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Nice. This can easily be turned into an activity wherein students compare different materials to see which would shrink the length by the most (or the least).

David,

It’s a difficult one because I think it would be hard to construct a mathematical model to determine how much the length has decreased by. It’s also interesting because people are known to underestimate the change in length – especially when the diameter of the rope/cable is large.

My original thought was to give them the diameter of the cable and the full length of the cable and simply see how they work out the change in length – no meauring involved. Having said that, I think you may be right about getting them measuring string/ropes with different diameters to see how the length changes. In that case, I guess there’s an added dimension with the tension in a rope the larger the diameter is or the tension in a cable compared with the tension in a length of string.