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07_InstSolManual_PDF_Part7 - Work and Energy 7-7 Reect Fon...

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Reflect: is always the force applied to one end of the spring, thus we did not need to double the 15.0 N force. Consider a free-body diagram of a spring at rest; forces of equal magnitude and opposite direction are always applied to both ends of every section of the spring examined. 7.28. Set Up: Use and for parts (a) and (b). Solve: (a) The corresponding work on the spring is: (b) Now resulting in To stretch the spring from to requires of additional work. Reflect: Doubling x , doubles Also, since the total work to stretch the spring from 0.0 m to 2.0 m is the total work increases by a factor of four. 7.29. Set Up: The work done is the area under the graph of versus x between the initial and final positions. Solve: (a) The area between and is a right triangle. The work is thus calculated as: (b) Since the area between and is a trapezoid, the work is calculated as: Reflect: The force is larger for than for 5.0 cm and the work done in (b) is greater than that done in (a), even though the displacement of the end of the spring is 5.0 cm in each case.
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