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| 183_notes:motionpredict [2015/09/02 17:36] – [Applying the Momentum Principle] 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 ===== |
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| **Your primary job in mechanics is to be able to predict or explain the motion of systems.** Previously, you read about the [[:183_notes:displacement_and_velocity#what_s_so_special_about_constant_velocity_motion|position update formula]], which allows you to predict the future location of a system given information about its current location and its velocity (or [[183_notes:momentum|momentum]]). | Your primary job in mechanics is to be able to predict or explain the motion of systems. Previously, you read about the [[:183_notes:displacement_and_velocity#what_s_so_special_about_constant_velocity_motion|position update formula]], which allows you to predict the future location of a system given information about its current location and its velocity (or [[183_notes:momentum|momentum]]). |
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| But, a system doesn't need to move with [[183_notes:displacement_and_velocity|constant velocity]] (or momentum); [[183_notes:momentum_principle|it can change its momentum (or velocity) as a result of interacting with it surroundings]]. In these notes, you will read how to predict the future motion of an system that interacts with its surroundings. | But, a system doesn't need to move with [[183_notes:displacement_and_velocity|constant velocity]] (or momentum); [[183_notes:momentum_principle|it can change its momentum (or velocity) as a result of interacting with it surroundings]]. In these notes, you will read how to predict the future motion of an system that interacts with its surroundings. |
| $$\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$$ | $$\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$$ |
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| It is critical that the time step over which we are doing the prediction be small enough such that the net force can be considered a constant vector. | It is critical that the time step over which we are doing the prediction be small enough such that the [[183_notes:constantf|net force can be considered a constant vector]]. |
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| In later notes, you will learn about the [[183_notes:constantf|special case of constant force motion]] -- in that case, the length of the time interval will not matter. But for all other cases you will work with (e.g., [[183_notes:springmotion|spring-like interactions]]), the length of the time interval absolutely matters. | In later notes, you will learn about the [[183_notes:constantf|special case of constant force motion]] -- in that case, the length of the time interval will not matter. But for all other cases you will work with (e.g., [[183_notes:gravitation|gravitational interactions]], [[183_notes:springmotion|spring-like interactions]]), the length of the time interval absolutely matters. |
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| === Separation of Components === | === Separation of Components === |
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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. | 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. |
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| ===== Examples ===== | ===== Examples ===== |
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| [[:183_notes:examples:finalP|Predicting the final momentum & velocity using the Momentum Principle]] | [[:183_notes:examples:finalP|Predicting the final momentum & velocity using the Momentum Principle]] |