07_InstSolManual_PDF_Part13 - Work and Energy 7-13 7.60 Set...

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7.60. Set Up: Applying with the change in mechanical energy is simply the differ- ence between the initial and final elastic potential energy of the stretched spring: Also define the initial position as the point of release and the final position as the lowest position after five complete cycles. Figure 7.60 Solve: (a) (b) The percentage lost is Reflect: Note that the spring, in its equilibrium position, is stretched by the weight of the hanging mass. Conse- quently, an alternative solution can be developed that explicitly incorporates gravitational potential energy. Let d be the distance the spring is stretched at equilibrium due to the weight of the object. Define a new reference point; let where the mass is 0.130 m below the equilibrium point. At this point, the spring is stretched The total potential energy is therefore: Then when the mass is 0.100 m below the equilibrium position, and the spring is stretched The total energy is then: The change in mechanical energy is thus
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