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**Unformatted text preview: **yoon (jy4326) – HW08 – markert – (58840) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Two spheres look identical and have the same mass. One is hollow and the other is solid. Which method would determine which is which? 1. Drop them from the same height. 2. Weigh them on a scale. 3. Roll them down an incline. correct 4. None of these Explanation: From conservation of mechanical energy, U = K trans + K rot mg h = 1 2 mv 2 f + 1 2 I ω 2 f I hollow = 2 3 mr 2 and I solid = 2 5 mr 2 Since the potential energy for each is the same at the top of the incline, the sphere with the greater moment of inertia would have the smaller speed at the bottom of the incline, and would lose the race. keywords: 002 (part 1 of 3) 10.0 points A 13 kg mass is attached to a cord that is wrapped around a wheel with a radius of 10 . 3 cm, as shown. The acceleration of the mass down the frictionless incline is measured to be 2 . 6 m / s 2 . Assume the axle of the wheel to be frictionless. 10 . 3 cm 1 3 k g 2 . 6 m / s 2 38 ◦ Find the force in the rope. The acceleration of gravity is 9 . 81 m / s 2 . Correct answer: 44 . 7153 N. Explanation: Let : m = 13 kg , a = 2 . 6 m / s 2 , θ = 38 . ◦ , and g = 9 . 81 m / s 2 . Parallel to the incline, F net = ma F = mg sin θ- ma = (13 kg)(9 . 81 m / s 2 )(sin38 ◦ )- (13 kg)(2 . 6 m / s 2 ) = 44 . 7153 N . 003 (part 2 of 3) 10.0 points Find the moment of inertia of the wheel. Correct answer: 0 . 182456 kg · m 2 . Explanation: Let : r = 10 . 3 cm = 0 . 103 m . a = r α and the torque is τ = I α F r = I parenleftBig a r parenrightBig I = F r 2 a = (44 . 7153 N)(0 . 103 m) 2 2 . 6 m / s 2 = . 182456 kg · m 2 ....

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