicalbig 2 g h = radicalBig 2 (9 . 8 m / s 2 ) (2 . 9 m) = 7 . 53923 m / s . keywords: 003 10.0 points A solid sphere has a radius of 0 . 46 m and a mass of 130 kg. How much work is required to get the sphere rolling with an angular speed of 12 rad / s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping. Correct answer: 2772 . 81 J. Explanation: Let : r = 0 . 46 m , m = 130 kg , and ω f = 12 rad / s . I = 2 5 mr 2 and v = r ω , so the work is W = Δ K = 1 2 mv 2 + 1 2 I ω 2 = 1 2 m ( r ω ) 2 + 1 2 parenleftbigg 2 5 mr 2 parenrightbigg ω 2 = 7 10 mr 2 ω 2 = 7 10 (130 kg) (0 . 46 m) 2 (12 rad / s) 2 = 2772 . 81 J . homework 27 – Turner – (58185) 1 hinojosa (jlh3938) – homework 27 – Turner – (58185) 2 keywords: 004 10.0 points A solid steel sphere of density 7 . 83 g / cm 3 and mass 0 . 7 kg spin on an axis through its center with a period of 3 . 7 s....
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## This note was uploaded on 05/02/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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hw27 - This print-out should have 12 questions....

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