=moda}[Momentum and External Force] plus [Mechanical Energy and Non-Conservative Work].
{note}Note that the rule we have derived above relies on the fact that the kinetic energy remains constant during the collision. For this reason, we have stated that we are using the mechanical energy model, though it will not be explicitly used in the solution. {note}{cloak}
{toggle-cloak:id=appa} *Approach:*
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{toggle-cloak:id=diaga} {color:red}{*}Diagrammatic Representation{*}{color}
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We begin with a picture. Since the initial direction of motion of the cue ball is not specified, we arbitrarily assign it to move along the x-axis prior to the collision. We also arbitrarily assign it positive x\- and y-velocity components after the collision.
|| Before Collision || After Collision ||
| !pool1.jpg! | !pool2.jpg! |
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{toggle-cloak:id=matha} {color:red}{*}Mathematical Representation{*}{color}
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Rather than implementing the elastic collision constraint of constant mechanical energy in the usual way, we will use the _right angle rule_ described above. Using that rule plus conservation of y-momentum, we know that the five ball will have a final velocity directed at 60° below the positive x-axis in our coordinates. With this information in hand, we can simply write the equations of momentum conservation for our system. {note}Recall that we are assuming external impulses are negligible compared to the internal impulse of the collision. {note}
{latex}\begin{large}\[ p^{cue}_{x,i} + p^{five}_{x,i} = p^{cue}_{x,f} + p^{five}_{x,f}\]
\[ p^{cue}_{y,f} + p^{five}_{y,f} = p^{cue}_{y,f} + p^{five}_{y,f}\]\end{large}{latex}
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