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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.
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So, what I do with this tension is
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I trade this guy for two forces.
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This is T.
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If that angle is θ; let me see,
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that angle is θ; so this is T · sin(θ),
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and this is T · cos(θ).