183_notes:motionpredict

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183_notes:motionpredict [2014/07/08 12:56] – caballero183_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)
 +
 ===== Applying the Momentum Principle ===== ===== Applying the Momentum Principle =====
  
-Your 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 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]]). 
- +
-But, a system doesn't need to move with 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 learn 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.
 ==== Predicting the Future Momentum ==== ==== Predicting the Future Momentum ====
  
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 $$\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$$ $$\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$$
  
-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]].  
 + 
 +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.
  
-In later notes, you will learn about the 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, the length of the time interval absolutely matters.+\\
  
 === Separation of Components === === Separation of Components ===
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 $$p_{fz} = p_{iz} + F_{net,z} \Delta t$$ $$p_{fz} = p_{iz} + F_{net,z} \Delta t$$
  
 +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 =====
  
 +[[:183_notes:examples:finalP|Predicting the final momentum & velocity using the Momentum Principle]]
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