# Silly rubber band. Why can’t you be more like a spring.

So last Tuesday evening I was lazying around on the forums as usual giving my two cent on how to solve simple math and physics problems. In particular there was this one gymnasium student who had done a physics lab in school with a rubber band and who was outlining how he wanted to interprete it. He didn’t post anything more so there was no discussion to be had and I do suspect that what I saw as a fundamental flaw or issue was really just a misrepresentation. Nevertheless the description itself still spurred me to do a little mini experiment that evening.

He had suspended a small weight from the rubber band and simply measured the elongation of the rubber band as a result of it’s induced gravitational force. Then he postulated that the rubber band would follow Hookes law

$F = k x$

determined the expected ‘spring constant’ $k$ from this single measurment and used this linear extrapolation to find the weight of another heavier object suspended in the same way from the elongation it caused. The problem is of course that rubber bands don’t elongate in a linear way when you apply a force to it as you would see if you took more than a single measurement. His error was a natural one but it gave me a bit of a laugh when it reminded me of the famous Coulomb torsion experiment for studying the electrostatic force where he apparently only disclosed 3 measurements (data points) and argued on their basis alone. There is naturally a bit of historical debate as to how he did his measurements and why but the point I take from it that it’s really rather silly not to make lots of measurements when the apparatus is right in front of you. It’s so much easier to catch your errors when you do.

So back to me. I decided to spend a couple of hours to set up a simple a experiment with household objects to loosely characterize a rubberbands elongation a a function of applied weight (load). So I attached a rubber to some strings along a rules and at the other end of the string attached to the rubber band I attached a small card board cup which I filled up with some standard weights in the form of some iron balls I had lying around as part of an old toy set. As I loaded up the cup with balls, one by one, I measured the elongation relative to the length when a single ball was in the cup and doing this twice with a day apart the elongation response is displayed in the graph below.

Only took me 3-4 hours total to work on and I was pretty happy with at least capturing the non-linearity with things I only had to stretch for. I do recognize a number of flaws though, the pribary one being that it was difficult to increase the load in a continuous way as I effectively had to drop the balls into the cup and the 1mm and the decrease in effective weight once the ball has stopped causes some oscillations and once elongated it won’t return to the same length as before the load making the graph a little misrepresentative. I also probably should have been in less of a rush to do the measurements as it sometimes took time for it to properly settle. In the last 5 measurements I observed that it would not actually settle into the proper elongation until after 45 seconds which I had missed to account for. Essentially all measurements in the second experiment past the jump in the red graph are probably too bad to be reliable but the two measurements done at different days agree pretty well which makes them look pretty reliable.

The natural length of the rubber band was about 6cm and it finally snapped when it was extented to 26cm. Pictures of the actual setup at: http://imgur.com/a/KmTyF