Force / elastic potential energy of a rubber band

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SUMMARY

The discussion focuses on the calculation of work and potential energy associated with stretching a rubber band, characterized by its elasticity constant k and initial radius r0. The potential energy difference when stretching the band to a larger radius r is expressed as 1/2 k (l - l0)^2, in accordance with Hooke's law. Additionally, the tension in the rubber band is debated, with considerations on whether it should be represented as dE/dr or dE/dl, highlighting the distinction between these two expressions in the context of circular shapes.

PREREQUISITES
  • Understanding of Hooke's Law and its application
  • Basic knowledge of potential energy concepts
  • Familiarity with circular geometry and its implications on tension
  • Ability to differentiate between derivatives in physical contexts
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  • Study the derivation of potential energy in elastic materials using Hooke's Law
  • Explore the relationship between tension and potential energy in circular objects
  • Investigate the implications of elasticity constants in various materials
  • Learn about energy conservation principles in mechanical systems
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Physics students, mechanical engineers, and anyone interested in the mechanics of elastic materials and energy calculations.

Heirot
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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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