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HW 10-solutions

# HW 10-solutions - kuruvila(lk5992 HW 10 opyrchal(11113 This...

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kuruvila (lk5992) – HW 10 – opyrchal – (11113) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A 4 . 1 kg mass is connected by a light cord to a 2 . 4 kg mass on a smooth surface as shown. The pulley rotates about a frictionless axle and has a moment of inertia of 0 . 59 kg · m 2 and a radius of 0 . 30 m. 4 . 1kg 2 . 4kg F 1 F 2 R What is the acceleration of the two masses? The acceleration of gravity is 9 . 81 m / s 2 . As- sume that the cord does not slip on the pulley. Correct answer: 3 . 08076 m / s 2 . Explanation: F 2 a F 1 m 1 g a Let : I = 0 . 59 kg · m 2 , R = 0 . 30 m , m 1 = 4 . 1 kg , m 2 = 2 . 4 kg , and g = 9 . 81 m / s 2 . Applying Newton’s second law to m 1 and m 2 , m 1 a = m 1 g - F 1 m 2 a = F 2 F net = F 1 - F 2 = ( m 1 g - m 1 a ) - m 2 a = m 1 g - ( m 1 + m 2 ) a a = αR , so applying Newton’s second law to the pulley, F net R = I α = I parenleftBig a R parenrightBig I a = F net R 2 I a = [ m 1 g - ( m 1 + m 2 ) a ] R 2 a = m 1 g R 2 I + ( m 1 + m 2 ) R 2 = (4 . 1kg)(9 . 81m / s 2 )(0 . 3m) 2 0 . 59kg · m 2 +(4 . 1kg+2 . 4kg)(0 . 3m) 2 = 3 . 08076 m / s 2 . 002 (part 2 of 3) 10.0 points What is the magnitude of the force F 1 ? Correct answer: 27 . 5899 N. Explanation: F 1 = m 1 g - m 1 a = (4 . 1kg)(9 . 81m / s 2 - 3 . 08076 m / s 2 ) = 27 . 5899 N . 003 (part 3 of 3) 10.0 points What is the magnitude of the force F 2 ? Correct answer: 7 . 39382 N. Explanation: F 2 = m 2 a = (2 . 4kg)(3 . 08076 m / s 2 ) = 7 . 39382 N . 004 10.0 points A uniform 1 kg rod with length 10 m has a frictionless pivot at one end. The rod is released from rest at an angle of 25 beneath the horizontal.

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kuruvila (lk5992) – HW 10 – opyrchal – (11113) 2 5 m 10 m 1 kg 25 What is the angular acceleration of the rod immediately after it is released? The moment of inertia of a rod about the center of mass is 1 12 m L 2 , where m is the mass of the rod and L is the length of the rod. The moment
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