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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.
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When can I use Conservation of Mechanical Energy?
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When can I not?
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A bullet driving into a chunk of wood,
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you better know you cannot use Conservation of Kinetic Energy.
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But once the combination is going up,
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trading kinetic for potential, you can.