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Unformatted text preview: kim (jkk547) HW05 Tsoi (58020) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points An elevator of mass m is initially at rest on the first floor of a building. It moves upward, and passes the second and third floors with a constant velocity, and finally stops at the fourth floor. The distance between adjacent floors is h . What is the net work done on the elevator during the entire trip, from the first floor to the fourth floor? 1. None of these. 2. W =- 3 mg h 3. W =- 4 mg h 4. W = 3 mg h 5. W = 0 correct 6. W = 4 mg h Explanation: The key to answering this question is find- ing the net work done on the elevator. The work-energy theorem states that the net work, summationdisplay W , done on an object is related to the change in kinetic energy of the object, K , by summationdisplay W = K . The elevator starts at rest at the first floor, thus K i = 0. The elevator ends at rest at the fourth floor and so K f = 0, and so K is zero! Another way to think about this is that the work done on the elevator by the elevator motor is the exact negative of the work done on the elevator by gravity. Adding these two together to find the net work done on the elevator gives zero! 002 (part 1 of 2) 10.0 points Consider a bungee cord of unstretched length L = 31 m. When the cord is stretched to L &gt; L it behaves like a spring and obeys Hookes law with the spring constant k = 56 N / m. However, unlike a spring, the cord folds instead of becoming compressed when the distance between its ends is less than the unstretched length: For L &lt; L the cord has zero tension and zero elastic energy. To test the cords reliability, one end is tied to a high bridge (height H = 141 m above the surface of a river) and the other end is tied to a steel ball of weight mg = 140 kg 9 . 8 m / s 2 . The ball is dropped off the bridge with zero initial speed. Fortunately, the cord works and the ball stops in the air before it hits the water and then the cord pulls it back up. Calculate the balls height h bot at the lowest point of its trajectory. For simplicity, neglects the cords own weight and inertia as well as the air drag on the ball and the cord. Correct answer: 39 . 4647 m. Explanation: In the absence of air drag and other resis- tive forces, there are only two forces acting on the ball the gravity force mvectorg and the cords tension T , which are both conserva- tive. Therefore, the system (the ball plus the cord) has conserved mechanical energy E mech = K + U grav + U cord = const , where K = mv 2 2 , U grav = mg h, U cord = braceleftbigg 1 2 k ( L- L ) 2 for L &gt; L , for L &lt; L ....
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- Fall '09