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2-8 (9) - Create assignment 00223 Homework 8 Oct 24 at 7:27...

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Create assignment, 00223, Homework 8, Oct 24 at 7:27 pm 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Cable Over a Pulley 10:07, trigonometry, numeric, > 1 min, nor- mal. 001 A cable passes over a pulley. Because the cable grips the pulley and the pulley has non- zero mass, the tension in the cable is not the same on opposite sides of the pulley. The force on one side is 120 N, and the force on the other side is 100 N. Assuming that the pulley is a uniform disk of mass 2 . 1 kg and ra- dius 0 . 81 m, determine the magnitude of its angular acceleration. Correct answer: 23 . 5156 rad / s 2 . Explanation: The resultant torque is given by (120 N)(0 . 81 m) - (100 N)(0 . 81 m) = 16 . 2 N m The moment of inertia is: I = 1 2 m r 2 = 1 2 (2 . 1 kg)(0 . 81 m) 2 = 0 . 688905 kg m 2 . Then, τ = I α gives α = τ I = 16 . 2 N m 0 . 688905 kg m 2 = 23 . 5156 rad / s 2 . Complex Atwood Machine 10:07, trigonometry, numeric, > 1 min, nor- mal. 002 An Atwood machine is constructed using two wheels (with the masses concentrated at the rims). The left wheel has a mass of 2 kg and radius 22 cm. The right wheel has a mass of 2 . 5 kg and radius 30 cm. The acceleration of gravity is 9 . 8 m / s 2 . 3 m 1 m 4 m 2 m The hanging mass on the left is 1 . 5 kg and on the right 1 kg. What is the acceleration of the system? Correct answer: 0 . 7 m / s 2 . Explanation: Basic Concepts: The net acceleration a = is in the direction of the heavier mass m 1 . Each pulley’s mass is concentrated on the rim, so I = m pulley r 2 3 m 1 1 m 4 m 2 2 2 m T 1 T 3 T a a r r For each pulley, τ net = = mr 2 a r · = mra so that for the leftmost pulley, T 1 r 1 - T 2 r 1 = m 1 r 1 a m 1 a = T 1 - T 2 (1) and for the rightmost pulley, T 2 r 2 - T 3 r 2 = m 2 r 2
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