hw8_solns - Answer Key Homework 8 David McIntyre 45123 This...

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Answer, Key – Homework 8 – David McIntyre – 45123 – May 10, 2004 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before making your selection. The due time is Central time. Chapter 8 problems. 001 (part 1 of 2) 5 points Note: A bungee cord can stretch, but it is never compressed. When the distance be- tween the two ends of the cord is less than its unstretched length L 0 , the cord folds and its tension is zero. For simplicity, neglect the cord’s own weight and inertia as well as the air drag on the ball and the cord. A bungee cord has length L 0 = 30 m when unstretched; when it’s stretched to L > L 0 , the cord’s tension obeys Hooke’s law with “spring” constant 45 N / m. To test the cord’s reliability, one end is tied to a high bridge of height 83 m above the surface of a river) and the other end is tied to a steel ball of mass 74 kg. The ball is dropped off the bridge with zero initial speed. Fortunately, the cord works and the ball stops in the air a few meters before it hits the water — and then the cord pulls it back up. The acceleration of gravity is 9 . 8 m / s 2 . Calculate the ball’s height above the wa- ter’s surface at this lowest point of its trajec- tory. Correct answer: 1 . 86096 m. Explanation: In the absence of air drag and other resistive forces, there are only two forces acting on the ball – the gravity force m~g and the cord’s tension T , both conservative. Therefore, the system (the ball plus the cord) has conserved mechanical energy E mech = K
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