Question

Consider a tug-of-war between two people who pull in opposite directions on the ends of a rope. By Newton’s third law, the force that A exerts on B is just as great as the force that B exerts on A. So what determines who wins? (Hint: Draw a free-body diagram showing all the forces that act on each person.)

Short answer

Newton’s Third cannot be applied because this opposing force is not action-reaction pair. If one person’s pulling force is greater than the other, then the direction of the non-zero net force will decide the winner.

Step-by-step solution

Tension in the string

When a pulling force is exerted on the ends of the string or rope, the force is transmitted axially throughout the length. This pulling force in the rope/string is called tension.

The given case

Tension is non-negative in nature. The tension is zero only when the rope is slack. The tension in the rope is equal to the force on the ends of the segment. Suppose a force of 100 N pulls the rope on both ends in opposite directions, then the tension is 100 N. Now, if one end is pulled with 200 N, the rope will accelerate towards this end with a net force of 100 N. But the tension in the rope will still be 100 N. Extra 100 N is used in accelerating the rope.

Here Newton’s Third cannot be applied because this opposing force is not action-reaction pair. The force between these people is transmitted through the rope. The tension in the rope is equal to the force on the ends of the segment. If one person’s pulling force is greater than the other, then the direction of the non-zero net force will decide the winner.

Thus, Newton’s Third cannot be applied because this opposing force is not action-reaction pair. If one person’s pulling force is greater than the other, then the direction of the non-zero net force will decide the winner.