Tension on a box made of stretchable material

[Yuppy]

Please take a look at the slides attached.

Suppose I apply a force F on the right hand side and another on the left hand side as shown in the following diagram. Suppose that the material can be stretched. Now one of my friends said that the extension is delta due to a force F while another friend said it is 2delta and they both gave me their reasons. The next slides shows their reasoning. Could you please tell me which reasoning is right?

 

[Doc Al]

Now one of my friends said that the extension is delta due to a force F while another friend said it is 2delta and they both gave me their reasons.

The tension created is F, not 2F. The extension, which is measured from end to end, is due to the tension F. If you measure from the center, then each end moves delta/2, of course. The total end-to-end extension is the same no matter how you think of it.

Point out to your second friend that if you measure from the center, the effective "spring constant" of the material is twice as much--since you are looking at only half of it--thus the extension of each end from the center is just half of the total extension.

Make sense?