07_InstSolManual_PDF_Part17

07_InstSolManual_PDF_Part17 - Work and Energy 7-17 7.77 Set...

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7.77. Set Up: In part (a), the conservation of energy results in or Similarly, the maximum speed may be calculated in part (b) as Solve: (a) (b) Reflect: The maximum permissible speed calculated in (b) is equivalent to roughly A practical design for a parking garage should be sufficient for speeds up to 7.78. Set Up: Applying in part (a) gives or In part (b), use: Solve: (a) (b) Reflect: Mechanical energy was converted to thermal energy by the negative work done by the air drag force. 7.79. Set Up: Construct a free-body diagram as shown to assess the contributing forces with respect to the path of motion. Note that for circular motion, the velocity vector is always tangent to the circle. Figure 7.79 Solve: (a) (i) The tension force in the string is always perpendicular to the displacement and thus does no work. (a) (ii) Considering a complete cycle, The work of the gravitational force is (b) (i) The tension does no work. (b) (ii) Considering a semi-circular portion of the path, and the work of gravity becomes: Reflect: Gravity does negative work as the ball moves upward and positive work as the ball moves downward. For
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