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Force balance in tug of war


The tug of war is a traditional game used to train seafaring peoples, settle inter-tribal debts, and celebrate bountiful harvests. At the start of the game, the players of each team grab hold of a rope—that starts evenly distributed across their midpoint—and try to pull the other team over the midpoint. Though its luster has been diminished over the years, the game remains one of the few examples of force balance to cut across cultural divides.

In this set, we'll learn about the crucial principles you need to win the tug of war, or determine if you should graciously bow out. In doing so, we'll apply several key concepts of mechanics including force balance, Newton's laws, and friction forces.

We begin by establishing a basic result about rope tension, and move on to understand how to swing the advantage to one side or the other.

A man ties one end of a rope to a tree and pulls on the other end from his waist. The rope tightens, pulling on both the man and the tree.

On which object, the tree or the man, will the rope exert greater force?

In the previous question the string pulls the man toward the tree. What stops him from being dragged toward the tree?

Suppose two people, standing in place, are holding a rope firmly and that it doesn't slip in their hands.

Which of the two people can apply a greater force on the rope?

In the previous case, which person will win the tug of war?

Suppose the man is standing straight up and down when he starts to pull on the rope. What will happen if he applies an extreme force on the rope?

In a tug of war, why are the athletes advised to keep their bodies as low as possible as shown below?

In this problem set, we learned about the physics that underlies the tug of war. In particular, we learned two surprising facts

  • the friction with the ground plays a crucial role in determining the victor.
  • two people of differing strength will apply identical forces to the rope, as long as they hold on.

With these lessons in the rearview mirror, you should be well prepared to win your next match, or at least have solid grounds on which to withdraw from the contest.


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