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Unformatted text preview: Version One Homework 9 Heinz 81204 Oct 25, 2004 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. Two Blocks 02 10:07, calculus, numeric, > 1 min, normal. 001 (part 1 of 3) 4 points The blocks shown in figure are connected by an inextensible string of negligible mass. The string passes over a frictionless pulley without slipping on the rim of the pulley. The acceleration of gravity is 9 . 8 m / s 2 . The block on the frictionless incline is mov ing with a constant acceleration up the in cline. 20 kg T 1 R = 0 . 25 m M 6 . 3 k g = T 2 6 m / s 2 30 Determine the tension T 1 in the vertical part of the string. Correct answer: 76 N. Explanation: Let : M = mass of pulley , R = 0 . 25 m a = 6 m / s 2 = 30 , m 1 = 20 kg , m 2 = 6 . 3 kg , g = 9 . 8 m / s 2 , = 0 , and W = m 1 g = 61 . 74 N . T 2 W k N W W m a W k From a freebody diagram (not shown) for the hanging mass m 1 = 20 kg , we see m 1 g T 1 = m 1 a , and we obtain T 1 = m 1 ( g a ) = (20 kg)(9 . 8 m / s 2 6 m / s 2 ) = 76 N . 002 (part 2 of 3) 3 points Determine the tension T 2 in the string parallel to the incline plane. Correct answer: 68 . 67 N. Explanation: From the freebody diagram (shown above) for the mass m 2 = 6 . 3 kg , we can obtain the other tension T 2 m 2 g sin = m 2 a so that T 2 = m 2 a + m 2 g sin or T 2 = m 2 ( a + g sin ) = (6 . 3 kg) h (6 m / s 2 ) + (9 . 8 m / s 2 )sin(30 ) i = 68 . 67 N . 003 (part 3 of 3) 3 points Assume: The pulley has uniform density and is shaped like a narrow cylindrical disk. Find the mass M of the pulley. Correct answer: 2 . 44333 kg. Explanation: Version One Homework 9 Heinz 81204 Oct 25, 2004 2 From the torque equation, applied to the pulley ( T 1 T 2 ) R = I = I a R we obtain I = [ T 1 T 2 ] R 2 a = [(76 N) (68 . 67 N)](0 . 25 m) 2 (6 m / s 2 ) = 0 . 0763542 kg m 2 . Since I disk = 1 2 M R 2 , we have M = 2 I R 2 = 2(0 . 0763542 kg m 2 ) (0 . 25 m) 2 = 2 . 44333 kg ....
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