# hw 9 sol - Patel(pnp223 homework 09 Turner(92160 This...

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Patel (pnp223) – homework 09 – Turner – (92160) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 oF 2) 10.0 points A light, inextensible cord passes over a light, Frictionless pulley with a radius oF 12 cm. It has a(n) 21 kg mass on the leFt and a(n) 4 kg mass on the right, both hanging Freely. Initially their center oF masses are a vertical distance 4 . 8 m apart. The acceleration oF gravity is 9 . 8 m / s 2 . 4 . 8 m 12 cm ω 21 kg 4 kg At what rate are the two masses accelerat- ing when they pass each other? Correct answer: 6 . 664 m / s 2 . Explanation: Let : R = 12 cm , m 1 = 4 kg , m 2 = 21 kg , h = 4 . 8 m , and v = ω R . Consider the Free body diagrams 21 kg 4 kg T m 2 g 1 a Since the larger mass will move down and the smaller mass up, we can take motion downward as positive For m 2 and motion up- ward as positive For m 1 . Apply Newton’s second law to m 1 and m 2 respectively and then combine the results: ±or mass 1: s F 1 : T - m 1 g = m 1 a (1) ±or mass 2: s F 2 : m 2 g - T = m 2 a (2) We can add Eqs. (1) and (2) above and obtain: m 2 g - m 1 g = m 1 a + m 2 a a = m 2 - m 1 m 1 + m 2 g = 21 kg - 4 kg 21 kg + 4 kg (9 . 8 m / s 2 ) = 6 . 664 m / s 2 . 002 (part 2 oF 2) 10.0 points What is the tension in the cord when they pass each other? Correct answer: 65 . 856 N. Explanation: T = m 1 ( g + a ) = (4 kg) (9 . 8 m / s 2 + 6 . 664 m / s 2 ) = 65 . 856 N .

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hw 9 sol - Patel(pnp223 homework 09 Turner(92160 This...

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