Spring constant of vex rubber bands?

Does anyone know the spring force constant of Vex rubber bands (size 32)?

Rubber bands are far from ideal springs.

You should characterize them yourself:
Get an inexpensive spring scale and track the force applied by the rubber band at various different stretch distances. Repeat many times to get a good sample size. Then compute a regression on the data.

That would be a good learning experience and shouldn’t take more than an hour or two once you get the hang of the process.

You can also try using a plastic milk jug or other lightweight container and pour X amount of water into it and observe Y amount of stretch. 1 cc of water weighs 1 gram. Or you can measure in ounces and make the conversion. You should try not only a fair number of different rubber bands, you should also test one rubber band multiple times to observe how the rubber bands change their effective spring constants after a certain number of stretches. Some rubber bands will change by 20% or more after a single stretch.

These are definitely worthwhile considerations too.

I calculated the spring constant of a size 64 band to be right around 60 by hanging some steel C channels from it, but like everyone’s been saying, it’s non linear. Anyhow, a size 32 band should have about half of that, so it should be ballpark of 30 for large displacements. I would assume it’d be smaller for smaller displacements but I have no idea what the function would look like. Good luck!

Thanks for all the advice, everyone! I’ve done some measurements where I took a spring scale and stretched a rubber band a certain distance (20 cm) and recorded the force that was measured on the spring scale. However, when I use Hooke’s law (k=-F/x), I end up with negative numbers for k. Is this normal or am I doing something wrong?

That’s because you’re mixing up your directions. The negative is there for the vector to indicate direction. If you draw a free-body diagram, you’ll have the elastic force aimed up and gravity aimed down. Let’s call upward positive y, with y=0 where the elastic’s bottom end is before stretching. (The starting period on each line is there because the auto-formatting was messing up my negative signs. Ignore those periods.)

. Fnet,y = Fe - Fg = 0
. Fe = Fg
. - k y = m g
. - k (-0.2 m) = (mass used in kg) (9.8 m/s^2)
. k= 49 * (mass in kg), with final units in N/m

Note the lack of a negative in k at the end.