Solve: Reflect: At the maximum compression the magnitude of the spring force is twice the weight of the object and the system is not in equilibrium. 7.54. Set Up: Use In part (a), setting we have the amount the spring will stretch. Also, since In part (b), where Solve: (a) (b) and x must be positive, so Reflect: In part (b) there is additional initial energy, so the spring is stretched more. 7.55. Set Up: Apply with and therefore, the lost mechanical energy is Solve: Reflect: Part of the initial mechanical energy is converted to thermal energy by the negative work done by friction. We did not use the stopping time in our solution. 7.56. Set Up: Apply with since the otter returns to the same height. Thus, Solve: Reflect: Part of the initial mechanical energy was converted to thermal energy by the negative work done by friction. 7.57. Set Up: Use with and Conservation of energy thus becomes: Solve: Reflect: In the absence of air resistance an object released from rest has a speed of after it has fallen
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