p201f04-homework09-sol

p201f04-homework09-sol - Version One Homework 9 Heinz 81204...

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Unformatted text preview: Version One Homework 9 Heinz 81204 Oct 25, 2004 1 This print-out should have 10 questions. Multiple-choice 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 free-body 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 free-body 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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p201f04-homework09-sol - Version One Homework 9 Heinz 81204...

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