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Unformatted text preview: Johnson, Matthew Quiz 3 Due: Apr 6 2005, 10:00 pm Inst: Kleinman 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points Consider the problem of the solid sphere rolling down an incline without slipping. The incline has an angle . The spheres length up the incline is , and its height is h . At the beginning, the sphere rests on the very top of the incline. The sphere has mass M and radius R . 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 . Choose the instantaneous axis through the contact point P as the axis of origin for the torque equation. R M h The acceleration of the center of mass is 1. a = 3 7 g cos . 2. a = 3 5 g sin . 3. a = 2 7 g sin . 4. a = 3 5 g cos . 5. a = 2 7 g cos . 6. a = 3 7 g sin . 7. a = 5 7 g sin . correct 8. a = 5 7 g cos . Explanation: Basic Concepts: X ~ F = m ~a X ~ = I ~. mg cos N f mg sin With the origin at the point of contact, X : M g R sin = I , (1) where I is obtained using the parallelaxis theorem I = 2 5 M R 2 + M R 2 = 7 5 M R 2 . (2) If the sphere rolls without slipping, = a R . (3) Now substituting I from Eq. 2 and from Eq. 3 into Eq. 1, we have M g R sin = 7 5 M R 2 a R , so a = 5 7 g sin . 002 (part 2 of 2) 10 points The minimum coefficient of friction such that the sphere rolls without slipping is 1. = 3 7 tan . 2. = 2 7 sin . 3. = 2 7 tan . correct 4. = 5 7 cos . 5. = 3 7 sin . Johnson, Matthew Quiz 3 Due: Apr 6 2005, 10:00 pm Inst: Kleinman 2 6. = 5 7 tan . 7. = 3 5 cos . 8. = 2 7 cos . Explanation: The net force along the direction of the incline is X F = M g sin  f = M 5 7 g sin , where f = N = M g cos . Then M g sin  M g cos = M 5 7 g sin , so = 2 7 tan . 003 (part 1 of 1) 10 points A 27 kg mass and a 14 kg mass are suspended by a pulley that has a radius of 12 cm and a mass of 7 kg. The cord has a negligible mass and causes the pulley to rotate without slipping. The pulley rotates without friction. The masses start from rest 2 . 8 m apart. Treat the pulley as a uniform disk. The acceleration of gravity is 9 . 8 m / s 2 . 2 . 8 m 12 cm 7 kg 27 kg 14 kg Determine the speeds of the two masses as they pass each other. Correct answer: 2 . 83129 m / s. Explanation: Let : M = 7 kg , R = 12 cm , m 1 = 27 kg , m 2 = 14 kg , h = 2 . 8 m , v = R, I = 1 2 M R 2 , and K disk = 1 2 I 2 = 1 4 M v 2 ....
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This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner

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