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I apply F = m · a,
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that's it;
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and I'm going to get everything by applying F = ma,
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to this guy.
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So, here is that mass.
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The tension on the rope can only be along the rope.
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The rope is not a rigid object.
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It cannot exert a force perpendicular to itself.
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It can only pull it along each direction.
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That's the tension on the rope.
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There is m · g, and that's it.
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Under these things it's going to obey F = m · a.