## Saturday, December 11, 2010

### Variations in Spring Rate From Similar Mini-Bungee Cords

I am working on an invention at the moment that requires some source of tightening, and I had thought that bungee cords might be one possible prototype model.  It turns out that while bungee cords do not produce enormous force individually, when you sum them, like any other spring, you sum the spring constant.

I am sure you all remember learning Hooke's Law in physics class (or am I one of the weird ones that still remembered it?)--one of the few really simple equations:
F = -kx
where F is the force, k is the spring constant, and x is the displacement of the spring under force F.  I experimentally verified that when you have multiple springs in parallel, the force is the result of summing the value for k of the different springs.  I did this by hanging a .78 kg weight on the end of each of five apparently identical mini-bungee cords from the same package, and putting the other hook over the end of a ruler, then measuring x and then computing k for each.

I was experimenting some variation, but not this much!  The values for k in newtons/meter were -92.6, -96.3, -218.87, -343.94, and -343.94.  The clumping of the data suggests that in spite of nearly identical appearance, the rubber that is used in these mini-bungees comes from a variety of sources, with the similarities in values suggesting a common origin for the materials used in similar spring rates.

I'm not sure that mini-bungees are going to be useful for my project, because it would take too many of these cords to achieve the desired force, but it was still startling to see the variation in spring rates!