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183_notes:motionpredict [2014/07/08 12:39] – created caballero | 183_notes:motionpredict [2021/02/04 23:25] (current) – [Predicting the Future Momentum] stumptyl | ||
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+ | Section 2.3 in Matter and Interactions (4th edition) | ||
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===== Applying the Momentum Principle ===== | ===== Applying the Momentum Principle ===== | ||
- | Your job in mechanics is to be able to predict or explain motion. Previously, you read about the [[: | + | Your primary |
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+ | But, a system doesn' | ||
+ | ==== Predicting the Future Momentum ==== | ||
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+ | [[183_notes: | ||
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+ | $$\Delta \vec{p} = \vec{p}_f - \vec{p}_i = \vec{F}_{net} \Delta t$$ | ||
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+ | which can be rewritten to predict the system' | ||
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+ | $$\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$$ | ||
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+ | It is critical that the time step over which we are doing the prediction be small enough such that the [[183_notes: | ||
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+ | In later notes, you will learn about the [[183_notes: | ||
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+ | \\ | ||
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+ | === Separation of Components === | ||
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+ | The Update Form of the Momentum Princple, like the Momentum Principle itself, is a vector principle. And thus each component of the momentum vector can be predicted, | ||
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+ | $$p_{fx} = p_{ix} + F_{net,x} \Delta t$$ | ||
+ | $$p_{fy} = p_{iy} + F_{net,y} \Delta t$$ | ||
+ | $$p_{fz} = p_{iz} + F_{net,z} \Delta t$$ | ||
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+ | This might seem trivial, but there is a critical implication. If the force in any direction is zero, then the momentum, and thus the velocity, does not change in that direction. | ||
+ | ===== Examples ===== | ||
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+ | [[: |