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Unformatted text preview: Bodet (ngb299) oldfinal 01 CC09 turner (57340) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine W (or fuel energy) required to launch a satellite of mass m at rest from a launching pad placed at the surface earth, to a circular orbit where the radius of the orbit is r = 3 R where R is the radius of the earth. Ignore the effect of the Earths rotation. The fuel energy required is 1. 5 GmM 6 R correct 2. 2 GmM R 3. 7 GmM 6 R 4. GmM R 5. GmM 6 R 6. 3 GmM 4 R 7. 3 GmM 2 R 8. GmM 4 R Explanation: The orbital satellite energies are E f =- GM m 2 r =- GM m 6 R E i =- GM m R . The fuel energy is W = E f- E i =- GM m 6 R-- GM m R = 1- 1 6 GmM R = 5 GmM 6 R . 002 10.0 points A pendulum consists of a very light sti ff rod with negligible mass of length L = 1 . 9 m hanging from a nearly frictionless axle, with a mass m = 0 . 5 kg at the end of the rod. Suppose you hit the stationary hanging mass so that it has an initial speed v i . What is the minimum initial speed in order that the pendulum go over the top ( = 180 )? (in units of m/s) L m s = L O Correct answer: 8 . 63 m / s. Explanation: Let : m = 0 . 5 kg , L = 1 . 9 m , and g = 9 . 8 m / s 2 . Energy principle leads K f + U f = K i + U i . For present problem, K f = 0, U f- U i = mg (2 L ), this leads to K i = U f- U i = mg (2 L ) mv 2 i 2 = mg (2 L ) v i = 4 g L = 4 (9 . 8 m / s 2 ) (1 . 9 m) = 8 . 63 m / s . 003 10.0 points Consider a electron-electron interaction sys- tem. Which figure given below represents the Bodet (ngb299) oldfinal 01 CC09 turner (57340) 2 system. In each figure K, U and K+U are rep- resented by the y-axis and the separation by x-axis. Choices: 1. A 2. C 3. D correct 4. B Explanation: Notice figure D contains all expected fea- tures of electron-electron interaction. Begin with some finite K at large r. As the two electrons approach each other, r decreases and K decreases. Eventually they stop at the distance of the closest approach, where K=0. K+U= constant. At K=0, the value of K+U line is determined by the U value there. U has the characteristic behavior of a sys- tem with a repulsive force, with U > throughout. As the separation gets closer and closer, the magnitude of U increases cor- respondingly. We reject the choices of figures A, B and, since each figure contains at least an error. Notice that in figure A, U < 0. But for electron-electron case, we must have U > 0. In figure B, K < 0. But K = mv 2 2 , which can never be negative. In figure C, as r approaches infinity K > K + U . This is again false. As r approaches infinity we should have instead, K+U ap- proaches K, since here U approaches 0....
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- Spring '08