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183_notes:examples:a_yo-yo [2014/10/31 16:22] – pwirving | 183_notes:examples:a_yo-yo [2014/11/06 02:40] – pwirving | ||
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=== Assumptions and Approximations === | === Assumptions and Approximations === | ||
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+ | You are able to maintain constant force when pulling up on yo-yo | ||
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+ | Assume no slipping of string around the axle. Spindle turns the same amount as string that has unravelled | ||
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+ | No wobble included | ||
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+ | String has no mass | ||
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=== Lacking === | === Lacking === | ||
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+ | Change in translational kinetic energy of the yo-yo | ||
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+ | Change in the rotational kinetic energy of the yo-yo | ||
=== Representations === | === Representations === | ||
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Surroundings: | Surroundings: | ||
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+ | {{course_planning: | ||
b: | b: | ||
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Surroundings: | Surroundings: | ||
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+ | {{course_planning: | ||
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+ | $\int_i^f \vec{F}_{net} \cdot d\vec{r}_{cm}$ | ||
=== Solution === | === Solution === | ||
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From the Energy Principle (point particle only has $K_{trans}$): | From the Energy Principle (point particle only has $K_{trans}$): | ||
- | $\DeltaK_{trans} = (F - mg)\Deltay_{CM}$ | + | $\Delta K_{trans} = (F - mg)\Delta y_{CM}$ |
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+ | $\Delta y_{CM} = -h (from\; digram)$ | ||
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+ | $\Delta K_{trans} = (F - mg)(-h) = (mg - F)h$ | ||
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+ | b: | ||
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+ | $\Delta E_{sys} = W_{hand} + W_{Earth}$ | ||
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+ | $\Delta K_{trans} + \Delta K_{rot} = Fd + (-mg)(-h)$ | ||
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+ | $\Delta K_{trans} = (mg - F)h$ (From part (a)) | ||
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+ | $(mg - F)h + \Delta K_{rot} = Fd + mgh$ | ||
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+ | $\Delta K_{rot} = F(d + h)$ | ||