hw24 - Overton, Mays Homework 24 Due: Mar 30 2005, 4:00 am...

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Overton, Mays – Homework 24 – Due: Mar 30 2005, 4:00 am – Inst: Turner 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. The due time is Central time. 001 (part 1 oF 3) 10 points AcylindricalpulleywithamassoF M = 7 . 8kg and a radius oF r = 0 . 669 m is used to lower a bucket with a mass oF m = 3 . 3 kg into a well. The bucket starts From rest and Falls For 3 . 5 s. The acceleration oF gravity is 9 . 8 m / s 2 . r M m What is the linear acceleration oF the Falling bucket? Correct answer: 4 . 49167 m / s 2 . Explanation: The disk has moment oF inertia, I = 1 2 M r 2 . Let T be the tension in the cord and let α be the angular acceleration oF the wheel. Newton’s equation For the disk is T r = I α. (1) Newton’s equation For the mass m is mg - T = ma. (2) The linear acceleration a oF the mass is related to the angular acceleration α oF the wheel by theFormula, a = αr . ±romEq.(2)thetension is T = m ( g - a ). Putting this into Eq. (1) and solving For a gives ( mg - ma ) r = 1 2 M r 2 a r · 2 mg - 2 ma = M a 2 mg = ( M + 2 m ) a a = 2 mg M + 2 m . Or a = g 1 1 + M 2 m = ( 9 . 8 m / s 2 ) 1 1 + (7 . 8 kg) 2(3 . 3 kg) = 4 . 49167 m / s 2 . 002 (part 2 oF 3) 10 points How Far does it drop? Correct answer: 27 . 5115 m. Explanation: To fnd how Far it drops, we use y = v 0 t + 1 2 at 2 = 0 + 1 2 ( 4 . 49167 m / s 2 ) (3 . 5 s) 2 = 27 . 5115 m . 003 (part 3 oF 3) 10 points ±ind the angular acceleration oF the cylinder. Correct answer: 6 . 714 rad / s 2 . Explanation: The angular acceleration is α = a r = ( 4 . 49167 m / s 2 ) (0 . 669 m) = 6 . 714 rad / s 2 . 004 (part 1 oF 1) 10 points A solid sphere oF radius 44 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 4 . 4 m above its position when at the bottom oF the incline. The sphere is released and moves down the incline. The acceleration oF gravity is 9 . 8 m / s 2 . Hint: The moment oF inertia oF a sphere with respect to an axis through its center is 2 5 M R 2 .
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Overton, Mays – Homework 24 – Due: Mar 30 2005, 4:00 am – Inst: Turner 2 44 cm M μ 27 4 . 4m Calculate the speed of the sphere when it reaches the bottom of the incline in the case where it rolls without slipping. Correct answer: 7
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This note was uploaded on 03/22/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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hw24 - Overton, Mays Homework 24 Due: Mar 30 2005, 4:00 am...

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