# Tension on rope

1. May 25, 2014

### Maxo

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?

2. May 25, 2014

### Staff: Mentor

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?

3. May 25, 2014

### Maxo

Ah that's a good explanation. Thank you my friend.