If it is a tug of war with one person on each side, the rope is only having to deal with the stress of the weight of two people pulling on it. One in either direction. Lets say each person is pulling with 50 lbs of force. The rope has 100lbs of force stored in it. If it breaks, the middle of the rope comes flying back at the participants with their 50lbs of force, a manageable amount.
But in a large game of tug of war, say one hundred people on each side, the rope is dealing with the force of two hundred people. One hundred on each side. Each person still pulls the same, lets say 50lbs per person. The Rope has a collective 10,000lbs of force stored in it. And if it snaps, now each side has its 5000lbs of force that is flying back at them. That is like getting hit by a car.
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