Which Rope Sustains Greater Tension: Tree or Tug-of-War?

In summary, a rope was used in a tug-of-war between two teams of five people each. Despite both teams being equally strong, neither team won. An identical rope was then tied to a tree and the same ten people pulled just as hard on the loose end as they did in the contest. The question is, which rope sustains the greater tension - the one tied to the tree or the one in the tug-of-war? The answer is actually (b), the rope in the tug-of-war, as the tension is determined by the magnitude of force applied, not the number of people. This is further explained by considering a scenario where weights are used instead of people, with the same conclusion that the rope in the tug-of-war sust
  • #1
Maxo
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A rope is used in a tug-of-war between two teams of five people each. Both teams are equally strong, so neither team wins. An identical rope is tied to a tree, and the same ten people pull just as hard on the loose end as they did in the contest. In both cases, the people pull steadily with no jerking. Which rope sustains the greater tension (a) the rope tied to the tree or (b) the rope in the tug-of-war, or (c) do the ropes sustain the same tension?

I thought the answer was (c) but according to my book it is not. I don't understand how it can be different. I mean, if people pull the same way both times there is the same maginitude of force in both cases, right? How can it then be different?
 
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  • #2
Imagine that we apply tension to the rope by running the end of the rope over a pulley and hanging a weight from it, instead of having people tug on it. In the first case we have five weights on each end of the rope; in the second case we have ten weights on one end of the rope and the other end tied to a solid object. What tension in the rope is needed to support the weights, stop them from movng downwards or upwards?
 
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  • #3
Ah that's a good explanation. Thank you my friend.
 

1. What factors affect the tension sustained by a rope?

The tension sustained by a rope depends on several factors including the material of the rope, its thickness, and its elasticity. Additionally, the amount of force applied to the rope and any external factors such as friction can also affect the tension sustained.

2. Is it possible to determine which rope can sustain greater tension just by looking at it?

No, it is not possible to determine which rope can sustain greater tension just by looking at it. As mentioned, there are multiple factors that contribute to the tension sustained by a rope and these cannot be determined by visual inspection alone.

3. Which rope is typically thicker: a tree or a tug-of-war rope?

The thickness of a rope can vary greatly depending on the specific tree or tug-of-war rope in question. Generally, tug-of-war ropes tend to be thicker as they are designed to withstand high levels of tension and force.

4. Can you explain why a tug-of-war rope may be able to sustain greater tension than a tree?

A tug-of-war rope is specifically designed to withstand high levels of tension and force, whereas a tree is not. Tug-of-war ropes are typically made of strong, durable materials such as nylon or polyester, while trees are made of natural fibers which are not as strong. Additionally, tug-of-war ropes are often thicker and have a more uniform structure, making them better equipped to handle tension and force.

5. How can one accurately compare the tension sustained by a tree and a tug-of-war rope?

To accurately compare the tension sustained by a tree and a tug-of-war rope, a controlled experiment would need to be conducted. This would involve applying equal amounts of force to both the tree and the rope and measuring the tension sustained by each. Other factors, such as the type and thickness of rope used, should also be taken into consideration.

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