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So, let me summarize this last result.
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In every collision,
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no matter what, momentum is conserved;
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the energy may or may not be.
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And if I give you a problem like this
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where in between there's some funny business going on
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which is not energy conserving,
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don't use energy conservation from start to finish.
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Use momentum conservation,
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find the speed of the composite object.
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This is what you've got to understand in your head.
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It's not this equation.