Advanced Membranes

Stretching energy

The stretching part of the energy is easiest to understand. First, think about a spring -- it takes effort to stretch or compress a spring from its normal length. We call the normal length the natural or equilibrium length of the spring. This is the length the spring has when no force is applied. Consider the model of a spring below:

Use the mouse to drag the block on the end of the spring. The force used to move the block is shown on the left graph (marked F) and the stored energy (marked E) is shown on the right.

Things to notice

  • The spring has a certain length when no force is applied (in fact we have draw the vertical axes on the graphs so that they go through this value of the extension, x). We say the force is positive to stretch (make longer) the spring and negative to compress (make shorter) it.
  • The energy stored in the spring increases if the spring is compressed or stretched from that length.
The stretch in a membrane, like the rubber of our balloon, works a bit like the stretch of a spring except that it works in all directions.

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