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Both sides previous revision Previous revision Next revision | Previous revision Next revisionBoth sides next revision | ||
183_notes:examples:sliding_to_a_stop [2014/09/22 04:29] – pwirving | 183_notes:examples:sliding_to_a_stop [2014/09/22 04:35] – pwirving | ||
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$ y: \Delta p_y = (F_N - mg)\Delta t = 0 $ | $ y: \Delta p_y = (F_N - mg)\Delta t = 0 $ | ||
+ | |||
+ | Write equation of y direction in terms of $F_N$ to sub into x direction equation. | ||
$ (F_N - mg) \Delta t = 0 $ | $ (F_N - mg) \Delta t = 0 $ | ||
- | $ F_N \Delta t - mg \Delta t = 0 \,\, | + | Multiply out |
+ | |||
+ | $ F_N \Delta t - mg \Delta t = 0 | ||
+ | |||
+ | Make equal to each other | ||
+ | |||
+ | $ F_N \Delta t = mg \Delta t | ||
- | $ F_N \Delta t = mg \Delta t \, | + | Cancel |
- | $ F_N = mg | + | $ F_N = mg |
- | Combining these two equations and substituting in mg for F_N and writing $ p_x = mv_x $, we get the following equation: | + | Combining these two equations and substituting in mg for $F_N$ and writing $ p_x = \Delta(mv_x) $, we get the following equation: |
$ \Delta(mv_x) = -mg\Delta t $ | $ \Delta(mv_x) = -mg\Delta t $ |