In which case is the rope more likely to break?

In assessing the likelihood of the rope breaking in each scenario, it's important to consider the forces exerted on the rope and how they differ between the two cases.

When two people engage in a tug-of-war, they apply tensile forces in opposite directions on the rope. The tension in the rope is essentially the sum of the forces exerted by both individuals. If both players pull with significant force, the cumulative effect can increase the likelihood of the rope reaching its tensile strength limit, potentially leading to a break.

In contrast, when two individuals pull the rope around a fixed pole, the situation alters slightly. The rope is still subjected to tension, but the fixed pole changes how this tension is distributed. The presence of the pole acts like a pivot point. The forces are still exerted in opposite directions; however, the interaction with the pole may result in a different distribution of forces in the rope.

The key aspect that makes both scenarios potentially lead to a rope breaking relies on the maximum force applied. In both cases, the overall forces acting on the rope can exceed its strength if the individuals exert strong enough pulls. Therefore, claiming that both cases are identical recognizes that the fundamental principle of tension and breakage risk does not fundamentally change based on the method of