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The breaking strength of the rope has to be stated in terms of the "tension" in the rope, and that has to be the 800N quoted here. If the ends of the rope are pulled in oppposite directions with a force of 500N on each end, then the tension in the rope at any point is 1000N, and yes, it will break.

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Q: A certain rope will break when a force of more than 800 N is exerted on it two men pull on the rope in oppositedirection with a force of 500 N eachWill the rope break?
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