Force / elastic potential energy of a rubber band

AI Thread Summary
The discussion centers on calculating the work needed to stretch a rubber band from its unstreched radius r0 to a larger radius r, using Hooke's law. The potential energy difference when stretching the band is proposed to be 1/2 k (l - l0)^2, aligning with Hooke's law principles. There is confusion regarding the tension in the band, specifically whether it should be expressed as dE/dr or dE/dl, highlighting the distinction between the two forces. The circular shape of the band complicates the application of these formulas. Overall, the conversation explores the relationship between elasticity, potential energy, and tension in rubber bands.
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Suppose we have a rubber band of some elasticity k and of unstreched radius r0 (the band is always kept in the shape of a circle). What work is necessary to strech it to some larger radius r? How do we apply Hooke's law in this situation?

Thanks
 
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I guess I misplaced my question... Sorry about that. This really isn't homework, but I'm just curious. Nevertheless... My problem is this. If we have an unstreched band of radius r0, and corresponding circumference (the length of the band) l0, and we strech it to some radius r (length l), what's the difference in potential energy? Is it 1/2 k (l - l0)^2. That would make sense due to Hooke's law. But what about the tension in the band? Is the tension dE/dr or dE/dl? The first expresion makes sense because of the circular shape. The second one follows strictly from Hooke's law. Note that the two forces are not the same. I hope this is not confusing to you as it is to me.

Thanks
 
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