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When you say the rope is under tension
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being pulled from both sides by a certain force,
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the tension is not 0 just because this T and that T cancel.
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It's true the net force is 0,
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but it doesn't mean you can ignore it.
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Suppose you are being pulled by my favorite animals --
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the elephants -- from both sides by equal force.
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You don't find any consolation
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in the fact that these forces add up to 0.
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You feel the pain.
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That pain is what--This gentleman doesn't agree.
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One of you guys nodding your head.