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OMPhQuiz_08_p67-75 - chapter 8 Conservation of Energy...

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Potential energy of a conservative force (Section 8.1) 1. Mass–spring system • Context in the textbook: Before Example 1 in Section 8.1. 2. Conservative force: Path integrals • Context in the textbook: Section 2.1 considers conservative force in one dimension. This example verifies the path-independent property of a conservative force in two dimensions. It may be used at the end of Section 8.1. Potential energy due to gravity plus spring force (Section 8.2) The following exercises may be used before Example 4 in Section 8.2: 3. Spring toy: Maximum height 4. Spring toy: Special points of U 5. Releasing a compressed spring 6. Spring–pulley system with friction Power (Section 8.5) Two exercises before Example 9 of Section 8.5: 7. Climbing up a hill 8. Maximum speed on a flat road Contents PhysiQuiz 67 chapter 8 Conservation of Energy
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Consider a mass–spring system. The spring force asserted on the block is given by Hooke’s Law: F spring k x . Denote the potential energy of the spring by U ( x ). At x 0 the spring is relaxed: U (0) 0. U ( x ) is the work done by the stretching force in going from x O to x x , which is given by which of the following? A B C D kx 2 kx 2 x 0 kxdx x 0 kxdx Extra: Release the mass from rest at x x . Determine the kinetic energy at x 0 in terms of x , k , m . Hint: Not all the quantities here need to be used. Explanation: When the spring is pulled to the right, both the pulling force and the displacement are in the same direction. The pulling force is opposite to the spring force. The latter obeys Hooke’s Law: F pull F spring k x . So work done in stretching the spring from x O to x x is given by Answer C.
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