Anyway, today I began thinking about mainsprings, the coiled springs typically used to power wind up clocks, watches, etc. While reading up on them I began to notice a trend where articles comment on how much energy they can contain (usually described as "a lot" rather than anything useful.) This lead me to try to find a source for the potential energy of a mainspring, something that I've found rather difficult to find.

The closest I've come is a webpage which says:

Mr. Dan Henderson, a Senior Manufacturing Technology Engineer at 3M, shared with me a formula for springs. All other factors being equal, the strength of the spring is proportional to its width: in other words, if we double the width, we double the strength. Similarly, the strength is proportional to the cube (to the power of 3) of the thickness: if we double the thickness, the spring is eight times stronger (2x2x2=8).

[math]f=kbh^3[/math]

where "b" is the width of the spring and "h" is the thickness. This bothers me because it doesn't provide any form of bending (or whatever the mainspring equivalent of elongation is) into the equation.

Thinking about it further I was wondering if it could simply be classified as a cantilever beam that is being bent way, WAY further than is usually covered (and thus out of the realms of my engineering textbooks I believe, however they are packed and unavailable for consultation for at least 3 weeks), since generally the bending is limited to smaller angles (at least probably less than 360 degrees).

So, to wrap it up, can anyone provide some direction for figuring out (or simply tell me) the potential energy of a mainspring.

Thanks